class: center, middle, inverse, title-slide .title[ # Multivariate distributions ] .author[ ### <a href="https://jmclip.github.io/MACSS_math_camp/">MACS 33000</a> <br /> University of Chicago ] --- `$$\newcommand{\E}{\mathrm{E}} \newcommand{\Var}{\mathrm{Var}} \newcommand{\Cov}{\mathrm{Cov}} \newcommand{\Cor}{\mathrm{Cor}}$$` # Misc * Calcs spoken for * Link for practice questions open on github / pset * Meetings with preceptors! --- # Acronym recap: * Discrete: pmf and CMF * Continuous: pdf and CDF * The lowercase reflects that we're associating it with particular values (e.g. f) * Uppercase is integrating (e.g. F) * Rules of probability: * `\(0 \leq p(x) \leq 1\)` * Total probability must sum to 1! * Expected values: tells us what we can anticipate getting from our function: IN THE LONG RUN * multiply your value times its probability * Moments: tell us about the function and multiply `\(x^n\)` by the probability for the `\(n^{th}\)` moment --- # Learning objectives * Define a joint probability density function * Condition pdfs on other random variables * Identify independence between two random variables * Define covariance and correlation * Examine sums of random variables * Define the multivariate normal distribution --- # Multivariate distribution `\(X\)` and `\(Y\)` are **jointly continuous** if, for all `\(x\in\Re\)` and `\(y\in \Re\)`, there exists a function `\(f(x,y)\)` such that `\(C \subset \Re^{2}\)`, `$$\Pr\{(X, Y) \in C \} = \iint_{(x,y)\in C} f(x,y)\, dx\, dy$$` -- What is `\(C \subset R^{2}\)`? -- * `\(R^{2} = R \underbrace{\times}_{\text{Cartesian Product}} R\)` * `\(C\)` is a subset of the 2-d plane --- ## `\(C = \{x, y: x \in [0,1] , y\in [0,1] \}\)` <img src="12-multivariate-pdf_files/figure-html/a-2d-rect-1.png" width="864" style="display: block; margin: auto;" /> --- # `\(C = \{x, y: x^2 + y^2 \leq 1 \}\)` <img src="12-multivariate-pdf_files/figure-html/a-2d-circle-1.png" width="864" style="display: block; margin: auto;" /> --- # `\(C = \{ x, y: x> y, x,y\in(0,2)\}\)` <img src="12-multivariate-pdf_files/figure-html/a-2d-triangle-1.png" width="864" style="display: block; margin: auto;" /> --- # Multivariate distribution: role of integrals `$$\begin{aligned} C &= \{ x, y: x \in A, y \in B \} \\ \Pr\{(X,Y) \in C \} &= \int_{B} \int_{A} f(x,y) \, dx\, dy \end{aligned}$$` --- # Examples of joint pdfs Consider a function `\(f:\Re \times \Re \rightarrow \Re\)`: * Input: an `\(x\)` value and a `\(y\)` value. * Output: a number from the real line * `\(f(x,y) = a\)` --- # Examples of joint pdfs: normal `\(f(x,y) = \frac{1}{2\pi}exp[\frac{(x^2+y^2)}{-2}]\)` <div class="plotly html-widget html-fill-item" id="htmlwidget-9eceb20dc2a931752ae4" style="width:864px;height:504px;"></div> <script type="application/json" data-for="htmlwidget-9eceb20dc2a931752ae4">{"x":{"visdat":{"d4314a085e75":["function () ","plotlyVisDat"]},"cur_data":"d4314a085e75","attrs":{"d4314a085e75":{"x":{},"y":{},"z":{},"alpha_stroke":1,"sizes":[10,100],"spans":[1,20],"type":"surface","inherit":true}},"layout":{"margin":{"b":100,"l":5,"t":0,"r":50,"pad":0},"scene":{"xaxis":{"title":"x"},"yaxis":{"title":"y"},"zaxis":{"title":"z_mat"}},"hovermode":"closest","showlegend":false,"legend":{"yanchor":"top","y":0.5}},"source":"A","config":{"modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"data":[{"colorbar":{"title":"z_mat","ticklen":2,"len":0.5,"lenmode":"fraction","y":1,"yanchor":"top"},"colorscale":[["0","rgba(68,1,84,1)"],["0.0416666666666667","rgba(70,19,97,1)"],["0.0833333333333333","rgba(72,32,111,1)"],["0.125","rgba(71,45,122,1)"],["0.166666666666667","rgba(68,58,128,1)"],["0.208333333333333","rgba(64,70,135,1)"],["0.25","rgba(60,82,138,1)"],["0.291666666666667","rgba(56,93,140,1)"],["0.333333333333333","rgba(49,104,142,1)"],["0.375","rgba(46,114,142,1)"],["0.416666666666667","rgba(42,123,142,1)"],["0.458333333333333","rgba(38,133,141,1)"],["0.5","rgba(37,144,140,1)"],["0.541666666666667","rgba(33,154,138,1)"],["0.583333333333333","rgba(39,164,133,1)"],["0.625","rgba(47,174,127,1)"],["0.666666666666667","rgba(53,183,121,1)"],["0.708333333333333","rgba(79,191,110,1)"],["0.75","rgba(98,199,98,1)"],["0.791666666666667","rgba(119,207,85,1)"],["0.833333333333333","rgba(147,214,70,1)"],["0.875","rgba(172,220,52,1)"],["0.916666666666667","rgba(199,225,42,1)"],["0.958333333333333","rgba(226,228,40,1)"],["1","rgba(253,231,37,1)"]],"showscale":true,"x":[-2,-1.96,-1.9199999999999999,-1.8799999999999999,-1.8400000000000001,-1.8,-1.76,-1.72,-1.6799999999999999,-1.6400000000000001,-1.6000000000000001,-1.5600000000000001,-1.52,-1.48,-1.4399999999999999,-1.3999999999999999,-1.3599999999999999,-1.3199999999999998,-1.28,-1.24,-1.2,-1.1600000000000001,-1.1200000000000001,-1.0800000000000001,-1.04,-1,-0.95999999999999996,-0.91999999999999993,-0.87999999999999989,-0.84000000000000008,-0.80000000000000004,-0.76000000000000001,-0.71999999999999997,-0.67999999999999994,-0.6399999999999999,-0.59999999999999987,-0.56000000000000005,-0.52000000000000002,-0.47999999999999998,-0.43999999999999995,-0.39999999999999991,-0.35999999999999988,-0.32000000000000006,-0.28000000000000003,-0.23999999999999999,-0.19999999999999996,-0.15999999999999992,-0.11999999999999988,-0.080000000000000071,-0.040000000000000036,0,0.040000000000000036,0.080000000000000071,0.12000000000000011,0.16000000000000014,0.20000000000000018,0.24000000000000021,0.28000000000000025,0.31999999999999984,0.35999999999999988,0.39999999999999991,0.43999999999999995,0.47999999999999998,0.52000000000000002,0.56000000000000005,0.60000000000000009,0.64000000000000012,0.68000000000000016,0.7200000000000002,0.76000000000000023,0.80000000000000027,0.83999999999999986,0.87999999999999989,0.91999999999999993,0.95999999999999996,1,1.04,1.0800000000000001,1.1200000000000001,1.1600000000000001,1.2000000000000002,1.2400000000000002,1.2800000000000002,1.3200000000000003,1.3599999999999999,1.3999999999999999,1.4399999999999999,1.48,1.52,1.5600000000000001,1.6000000000000001,1.6400000000000001,1.6800000000000002,1.7200000000000002,1.7600000000000002,1.8000000000000003,1.8399999999999999,1.8799999999999999,1.9199999999999999,1.96,2],"y":[-2,-1.96,-1.9199999999999999,-1.8799999999999999,-1.8400000000000001,-1.8,-1.76,-1.72,-1.6799999999999999,-1.6400000000000001,-1.6000000000000001,-1.5600000000000001,-1.52,-1.48,-1.4399999999999999,-1.3999999999999999,-1.3599999999999999,-1.3199999999999998,-1.28,-1.24,-1.2,-1.1600000000000001,-1.1200000000000001,-1.0800000000000001,-1.04,-1,-0.95999999999999996,-0.91999999999999993,-0.87999999999999989,-0.84000000000000008,-0.80000000000000004,-0.76000000000000001,-0.71999999999999997,-0.67999999999999994,-0.6399999999999999,-0.59999999999999987,-0.56000000000000005,-0.52000000000000002,-0.47999999999999998,-0.43999999999999995,-0.39999999999999991,-0.35999999999999988,-0.32000000000000006,-0.28000000000000003,-0.23999999999999999,-0.19999999999999996,-0.15999999999999992,-0.11999999999999988,-0.080000000000000071,-0.040000000000000036,0,0.040000000000000036,0.080000000000000071,0.12000000000000011,0.16000000000000014,0.20000000000000018,0.24000000000000021,0.28000000000000025,0.31999999999999984,0.35999999999999988,0.39999999999999991,0.43999999999999995,0.47999999999999998,0.52000000000000002,0.56000000000000005,0.60000000000000009,0.64000000000000012,0.68000000000000016,0.7200000000000002,0.76000000000000023,0.80000000000000027,0.83999999999999986,0.87999999999999989,0.91999999999999993,0.95999999999999996,1,1.04,1.0800000000000001,1.1200000000000001,1.1600000000000001,1.2000000000000002,1.2400000000000002,1.2800000000000002,1.3200000000000003,1.3599999999999999,1.3999999999999999,1.4399999999999999,1.48,1.52,1.5600000000000001,1.6000000000000001,1.6400000000000001,1.6800000000000002,1.7200000000000002,1.7600000000000002,1.8000000000000003,1.8399999999999999,1.8799999999999999,1.9199999999999999,1.96,2],"z":[[0.0029150244650281948,0.0031552830685064662,0.0034098837935359152,0.0036791369954507149,0.0039633047599361097,0.0042625953530344724,0.0045771576844913604,0.0049070758405529548,0.0052523637458022042,0.005612960016569659,0.0059887230707933534,0.0063794265608507874,0.006784755196771599,0.0072043010272956369,0.0076375602454110186,0.0080839305832440186,0.0085427093584435534,0.0090130922304875512,0.0094941727206312616,0.0099849425435298688,0.010484292791926746,0.010991016008249595,0.011503809168561334,0.012021277595150495,0.012541939804212972,0.013064233284684923,0.013586521193461716,0.014107099941119392,0.014624207630993185,0.015136033303221483,0.015640726924298666,0.016136410051965418,0.016621187095070565,0.017093157078531655,0.017550425814864774,0.017991118376101546,0.01841339175340518,0.018815447586466555,0.01919554484091637,0.019552012309622557,0.019883260812923801,0.020187794973626452,0.020464224444986568,0.0207112744739067,0.020927795687169945,0.021112772995655688,0.021265333520051336,0.021384753451487722,0.021470463771653604,0.021522054769138883,0.021539279301848634,0.021522054769138883,0.021470463771653604,0.021384753451487722,0.021265333520051336,0.021112772995655685,0.020927795687169942,0.020711274473906697,0.020464224444986572,0.020187794973626452,0.019883260812923801,0.019552012309622557,0.01919554484091637,0.018815447586466555,0.01841339175340518,0.017991118376101546,0.017550425814864771,0.017093157078531651,0.016621187095070565,0.016136410051965418,0.015640726924298663,0.015136033303221486,0.014624207630993185,0.014107099941119392,0.013586521193461716,0.013064233284684923,0.012541939804212972,0.012021277595150495,0.011503809168561334,0.010991016008249595,0.010484292791926746,0.0099849425435298653,0.0094941727206312582,0.0090130922304875443,0.0085427093584435534,0.0080839305832440186,0.0076375602454110186,0.0072043010272956369,0.006784755196771599,0.0063794265608507874,0.0059887230707933534,0.005612960016569659,0.0052523637458022025,0.0049070758405529522,0.0045771576844913587,0.0042625953530344707,0.0039633047599361105,0.0036791369954507149,0.0034098837935359152,0.0031552830685064662,0.0029150244650281948],[0.0031552830685064662,0.0034153439745855732,0.0036909290911266526,0.0039823743531940169,0.0042899634477807152,0.0046139218063797364,0.0049544106119946956,0.0053115208813261589,0.0056852676866321261,0.0060755845849529491,0.0064823183249220345,0.0069052239031682479,0.0073439600432744986,0.0077980851703177033,0.0082670539531167833,0.0087502144844073346,0.0092468061662075839,0.0097559583636185644,0.010276689885206174,0.0108079093419564,0.011348416429606495,0.011896904170983703,0.012451962145895727,0.013012080726199879,0.013575656323034577,0.014140997641948178,0.014706332929943137,0.015269818186418567,0.015829546297804243,0.016383557043505914,0.016929847908804932,0.017466385628757176,0.017991118376101546,0.018501988495897827,0.018996945680243547,0.019473960468136136,0.019931037948504489,0.020366231538771852,0.020777656707150222,0.021163504504304514,0.021522054769138883,0.021851688874298138,0.022150901879568859,0.022418313965703162,0.022652681027241835,0.022852904310622518,0.023018038993134829,0.023147301609014723,0.023240076241015303,0.023295919408990597,0.023314563601200315,0.023295919408990597,0.023240076241015303,0.023147301609014723,0.023018038993134829,0.022852904310622514,0.022652681027241831,0.022418313965703159,0.022150901879568863,0.021851688874298138,0.021522054769138883,0.021163504504304514,0.020777656707150222,0.020366231538771852,0.019931037948504489,0.019473960468136136,0.018996945680243543,0.018501988495897823,0.017991118376101543,0.017466385628757172,0.016929847908804928,0.016383557043505918,0.015829546297804243,0.015269818186418567,0.014706332929943137,0.014140997641948178,0.013575656323034577,0.013012080726199879,0.012451962145895727,0.011896904170983703,0.011348416429606493,0.010807909341956396,0.010276689885206171,0.0097559583636185575,0.0092468061662075839,0.0087502144844073346,0.0082670539531167833,0.0077980851703177033,0.0073439600432744986,0.0069052239031682479,0.0064823183249220345,0.0060755845849529491,0.0056852676866321235,0.0053115208813261563,0.0049544106119946947,0.0046139218063797347,0.004289963447780717,0.0039823743531940169,0.0036909290911266526,0.0034153439745855732,0.0031552830685064662],[0.0034098837935359152,0.0036909290911266526,0.003988751252318022,0.0043037133188741422,0.0046361218685755266,0.0049862205230490802,0.0053541834712027038,0.0057401090739014797,0.0061440136195883696,0.0065658253040016389,0.0070053785098765477,0.0074624084644474018,0.0079365463536019715,0.0084273149716058825,0.0089341249843435961,0.0094562718819605172,0.0099929336935985266,0.010543169532570874,0.011105919034816126,0.011680002746817587,0.012264123511406154,0.012856868891034025,0.013456714658285983,0.01406202937267753,0.01467108005128704,0.015282038928612808,0.015892991288383319,0.016501944337043228,0.017106837075463652,0.017705551112270207,0.018295922349238675,0.018875753456674582,0.019442827044767613,0.01999491942579118,0.020529814851891107,0.021045320104255621,0.021539279301848638,0.022009588791768921,0.022454211978800521,0.022871193948950898,0.023258675740816071,0.023614908119520307,0.023938264710778773,0.024227254357319934,0.024480532566446708,0.024696911925846471,0.024875371374784586,0.025015064229412538,0.025115324873938413,0.02517567404367195,0.025195822641271334,0.02517567404367195,0.025115324873938413,0.025015064229412538,0.024875371374784586,0.024696911925846467,0.024480532566446705,0.024227254357319931,0.023938264710778777,0.023614908119520307,0.023258675740816071,0.022871193948950898,0.022454211978800521,0.022009588791768921,0.021539279301848638,0.021045320104255621,0.020529814851891103,0.019994919425791177,0.019442827044767609,0.018875753456674579,0.018295922349238672,0.01770555111227021,0.017106837075463652,0.016501944337043228,0.015892991288383319,0.015282038928612808,0.01467108005128704,0.01406202937267753,0.013456714658285983,0.012856868891034025,0.01226412351140615,0.011680002746817584,0.011105919034816123,0.010543169532570867,0.0099929336935985266,0.0094562718819605172,0.0089341249843435961,0.0084273149716058825,0.0079365463536019715,0.0074624084644474018,0.0070053785098765477,0.0065658253040016389,0.006144013619588367,0.0057401090739014771,0.0053541834712027021,0.0049862205230490784,0.0046361218685755292,0.0043037133188741422,0.003988751252318022,0.0036909290911266526,0.0034098837935359152],[0.0036791369954507149,0.0039823743531940169,0.0043037133188741422,0.0046435456009674319,0.0050022019854251273,0.0053799453308649142,0.0057769635805992505,0.0061933628623203237,0.0066291607506484777,0.007084279771472639,0.0075585412299625163,0.0080516594462132721,0.0085632364836009875,0.0090927574549980999,0.0096395864909502686,0.010202963451691261,0.010782001461428119,0.011375685338639316,0.011982870990187584,0.012602285829870448,0.013232530273649649,0.013872080354272774,0.014519291487404298,0.015172403409819481,0.015829546297804239,0.016488748060787893,0.017147942791573351,0.017804980340496372,0.018457636966631524,0.019103627004968423,0.019740615474516342,0.020366231538771856,0.020978082717117316,0.02157376973371913,0.022150901879568863,0.022707112753651681,0.023240076241015307,0.023747522578910298,0.024227254357319927,0.024677162297210554,0.02509524064880048,0.025479602053125369,0.025828491713200331,0.026140300726137187,0.026413578434634558,0.026647043665247026,0.026839594731655987,0.026990318093676739,0.027098495576781047,0.027163610072305,0.027185349655036491,0.027163610072305,0.027098495576781047,0.026990318093676739,0.026839594731655987,0.026647043665247023,0.026413578434634554,0.026140300726137183,0.025828491713200334,0.025479602053125369,0.02509524064880048,0.024677162297210554,0.024227254357319927,0.023747522578910298,0.023240076241015307,0.022707112753651681,0.022150901879568859,0.021573769733719127,0.020978082717117312,0.020366231538771849,0.019740615474516339,0.019103627004968426,0.018457636966631524,0.017804980340496372,0.017147942791573351,0.016488748060787893,0.015829546297804239,0.015172403409819481,0.014519291487404298,0.013872080354272774,0.013232530273649647,0.012602285829870444,0.011982870990187581,0.011375685338639309,0.010782001461428119,0.010202963451691261,0.0096395864909502686,0.0090927574549980999,0.0085632364836009875,0.0080516594462132721,0.0075585412299625163,0.007084279771472639,0.0066291607506484751,0.0061933628623203202,0.0057769635805992488,0.0053799453308649115,0.005002201985425129,0.0046435456009674319,0.0043037133188741422,0.0039823743531940169,0.0036791369954507149],[0.0039633047599361097,0.0042899634477807152,0.0046361218685755266,0.0050022019854251273,0.0053885601333985003,0.0057954794736858797,0.0062231624658928165,0.0066717234347612592,0.0071411813123333032,0.0076314526405823584,0.0081423449227157416,0.0086735504135942894,0.0092246404409185804,0.0097950603489076471,0.010384125155067441,0.010991016008249596,0.011614777532490659,0.012254316136070222,0.012908399358826475,0.013575656323034575,0.014254579344124033,0.014943526747247476,0.015640726924298663,0.016344283653520707,0.017052182690476543,0.017762299625024486,0.018472408984224021,0.01918019454598029,0.019883260812923798,0.020579145580731498,0.021265333520051333,0.021939270676624271,0.022598379780337335,0.023240076241015307,0.023861784696989279,0.024460955972075381,0.025035084287751662,0.02558172457020871,0.026098509686722313,0.026583167442578218,0.027033537168666549,0.02744758573091911,0.027823422796018172,0.028159315193254722,0.028453700220018148,0.028705197748082504,0.028912620999506148,0.029074985874439879,0.029191518728268195,0.029261662512087613,0.02928508120832678,0.029261662512087613,0.029191518728268195,0.029074985874439879,0.028912620999506148,0.0287051977480825,0.028453700220018141,0.028159315193254715,0.027823422796018175,0.02744758573091911,0.027033537168666549,0.026583167442578218,0.026098509686722313,0.02558172457020871,0.025035084287751662,0.024460955972075381,0.023861784696989276,0.023240076241015303,0.022598379780337331,0.021939270676624267,0.021265333520051326,0.020579145580731501,0.019883260812923798,0.01918019454598029,0.018472408984224021,0.017762299625024486,0.017052182690476543,0.016344283653520707,0.015640726924298663,0.014943526747247476,0.014254579344124031,0.013575656323034571,0.012908399358826471,0.012254316136070215,0.011614777532490659,0.010991016008249596,0.010384125155067441,0.0097950603489076471,0.0092246404409185804,0.0086735504135942894,0.0081423449227157416,0.0076314526405823584,0.0071411813123333006,0.0066717234347612566,0.0062231624658928147,0.0057954794736858779,0.0053885601333985029,0.0050022019854251273,0.0046361218685755266,0.0042899634477807152,0.0039633047599361097],[0.0042625953530344724,0.0046139218063797364,0.0049862205230490802,0.0053799453308649142,0.0057954794736858797,0.0062331274957362452,0.0066931071454421525,0.0071755413808255774,0.0076804505635895796,0.0082077449333402795,0.0087572174568103251,0.0093285371493594775,0.0099212429673228766,0.01053473836985956,0.011168286647740003,0.011821007113933748,0.012491872246867534,0.013179705871791283,0.013883182458805893,0.014600827607789892,0.015331019780750797,0.016071993331088243,0.016821842866979374,0.01757852897269948,0.018339885297312321,0.01910362700496842,0.019867360565220551,0.020628594845507338,0.021384753451487718,0.022133188244463968,0.022871193948950892,0.02359602374778054,0.024304905747224687,0.024995060180715359,0.025663717207085348,0.026308135148060175,0.026925619000219621,0.027513539048997407,0.028069349406665632,0.028590606292789318,0.029074985874439879,0.02952030148459165,0.029924520040626998,0.030285777490736184,0.030602393124176629,0.030872882591770352,0.031095969495550112,0.031270595420960834,0.031395928301294874,0.031471369021871136,0.031496556190612812,0.031471369021871136,0.031395928301294874,0.031270595420960834,0.031095969495550112,0.030872882591770349,0.030602393124176626,0.030285777490736177,0.029924520040627001,0.02952030148459165,0.029074985874439879,0.028590606292789318,0.028069349406665632,0.027513539048997407,0.026925619000219621,0.026308135148060175,0.025663717207085341,0.024995060180715355,0.024304905747224683,0.023596023747780536,0.022871193948950888,0.022133188244463975,0.021384753451487718,0.020628594845507338,0.019867360565220551,0.01910362700496842,0.018339885297312321,0.01757852897269948,0.016821842866979374,0.016071993331088243,0.015331019780750795,0.014600827607789888,0.01388318245880589,0.013179705871791274,0.012491872246867534,0.011821007113933748,0.011168286647740003,0.01053473836985956,0.0099212429673228766,0.0093285371493594775,0.0087572174568103251,0.0082077449333402795,0.007680450563589577,0.0071755413808255739,0.0066931071454421507,0.0062331274957362435,0.0057954794736858823,0.0053799453308649142,0.0049862205230490802,0.0046139218063797364,0.0042625953530344724],[0.0045771576844913604,0.0049544106119946956,0.0053541834712027038,0.0057769635805992505,0.0062231624658928165,0.0066931071454421525,0.0071870314366283281,0.0077050673712790313,0.0082472368137088189,0.0088134433795690539,0.0094034647573729251,0.010016945537149735,0.01065339065207312,0.011312159538995937,0.011992461122521192,0.01269334972447039,0.013413721996325671,0.014152314966387922,0.014907705286001879,0.01567830975026839,0.016462387158236332,0.017258041565713103,0.018063226970650274,0.018875753456674579,0.019693294804894967,0.020513397567798811,0.021333491582053162,0.022150901879568859,0.02296286193850185,0.023766528198207511,0.024558995744789446,0.025337315057059998,0.026098509686722313,0.026839594731655987,0.027557595947595888,0.028249569331477438,0.028912620999506148,0.029543927174795367,0.030140754093379123,0.030700477633690451,0.031220602473310582,0.031698780578013654,0.032132828831891204,0.03252074562363403,0.032860726212830794,0.033151176711325621,0.033390726528133352,0.033578239141976954,0.033712821082984332,0.033793829024229186,0.033820874904358172,0.033793829024229186,0.033712821082984332,0.033578239141976954,0.033390726528133352,0.033151176711325614,0.032860726212830788,0.03252074562363403,0.032132828831891211,0.031698780578013654,0.031220602473310582,0.030700477633690451,0.030140754093379123,0.029543927174795367,0.028912620999506148,0.028249569331477438,0.027557595947595884,0.02683959473165598,0.02609850968672231,0.025337315057059995,0.024558995744789439,0.023766528198207515,0.02296286193850185,0.022150901879568859,0.021333491582053162,0.020513397567798811,0.019693294804894967,0.018875753456674579,0.018063226970650274,0.017258041565713103,0.016462387158236329,0.015678309750268387,0.014907705286001875,0.014152314966387913,0.013413721996325671,0.01269334972447039,0.011992461122521192,0.011312159538995937,0.01065339065207312,0.010016945537149735,0.0094034647573729251,0.0088134433795690539,0.0082472368137088154,0.0077050673712790278,0.0071870314366283255,0.0066931071454421499,0.0062231624658928191,0.0057769635805992505,0.0053541834712027038,0.0049544106119946956,0.0045771576844913604],[0.0049070758405529548,0.0053115208813261589,0.0057401090739014797,0.0061933628623203237,0.0066717234347612592,0.0071755413808255774,0.0077050673712790313,0.0082604429547062427,0.0088416915713854655,0.0094487098896551738,0.010081259573980258,0.010738959596700997,0.011421279206938664,0.012127531670226073,0.012856868891034027,0.013608277027397159,0.014380573202248762,0.015172403409819485,0.015982241707530903,0.016808390774240338,0.017648983904514026,0.01850198849589782,0.019365211072021962,0.020236303868953278,0.021112772995655688,0.021991988161926147,0.022871193948950898,0.023747522578910302,0.024618008121102587,0.025479602053125369,0.026329190077027283,0.027163610072304997,0.027979671050459759,0.028774172959823895,0.029543927174795377,0.030285777490736188,0.030996621434838497,0.031673431694456605,0.032313277457930549,0.032913345458942776,0.033470960514071703,0.033983605344513147,0.034448939476971252,0.034864817025467287,0.035229303165229757,0.035540689121817987,0.035797505513057687,0.035998533898054901,0.03614281640628695,0.036229663340296328,0.036258658667553054,0.036229663340296328,0.03614281640628695,0.035998533898054901,0.035797505513057687,0.03554068912181798,0.03522930316522975,0.03486481702546728,0.034448939476971259,0.033983605344513147,0.033470960514071703,0.032913345458942776,0.032313277457930549,0.031673431694456605,0.030996621434838497,0.030285777490736188,0.029543927174795374,0.028774172959823891,0.027979671050459752,0.027163610072304993,0.026329190077027279,0.025479602053125373,0.024618008121102587,0.023747522578910302,0.022871193948950898,0.021991988161926147,0.021112772995655688,0.020236303868953278,0.019365211072021962,0.01850198849589782,0.017648983904514026,0.016808390774240334,0.0159822417075309,0.015172403409819476,0.014380573202248762,0.013608277027397159,0.012856868891034027,0.012127531670226073,0.011421279206938664,0.010738959596700997,0.010081259573980258,0.0094487098896551738,0.008841691571385462,0.0082604429547062392,0.0077050673712790287,0.0071755413808255748,0.0066717234347612618,0.0061933628623203237,0.0057401090739014797,0.0053115208813261589,0.0049070758405529548],[0.0052523637458022042,0.0056852676866321261,0.0061440136195883696,0.0066291607506484777,0.0071411813123333032,0.0076804505635895796,0.0082472368137088189,0.0088416915713854655,0.0094638399262801844,0.010113571275767206,0.010790630513757976,0.011494609801463957,0.012224941041557115,0.012980889177287638,0.013761546436622795,0.01456582763829458,0.015392466671726591,0.016240014256115841,0.017106837075463649,0.017991118376101546,0.018890860101292081,0.019803886623882407,0.020727850122861366,0.021660237633162393,0.022598379780337338,0.023539461193001633,0.024480532566446708,0.025418524330781987,0.026350261856676941,0.027272482111509948,0.028181851658793593,0.029074985874439883,0.029948469235059991,0.030798876516363514,0.031622794724124298,0.032416845566391364,0.0331777082639007,0.03390214248621843,0.034587011194218059,0.035229303165229757,0.035826154975725236,0.036374872217800745,0.036872949730034965,0.037318090630520315,0.037708223949943408,0.038041520675422935,0.038316408031254613,0.038531581840575146,0.038686016832007036,0.038778974777318426,0.038810010369722009,0.038778974777318426,0.038686016832007036,0.038531581840575146,0.038316408031254613,0.038041520675422928,0.037708223949943408,0.037318090630520308,0.036872949730034972,0.036374872217800745,0.035826154975725236,0.035229303165229757,0.034587011194218059,0.03390214248621843,0.0331777082639007,0.032416845566391364,0.031622794724124298,0.030798876516363507,0.029948469235059987,0.029074985874439876,0.028181851658793586,0.027272482111509955,0.026350261856676941,0.025418524330781987,0.024480532566446708,0.023539461193001633,0.022598379780337338,0.021660237633162393,0.020727850122861366,0.019803886623882407,0.018890860101292078,0.017991118376101539,0.017106837075463645,0.01624001425611583,0.015392466671726591,0.01456582763829458,0.013761546436622795,0.012980889177287638,0.012224941041557115,0.011494609801463957,0.010790630513757976,0.010113571275767206,0.009463839926280181,0.008841691571385462,0.0082472368137088171,0.007680450563589577,0.0071411813123333067,0.0066291607506484777,0.0061440136195883696,0.0056852676866321261,0.0052523637458022042],[0.005612960016569659,0.0060755845849529491,0.0065658253040016389,0.007084279771472639,0.0076314526405823584,0.0082077449333402795,0.0088134433795690539,0.0094487098896551738,0.010113571275767206,0.010807909341956395,0.01153145146805697,0.012283761815478149,0.013064233284684921,0.013872080354272776,0.01470633292994313,0.015565831328291937,0.016449222515069122,0.017354957710412202,0.018281291464493494,0.019226282296068629,0.020187794973626445,0.021163504504304504,0.022150901879568849,0.023147301609014716,0.024149851054711482,0.025155541558504801,0.026161221333845405,0.027163610072304993,0.028159315193254715,0.029144849643526829,0.030116651132574227,0.031071102668010917,0.032004554236786595,0.032913345458942769,0.033793829024229186,0.034642394707123977,0.035455493743273642,0.036229663340296314,0.036961551088488531,0.037647939032418289,0.038285767162811166,0.038872156089631731,0.039404428661872666,0.039880130307281554,0.040297047876024499,0.040653226785999134,0.040946986284011236,0.041176932656117389,0.041341970241863292,0.041441310130627143,0.041474476443487916,0.041441310130627143,0.041341970241863292,0.041176932656117389,0.040946986284011236,0.040653226785999128,0.040297047876024492,0.039880130307281547,0.039404428661872673,0.038872156089631731,0.038285767162811166,0.037647939032418289,0.036961551088488531,0.036229663340296314,0.035455493743273642,0.034642394707123977,0.033793829024229179,0.032913345458942762,0.032004554236786588,0.03107110266801091,0.03011665113257422,0.029144849643526833,0.028159315193254715,0.027163610072304993,0.026161221333845405,0.025155541558504801,0.024149851054711482,0.023147301609014716,0.022150901879568849,0.021163504504304504,0.020187794973626442,0.019226282296068622,0.018281291464493487,0.017354957710412188,0.016449222515069122,0.015565831328291937,0.01470633292994313,0.013872080354272776,0.013064233284684921,0.012283761815478149,0.01153145146805697,0.010807909341956395,0.010113571275767202,0.0094487098896551686,0.0088134433795690522,0.0082077449333402761,0.007631452640582361,0.007084279771472639,0.0065658253040016389,0.0060755845849529491,0.005612960016569659],[0.0059887230707933534,0.0064823183249220345,0.0070053785098765477,0.0075585412299625163,0.0081423449227157416,0.0087572174568103251,0.0094034647573729251,0.010081259573980258,0.010790630513757976,0.01153145146805697,0.012303431565987108,0.013106105791475574,0.013938826402336273,0.014800755289952028,0.015690857416465871,0.016607895462756317,0.017550425814864767,0.018516796008910014,0.019505143744854091,0.020513397567798807,0.021539279301848627,0.022580308306066572,0.023633807604802045,0.024696911925846457,0.025766577659671622,0.02683959473165598,0.027912600356964769,0.028982094624908104,0.030044457836464162,0.031095969495550109,0.032132828831891197,0.033151176711325607,0.034147118768438567,0.035116749576888068,0.036056177655,0.036961551088488538,0.037829083538791879,0.038655080394766256,0.039435964817582519,0.040168303423806673,0.04084883134996483,0.041474476443487916,0.042042382329850872,0.042549930113954922,0.042994758485291842,0.043374782011060473,0.043688207419012137,0.043933547692167868,0.044109633820411574,0.044215624079015574,0.044251010731052316,0.044215624079015574,0.044109633820411574,0.043933547692167868,0.043688207419012137,0.043374782011060466,0.042994758485291835,0.042549930113954915,0.042042382329850879,0.041474476443487916,0.04084883134996483,0.040168303423806673,0.039435964817582519,0.038655080394766256,0.037829083538791879,0.036961551088488538,0.036056177654999993,0.035116749576888061,0.03414711876843856,0.0331511767113256,0.03213282883189119,0.031095969495550116,0.030044457836464162,0.028982094624908104,0.027912600356964769,0.02683959473165598,0.025766577659671622,0.024696911925846457,0.023633807604802045,0.022580308306066572,0.021539279301848624,0.020513397567798804,0.019505143744854084,0.01851679600891,0.017550425814864767,0.016607895462756317,0.015690857416465871,0.014800755289952028,0.013938826402336273,0.013106105791475574,0.012303431565987108,0.01153145146805697,0.010790630513757971,0.010081259573980253,0.0094034647573729216,0.0087572174568103216,0.0081423449227157451,0.0075585412299625163,0.0070053785098765477,0.0064823183249220345,0.0059887230707933534],[0.0063794265608507874,0.0069052239031682479,0.0074624084644474018,0.0080516594462132721,0.0086735504135942894,0.0093285371493594775,0.010016945537149735,0.010738959596700997,0.011494609801463957,0.012283761815478149,0.013106105791475574,0.013961146375797184,0.014848193567643525,0.015766354580303624,0.016714526850189523,0.017691392335646171,0.018695413241533902,0.019724829297449484,0.020777656707150219,0.021851688874298131,0.022944498995107757,0.024053444591960047,0.025175674043671933,0.026308135148060172,0.027447585730919103,0.028590606292789318,0.029733614661204388,0.030872882591770349,0.032004554236786595,0.033124666375504763,0.034229170275907057,0.035313955034436448,0.036374872217800731,0.03740776161016706,0.03840847785011875,0.039372917724998506,0.040297047876024492,0.041176932656117382,0.042008761873962443,0.042788878152650867,0.043513803629453542,0.04418026572497976,0.044785221715213486,0.045325881848690887,0.045799730763322839,0.046204546972951878,0.046538420212488309,0.046799766452164861,0.046987340415802235,0.047100245464664382,0.04713794073713469,0.047100245464664382,0.046987340415802235,0.046799766452164861,0.046538420212488309,0.046204546972951871,0.045799730763322832,0.04532588184869088,0.044785221715213493,0.04418026572497976,0.043513803629453542,0.042788878152650867,0.042008761873962443,0.041176932656117382,0.040297047876024492,0.039372917724998506,0.038408477850118743,0.037407761610167053,0.036374872217800724,0.035313955034436441,0.03422917027590705,0.03312466637550477,0.032004554236786595,0.030872882591770349,0.029733614661204388,0.028590606292789318,0.027447585730919103,0.026308135148060172,0.025175674043671933,0.024053444591960047,0.022944498995107754,0.021851688874298125,0.020777656707150212,0.019724829297449474,0.018695413241533902,0.017691392335646171,0.016714526850189523,0.015766354580303624,0.014848193567643525,0.013961146375797184,0.013106105791475574,0.012283761815478149,0.011494609801463952,0.010738959596700992,0.010016945537149732,0.009328537149359474,0.0086735504135942929,0.0080516594462132721,0.0074624084644474018,0.0069052239031682479,0.0063794265608507874],[0.006784755196771599,0.0073439600432744986,0.0079365463536019715,0.0085632364836009875,0.0092246404409185804,0.0099212429673228766,0.01065339065207312,0.011421279206938664,0.012224941041557115,0.013064233284684921,0.013938826402336273,0.014848193567643525,0.015791600939333447,0.016768099005844285,0.017776515150176406,0.018815447586466558,0.019883260812923801,0.020978082717117319,0.022097803458650235,0.023240076241015307,0.024402320068971358,0.02558172457020871,0.026775256940531494,0.027979671050459756,0.029191518728268202,0.030407163210290657,0.031622794724124298,0.032834448144489367,0.034038022635287969,0.03522930316522975,0.036403983758638694,0.037557692318116072,0.038686016832007043,0.039784532757490651,0.040848831349964844,0.04187454869158614,0.042857395156681383,0.043793185039573197,0.044677866061412254,0.045507548467100381,0.046278533421483671,0.046987340415802256,0.047630733400956235,0.048205745373475724,0.048709701153100679,0.049140238107452217,0.049495324599223928,0.049773275954394902,0.049972767775866393,0.050092846455306046,0.050132936766456603,0.050092846455306046,0.049972767775866393,0.049773275954394902,0.049495324599223928,0.04914023810745221,0.048709701153100672,0.048205745373475717,0.047630733400956242,0.046987340415802256,0.046278533421483671,0.045507548467100381,0.044677866061412254,0.043793185039573197,0.042857395156681383,0.04187454869158614,0.040848831349964837,0.039784532757490644,0.038686016832007036,0.037557692318116065,0.036403983758638687,0.035229303165229757,0.034038022635287969,0.032834448144489367,0.031622794724124298,0.030407163210290657,0.029191518728268202,0.027979671050459756,0.026775256940531494,0.02558172457020871,0.024402320068971355,0.0232400762410153,0.022097803458650228,0.020978082717117305,0.019883260812923801,0.018815447586466558,0.017776515150176406,0.016768099005844285,0.015791600939333447,0.014848193567643525,0.013938826402336273,0.013064233284684921,0.01222494104155711,0.011421279206938658,0.010653390652073116,0.0099212429673228731,0.0092246404409185839,0.0085632364836009875,0.0079365463536019715,0.0073439600432744986,0.006784755196771599],[0.0072043010272956369,0.0077980851703177033,0.0084273149716058825,0.0090927574549980999,0.0097950603489076471,0.01053473836985956,0.011312159538995937,0.012127531670226073,0.012980889177287638,0.013872080354272776,0.014800755289952028,0.015766354580303624,0.016768099005844285,0.017804980340496372,0.018875753456674579,0.019978929886918871,0.021112772995655688,0.022275294905486749,0.02346425531077127,0.024677162297210557,0.025911275269731068,0.02716361007230499,0.028430946362598634,0.029709837281695361,0.030996621434838494,0.032287437173456141,0.033578239141976961,0.03486481702546728,0.036142816406286957,0.037407761610167067,0.03865508039476627,0.039880130307281554,0.041078226512494008,0.04224467086913461,0.043374782011060486,0.044463926170819332,0.045507548467100381,0.046501204364642307,0.047440591005666118,0.048321578106051442,0.049140238107452223,0.04989287527846667,0.050576053463894079,0.051186622191016405,0.051721740855664944,0.052178900728433744,0.052555944542581522,0.052851083449663869,0.053062911156439206,0.053190415086729136,0.053232984444271166,0.053190415086729136,0.053062911156439206,0.052851083449663869,0.052555944542581522,0.052178900728433737,0.051721740855664937,0.051186622191016398,0.050576053463894086,0.04989287527846667,0.049140238107452223,0.048321578106051442,0.047440591005666118,0.046501204364642307,0.045507548467100381,0.044463926170819332,0.04337478201106048,0.042244670869134603,0.041078226512494001,0.039880130307281547,0.038655080394766263,0.037407761610167074,0.036142816406286957,0.03486481702546728,0.033578239141976961,0.032287437173456141,0.030996621434838494,0.029709837281695361,0.028430946362598634,0.02716361007230499,0.025911275269731065,0.02467716229721055,0.023464255310771263,0.022275294905486735,0.021112772995655688,0.019978929886918871,0.018875753456674579,0.017804980340496372,0.016768099005844285,0.015766354580303624,0.014800755289952028,0.013872080354272776,0.012980889177287631,0.012127531670226068,0.011312159538995933,0.010534738369859555,0.0097950603489076523,0.0090927574549980999,0.0084273149716058825,0.0077980851703177033,0.0072043010272956369],[0.0076375602454110186,0.0082670539531167833,0.0089341249843435961,0.0096395864909502686,0.010384125155067441,0.011168286647740003,0.011992461122521192,0.012856868891034027,0.013761546436622795,0.01470633292994313,0.015690857416465871,0.016714526850189523,0.017776515150176406,0.018875753456674579,0.020010921761412597,0.021180442082035712,0.022382473343501793,0.023614908119520304,0.024875371374784579,0.026161221333845408,0.027469552585073935,0.028797201508382976,0.030140754093379116,0.031496556190612812,0.032860726212830794,0.034229170275907064,0.035597599740767115,0.036961551088488538,0.038316408031254613,0.039657425732371507,0.040979756979568897,0.042278480127730181,0.043548628600488186,0.044785221715213493,0.045983296573241628,0.04713794073713469,0.048244325399727388,0.049297738736001212,0.050293619118757349,0.051227587872857104,0.052095481240654627,0.052893381233281161,0.053617645048713525,0.054264932748060428,0.054832232896154222,0.055316885891195267,0.055716604730650009,0.056029492986577369,0.056254059792713619,0.056389231677595499,0.05643436111230455,0.056389231677595499,0.056254059792713619,0.056029492986577369,0.055716604730650009,0.05531688589119526,0.054832232896154215,0.054264932748060414,0.053617645048713532,0.052893381233281161,0.052095481240654627,0.051227587872857104,0.050293619118757349,0.049297738736001212,0.048244325399727388,0.04713794073713469,0.045983296573241614,0.044785221715213486,0.043548628600488179,0.042278480127730174,0.04097975697956889,0.039657425732371514,0.038316408031254613,0.036961551088488538,0.035597599740767115,0.034229170275907064,0.032860726212830794,0.031496556190612812,0.030140754093379116,0.028797201508382976,0.027469552585073932,0.026161221333845401,0.024875371374784572,0.023614908119520286,0.022382473343501793,0.021180442082035712,0.020010921761412597,0.018875753456674579,0.017776515150176406,0.016714526850189523,0.015690857416465871,0.01470633292994313,0.013761546436622788,0.012856868891034021,0.011992461122521189,0.011168286647739998,0.010384125155067446,0.0096395864909502686,0.0089341249843435961,0.0082670539531167833,0.0076375602454110186],[0.0080839305832440186,0.0087502144844073346,0.0094562718819605172,0.010202963451691261,0.010991016008249596,0.011821007113933748,0.01269334972447039,0.013608277027397159,0.01456582763829458,0.015565831328291937,0.016607895462756317,0.017691392335646171,0.018815447586466558,0.019978929886918871,0.021180442082035712,0.022418313965703162,0.023690596862904468,0.024995060180715369,0.026329190077027286,0.027690190380201391,0.029074985874439883,0.030480228044725551,0.031902303351898774,0.033337344083032683,0.034781241794998828,0.036229663340296328,0.037678069434197992,0.039121735691433353,0.040555776029397028,0.041975168303683051,0.04337478201106048,0.044749407865291364,0.046093789022920655,0.047402653709803254,0.04867074897512684,0.04989287527846667,0.051063921597366627,0.05217890072843373,0.053232984444271166,0.054221538162010779,0.055140154776936796,0.055984687316845652,0.056751280079426938,0.057436397926065474,0.058036853420974303,0.058549831524319182,0.058972911571760836,0.059304086300333195,0.059541777711434929,0.059684849595528798,0.059732616579451212,0.059684849595528798,0.059541777711434929,0.059304086300333195,0.058972911571760836,0.058549831524319168,0.058036853420974296,0.057436397926065468,0.056751280079426945,0.055984687316845652,0.055140154776936796,0.054221538162010779,0.053232984444271166,0.05217890072843373,0.051063921597366627,0.04989287527846667,0.048670748975126833,0.047402653709803247,0.046093789022920648,0.044749407865291357,0.043374782011060473,0.041975168303683058,0.040555776029397028,0.039121735691433353,0.037678069434197992,0.036229663340296328,0.034781241794998828,0.033337344083032683,0.031902303351898774,0.030480228044725551,0.029074985874439879,0.027690190380201381,0.026329190077027276,0.024995060180715355,0.023690596862904468,0.022418313965703162,0.021180442082035712,0.019978929886918871,0.018815447586466558,0.017691392335646171,0.016607895462756317,0.015565831328291937,0.014565827638294573,0.013608277027397152,0.012693349724470386,0.011821007113933742,0.010991016008249602,0.010202963451691261,0.0094562718819605172,0.0087502144844073346,0.0080839305832440186],[0.0085427093584435534,0.0092468061662075839,0.0099929336935985266,0.010782001461428119,0.011614777532490659,0.012491872246867534,0.013413721996325671,0.014380573202248762,0.015392466671726591,0.016449222515069122,0.017550425814864767,0.018695413241533902,0.019883260812923801,0.021112772995655688,0.022382473343501793,0.023690596862904468,0.025035084287751665,0.026413578434634565,0.027823422796018175,0.029261662512087616,0.03072504784257055,0.032210040237713254,0.033712821082984332,0.03522930316522975,0.036755144879186998,0.038285767162811166,0.039816373118142755,0.041341970241863306,0.04285739515668139,0.044357340701733285,0.045836385207756368,0.047289023751392191,0.048709701153100679,0.050092846455306046,0.051432908592026004,0.052724392938809143,0.053961898412739503,0.055140154776936783,0.056254059792713633,0.057298715855614836,0.058269465749164903,0.059161927152426269,0.059972025544487217,0.060696025160744072,0.061330557672232819,0.061872648280136368,0.062319738942708612,0.062669708480908165,0.062920889341645539,0.063072080833283556,0.063122558686399266,0.063072080833283556,0.062920889341645539,0.062669708480908165,0.062319738942708612,0.061872648280136361,0.061330557672232812,0.060696025160744058,0.059972025544487224,0.059161927152426269,0.058269465749164903,0.057298715855614836,0.056254059792713633,0.055140154776936783,0.053961898412739503,0.052724392938809143,0.05143290859202599,0.050092846455306039,0.048709701153100665,0.047289023751392177,0.045836385207756361,0.044357340701733299,0.04285739515668139,0.041341970241863306,0.039816373118142755,0.038285767162811166,0.036755144879186998,0.03522930316522975,0.033712821082984332,0.032210040237713254,0.030725047842570543,0.029261662512087606,0.027823422796018165,0.026413578434634547,0.025035084287751665,0.023690596862904468,0.022382473343501793,0.021112772995655688,0.019883260812923801,0.018695413241533902,0.017550425814864767,0.016449222515069122,0.015392466671726586,0.014380573202248755,0.013413721996325666,0.012491872246867531,0.011614777532490664,0.010782001461428119,0.0099929336935985266,0.0092468061662075839,0.0085427093584435534],[0.0090130922304875512,0.0097559583636185644,0.010543169532570874,0.011375685338639316,0.012254316136070222,0.013179705871791283,0.014152314966387922,0.015172403409819485,0.016240014256115841,0.017354957710412202,0.018516796008910014,0.019724829297449484,0.020978082717117319,0.022275294905486749,0.023614908119520304,0.024995060180715369,0.026413578434634565,0.027867975905474716,0.02935544981177398,0.030872882591770363,0.032416845566391364,0.03398360534451314,0.035569133049169366,0.037169116415061383,0.038778974777318426,0.040393876939324981,0.042008761873962457,0.043618362178234678,0.045217230166425565,0.046799766452164875,0.048360250835565548,0.04989287527846667,0.051391778719295067,0.052851083449663883,0.054264932748060442,0.055627529442314388,0.05693317505242089,0.05817630914911967,0.059351548551742711,0.060453725981525021,0.061477927784042721,0.062419530336843443,0.063274234765737333,0.064038099605609342,0.06470757105890633,0.065279510526972923,0.06575121911590795,0.066120458849264444,0.066385470354323017,0.066544986826371971,0.066598244115908492,0.066544986826371971,0.066385470354323017,0.066120458849264444,0.06575121911590795,0.065279510526972923,0.064707571058906316,0.064038099605609328,0.063274234765737333,0.062419530336843443,0.061477927784042721,0.060453725981525021,0.059351548551742711,0.05817630914911967,0.05693317505242089,0.055627529442314388,0.054264932748060435,0.052851083449663869,0.05139177871929506,0.049892875278466663,0.048360250835565541,0.046799766452164882,0.045217230166425565,0.043618362178234678,0.042008761873962457,0.040393876939324981,0.038778974777318426,0.037169116415061383,0.035569133049169366,0.03398360534451314,0.032416845566391357,0.030872882591770352,0.029355449811773973,0.027867975905474698,0.026413578434634565,0.024995060180715369,0.023614908119520304,0.022275294905486749,0.020978082717117319,0.019724829297449484,0.018516796008910014,0.017354957710412202,0.016240014256115834,0.015172403409819478,0.014152314966387919,0.01317970587179128,0.012254316136070227,0.011375685338639316,0.010543169532570874,0.0097559583636185644,0.0090130922304875512],[0.0094941727206312616,0.010276689885206174,0.011105919034816126,0.011982870990187584,0.012908399358826475,0.013883182458805893,0.014907705286001879,0.015982241707530903,0.017106837075463649,0.018281291464493494,0.019505143744854091,0.020777656707150219,0.022097803458650235,0.02346425531077127,0.024875371374784579,0.026329190077027286,0.027823422796018175,0.02935544981177398,0.030922318742291226,0.03252074562363403,0.034147118768438574,0.035797505513057673,0.037467661936225437,0.039153045602280973,0.04084883134996483,0.042549930113954922,0.044251010731052323,0.045946524646714809,0.047630733400956235,0.049297738736001219,0.050941515132046415,0.052555944542581515,0.054134853067519965,0.055672049271425481,0.057161363825925959,0.058596690130481965,0.059972025544487217,0.061281512846640976,0.062519481525009982,0.063680488493488396,0.064759357827698996,0.065751219115907936,0.066651544028323503,0.067456180721203532,0.068161385710411748,0.068763852872259099,0.069260739257378467,0.069649687435668295,0.069928844126583956,0.070096874908771631,0.070152974845681407,0.070096874908771631,0.069928844126583956,0.069649687435668295,0.069260739257378467,0.068763852872259099,0.068161385710411734,0.067456180721203518,0.066651544028323503,0.065751219115907936,0.064759357827698996,0.063680488493488396,0.062519481525009982,0.061281512846640976,0.059972025544487217,0.058596690130481965,0.057161363825925945,0.055672049271425474,0.054134853067519959,0.052555944542581508,0.050941515132046401,0.049297738736001233,0.047630733400956235,0.045946524646714809,0.044251010731052323,0.042549930113954922,0.04084883134996483,0.039153045602280973,0.037467661936225437,0.035797505513057673,0.034147118768438567,0.032520745623634023,0.030922318742291215,0.029355449811773963,0.027823422796018175,0.026329190077027286,0.024875371374784579,0.02346425531077127,0.022097803458650235,0.020777656707150219,0.019505143744854091,0.018281291464493494,0.017106837075463642,0.015982241707530896,0.014907705286001875,0.013883182458805888,0.01290839935882648,0.011982870990187584,0.011105919034816126,0.010276689885206174,0.0094941727206312616],[0.0099849425435298688,0.0108079093419564,0.011680002746817587,0.012602285829870448,0.013575656323034575,0.014600827607789892,0.01567830975026839,0.016808390774240338,0.017991118376101546,0.019226282296068629,0.020513397567798807,0.021851688874298131,0.023240076241015307,0.024677162297210557,0.026161221333845408,0.027690190380201391,0.029261662512087616,0.030872882591770363,0.03252074562363403,0.034201797890100527,0.035912241009586308,0.037647939032418289,0.039404428661872666,0.041176932656117396,0.042960376433158178,0.044749407865291364,0.046538420212488323,0.048321578106051442,0.050092846455306046,0.051846022111570626,0.053574768085746516,0.055272650079166367,0.056933175052420883,0.058549831524319175,0.060116131263486056,0.061625652008886596,0.063072080833283542,0.064449257745714722,0.065751219115907936,0.066972240495443564,0.068106878407671587,0.069150010681049826,0.070096874908771631,0.070943104631279646,0.07168476285742012,0.07231837256438671,0.072840943845957962,0.073249997412488846,0.07354358418423336,0.073720300761344115,0.073779300598741493,0.073720300761344115,0.07354358418423336,0.073249997412488846,0.072840943845957962,0.072318372564386696,0.071684762857420106,0.070943104631279633,0.070096874908771631,0.069150010681049826,0.068106878407671587,0.066972240495443564,0.065751219115907936,0.064449257745714722,0.063072080833283542,0.061625652008886596,0.060116131263486042,0.058549831524319161,0.056933175052420869,0.055272650079166354,0.053574768085746502,0.051846022111570633,0.050092846455306046,0.048321578106051442,0.046538420212488323,0.044749407865291364,0.042960376433158178,0.041176932656117396,0.039404428661872666,0.037647939032418289,0.035912241009586301,0.03420179789010052,0.032520745623634023,0.030872882591770342,0.029261662512087616,0.027690190380201391,0.026161221333845408,0.024677162297210557,0.023240076241015307,0.021851688874298131,0.020513397567798807,0.019226282296068629,0.017991118376101539,0.016808390774240331,0.015678309750268387,0.014600827607789886,0.01357565632303458,0.012602285829870448,0.011680002746817587,0.0108079093419564,0.0099849425435298688],[0.010484292791926746,0.011348416429606495,0.012264123511406154,0.013232530273649649,0.014254579344124033,0.015331019780750797,0.016462387158236332,0.017648983904514026,0.018890860101292081,0.020187794973626445,0.021539279301848627,0.022944498995107757,0.024402320068971358,0.025911275269731068,0.027469552585073935,0.029074985874439883,0.03072504784257055,0.032416845566391364,0.034147118768438574,0.035912241009586308,0.037708223949943401,0.039530724799638393,0.041375057051015816,0.043236204550814221,0.045108838935530991,0.046987340415802249,0.048865821856693366,0.050738156060806075,0.052598006120603516,0.054438858665906011,0.056254059792713619,0.058036853420974296,0.05978042179225028,0.0614779277840427,0.063122558686399266,0.064707571058906316,0.066226336262766861,0.067672386243852259,0.069039459128786271,0.070321544187608082,0.071512925713616698,0.072608225373792759,0.073602442591804665,0.074490992540021839,0.075269741337072898,0.075935038073101604,0.07648374331569667,0.076913253785125535,0.077221522927525418,0.077407077158562709,0.077469027597160969,0.077407077158562709,0.077221522927525418,0.076913253785125535,0.07648374331569667,0.075935038073101591,0.075269741337072885,0.074490992540021839,0.073602442591804665,0.072608225373792759,0.071512925713616698,0.070321544187608082,0.069039459128786271,0.067672386243852259,0.066226336262766861,0.064707571058906316,0.063122558686399266,0.061477927784042687,0.059780421792250266,0.058036853420974283,0.056254059792713612,0.054438858665906024,0.052598006120603516,0.050738156060806075,0.048865821856693366,0.046987340415802249,0.045108838935530991,0.043236204550814221,0.041375057051015816,0.039530724799638393,0.037708223949943401,0.035912241009586295,0.03414711876843856,0.032416845566391343,0.03072504784257055,0.029074985874439883,0.027469552585073935,0.025911275269731068,0.024402320068971358,0.022944498995107757,0.021539279301848627,0.020187794973626445,0.018890860101292074,0.017648983904514019,0.016462387158236325,0.015331019780750792,0.014254579344124038,0.013232530273649649,0.012264123511406154,0.011348416429606495,0.010484292791926746],[0.010991016008249595,0.011896904170983703,0.012856868891034025,0.013872080354272774,0.014943526747247476,0.016071993331088243,0.017258041565713103,0.01850198849589782,0.019803886623882407,0.021163504504304504,0.022580308306066572,0.024053444591960047,0.02558172457020871,0.02716361007230499,0.028797201508382976,0.030480228044725551,0.032210040237713254,0.03398360534451314,0.035797505513057673,0.037647939032418289,0.039530724799638393,0.041441310130627122,0.043374782011060459,0.045325881848690873,0.047289023751392177,0.049258316316082906,0.051227587872857097,0.053190415086729115,0.055140154776936776,0.057069978771343594,0.058972911571760808,0.060841870565609878,0.062669708480908137,0.064449257745714708,0.066173376380534055,0.067834995023320646,0.069427164662197755,0.070943104631279605,0.072376250410489812,0.073720300761344087,0.074969263727580282,0.076117501032446022,0.077159770413482459,0.078091265450754274,0.078907652465564096,0.079605104093542128,0.080180329168314635,0.080630598589332581,0.080953766889399079,0.081148289263411735,0.081213233869201068,0.081148289263411735,0.080953766889399079,0.080630598589332581,0.080180329168314635,0.079605104093542128,0.078907652465564082,0.07809126545075426,0.077159770413482473,0.076117501032446022,0.074969263727580282,0.073720300761344087,0.072376250410489812,0.070943104631279605,0.069427164662197755,0.067834995023320646,0.066173376380534055,0.064449257745714708,0.062669708480908123,0.060841870565609864,0.058972911571760794,0.057069978771343607,0.055140154776936776,0.053190415086729115,0.051227587872857097,0.049258316316082906,0.047289023751392177,0.045325881848690873,0.043374782011060459,0.041441310130627122,0.039530724799638386,0.037647939032418275,0.035797505513057659,0.033983605344513119,0.032210040237713254,0.030480228044725551,0.028797201508382976,0.02716361007230499,0.02558172457020871,0.024053444591960047,0.022580308306066572,0.021163504504304504,0.019803886623882397,0.018501988495897813,0.017258041565713096,0.016071993331088236,0.014943526747247481,0.013872080354272774,0.012856868891034025,0.011896904170983703,0.010991016008249595],[0.011503809168561334,0.012451962145895727,0.013456714658285983,0.014519291487404298,0.015640726924298663,0.016821842866979374,0.018063226970650274,0.019365211072021962,0.020727850122861366,0.022150901879568849,0.023633807604802045,0.025175674043671933,0.026775256940531494,0.028430946362598634,0.030140754093379116,0.031902303351898774,0.033712821082984332,0.035569133049169366,0.037467661936225437,0.039404428661872666,0.041375057051015816,0.043374782011060459,0.045398461307732389,0.047440591005666104,0.049495324599223914,0.051556495817996144,0.053617645048713518,0.055672049271425467,0.057712755363353983,0.059732616579451191,0.061724331975021973,0.063680488493488382,0.065593605402140848,0.067456180721203518,0.069260739257378454,0.07099988182283315,0.072666335194921036,0.074253002351280656,0.075753012499786387,0.077159770413482473,0.078467004577403007,0.079668813657244611,0.08075971080930755,0.081734665366938422,0.082589141460778573,0.083319133158228531,0.083921195741358923,0.084392472781619918,0.084730718713615927,0.084934316658335271,0.085002291297892441,0.084934316658335271,0.084730718713615927,0.084392472781619918,0.083921195741358923,0.083319133158228517,0.082589141460778559,0.081734665366938408,0.080759710809307564,0.079668813657244611,0.078467004577403007,0.077159770413482473,0.075753012499786387,0.074253002351280656,0.072666335194921036,0.07099988182283315,0.06926073925737844,0.067456180721203504,0.065593605402140834,0.063680488493488369,0.061724331975021959,0.059732616579451205,0.057712755363353983,0.055672049271425467,0.053617645048713518,0.051556495817996144,0.049495324599223914,0.047440591005666104,0.045398461307732389,0.043374782011060459,0.041375057051015809,0.039404428661872652,0.037467661936225423,0.035569133049169345,0.033712821082984332,0.031902303351898774,0.030140754093379116,0.028430946362598634,0.026775256940531494,0.025175674043671933,0.023633807604802045,0.022150901879568849,0.020727850122861356,0.019365211072021955,0.01806322697065027,0.016821842866979367,0.015640726924298669,0.014519291487404298,0.013456714658285983,0.012451962145895727,0.011503809168561334],[0.012021277595150495,0.013012080726199879,0.01406202937267753,0.015172403409819481,0.016344283653520707,0.01757852897269948,0.018875753456674579,0.020236303868953278,0.021660237633162393,0.023147301609014716,0.024696911925846457,0.026308135148060172,0.027979671050459756,0.029709837281695361,0.031496556190612812,0.033337344083032683,0.03522930316522975,0.037169116415061383,0.039153045602280973,0.041176932656117396,0.043236204550814221,0.045325881848690873,0.047440591005666104,0.049574580506400498,0.051721740855664937,0.053875628409685822,0.056029492986577376,0.058176309149119663,0.060308811006698319,0.062419530336843415,0.064500837781174533,0.066544986826371944,0.068544160238752497,0.070490518581823702,0.07237625041048984,0.074193623704025422,0.075935038073101591,0.077593077254578424,0.0791605613919205,0.080630598589332594,0.081996635224336908,0.083252504506716105,0.084392472781619918,0.085411283091162263,0.086304195531899219,0.08706702397494949,0.08769616875085931,0.088188644942196096,0.088542105972744714,0.088754862232467993,0.088825894531385133,0.088754862232467993,0.088542105972744714,0.088188644942196096,0.08769616875085931,0.087067023974949476,0.086304195531899205,0.085411283091162249,0.084392472781619932,0.083252504506716105,0.081996635224336908,0.080630598589332594,0.0791605613919205,0.077593077254578424,0.075935038073101591,0.074193623704025422,0.072376250410489826,0.070490518581823688,0.068544160238752483,0.06654498682637193,0.064500837781174533,0.062419530336843429,0.060308811006698319,0.058176309149119663,0.056029492986577376,0.053875628409685822,0.051721740855664937,0.049574580506400498,0.047440591005666104,0.045325881848690873,0.043236204550814214,0.041176932656117382,0.039153045602280959,0.037169116415061362,0.03522930316522975,0.033337344083032683,0.031496556190612812,0.029709837281695361,0.027979671050459756,0.026308135148060172,0.024696911925846457,0.023147301609014716,0.021660237633162382,0.020236303868953268,0.018875753456674572,0.017578528972699473,0.016344283653520711,0.015172403409819481,0.01406202937267753,0.013012080726199879,0.012021277595150495],[0.012541939804212972,0.013575656323034577,0.01467108005128704,0.015829546297804239,0.017052182690476543,0.018339885297312321,0.019693294804894967,0.021112772995655688,0.022598379780337338,0.024149851054711482,0.025766577659671622,0.027447585730919103,0.029191518728268202,0.030996621434838494,0.032860726212830794,0.034781241794998828,0.036755144879186998,0.038778974777318426,0.04084883134996483,0.042960376433158178,0.045108838935530991,0.047289023751392177,0.049495324599223914,0.051721740855664937,0.053961898412739503,0.056209074541379203,0.058456226697710577,0.060696025160744058,0.062920889341645539,0.065123027556384702,0.067294480005947274,0.069427164662197768,0.071512925713616698,0.073543584184233374,0.075510990301829395,0.077407077158562709,0.079223915179170074,0.080953766889399106,0.082589141460778587,0.084122848497652447,0.085548050528881245,0.086858313669956541,0.088047655931574723,0.08911059266796173,0.090042178682302965,0.090838046537275188,0.091494440655549208,0.092008246837784427,0.092377016873513754,0.092598987972783209,0.09267309680274094,0.092598987972783209,0.092377016873513754,0.092008246837784427,0.091494440655549208,0.090838046537275174,0.090042178682302951,0.089110592667961716,0.088047655931574736,0.086858313669956541,0.085548050528881245,0.084122848497652447,0.082589141460778587,0.080953766889399106,0.079223915179170074,0.077407077158562709,0.075510990301829381,0.07354358418423336,0.071512925713616685,0.069427164662197755,0.06729448000594726,0.065123027556384716,0.062920889341645539,0.060696025160744058,0.058456226697710577,0.056209074541379203,0.053961898412739503,0.051721740855664937,0.049495324599223914,0.047289023751392177,0.045108838935530984,0.042960376433158171,0.040848831349964816,0.038778974777318405,0.036755144879186998,0.034781241794998828,0.032860726212830794,0.030996621434838494,0.029191518728268202,0.027447585730919103,0.025766577659671622,0.024149851054711482,0.022598379780337328,0.021112772995655678,0.01969329480489496,0.018339885297312314,0.01705218269047655,0.015829546297804239,0.01467108005128704,0.013575656323034577,0.012541939804212972],[0.013064233284684923,0.014140997641948178,0.015282038928612808,0.016488748060787893,0.017762299625024486,0.01910362700496842,0.020513397567798811,0.021991988161926147,0.023539461193001633,0.025155541558504801,0.02683959473165598,0.028590606292789318,0.030407163210290657,0.032287437173456141,0.034229170275907064,0.036229663340296328,0.038285767162811166,0.040393876939324981,0.042549930113954922,0.044749407865291364,0.046987340415802249,0.049258316316082906,0.051556495817996144,0.053875628409685822,0.056209074541379203,0.058549831524319168,0.060890563536653841,0.063223635620281535,0.065541151502176667,0.06783499502332066,0.070096874908771617,0.072318372564386696,0.074490992540021839,0.076606215256427024,0.078655551554258477,0.080630598589332608,0.08252309656908903,0.084324985801785865,0.086028463512719103,0.08762603987115071,0.089110592667961744,0.090475420087527389,0.091714291028041336,0.092821492442479392,0.093791873197457618,0.094620883979158729,0.095304612813907744,0.095839815815406723,0.096223942820509334,0.096455157630066943,0.096532352630053914,0.096455157630066943,0.096223942820509334,0.095839815815406723,0.095304612813907744,0.094620883979158715,0.093791873197457604,0.092821492442479378,0.09171429102804135,0.090475420087527389,0.089110592667961744,0.08762603987115071,0.086028463512719103,0.084324985801785865,0.08252309656908903,0.080630598589332608,0.078655551554258463,0.07660621525642701,0.074490992540021825,0.072318372564386682,0.070096874908771603,0.067834995023320674,0.065541151502176667,0.063223635620281535,0.060890563536653841,0.058549831524319168,0.056209074541379203,0.053875628409685822,0.051556495817996144,0.049258316316082906,0.046987340415802242,0.04474940786529135,0.042549930113954915,0.040393876939324953,0.038285767162811166,0.036229663340296328,0.034229170275907064,0.032287437173456141,0.030407163210290657,0.028590606292789318,0.02683959473165598,0.025155541558504801,0.023539461193001623,0.021991988161926136,0.020513397567798804,0.019103627004968413,0.017762299625024493,0.016488748060787893,0.015282038928612808,0.014140997641948178,0.013064233284684923],[0.013586521193461716,0.014706332929943137,0.015892991288383319,0.017147942791573351,0.018472408984224021,0.019867360565220551,0.021333491582053162,0.022871193948950898,0.024480532566446708,0.026161221333845405,0.027912600356964769,0.029733614661204388,0.031622794724124298,0.033578239141976961,0.035597599740767115,0.037678069434197992,0.039816373118142755,0.042008761873962457,0.044251010731052323,0.046538420212488323,0.048865821856693366,0.051227587872857097,0.053617645048713518,0.056029492986577376,0.058456226697710577,0.060890563536653841,0.06332487440670552,0.065751219115907936,0.068161385710411748,0.070546933559671496,0.072899239916353747,0.075209549623898725,0.077469027597160969,0.079668813657244625,0.081800079261301006,0.083854085632388664,0.085822242764172788,0.08769616875085931,0.089467748874839187,0.091129193873486711,0.092673096802740954,0.094092487918718992,0.095380887009769252,0.096532352630053928,0.09754152771181665,0.09840368106668626,0.099114744326310414,0.099671343918817268,0.10007082772946889,0.10031128615070507,0.10039156728779881,0.10031128615070507,0.10007082772946889,0.099671343918817268,0.099114744326310414,0.098403681066686247,0.097541527711816636,0.096532352630053914,0.095380887009769266,0.094092487918718992,0.092673096802740954,0.091129193873486711,0.089467748874839187,0.08769616875085931,0.085822242764172788,0.083854085632388664,0.081800079261300992,0.079668813657244611,0.077469027597160955,0.075209549623898711,0.072899239916353734,0.07054693355967151,0.068161385710411748,0.065751219115907936,0.06332487440670552,0.060890563536653841,0.058456226697710577,0.056029492986577376,0.053617645048713518,0.051227587872857097,0.048865821856693359,0.046538420212488309,0.044251010731052309,0.042008761873962429,0.039816373118142755,0.037678069434197992,0.035597599740767115,0.033578239141976961,0.031622794724124298,0.029733614661204388,0.027912600356964769,0.026161221333845405,0.024480532566446698,0.022871193948950888,0.021333491582053155,0.019867360565220545,0.018472408984224028,0.017147942791573351,0.015892991288383319,0.014706332929943137,0.013586521193461716],[0.014107099941119392,0.015269818186418567,0.016501944337043228,0.017804980340496372,0.01918019454598029,0.020628594845507338,0.022150901879568859,0.023747522578910302,0.025418524330781987,0.027163610072304993,0.028982094624908104,0.030872882591770349,0.032834448144489367,0.03486481702546728,0.036961551088488538,0.039121735691433353,0.041341970241863306,0.043618362178234678,0.045946524646714809,0.048321578106051442,0.050738156060806075,0.053190415086729115,0.055672049271425467,0.058176309149119663,0.060696025160744058,0.063223635620281535,0.065751219115907936,0.06827053122067224,0.070773045332951021,0.073249997412488846,0.0756924343242876,0.078091265450754288,0.080437317183180645,0.082721389857620328,0.084934316658335299,0.08706702397494949,0.08911059266796173,0.091056319671955155,0.092895779347233295,0.094620883979158715,0.096223942820509362,0.097697719075926018,0.099035484239111446,0.10023106921283791,0.10127891166888656,0.1021740991395078,0.10291240737346569,0.10349033353770404,0.10390512389952482,0.10415479568318164,0.10423815285815245,0.10415479568318164,0.10390512389952482,0.10349033353770404,0.10291240737346569,0.10217409913950778,0.10127891166888654,0.10023106921283789,0.09903548423911146,0.097697719075926018,0.096223942820509362,0.094620883979158715,0.092895779347233295,0.091056319671955155,0.08911059266796173,0.08706702397494949,0.084934316658335285,0.082721389857620314,0.080437317183180632,0.07809126545075426,0.075692434324287586,0.07324999741248886,0.070773045332951021,0.06827053122067224,0.065751219115907936,0.063223635620281535,0.060696025160744058,0.058176309149119663,0.055672049271425467,0.053190415086729115,0.050738156060806068,0.048321578106051429,0.045946524646714795,0.04361836217823465,0.041341970241863306,0.039121735691433353,0.036961551088488538,0.03486481702546728,0.032834448144489367,0.030872882591770349,0.028982094624908104,0.027163610072304993,0.025418524330781976,0.023747522578910291,0.022150901879568849,0.020628594845507331,0.019180194545980297,0.017804980340496372,0.016501944337043228,0.015269818186418567,0.014107099941119392],[0.014624207630993185,0.015829546297804243,0.017106837075463652,0.018457636966631524,0.019883260812923798,0.021384753451487718,0.02296286193850185,0.024618008121102587,0.026350261856676941,0.028159315193254715,0.030044457836464162,0.032004554236786595,0.034038022635287969,0.036142816406286957,0.038316408031254613,0.040555776029397028,0.04285739515668139,0.045217230166425565,0.047630733400956235,0.050092846455306046,0.052598006120603516,0.055140154776936776,0.057712755363353983,0.060308811006698319,0.062920889341645539,0.065541151502176667,0.068161385710411748,0.070773045332951021,0.073367291218370864,0.075935038073101604,0.078467004577403021,0.080953766889399106,0.083385815133989072,0.085753612425757117,0.08804765593157475,0.090258539440196822,0.092377016873513768,0.094394066147878819,0.096300952774640208,0.098089292577134279,0.099751112897289385,0.10127891166888656,0.10266571374653462,0.10390512389952485,0.10499137590778909,0.10591937723291403,0.10668474878015885,0.10728385931715663,0.10771385417080621,0.10797267788503788,0.10805909058781833,0.10797267788503788,0.10771385417080621,0.10728385931715663,0.10668474878015885,0.10591937723291402,0.10499137590778908,0.10390512389952483,0.10266571374653463,0.10127891166888656,0.099751112897289385,0.098089292577134279,0.096300952774640208,0.094394066147878819,0.092377016873513768,0.090258539440196822,0.088047655931574736,0.085753612425757103,0.083385815133989058,0.080953766889399092,0.078467004577402993,0.075935038073101618,0.073367291218370864,0.070773045332951021,0.068161385710411748,0.065541151502176667,0.062920889341645539,0.060308811006698319,0.057712755363353983,0.055140154776936776,0.052598006120603509,0.050092846455306032,0.047630733400956221,0.045217230166425537,0.04285739515668139,0.040555776029397028,0.038316408031254613,0.036142816406286957,0.034038022635287969,0.032004554236786595,0.030044457836464162,0.028159315193254715,0.026350261856676931,0.024618008121102573,0.02296286193850184,0.021384753451487711,0.019883260812923804,0.018457636966631524,0.017106837075463652,0.015829546297804243,0.014624207630993185],[0.015136033303221483,0.016383557043505914,0.017705551112270207,0.019103627004968423,0.020579145580731498,0.022133188244463968,0.023766528198207511,0.025479602053125369,0.027272482111509948,0.029144849643526829,0.031095969495550109,0.033124666375504763,0.03522930316522975,0.037407761610167067,0.039657425732371507,0.041975168303683051,0.044357340701733285,0.046799766452164875,0.049297738736001219,0.051846022111570626,0.054438858665906011,0.057069978771343594,0.059732616579451191,0.062419530336843415,0.065123027556384702,0.06783499502332066,0.070546933559671496,0.073249997412488846,0.075935038073101604,0.078592652276080963,0.081213233869201082,0.083787029190036014,0.086304195531899219,0.088754862232467993,0.091129193873486725,0.093417455040206362,0.095610076055436782,0.09769771907592599,0.099671343918817254,0.10152227297364416,0.10324225455107541,0.10482352402365233,0.10625886212619486,0.10754164980436302,0.10866591902890098,0.10962639903007085,0.11041855745128229,0.11103863597239758,0.11148368001097241,0.11175156217300977,0.11184099919278612,0.11175156217300977,0.11148368001097241,0.11103863597239758,0.11041855745128229,0.10962639903007083,0.10866591902890096,0.10754164980436301,0.10625886212619487,0.10482352402365233,0.10324225455107541,0.10152227297364416,0.099671343918817254,0.09769771907592599,0.095610076055436782,0.093417455040206362,0.091129193873486711,0.088754862232467979,0.086304195531899205,0.083787029190036,0.081213233869201054,0.078592652276080976,0.075935038073101604,0.073249997412488846,0.070546933559671496,0.06783499502332066,0.065123027556384702,0.062419530336843415,0.059732616579451191,0.057069978771343594,0.054438858665906004,0.051846022111570605,0.049297738736001205,0.04679976645216484,0.044357340701733285,0.041975168303683051,0.039657425732371507,0.037407761610167067,0.03522930316522975,0.033124666375504763,0.031095969495550109,0.029144849643526829,0.027272482111509937,0.025479602053125359,0.023766528198207505,0.022133188244463961,0.020579145580731505,0.019103627004968423,0.017705551112270207,0.016383557043505914,0.015136033303221483],[0.015640726924298666,0.016929847908804932,0.018295922349238675,0.019740615474516342,0.021265333520051333,0.022871193948950892,0.024558995744789446,0.026329190077027283,0.028181851658793593,0.030116651132574227,0.032132828831891197,0.034229170275907057,0.036403983758638694,0.03865508039476627,0.040979756979568897,0.04337478201106048,0.045836385207756368,0.048360250835565548,0.050941515132046415,0.053574768085746516,0.056254059792713619,0.058972911571760808,0.061724331975021973,0.064500837781174533,0.067294480005947274,0.070096874908771617,0.072899239916353747,0.0756924343242876,0.078467004577403021,0.081213233869201082,0.083921195741358937,0.086580811306795694,0.089181909665091375,0.091714291028041336,0.094167792026680922,0.096532352630053914,0.098798084071091266,0.10095533714689815,0.10299477024011842,0.10490741639534565,0.10668474878015885,0.10831874386452758,0.10980194166517793,0.11112750242301619,0.11228925911171539,0.11328176521378314,0.11410033724641171,0.11474109157260118,0.11520097509275401,0.11547778947736728,0.11557020867169789,0.11547778947736728,0.11520097509275401,0.11474109157260118,0.11410033724641171,0.11328176521378312,0.11228925911171538,0.11112750242301618,0.10980194166517795,0.10831874386452758,0.10668474878015885,0.10490741639534565,0.10299477024011842,0.10095533714689815,0.098798084071091266,0.096532352630053914,0.094167792026680908,0.091714291028041323,0.089181909665091347,0.08658081130679568,0.083921195741358909,0.081213233869201096,0.078467004577403021,0.0756924343242876,0.072899239916353747,0.070096874908771617,0.067294480005947274,0.064500837781174533,0.061724331975021973,0.058972911571760808,0.056254059792713612,0.053574768085746502,0.050941515132046394,0.048360250835565513,0.045836385207756368,0.04337478201106048,0.040979756979568897,0.03865508039476627,0.036403983758638694,0.034229170275907057,0.032132828831891197,0.030116651132574227,0.028181851658793583,0.026329190077027272,0.024558995744789435,0.022871193948950885,0.02126533352005134,0.019740615474516342,0.018295922349238675,0.016929847908804932,0.015640726924298666],[0.016136410051965418,0.017466385628757176,0.018875753456674582,0.020366231538771856,0.021939270676624271,0.02359602374778054,0.025337315057059998,0.027163610072304997,0.029074985874439883,0.031071102668010917,0.033151176711325607,0.035313955034436448,0.037557692318116072,0.039880130307281554,0.042278480127730181,0.044749407865291364,0.047289023751392191,0.04989287527846667,0.052555944542581515,0.055272650079166367,0.058036853420974296,0.060841870565609878,0.063680488493488382,0.066544986826371944,0.069427164662197768,0.072318372564386696,0.075209549623898725,0.078091265450754288,0.080953766889399106,0.083787029190036014,0.086580811306795694,0.089324714934305757,0.092008246837784413,0.094620883979158715,0.097152140893787722,0.099591638730008675,0.10192917532771055,0.10415479568318162,0.10625886212619486,0.10823212352219264,0.11006578280790193,0.11175156217300977,0.11328176521378312,0.11464933540670313,0.11584791028114454,0.11687187070955418,0.11771638478102261,0.11837744577901889,0.11885190384565765,0.11913749098236948,0.11923283910932092,0.11913749098236948,0.11885190384565765,0.11837744577901889,0.11771638478102261,0.11687187070955417,0.11584791028114452,0.11464933540670312,0.11328176521378314,0.11175156217300977,0.11006578280790193,0.10823212352219264,0.10625886212619486,0.10415479568318162,0.10192917532771055,0.099591638730008675,0.097152140893787708,0.094620883979158701,0.092008246837784399,0.089324714934305743,0.08658081130679568,0.083787029190036041,0.080953766889399106,0.078091265450754288,0.075209549623898725,0.072318372564386696,0.069427164662197768,0.066544986826371944,0.063680488493488382,0.060841870565609878,0.058036853420974283,0.055272650079166347,0.052555944542581501,0.049892875278466635,0.047289023751392191,0.044749407865291364,0.042278480127730181,0.039880130307281554,0.037557692318116072,0.035313955034436448,0.033151176711325607,0.031071102668010917,0.029074985874439869,0.027163610072304986,0.025337315057059991,0.023596023747780533,0.021939270676624281,0.020366231538771856,0.018875753456674582,0.017466385628757176,0.016136410051965418],[0.016621187095070565,0.017991118376101546,0.019442827044767613,0.020978082717117316,0.022598379780337335,0.024304905747224687,0.026098509686722313,0.027979671050459759,0.029948469235059991,0.032004554236786595,0.034147118768438567,0.036374872217800731,0.038686016832007043,0.041078226512494008,0.043548628600488186,0.046093789022920655,0.048709701153100679,0.051391778719295067,0.054134853067519965,0.056933175052420883,0.05978042179225028,0.062669708480908137,0.065593605402140848,0.068544160238752497,0.071512925713616698,0.074490992540021839,0.077469027597160969,0.080437317183180645,0.083385815133989072,0.086304195531899219,0.089181909665091375,0.092008246837784413,0.094772398572877239,0.097463525694614181,0.1000708277294689,0.10258361401980673,0.10499137590778908,0.1072838593171566,0.10945113703860512,0.11148368001097242,0.11337242688578771,0.11510885116716335,0.11668502523266076,0.11809368056361504,0.11932826354529348,0.12038298623787108,0.12125287156807107,0.12193379244784334,0.12242250438990307,0.12271667125948227,0.12281488387629858,0.12271667125948227,0.12242250438990307,0.12193379244784334,0.12125287156807107,0.12038298623787107,0.11932826354529347,0.11809368056361502,0.11668502523266079,0.11510885116716335,0.11337242688578771,0.11148368001097242,0.10945113703860512,0.1072838593171566,0.10499137590778908,0.10258361401980673,0.10007082772946889,0.097463525694614167,0.094772398572877226,0.092008246837784399,0.089181909665091347,0.086304195531899233,0.083385815133989072,0.080437317183180645,0.077469027597160969,0.074490992540021839,0.071512925713616698,0.068544160238752497,0.065593605402140848,0.062669708480908137,0.059780421792250266,0.056933175052420862,0.054134853067519952,0.051391778719295032,0.048709701153100679,0.046093789022920655,0.043548628600488186,0.041078226512494008,0.038686016832007043,0.036374872217800731,0.034147118768438567,0.032004554236786595,0.02994846923505998,0.027979671050459745,0.026098509686722306,0.02430490574722468,0.022598379780337342,0.020978082717117316,0.019442827044767613,0.017991118376101546,0.016621187095070565],[0.017093157078531655,0.018501988495897827,0.01999491942579118,0.02157376973371913,0.023240076241015307,0.024995060180715359,0.026839594731655987,0.028774172959823895,0.030798876516363514,0.032913345458942769,0.035116749576888068,0.03740776161016706,0.039784532757490651,0.04224467086913461,0.044785221715213493,0.047402653709803254,0.050092846455306046,0.052851083449663883,0.055672049271425481,0.058549831524319175,0.0614779277840427,0.064449257745714708,0.067456180721203518,0.070490518581823702,0.073543584184233374,0.076606215256427024,0.079668813657244625,0.082721389857620328,0.085753612425757117,0.088754862232467993,0.091714291028041336,0.094620883979158715,0.097463525694614181,0.10023106921283791,0.1029124073734657,0.10549654595032244,0.10797267788503787,0.11033025792983915,0.11255907698551951,0.11464933540670313,0.11659171454172762,0.11837744577901892,0.11999837638587342,0.12144703144906403,0.12271667125948227,0.12380134352479043,0.12469592984430961,0.12539618593849985,0.12589877519063927,0.12620129512981429,0.12630229656110392,0.12620129512981429,0.12589877519063927,0.12539618593849985,0.12469592984430961,0.12380134352479041,0.12271667125948225,0.12144703144906402,0.11999837638587345,0.11837744577901892,0.11659171454172762,0.11464933540670313,0.11255907698551951,0.11033025792983915,0.10797267788503787,0.10549654595032244,0.10291240737346569,0.10023106921283788,0.097463525694614167,0.094620883979158701,0.091714291028041323,0.088754862232468007,0.085753612425757117,0.082721389857620328,0.079668813657244625,0.076606215256427024,0.073543584184233374,0.070490518581823702,0.067456180721203518,0.064449257745714708,0.061477927784042687,0.058549831524319154,0.05567204927142546,0.052851083449663848,0.050092846455306046,0.047402653709803254,0.044785221715213493,0.04224467086913461,0.039784532757490651,0.03740776161016706,0.035116749576888068,0.032913345458942769,0.0307988765163635,0.028774172959823881,0.026839594731655977,0.024995060180715352,0.023240076241015314,0.02157376973371913,0.01999491942579118,0.018501988495897827,0.017093157078531655],[0.017550425814864774,0.018996945680243547,0.020529814851891107,0.022150901879568863,0.023861784696989279,0.025663717207085348,0.027557595947595888,0.029543927174795377,0.031622794724124298,0.033793829024229186,0.036056177655,0.03840847785011875,0.040848831349964844,0.043374782011060486,0.045983296573241628,0.04867074897512684,0.051432908592026004,0.054264932748060442,0.057161363825925959,0.060116131263486056,0.063122558686399266,0.066173376380534055,0.069260739257378454,0.07237625041048984,0.075510990301829395,0.078655551554258477,0.081800079261301006,0.084934316658335299,0.08804765593157475,0.091129193873486725,0.094167792026680922,0.097152140893787722,0.1000708277294689,0.1029124073734657,0.10566547553146959,0.1083187438645276,0.11086111620852374,0.11328176521378314,0.1155702086716979,0.11771638478102263,0.1197107256015609,0.1215442279476389,0.12320852098817812,0.12469592984430963,0.12599953450914539,0.12711322345720058,0.12803174136255779,0.12875073040454865,0.12926676470672563,0.12957737752831355,0.12968108090615649,0.12957737752831355,0.12926676470672563,0.12875073040454865,0.12803174136255779,0.12711322345720058,0.12599953450914539,0.12469592984430962,0.12320852098817814,0.1215442279476389,0.1197107256015609,0.11771638478102263,0.1155702086716979,0.11328176521378314,0.11086111620852374,0.1083187438645276,0.10566547553146956,0.10291240737346569,0.10007082772946889,0.097152140893787708,0.094167792026680908,0.091129193873486738,0.08804765593157475,0.084934316658335299,0.081800079261301006,0.078655551554258477,0.075510990301829395,0.07237625041048984,0.069260739257378454,0.066173376380534055,0.063122558686399266,0.060116131263486035,0.057161363825925939,0.054264932748060407,0.051432908592026004,0.04867074897512684,0.045983296573241628,0.043374782011060486,0.040848831349964844,0.03840847785011875,0.036056177655,0.033793829024229186,0.031622794724124284,0.029543927174795363,0.027557595947595877,0.025663717207085338,0.023861784696989286,0.022150901879568863,0.020529814851891107,0.018996945680243547,0.017550425814864774],[0.017991118376101546,0.019473960468136136,0.021045320104255621,0.022707112753651681,0.024460955972075381,0.026308135148060175,0.028249569331477438,0.030285777490736188,0.032416845566391364,0.034642394707123977,0.036961551088488538,0.039372917724998506,0.04187454869158614,0.044463926170819332,0.04713794073713469,0.04989287527846667,0.052724392938809143,0.055627529442314388,0.058596690130481965,0.061625652008886596,0.064707571058906316,0.067834995023320646,0.07099988182283315,0.074193623704025422,0.077407077158562709,0.080630598589332608,0.083854085632388664,0.08706702397494949,0.090258539440196822,0.093417455040206362,0.096532352630053914,0.099591638730008675,0.10258361401980673,0.10549654595032244,0.1083187438645276,0.11103863597239759,0.11364484748426988,0.1161262791748747,0.11847218562652832,0.12067225238537123,0.12271667125948228,0.12459621299249314,0.12630229656110389,0.12782705436963859,0.12916339264929638,0.13030504641371085,0.13124662837532078,0.13198367128824096,0.13251266325199898,0.13283107558576643,0.1329373829635164,0.13283107558576643,0.13251266325199898,0.13198367128824096,0.13124662837532078,0.13030504641371082,0.12916339264929638,0.12782705436963857,0.12630229656110392,0.12459621299249314,0.12271667125948228,0.12067225238537123,0.11847218562652832,0.1161262791748747,0.11364484748426988,0.11103863597239759,0.10831874386452758,0.10549654595032243,0.10258361401980672,0.099591638730008647,0.0965323526300539,0.09341745504020639,0.090258539440196822,0.08706702397494949,0.083854085632388664,0.080630598589332608,0.077407077158562709,0.074193623704025422,0.07099988182283315,0.067834995023320646,0.064707571058906302,0.061625652008886575,0.058596690130481945,0.055627529442314354,0.052724392938809143,0.04989287527846667,0.04713794073713469,0.044463926170819332,0.04187454869158614,0.039372917724998506,0.036961551088488538,0.034642394707123977,0.03241684556639135,0.030285777490736174,0.028249569331477428,0.026308135148060165,0.024460955972075392,0.022707112753651681,0.021045320104255621,0.019473960468136136,0.017991118376101546],[0.01841339175340518,0.019931037948504489,0.021539279301848638,0.023240076241015307,0.025035084287751662,0.026925619000219621,0.028912620999506148,0.030996621434838497,0.0331777082639007,0.035455493743273642,0.037829083538791879,0.040297047876024492,0.042857395156681383,0.045507548467100381,0.048244325399727388,0.051063921597366627,0.053961898412739503,0.05693317505242089,0.059972025544487217,0.063072080833283542,0.066226336262766861,0.069427164662197755,0.072666335194921036,0.075935038073101591,0.079223915179170074,0.08252309656908903,0.085822242764172788,0.08911059266796173,0.092377016873513768,0.095610076055436782,0.098798084071091266,0.10192917532771055,0.10499137590778908,0.10797267788503787,0.11086111620852374,0.11364484748426988,0.11631222994249912,0.11885190384565765,0.12125287156807109,0.12350457656313303,0.1255969804287575,0.12752063728673113,0.1292667647067256,0.13082731043104853,0.13219501419153831,0.13336346395499699,0.13432714598768786,0.13508148819204452,0.13562289623902943,0.13594878209660702,0.13605758463749787,0.13594878209660702,0.13562289623902943,0.13508148819204452,0.13432714598768786,0.13336346395499696,0.13219501419153828,0.1308273104310485,0.12926676470672563,0.12752063728673113,0.1255969804287575,0.12350457656313303,0.12125287156807109,0.11885190384565765,0.11631222994249912,0.11364484748426988,0.11086111620852372,0.10797267788503785,0.10499137590778906,0.10192917532771052,0.098798084071091252,0.095610076055436796,0.092377016873513768,0.08911059266796173,0.085822242764172788,0.08252309656908903,0.079223915179170074,0.075935038073101591,0.072666335194921036,0.069427164662197755,0.066226336262766861,0.063072080833283528,0.059972025544487197,0.056933175052420855,0.053961898412739503,0.051063921597366627,0.048244325399727388,0.045507548467100381,0.042857395156681383,0.040297047876024492,0.037829083538791879,0.035455493743273642,0.033177708263900686,0.030996621434838483,0.028912620999506138,0.02692561900021961,0.025035084287751672,0.023240076241015307,0.021539279301848638,0.019931037948504489,0.01841339175340518],[0.018815447586466555,0.020366231538771852,0.022009588791768921,0.023747522578910298,0.02558172457020871,0.027513539048997407,0.029543927174795367,0.031673431694456605,0.03390214248621843,0.036229663340296314,0.038655080394766256,0.041176932656117382,0.043793185039573197,0.046501204364642307,0.049297738736001212,0.05217890072843373,0.055140154776936783,0.05817630914911967,0.061281512846640976,0.064449257745714722,0.067672386243852259,0.070943104631279605,0.074253002351280656,0.077593077254578424,0.080953766889399106,0.084324985801785865,0.08769616875085931,0.091056319671955155,0.094394066147878819,0.09769771907592599,0.10095533714689815,0.10415479568318162,0.1072838593171566,0.11033025792983915,0.11328176521378314,0.1161262791748747,0.11885190384565765,0.12144703144906399,0.12390042422660665,0.12620129512981426,0.12833938656840524,0.13030504641371082,0.13208930047131121,0.13368392066271903,0.13508148819204449,0.13627545101954533,0.13726017501928109,0.13803098826207802,0.13858421793683645,0.13891721950192223,0.13902839774289066,0.13891721950192223,0.13858421793683645,0.13803098826207802,0.13726017501928109,0.1362754510195453,0.13508148819204446,0.133683920662719,0.13208930047131121,0.13030504641371082,0.12833938656840524,0.12620129512981426,0.12390042422660665,0.12144703144906399,0.11885190384565765,0.1161262791748747,0.11328176521378312,0.11033025792983912,0.10728385931715659,0.10415479568318159,0.10095533714689812,0.097697719075926018,0.094394066147878819,0.091056319671955155,0.08769616875085931,0.084324985801785865,0.080953766889399106,0.077593077254578424,0.074253002351280656,0.070943104631279605,0.067672386243852245,0.064449257745714708,0.061281512846640955,0.058176309149119636,0.055140154776936783,0.05217890072843373,0.049297738736001212,0.046501204364642307,0.043793185039573197,0.041176932656117382,0.038655080394766256,0.036229663340296314,0.033902142486218416,0.031673431694456591,0.029543927174795356,0.0275135390489974,0.025581724570208721,0.023747522578910298,0.022009588791768921,0.020366231538771852,0.018815447586466555],[0.01919554484091637,0.020777656707150222,0.022454211978800521,0.024227254357319927,0.026098509686722313,0.028069349406665632,0.030140754093379123,0.032313277457930549,0.034587011194218059,0.036961551088488531,0.039435964817582519,0.042008761873962443,0.044677866061412254,0.047440591005666118,0.050293619118757349,0.053232984444271166,0.056254059792713633,0.059351548551742711,0.062519481525009982,0.065751219115907936,0.069039459128786271,0.072376250410489812,0.075753012499786387,0.0791605613919205,0.082589141460778587,0.086028463512719103,0.089467748874839187,0.092895779347233295,0.096300952774640208,0.099671343918817254,0.10299477024011842,0.10625886212619486,0.10945113703860512,0.11255907698551951,0.1155702086716979,0.11847218562652832,0.12125287156807109,0.12390042422660665,0.12640337882586763,0.12875073040454862,0.13093201415529887,0.1329373829635164,0.13475768134402849,0.13638451500013646,0.1378103152663322,0.13902839774289069,0.14003301448697761,0.1408193991901894,0.14138380484572052,0.14172353348865208,0.14183695767906987,0.14172353348865208,0.14138380484572052,0.1408193991901894,0.14003301448697761,0.13902839774289066,0.1378103152663322,0.13638451500013646,0.13475768134402849,0.1329373829635164,0.13093201415529887,0.12875073040454862,0.12640337882586763,0.12390042422660665,0.12125287156807109,0.11847218562652832,0.11557020867169789,0.11255907698551949,0.10945113703860511,0.10625886212619483,0.1029947702401184,0.099671343918817282,0.096300952774640208,0.092895779347233295,0.089467748874839187,0.086028463512719103,0.082589141460778587,0.0791605613919205,0.075753012499786387,0.072376250410489812,0.069039459128786271,0.065751219115907922,0.062519481525009968,0.059351548551742669,0.056254059792713633,0.053232984444271166,0.050293619118757349,0.047440591005666118,0.044677866061412254,0.042008761873962443,0.039435964817582519,0.036961551088488531,0.034587011194218045,0.032313277457930535,0.030140754093379112,0.028069349406665622,0.026098509686722324,0.024227254357319927,0.022454211978800521,0.020777656707150222,0.01919554484091637],[0.019552012309622557,0.021163504504304514,0.022871193948950898,0.024677162297210554,0.026583167442578218,0.028590606292789318,0.030700477633690451,0.032913345458942776,0.035229303165229757,0.037647939032418289,0.040168303423806673,0.042788878152650867,0.045507548467100381,0.048321578106051442,0.051227587872857104,0.054221538162010779,0.057298715855614836,0.060453725981525021,0.063680488493488396,0.066972240495443564,0.070321544187608082,0.073720300761344087,0.077159770413482473,0.080630598589332594,0.084122848497652447,0.08762603987115071,0.091129193873486711,0.094620883979158715,0.098089292577134279,0.10152227297364416,0.10490741639534565,0.10823212352219264,0.11148368001097242,0.11464933540670313,0.11771638478102263,0.12067225238537123,0.12350457656313303,0.12620129512981426,0.12875073040454862,0.13114167306034413,0.13336346395499699,0.13540607310980599,0.13726017501928109,0.13891721950192226,0.14036949733965784,0.14161020000130053,0.14263347280286082,0.14343446092404832,0.14400934777493066,0.1443553852885088,0.14447091580278371,0.1443553852885088,0.14400934777493066,0.14343446092404832,0.14263347280286082,0.14161020000130051,0.14036949733965781,0.13891721950192223,0.13726017501928112,0.13540607310980599,0.13336346395499699,0.13114167306034413,0.12875073040454862,0.12620129512981426,0.12350457656313303,0.12067225238537123,0.11771638478102261,0.11464933540670311,0.11148368001097241,0.10823212352219261,0.10490741639534563,0.10152227297364418,0.098089292577134279,0.094620883979158715,0.091129193873486711,0.08762603987115071,0.084122848497652447,0.080630598589332594,0.077159770413482473,0.073720300761344087,0.070321544187608068,0.06697224049544355,0.063680488493488369,0.060453725981524979,0.057298715855614836,0.054221538162010779,0.051227587872857104,0.048321578106051442,0.045507548467100381,0.042788878152650867,0.040168303423806673,0.037647939032418289,0.035229303165229736,0.032913345458942762,0.030700477633690441,0.028590606292789308,0.026583167442578225,0.024677162297210554,0.022871193948950898,0.021163504504304514,0.019552012309622557],[0.019883260812923801,0.021522054769138883,0.023258675740816071,0.02509524064880048,0.027033537168666549,0.029074985874439879,0.031220602473310582,0.033470960514071703,0.035826154975725236,0.038285767162811166,0.04084883134996483,0.043513803629453542,0.046278533421483671,0.049140238107452223,0.052095481240654627,0.055140154776936796,0.058269465749164903,0.061477927784042721,0.064759357827698996,0.068106878407671587,0.071512925713616698,0.074969263727580282,0.078467004577403007,0.081996635224336908,0.085548050528881245,0.089110592667961744,0.092673096802740954,0.096223942820509362,0.099751112897289385,0.10324225455107541,0.10668474878015885,0.11006578280790193,0.11337242688578771,0.11659171454172762,0.1197107256015609,0.12271667125948228,0.1255969804287575,0.12833938656840524,0.13093201415529887,0.13336346395499699,0.13562289623902948,0.13770011110166258,0.13958562504549793,0.14127074303259921,0.14274762523598827,0.14400934777493071,0.14504995677588664,0.14586451516861978,0.14644914170286089,0.14680104175409725,0.14691852957636339,0.14680104175409725,0.14644914170286089,0.14586451516861978,0.14504995677588664,0.14400934777493068,0.14274762523598825,0.14127074303259921,0.13958562504549796,0.13770011110166258,0.13562289623902948,0.13336346395499699,0.13093201415529887,0.12833938656840524,0.1255969804287575,0.12271667125948228,0.11971072560156089,0.11659171454172759,0.11337242688578768,0.1100657828079019,0.10668474878015884,0.10324225455107544,0.099751112897289385,0.096223942820509362,0.092673096802740954,0.089110592667961744,0.085548050528881245,0.081996635224336908,0.078467004577403007,0.074969263727580282,0.071512925713616698,0.068106878407671559,0.064759357827698982,0.06147792778404268,0.058269465749164903,0.055140154776936796,0.052095481240654627,0.049140238107452223,0.046278533421483671,0.043513803629453542,0.04084883134996483,0.038285767162811166,0.035826154975725222,0.033470960514071689,0.031220602473310571,0.029074985874439869,0.02703353716866656,0.02509524064880048,0.023258675740816071,0.021522054769138883,0.019883260812923801],[0.020187794973626452,0.021851688874298138,0.023614908119520307,0.025479602053125369,0.02744758573091911,0.02952030148459165,0.031698780578013654,0.033983605344513147,0.036374872217800745,0.038872156089631731,0.041474476443487916,0.04418026572497976,0.046987340415802256,0.04989287527846667,0.052893381233281161,0.055984687316845652,0.059161927152426269,0.062419530336843443,0.065751219115907936,0.069150010681049826,0.072608225373792759,0.076117501032446022,0.079668813657244611,0.083252504506716105,0.086858313669956541,0.090475420087527389,0.094092487918718992,0.097697719075926018,0.10127891166888656,0.10482352402365233,0.10831874386452758,0.11175156217300977,0.11510885116716335,0.11837744577901892,0.1215442279476389,0.12459621299249314,0.12752063728673113,0.13030504641371082,0.1329373829635164,0.13540607310980599,0.13770011110166258,0.13980914081049939,0.14172353348865208,0.14343446092404835,0.14493396321407698,0.14621501043110172,0.14727155751141532,0.14809859176808288,0.14869217250518862,0.14904946229545032,0.14916874957383605,0.14904946229545032,0.14869217250518862,0.14809859176808288,0.14727155751141532,0.14621501043110172,0.14493396321407695,0.14343446092404832,0.14172353348865208,0.13980914081049939,0.13770011110166258,0.13540607310980599,0.1329373829635164,0.13030504641371082,0.12752063728673113,0.12459621299249314,0.12154422794763889,0.11837744577901889,0.11510885116716334,0.11175156217300976,0.10831874386452756,0.10482352402365235,0.10127891166888656,0.097697719075926018,0.094092487918718992,0.090475420087527389,0.086858313669956541,0.083252504506716105,0.079668813657244611,0.076117501032446022,0.072608225373792745,0.069150010681049812,0.065751219115907922,0.062419530336843401,0.059161927152426269,0.055984687316845652,0.052893381233281161,0.04989287527846667,0.046987340415802256,0.04418026572497976,0.041474476443487916,0.038872156089631731,0.036374872217800724,0.033983605344513133,0.03169878057801364,0.02952030148459164,0.02744758573091912,0.025479602053125369,0.023614908119520307,0.021851688874298138,0.020187794973626452],[0.020464224444986568,0.022150901879568859,0.023938264710778773,0.025828491713200331,0.027823422796018172,0.029924520040626998,0.032132828831891204,0.034448939476971252,0.036872949730034965,0.039404428661872666,0.042042382329850872,0.044785221715213486,0.047630733400956235,0.050576053463894079,0.053617645048713525,0.056751280079426938,0.059972025544487217,0.063274234765737333,0.066651544028323503,0.070096874908771631,0.073602442591804665,0.077159770413482459,0.08075971080930755,0.084392472781619918,0.088047655931574723,0.091714291028041336,0.095380887009769252,0.099035484239111446,0.10266571374653462,0.10625886212619486,0.10980194166517793,0.11328176521378312,0.11668502523266076,0.11999837638587342,0.12320852098817812,0.12630229656110389,0.1292667647067256,0.13208930047131121,0.13475768134402849,0.13726017501928109,0.13958562504549793,0.14172353348865208,0.14366413975559386,0.14539849475041997,0.14691852957636337,0.14821711804568696,0.14928813232022656,0.15012649107482298,0.15072819965400272,0.15109038177787359,0.15121130244511369,0.15109038177787359,0.15072819965400272,0.15012649107482298,0.14928813232022656,0.14821711804568694,0.14691852957636337,0.14539849475041997,0.14366413975559389,0.14172353348865208,0.13958562504549793,0.13726017501928109,0.13475768134402849,0.13208930047131121,0.1292667647067256,0.12630229656110389,0.1232085209881781,0.11999837638587341,0.11668502523266075,0.11328176521378311,0.10980194166517791,0.10625886212619487,0.10266571374653462,0.099035484239111446,0.095380887009769252,0.091714291028041336,0.088047655931574723,0.084392472781619918,0.08075971080930755,0.077159770413482459,0.073602442591804651,0.070096874908771603,0.066651544028323476,0.063274234765737278,0.059972025544487217,0.056751280079426938,0.053617645048713525,0.050576053463894079,0.047630733400956235,0.044785221715213486,0.042042382329850872,0.039404428661872666,0.036872949730034944,0.034448939476971238,0.032132828831891197,0.029924520040626984,0.027823422796018182,0.025828491713200331,0.023938264710778773,0.022150901879568859,0.020464224444986568],[0.0207112744739067,0.022418313965703162,0.024227254357319934,0.026140300726137187,0.028159315193254722,0.030285777490736184,0.03252074562363403,0.034864817025467287,0.037318090630520315,0.039880130307281554,0.042549930113954922,0.045325881848690887,0.048205745373475724,0.051186622191016405,0.054264932748060428,0.057436397926065474,0.060696025160744072,0.064038099605609342,0.067456180721203532,0.070943104631279646,0.074490992540021839,0.078091265450754274,0.081734665366938422,0.085411283091162263,0.08911059266796173,0.092821492442479392,0.096532352630053928,0.10023106921283791,0.10390512389952485,0.10754164980436302,0.11112750242301619,0.11464933540670313,0.11809368056361504,0.12144703144906403,0.12469592984430963,0.12782705436963859,0.13082731043104853,0.13368392066271903,0.13638451500013646,0.13891721950192226,0.14127074303259921,0.14343446092404835,0.14539849475041997,0.14715378737973997,0.14869217250518865,0.15000643790963206,0.15109038177787359,0.15193886144152891,0.15254783402048971,0.15291438851158207,0.15303676896804697,0.15291438851158207,0.15254783402048971,0.15193886144152891,0.15109038177787359,0.15000643790963206,0.14869217250518862,0.14715378737973994,0.14539849475041999,0.14343446092404835,0.14127074303259921,0.13891721950192226,0.13638451500013646,0.13368392066271903,0.13082731043104853,0.12782705436963859,0.12469592984430962,0.12144703144906402,0.11809368056361502,0.11464933540670311,0.11112750242301618,0.10754164980436304,0.10390512389952485,0.10023106921283791,0.096532352630053928,0.092821492442479392,0.08911059266796173,0.085411283091162263,0.081734665366938422,0.078091265450754274,0.074490992540021839,0.070943104631279633,0.067456180721203504,0.0640380996056093,0.060696025160744072,0.057436397926065474,0.054264932748060428,0.051186622191016405,0.048205745373475724,0.045325881848690887,0.042549930113954922,0.039880130307281554,0.037318090630520301,0.034864817025467267,0.032520745623634023,0.030285777490736174,0.028159315193254732,0.026140300726137187,0.024227254357319934,0.022418313965703162,0.0207112744739067],[0.020927795687169945,0.022652681027241835,0.024480532566446708,0.026413578434634558,0.028453700220018148,0.030602393124176629,0.032860726212830794,0.035229303165229757,0.037708223949943408,0.040297047876024499,0.042994758485291842,0.045799730763322839,0.048709701153100679,0.051721740855664944,0.054832232896154222,0.058036853420974303,0.061330557672232819,0.06470757105890633,0.068161385710411748,0.07168476285742012,0.075269741337072898,0.078907652465564096,0.082589141460778573,0.086304195531899219,0.090042178682302965,0.093791873197457618,0.09754152771181665,0.10127891166888656,0.10499137590778909,0.10866591902890098,0.11228925911171539,0.11584791028114454,0.11932826354529348,0.12271667125948227,0.12599953450914539,0.12916339264929638,0.13219501419153831,0.13508148819204449,0.1378103152663322,0.14036949733965784,0.14274762523598827,0.14493396321407698,0.14691852957636337,0.14869217250518865,0.15024664032097335,0.15157464540813301,0.152669921116033,0.1535272710134557,0.15414260995494075,0.15451299650490707,0.15463665635945761,0.15451299650490707,0.15414260995494075,0.1535272710134557,0.152669921116033,0.15157464540813298,0.15024664032097335,0.14869217250518862,0.14691852957636339,0.14493396321407698,0.14274762523598827,0.14036949733965784,0.1378103152663322,0.13508148819204449,0.13219501419153831,0.12916339264929638,0.12599953450914536,0.12271667125948225,0.11932826354529345,0.11584791028114452,0.11228925911171536,0.10866591902890101,0.10499137590778909,0.10127891166888656,0.09754152771181665,0.093791873197457618,0.090042178682302965,0.086304195531899219,0.082589141460778573,0.078907652465564096,0.075269741337072885,0.071684762857420106,0.06816138571041172,0.064707571058906288,0.061330557672232819,0.058036853420974303,0.054832232896154222,0.051721740855664944,0.048709701153100679,0.045799730763322839,0.042994758485291842,0.040297047876024499,0.037708223949943394,0.035229303165229743,0.032860726212830781,0.030602393124176619,0.028453700220018158,0.026413578434634558,0.024480532566446708,0.022652681027241835,0.020927795687169945],[0.021112772995655688,0.022852904310622518,0.024696911925846471,0.026647043665247026,0.028705197748082504,0.030872882591770352,0.033151176711325621,0.035540689121817987,0.038041520675422935,0.040653226785999134,0.043374782011060473,0.046204546972951878,0.049140238107452217,0.052178900728433744,0.055316885891195267,0.058549831524319182,0.061872648280136368,0.065279510526972923,0.068763852872259099,0.07231837256438671,0.075935038073101604,0.079605104093542128,0.083319133158228531,0.08706702397494949,0.090838046537275188,0.094620883979158729,0.09840368106668626,0.1021740991395078,0.10591937723291403,0.10962639903007085,0.11328176521378314,0.11687187070955418,0.12038298623787108,0.12380134352479043,0.12711322345720058,0.13030504641371085,0.13336346395499699,0.13627545101954533,0.13902839774289069,0.14161020000130053,0.14400934777493071,0.14621501043110172,0.14821711804568696,0.15000643790963206,0.15157464540813301,0.15291438851158209,0.15401934517946114,0.15488427305016045,0.15550505087029778,0.15587871120543176,0.15600346406888799,0.15587871120543176,0.15550505087029778,0.15488427305016045,0.15401934517946114,0.15291438851158207,0.15157464540813298,0.15000643790963206,0.14821711804568699,0.14621501043110172,0.14400934777493071,0.14161020000130053,0.13902839774289069,0.13627545101954533,0.13336346395499699,0.13030504641371085,0.12711322345720055,0.1238013435247904,0.12038298623787105,0.11687187070955415,0.11328176521378312,0.10962639903007088,0.10591937723291403,0.1021740991395078,0.09840368106668626,0.094620883979158729,0.090838046537275188,0.08706702397494949,0.083319133158228531,0.079605104093542128,0.075935038073101591,0.072318372564386682,0.068763852872259085,0.065279510526972881,0.061872648280136368,0.058549831524319182,0.055316885891195267,0.052178900728433744,0.049140238107452217,0.046204546972951878,0.043374782011060473,0.040653226785999134,0.038041520675422914,0.035540689121817973,0.033151176711325607,0.030872882591770342,0.028705197748082514,0.026647043665247026,0.024696911925846471,0.022852904310622518,0.021112772995655688],[0.021265333520051336,0.023018038993134829,0.024875371374784586,0.026839594731655987,0.028912620999506148,0.031095969495550112,0.033390726528133352,0.035797505513057687,0.038316408031254613,0.040946986284011236,0.043688207419012137,0.046538420212488309,0.049495324599223928,0.052555944542581522,0.055716604730650009,0.058972911571760836,0.062319738942708612,0.06575121911590795,0.069260739257378467,0.072840943845957962,0.07648374331569667,0.080180329168314635,0.083921195741358923,0.08769616875085931,0.091494440655549208,0.095304612813907744,0.099114744326310414,0.10291240737346569,0.10668474878015885,0.11041855745128229,0.11410033724641171,0.11771638478102261,0.12125287156807107,0.12469592984430961,0.12803174136255779,0.13124662837532078,0.13432714598768786,0.13726017501928109,0.14003301448697761,0.14263347280286082,0.14504995677588664,0.14727155751141532,0.14928813232022656,0.15109038177787359,0.152669921116033,0.15401934517946114,0.15513228624468681,0.15600346406888796,0.15662872761857838,0.15700508801668775,0.1571307423421297,0.15700508801668775,0.15662872761857838,0.15600346406888796,0.15513228624468681,0.15401934517946111,0.15266992111603297,0.15109038177787359,0.14928813232022659,0.14727155751141532,0.14504995677588664,0.14263347280286082,0.14003301448697761,0.13726017501928109,0.13432714598768786,0.13124662837532078,0.12803174136255777,0.12469592984430959,0.12125287156807106,0.11771638478102259,0.11410033724641168,0.1104185574512823,0.10668474878015885,0.10291240737346569,0.099114744326310414,0.095304612813907744,0.091494440655549208,0.08769616875085931,0.083921195741358923,0.080180329168314635,0.076483743315696656,0.072840943845957934,0.06926073925737844,0.065751219115907908,0.062319738942708612,0.058972911571760836,0.055716604730650009,0.052555944542581522,0.049495324599223928,0.046538420212488309,0.043688207419012137,0.040946986284011236,0.038316408031254599,0.035797505513057666,0.033390726528133345,0.031095969495550102,0.028912620999506158,0.026839594731655987,0.024875371374784586,0.023018038993134829,0.021265333520051336],[0.021384753451487722,0.023147301609014723,0.025015064229412538,0.026990318093676739,0.029074985874439879,0.031270595420960834,0.033578239141976954,0.035998533898054901,0.038531581840575146,0.041176932656117389,0.043933547692167868,0.046799766452164861,0.049773275954394902,0.052851083449663869,0.056029492986577369,0.059304086300333195,0.062669708480908165,0.066120458849264444,0.069649687435668295,0.073249997412488846,0.076913253785125535,0.080630598589332581,0.084392472781619918,0.088188644942196096,0.092008246837784427,0.095839815815406723,0.099671343918817268,0.10349033353770404,0.10728385931715663,0.11103863597239758,0.11474109157260118,0.11837744577901889,0.12193379244784334,0.12539618593849985,0.12875073040454865,0.13198367128824096,0.13508148819204452,0.13803098826207802,0.1408193991901894,0.14343446092404832,0.14586451516861978,0.14809859176808288,0.15012649107482298,0.15193886144152891,0.1535272710134557,0.15488427305016045,0.15600346406888796,0.15687953417450748,0.15750830902253529,0.15788678295123637,0.15801314291484361,0.15788678295123637,0.15750830902253529,0.15687953417450748,0.15600346406888796,0.15488427305016042,0.15352727101345567,0.15193886144152891,0.15012649107482301,0.14809859176808288,0.14586451516861978,0.14343446092404832,0.1408193991901894,0.13803098826207802,0.13508148819204452,0.13198367128824096,0.12875073040454862,0.12539618593849983,0.12193379244784333,0.11837744577901887,0.11474109157260116,0.1110386359723976,0.10728385931715663,0.10349033353770404,0.099671343918817268,0.095839815815406723,0.092008246837784427,0.088188644942196096,0.084392472781619918,0.080630598589332581,0.076913253785125521,0.073249997412488832,0.069649687435668267,0.066120458849264388,0.062669708480908165,0.059304086300333195,0.056029492986577369,0.052851083449663869,0.049773275954394902,0.046799766452164861,0.043933547692167868,0.041176932656117389,0.038531581840575133,0.03599853389805488,0.033578239141976947,0.03127059542096082,0.029074985874439893,0.026990318093676739,0.025015064229412538,0.023147301609014723,0.021384753451487722],[0.021470463771653604,0.023240076241015303,0.025115324873938413,0.027098495576781047,0.029191518728268195,0.031395928301294874,0.033712821082984332,0.03614281640628695,0.038686016832007036,0.041341970241863292,0.044109633820411574,0.046987340415802235,0.049972767775866393,0.053062911156439206,0.056254059792713619,0.059541777711434929,0.062920889341645539,0.066385470354323017,0.069928844126583956,0.07354358418423336,0.077221522927525418,0.080953766889399079,0.084730718713615927,0.088542105972744714,0.092377016873513754,0.096223942820509334,0.10007082772946889,0.10390512389952482,0.10771385417080621,0.11148368001097241,0.11520097509275401,0.11885190384565765,0.12242250438990307,0.12589877519063927,0.12926676470672563,0.13251266325199898,0.13562289623902943,0.13858421793683645,0.14138380484572052,0.14400934777493066,0.14644914170286089,0.14869217250518862,0.15072819965400272,0.15254783402048971,0.15414260995494075,0.15550505087029778,0.15662872761857838,0.15750830902253529,0.15813960400686766,0.15851959486311606,0.15864646127880663,0.15851959486311606,0.15813960400686766,0.15750830902253529,0.15662872761857838,0.15550505087029776,0.15414260995494075,0.15254783402048969,0.15072819965400275,0.14869217250518862,0.14644914170286089,0.14400934777493066,0.14138380484572052,0.13858421793683645,0.13562289623902943,0.13251266325199898,0.1292667647067256,0.12589877519063927,0.12242250438990306,0.11885190384565762,0.11520097509275398,0.11148368001097243,0.10771385417080621,0.10390512389952482,0.10007082772946889,0.096223942820509334,0.092377016873513754,0.088542105972744714,0.084730718713615927,0.080953766889399079,0.077221522927525404,0.073543584184233332,0.069928844126583942,0.066385470354322976,0.062920889341645539,0.059541777711434929,0.056254059792713619,0.053062911156439206,0.049972767775866393,0.046987340415802235,0.044109633820411574,0.041341970241863292,0.038686016832007022,0.036142816406286936,0.033712821082984325,0.031395928301294868,0.029191518728268206,0.027098495576781047,0.025115324873938413,0.023240076241015303,0.021470463771653604],[0.021522054769138883,0.023295919408990597,0.02517567404367195,0.027163610072305,0.029261662512087613,0.031471369021871136,0.033793829024229186,0.036229663340296328,0.038778974777318426,0.041441310130627143,0.044215624079015574,0.047100245464664382,0.050092846455306046,0.053190415086729136,0.056389231677595499,0.059684849595528798,0.063072080833283556,0.066544986826371971,0.070096874908771631,0.073720300761344115,0.077407077158562709,0.081148289263411735,0.084934316658335271,0.088754862232467993,0.092598987972783209,0.096455157630066943,0.10031128615070507,0.10415479568318164,0.10797267788503788,0.11175156217300977,0.11547778947736728,0.11913749098236948,0.12271667125948227,0.12620129512981429,0.12957737752831355,0.13283107558576643,0.13594878209660702,0.13891721950192223,0.14172353348865208,0.1443553852885088,0.14680104175409725,0.14904946229545032,0.15109038177787359,0.15291438851158207,0.15451299650490707,0.15587871120543176,0.15700508801668775,0.15788678295123637,0.15851959486311606,0.15890049879266918,0.15902767005342514,0.15890049879266918,0.15851959486311606,0.15788678295123637,0.15700508801668775,0.15587871120543173,0.15451299650490705,0.15291438851158207,0.15109038177787362,0.14904946229545032,0.14680104175409725,0.1443553852885088,0.14172353348865208,0.13891721950192223,0.13594878209660702,0.13283107558576643,0.12957737752831353,0.12620129512981426,0.12271667125948225,0.11913749098236946,0.11547778947736725,0.1117515621730098,0.10797267788503788,0.10415479568318164,0.10031128615070507,0.096455157630066943,0.092598987972783209,0.088754862232467993,0.084934316658335271,0.081148289263411735,0.077407077158562695,0.073720300761344087,0.070096874908771603,0.06654498682637193,0.063072080833283556,0.059684849595528798,0.056389231677595499,0.053190415086729136,0.050092846455306046,0.047100245464664382,0.044215624079015574,0.041441310130627143,0.038778974777318412,0.036229663340296314,0.033793829024229179,0.031471369021871129,0.029261662512087627,0.027163610072305,0.02517567404367195,0.023295919408990597,0.021522054769138883],[0.021539279301848634,0.023314563601200315,0.025195822641271334,0.027185349655036491,0.02928508120832678,0.031496556190612812,0.033820874904358172,0.036258658667553054,0.038810010369722009,0.041474476443487916,0.044251010731052316,0.04713794073713469,0.050132936766456603,0.053232984444271166,0.05643436111230455,0.059732616579451212,0.063122558686399266,0.066598244115908492,0.070152974845681407,0.073779300598741493,0.077469027597160969,0.081213233869201068,0.085002291297892441,0.088825894531385133,0.09267309680274094,0.096532352630053914,0.10039156728779881,0.10423815285815245,0.10805909058781833,0.11184099919278612,0.11557020867169789,0.11923283910932092,0.12281488387629858,0.12630229656110392,0.12968108090615649,0.1329373829635164,0.13605758463749787,0.13902839774289066,0.14183695767906987,0.14447091580278371,0.14691852957636339,0.14916874957383605,0.15121130244511369,0.15303676896804697,0.15463665635945761,0.15600346406888799,0.1571307423421297,0.15801314291484361,0.15864646127880663,0.15902767005342514,0.15915494309189535,0.15902767005342514,0.15864646127880663,0.15801314291484361,0.1571307423421297,0.15600346406888796,0.15463665635945759,0.15303676896804694,0.15121130244511369,0.14916874957383605,0.14691852957636339,0.14447091580278371,0.14183695767906987,0.13902839774289066,0.13605758463749787,0.1329373829635164,0.12968108090615646,0.12630229656110389,0.12281488387629855,0.11923283910932089,0.11557020867169786,0.11184099919278614,0.10805909058781833,0.10423815285815245,0.10039156728779881,0.096532352630053914,0.09267309680274094,0.088825894531385133,0.085002291297892441,0.081213233869201068,0.077469027597160955,0.073779300598741465,0.070152974845681393,0.06659824411590845,0.063122558686399266,0.059732616579451212,0.05643436111230455,0.053232984444271166,0.050132936766456603,0.04713794073713469,0.044251010731052316,0.041474476443487916,0.038810010369721995,0.036258658667553033,0.033820874904358166,0.031496556190612805,0.029285081208326794,0.027185349655036491,0.025195822641271334,0.023314563601200315,0.021539279301848634],[0.021522054769138883,0.023295919408990597,0.02517567404367195,0.027163610072305,0.029261662512087613,0.031471369021871136,0.033793829024229186,0.036229663340296328,0.038778974777318426,0.041441310130627143,0.044215624079015574,0.047100245464664382,0.050092846455306046,0.053190415086729136,0.056389231677595499,0.059684849595528798,0.063072080833283556,0.066544986826371971,0.070096874908771631,0.073720300761344115,0.077407077158562709,0.081148289263411735,0.084934316658335271,0.088754862232467993,0.092598987972783209,0.096455157630066943,0.10031128615070507,0.10415479568318164,0.10797267788503788,0.11175156217300977,0.11547778947736728,0.11913749098236948,0.12271667125948227,0.12620129512981429,0.12957737752831355,0.13283107558576643,0.13594878209660702,0.13891721950192223,0.14172353348865208,0.1443553852885088,0.14680104175409725,0.14904946229545032,0.15109038177787359,0.15291438851158207,0.15451299650490707,0.15587871120543176,0.15700508801668775,0.15788678295123637,0.15851959486311606,0.15890049879266918,0.15902767005342514,0.15890049879266918,0.15851959486311606,0.15788678295123637,0.15700508801668775,0.15587871120543173,0.15451299650490705,0.15291438851158207,0.15109038177787362,0.14904946229545032,0.14680104175409725,0.1443553852885088,0.14172353348865208,0.13891721950192223,0.13594878209660702,0.13283107558576643,0.12957737752831353,0.12620129512981426,0.12271667125948225,0.11913749098236946,0.11547778947736725,0.1117515621730098,0.10797267788503788,0.10415479568318164,0.10031128615070507,0.096455157630066943,0.092598987972783209,0.088754862232467993,0.084934316658335271,0.081148289263411735,0.077407077158562695,0.073720300761344087,0.070096874908771603,0.06654498682637193,0.063072080833283556,0.059684849595528798,0.056389231677595499,0.053190415086729136,0.050092846455306046,0.047100245464664382,0.044215624079015574,0.041441310130627143,0.038778974777318412,0.036229663340296314,0.033793829024229179,0.031471369021871129,0.029261662512087627,0.027163610072305,0.02517567404367195,0.023295919408990597,0.021522054769138883],[0.021470463771653604,0.023240076241015303,0.025115324873938413,0.027098495576781047,0.029191518728268195,0.031395928301294874,0.033712821082984332,0.03614281640628695,0.038686016832007036,0.041341970241863292,0.044109633820411574,0.046987340415802235,0.049972767775866393,0.053062911156439206,0.056254059792713619,0.059541777711434929,0.062920889341645539,0.066385470354323017,0.069928844126583956,0.07354358418423336,0.077221522927525418,0.080953766889399079,0.084730718713615927,0.088542105972744714,0.092377016873513754,0.096223942820509334,0.10007082772946889,0.10390512389952482,0.10771385417080621,0.11148368001097241,0.11520097509275401,0.11885190384565765,0.12242250438990307,0.12589877519063927,0.12926676470672563,0.13251266325199898,0.13562289623902943,0.13858421793683645,0.14138380484572052,0.14400934777493066,0.14644914170286089,0.14869217250518862,0.15072819965400272,0.15254783402048971,0.15414260995494075,0.15550505087029778,0.15662872761857838,0.15750830902253529,0.15813960400686766,0.15851959486311606,0.15864646127880663,0.15851959486311606,0.15813960400686766,0.15750830902253529,0.15662872761857838,0.15550505087029776,0.15414260995494075,0.15254783402048969,0.15072819965400275,0.14869217250518862,0.14644914170286089,0.14400934777493066,0.14138380484572052,0.13858421793683645,0.13562289623902943,0.13251266325199898,0.1292667647067256,0.12589877519063927,0.12242250438990306,0.11885190384565762,0.11520097509275398,0.11148368001097243,0.10771385417080621,0.10390512389952482,0.10007082772946889,0.096223942820509334,0.092377016873513754,0.088542105972744714,0.084730718713615927,0.080953766889399079,0.077221522927525404,0.073543584184233332,0.069928844126583942,0.066385470354322976,0.062920889341645539,0.059541777711434929,0.056254059792713619,0.053062911156439206,0.049972767775866393,0.046987340415802235,0.044109633820411574,0.041341970241863292,0.038686016832007022,0.036142816406286936,0.033712821082984325,0.031395928301294868,0.029191518728268206,0.027098495576781047,0.025115324873938413,0.023240076241015303,0.021470463771653604],[0.021384753451487722,0.023147301609014723,0.025015064229412538,0.026990318093676739,0.029074985874439879,0.031270595420960834,0.033578239141976954,0.035998533898054901,0.038531581840575146,0.041176932656117389,0.043933547692167868,0.046799766452164861,0.049773275954394902,0.052851083449663869,0.056029492986577369,0.059304086300333195,0.062669708480908165,0.066120458849264444,0.069649687435668295,0.073249997412488846,0.076913253785125535,0.080630598589332581,0.084392472781619918,0.088188644942196096,0.092008246837784427,0.095839815815406723,0.099671343918817268,0.10349033353770404,0.10728385931715663,0.11103863597239758,0.11474109157260118,0.11837744577901889,0.12193379244784334,0.12539618593849985,0.12875073040454865,0.13198367128824096,0.13508148819204452,0.13803098826207802,0.1408193991901894,0.14343446092404832,0.14586451516861978,0.14809859176808288,0.15012649107482298,0.15193886144152891,0.1535272710134557,0.15488427305016045,0.15600346406888796,0.15687953417450748,0.15750830902253529,0.15788678295123637,0.15801314291484361,0.15788678295123637,0.15750830902253529,0.15687953417450748,0.15600346406888796,0.15488427305016042,0.15352727101345567,0.15193886144152891,0.15012649107482301,0.14809859176808288,0.14586451516861978,0.14343446092404832,0.1408193991901894,0.13803098826207802,0.13508148819204452,0.13198367128824096,0.12875073040454862,0.12539618593849983,0.12193379244784333,0.11837744577901887,0.11474109157260116,0.1110386359723976,0.10728385931715663,0.10349033353770404,0.099671343918817268,0.095839815815406723,0.092008246837784427,0.088188644942196096,0.084392472781619918,0.080630598589332581,0.076913253785125521,0.073249997412488832,0.069649687435668267,0.066120458849264388,0.062669708480908165,0.059304086300333195,0.056029492986577369,0.052851083449663869,0.049773275954394902,0.046799766452164861,0.043933547692167868,0.041176932656117389,0.038531581840575133,0.03599853389805488,0.033578239141976947,0.03127059542096082,0.029074985874439893,0.026990318093676739,0.025015064229412538,0.023147301609014723,0.021384753451487722],[0.021265333520051336,0.023018038993134829,0.024875371374784586,0.026839594731655987,0.028912620999506148,0.031095969495550112,0.033390726528133352,0.035797505513057687,0.038316408031254613,0.040946986284011236,0.043688207419012137,0.046538420212488309,0.049495324599223928,0.052555944542581522,0.055716604730650009,0.058972911571760836,0.062319738942708612,0.06575121911590795,0.069260739257378467,0.072840943845957962,0.07648374331569667,0.080180329168314635,0.083921195741358923,0.08769616875085931,0.091494440655549208,0.095304612813907744,0.099114744326310414,0.10291240737346569,0.10668474878015885,0.11041855745128229,0.11410033724641171,0.11771638478102261,0.12125287156807107,0.12469592984430961,0.12803174136255779,0.13124662837532078,0.13432714598768786,0.13726017501928109,0.14003301448697761,0.14263347280286082,0.14504995677588664,0.14727155751141532,0.14928813232022656,0.15109038177787359,0.152669921116033,0.15401934517946114,0.15513228624468681,0.15600346406888796,0.15662872761857838,0.15700508801668775,0.1571307423421297,0.15700508801668775,0.15662872761857838,0.15600346406888796,0.15513228624468681,0.15401934517946111,0.15266992111603297,0.15109038177787359,0.14928813232022659,0.14727155751141532,0.14504995677588664,0.14263347280286082,0.14003301448697761,0.13726017501928109,0.13432714598768786,0.13124662837532078,0.12803174136255777,0.12469592984430959,0.12125287156807106,0.11771638478102259,0.11410033724641168,0.1104185574512823,0.10668474878015885,0.10291240737346569,0.099114744326310414,0.095304612813907744,0.091494440655549208,0.08769616875085931,0.083921195741358923,0.080180329168314635,0.076483743315696656,0.072840943845957934,0.06926073925737844,0.065751219115907908,0.062319738942708612,0.058972911571760836,0.055716604730650009,0.052555944542581522,0.049495324599223928,0.046538420212488309,0.043688207419012137,0.040946986284011236,0.038316408031254599,0.035797505513057666,0.033390726528133345,0.031095969495550102,0.028912620999506158,0.026839594731655987,0.024875371374784586,0.023018038993134829,0.021265333520051336],[0.021112772995655685,0.022852904310622514,0.024696911925846467,0.026647043665247023,0.0287051977480825,0.030872882591770349,0.033151176711325614,0.03554068912181798,0.038041520675422928,0.040653226785999128,0.043374782011060466,0.046204546972951871,0.04914023810745221,0.052178900728433737,0.05531688589119526,0.058549831524319168,0.061872648280136361,0.065279510526972923,0.068763852872259099,0.072318372564386696,0.075935038073101591,0.079605104093542128,0.083319133158228517,0.087067023974949476,0.090838046537275174,0.094620883979158715,0.098403681066686247,0.10217409913950778,0.10591937723291402,0.10962639903007083,0.11328176521378312,0.11687187070955417,0.12038298623787107,0.12380134352479041,0.12711322345720058,0.13030504641371082,0.13336346395499696,0.1362754510195453,0.13902839774289066,0.14161020000130051,0.14400934777493068,0.14621501043110172,0.14821711804568694,0.15000643790963206,0.15157464540813298,0.15291438851158207,0.15401934517946111,0.15488427305016042,0.15550505087029776,0.15587871120543173,0.15600346406888796,0.15587871120543173,0.15550505087029776,0.15488427305016042,0.15401934517946111,0.15291438851158204,0.15157464540813295,0.15000643790963203,0.14821711804568696,0.14621501043110172,0.14400934777493068,0.14161020000130051,0.13902839774289066,0.1362754510195453,0.13336346395499696,0.13030504641371082,0.12711322345720055,0.12380134352479039,0.12038298623787104,0.11687187070955414,0.11328176521378309,0.10962639903007086,0.10591937723291402,0.10217409913950778,0.098403681066686247,0.094620883979158715,0.090838046537275174,0.087067023974949476,0.083319133158228517,0.079605104093542128,0.075935038073101577,0.072318372564386682,0.068763852872259071,0.065279510526972881,0.061872648280136361,0.058549831524319168,0.05531688589119526,0.052178900728433737,0.04914023810745221,0.046204546972951871,0.043374782011060466,0.040653226785999128,0.038041520675422907,0.035540689121817966,0.0331511767113256,0.030872882591770338,0.028705197748082511,0.026647043665247023,0.024696911925846467,0.022852904310622514,0.021112772995655685],[0.020927795687169942,0.022652681027241831,0.024480532566446705,0.026413578434634554,0.028453700220018141,0.030602393124176626,0.032860726212830788,0.03522930316522975,0.037708223949943408,0.040297047876024492,0.042994758485291835,0.045799730763322832,0.048709701153100672,0.051721740855664937,0.054832232896154215,0.058036853420974296,0.061330557672232812,0.064707571058906316,0.068161385710411734,0.071684762857420106,0.075269741337072885,0.078907652465564082,0.082589141460778559,0.086304195531899205,0.090042178682302951,0.093791873197457604,0.097541527711816636,0.10127891166888654,0.10499137590778908,0.10866591902890096,0.11228925911171538,0.11584791028114452,0.11932826354529347,0.12271667125948225,0.12599953450914539,0.12916339264929638,0.13219501419153828,0.13508148819204446,0.1378103152663322,0.14036949733965781,0.14274762523598825,0.14493396321407695,0.14691852957636337,0.14869217250518862,0.15024664032097335,0.15157464540813298,0.15266992111603297,0.15352727101345567,0.15414260995494075,0.15451299650490705,0.15463665635945759,0.15451299650490705,0.15414260995494075,0.15352727101345567,0.15266992111603297,0.15157464540813295,0.15024664032097332,0.1486921725051886,0.14691852957636337,0.14493396321407695,0.14274762523598825,0.14036949733965781,0.1378103152663322,0.13508148819204446,0.13219501419153828,0.12916339264929638,0.12599953450914536,0.12271667125948223,0.11932826354529344,0.11584791028114449,0.11228925911171535,0.10866591902890098,0.10499137590778908,0.10127891166888654,0.097541527711816636,0.093791873197457604,0.090042178682302951,0.086304195531899205,0.082589141460778559,0.078907652465564082,0.075269741337072871,0.071684762857420092,0.06816138571041172,0.064707571058906274,0.061330557672232812,0.058036853420974296,0.054832232896154215,0.051721740855664937,0.048709701153100672,0.045799730763322832,0.042994758485291835,0.040297047876024492,0.037708223949943387,0.035229303165229736,0.032860726212830781,0.030602393124176615,0.028453700220018155,0.026413578434634554,0.024480532566446705,0.022652681027241831,0.020927795687169942],[0.020711274473906697,0.022418313965703159,0.024227254357319931,0.026140300726137183,0.028159315193254715,0.030285777490736177,0.03252074562363403,0.03486481702546728,0.037318090630520308,0.039880130307281547,0.042549930113954915,0.04532588184869088,0.048205745373475717,0.051186622191016398,0.054264932748060414,0.057436397926065468,0.060696025160744058,0.064038099605609328,0.067456180721203518,0.070943104631279633,0.074490992540021839,0.07809126545075426,0.081734665366938408,0.085411283091162249,0.089110592667961716,0.092821492442479378,0.096532352630053914,0.10023106921283789,0.10390512389952483,0.10754164980436301,0.11112750242301618,0.11464933540670312,0.11809368056361502,0.12144703144906402,0.12469592984430962,0.12782705436963857,0.1308273104310485,0.133683920662719,0.13638451500013646,0.13891721950192223,0.14127074303259921,0.14343446092404832,0.14539849475041997,0.14715378737973994,0.14869217250518862,0.15000643790963206,0.15109038177787359,0.15193886144152891,0.15254783402048969,0.15291438851158207,0.15303676896804694,0.15291438851158207,0.15254783402048969,0.15193886144152891,0.15109038177787359,0.15000643790963203,0.1486921725051886,0.14715378737973991,0.14539849475041997,0.14343446092404832,0.14127074303259921,0.13891721950192223,0.13638451500013646,0.133683920662719,0.1308273104310485,0.12782705436963857,0.12469592984430959,0.12144703144906399,0.11809368056361501,0.11464933540670309,0.11112750242301617,0.10754164980436302,0.10390512389952483,0.10023106921283789,0.096532352630053914,0.092821492442479378,0.089110592667961716,0.085411283091162249,0.081734665366938408,0.07809126545075426,0.074490992540021825,0.070943104631279619,0.067456180721203504,0.064038099605609286,0.060696025160744058,0.057436397926065468,0.054264932748060414,0.051186622191016398,0.048205745373475717,0.04532588184869088,0.042549930113954915,0.039880130307281547,0.037318090630520294,0.03486481702546726,0.032520745623634016,0.030285777490736167,0.028159315193254725,0.026140300726137183,0.024227254357319931,0.022418313965703159,0.020711274473906697],[0.020464224444986572,0.022150901879568863,0.023938264710778777,0.025828491713200334,0.027823422796018175,0.029924520040627001,0.032132828831891211,0.034448939476971259,0.036872949730034972,0.039404428661872673,0.042042382329850879,0.044785221715213493,0.047630733400956242,0.050576053463894086,0.053617645048713532,0.056751280079426945,0.059972025544487224,0.063274234765737333,0.066651544028323503,0.070096874908771631,0.073602442591804665,0.077159770413482473,0.080759710809307564,0.084392472781619932,0.088047655931574736,0.09171429102804135,0.095380887009769266,0.09903548423911146,0.10266571374653463,0.10625886212619487,0.10980194166517795,0.11328176521378314,0.11668502523266079,0.11999837638587345,0.12320852098817814,0.12630229656110392,0.12926676470672563,0.13208930047131121,0.13475768134402849,0.13726017501928112,0.13958562504549796,0.14172353348865208,0.14366413975559389,0.14539849475041999,0.14691852957636339,0.14821711804568699,0.14928813232022659,0.15012649107482301,0.15072819965400275,0.15109038177787362,0.15121130244511369,0.15109038177787362,0.15072819965400275,0.15012649107482301,0.14928813232022659,0.14821711804568696,0.14691852957636337,0.14539849475041997,0.14366413975559389,0.14172353348865208,0.13958562504549796,0.13726017501928112,0.13475768134402849,0.13208930047131121,0.12926676470672563,0.12630229656110392,0.12320852098817812,0.11999837638587342,0.11668502523266076,0.11328176521378312,0.10980194166517793,0.10625886212619488,0.10266571374653463,0.09903548423911146,0.095380887009769266,0.09171429102804135,0.088047655931574736,0.084392472781619932,0.080759710809307564,0.077159770413482473,0.073602442591804665,0.070096874908771617,0.066651544028323489,0.063274234765737292,0.059972025544487224,0.056751280079426945,0.053617645048713532,0.050576053463894086,0.047630733400956242,0.044785221715213493,0.042042382329850879,0.039404428661872673,0.036872949730034951,0.034448939476971238,0.032132828831891197,0.029924520040626991,0.027823422796018186,0.025828491713200334,0.023938264710778777,0.022150901879568863,0.020464224444986572],[0.020187794973626452,0.021851688874298138,0.023614908119520307,0.025479602053125369,0.02744758573091911,0.02952030148459165,0.031698780578013654,0.033983605344513147,0.036374872217800745,0.038872156089631731,0.041474476443487916,0.04418026572497976,0.046987340415802256,0.04989287527846667,0.052893381233281161,0.055984687316845652,0.059161927152426269,0.062419530336843443,0.065751219115907936,0.069150010681049826,0.072608225373792759,0.076117501032446022,0.079668813657244611,0.083252504506716105,0.086858313669956541,0.090475420087527389,0.094092487918718992,0.097697719075926018,0.10127891166888656,0.10482352402365233,0.10831874386452758,0.11175156217300977,0.11510885116716335,0.11837744577901892,0.1215442279476389,0.12459621299249314,0.12752063728673113,0.13030504641371082,0.1329373829635164,0.13540607310980599,0.13770011110166258,0.13980914081049939,0.14172353348865208,0.14343446092404835,0.14493396321407698,0.14621501043110172,0.14727155751141532,0.14809859176808288,0.14869217250518862,0.14904946229545032,0.14916874957383605,0.14904946229545032,0.14869217250518862,0.14809859176808288,0.14727155751141532,0.14621501043110172,0.14493396321407695,0.14343446092404832,0.14172353348865208,0.13980914081049939,0.13770011110166258,0.13540607310980599,0.1329373829635164,0.13030504641371082,0.12752063728673113,0.12459621299249314,0.12154422794763889,0.11837744577901889,0.11510885116716334,0.11175156217300976,0.10831874386452756,0.10482352402365235,0.10127891166888656,0.097697719075926018,0.094092487918718992,0.090475420087527389,0.086858313669956541,0.083252504506716105,0.079668813657244611,0.076117501032446022,0.072608225373792745,0.069150010681049812,0.065751219115907922,0.062419530336843401,0.059161927152426269,0.055984687316845652,0.052893381233281161,0.04989287527846667,0.046987340415802256,0.04418026572497976,0.041474476443487916,0.038872156089631731,0.036374872217800724,0.033983605344513133,0.03169878057801364,0.02952030148459164,0.02744758573091912,0.025479602053125369,0.023614908119520307,0.021851688874298138,0.020187794973626452],[0.019883260812923801,0.021522054769138883,0.023258675740816071,0.02509524064880048,0.027033537168666549,0.029074985874439879,0.031220602473310582,0.033470960514071703,0.035826154975725236,0.038285767162811166,0.04084883134996483,0.043513803629453542,0.046278533421483671,0.049140238107452223,0.052095481240654627,0.055140154776936796,0.058269465749164903,0.061477927784042721,0.064759357827698996,0.068106878407671587,0.071512925713616698,0.074969263727580282,0.078467004577403007,0.081996635224336908,0.085548050528881245,0.089110592667961744,0.092673096802740954,0.096223942820509362,0.099751112897289385,0.10324225455107541,0.10668474878015885,0.11006578280790193,0.11337242688578771,0.11659171454172762,0.1197107256015609,0.12271667125948228,0.1255969804287575,0.12833938656840524,0.13093201415529887,0.13336346395499699,0.13562289623902948,0.13770011110166258,0.13958562504549793,0.14127074303259921,0.14274762523598827,0.14400934777493071,0.14504995677588664,0.14586451516861978,0.14644914170286089,0.14680104175409725,0.14691852957636339,0.14680104175409725,0.14644914170286089,0.14586451516861978,0.14504995677588664,0.14400934777493068,0.14274762523598825,0.14127074303259921,0.13958562504549796,0.13770011110166258,0.13562289623902948,0.13336346395499699,0.13093201415529887,0.12833938656840524,0.1255969804287575,0.12271667125948228,0.11971072560156089,0.11659171454172759,0.11337242688578768,0.1100657828079019,0.10668474878015884,0.10324225455107544,0.099751112897289385,0.096223942820509362,0.092673096802740954,0.089110592667961744,0.085548050528881245,0.081996635224336908,0.078467004577403007,0.074969263727580282,0.071512925713616698,0.068106878407671559,0.064759357827698982,0.06147792778404268,0.058269465749164903,0.055140154776936796,0.052095481240654627,0.049140238107452223,0.046278533421483671,0.043513803629453542,0.04084883134996483,0.038285767162811166,0.035826154975725222,0.033470960514071689,0.031220602473310571,0.029074985874439869,0.02703353716866656,0.02509524064880048,0.023258675740816071,0.021522054769138883,0.019883260812923801],[0.019552012309622557,0.021163504504304514,0.022871193948950898,0.024677162297210554,0.026583167442578218,0.028590606292789318,0.030700477633690451,0.032913345458942776,0.035229303165229757,0.037647939032418289,0.040168303423806673,0.042788878152650867,0.045507548467100381,0.048321578106051442,0.051227587872857104,0.054221538162010779,0.057298715855614836,0.060453725981525021,0.063680488493488396,0.066972240495443564,0.070321544187608082,0.073720300761344087,0.077159770413482473,0.080630598589332594,0.084122848497652447,0.08762603987115071,0.091129193873486711,0.094620883979158715,0.098089292577134279,0.10152227297364416,0.10490741639534565,0.10823212352219264,0.11148368001097242,0.11464933540670313,0.11771638478102263,0.12067225238537123,0.12350457656313303,0.12620129512981426,0.12875073040454862,0.13114167306034413,0.13336346395499699,0.13540607310980599,0.13726017501928109,0.13891721950192226,0.14036949733965784,0.14161020000130053,0.14263347280286082,0.14343446092404832,0.14400934777493066,0.1443553852885088,0.14447091580278371,0.1443553852885088,0.14400934777493066,0.14343446092404832,0.14263347280286082,0.14161020000130051,0.14036949733965781,0.13891721950192223,0.13726017501928112,0.13540607310980599,0.13336346395499699,0.13114167306034413,0.12875073040454862,0.12620129512981426,0.12350457656313303,0.12067225238537123,0.11771638478102261,0.11464933540670311,0.11148368001097241,0.10823212352219261,0.10490741639534563,0.10152227297364418,0.098089292577134279,0.094620883979158715,0.091129193873486711,0.08762603987115071,0.084122848497652447,0.080630598589332594,0.077159770413482473,0.073720300761344087,0.070321544187608068,0.06697224049544355,0.063680488493488369,0.060453725981524979,0.057298715855614836,0.054221538162010779,0.051227587872857104,0.048321578106051442,0.045507548467100381,0.042788878152650867,0.040168303423806673,0.037647939032418289,0.035229303165229736,0.032913345458942762,0.030700477633690441,0.028590606292789308,0.026583167442578225,0.024677162297210554,0.022871193948950898,0.021163504504304514,0.019552012309622557],[0.01919554484091637,0.020777656707150222,0.022454211978800521,0.024227254357319927,0.026098509686722313,0.028069349406665632,0.030140754093379123,0.032313277457930549,0.034587011194218059,0.036961551088488531,0.039435964817582519,0.042008761873962443,0.044677866061412254,0.047440591005666118,0.050293619118757349,0.053232984444271166,0.056254059792713633,0.059351548551742711,0.062519481525009982,0.065751219115907936,0.069039459128786271,0.072376250410489812,0.075753012499786387,0.0791605613919205,0.082589141460778587,0.086028463512719103,0.089467748874839187,0.092895779347233295,0.096300952774640208,0.099671343918817254,0.10299477024011842,0.10625886212619486,0.10945113703860512,0.11255907698551951,0.1155702086716979,0.11847218562652832,0.12125287156807109,0.12390042422660665,0.12640337882586763,0.12875073040454862,0.13093201415529887,0.1329373829635164,0.13475768134402849,0.13638451500013646,0.1378103152663322,0.13902839774289069,0.14003301448697761,0.1408193991901894,0.14138380484572052,0.14172353348865208,0.14183695767906987,0.14172353348865208,0.14138380484572052,0.1408193991901894,0.14003301448697761,0.13902839774289066,0.1378103152663322,0.13638451500013646,0.13475768134402849,0.1329373829635164,0.13093201415529887,0.12875073040454862,0.12640337882586763,0.12390042422660665,0.12125287156807109,0.11847218562652832,0.11557020867169789,0.11255907698551949,0.10945113703860511,0.10625886212619483,0.1029947702401184,0.099671343918817282,0.096300952774640208,0.092895779347233295,0.089467748874839187,0.086028463512719103,0.082589141460778587,0.0791605613919205,0.075753012499786387,0.072376250410489812,0.069039459128786271,0.065751219115907922,0.062519481525009968,0.059351548551742669,0.056254059792713633,0.053232984444271166,0.050293619118757349,0.047440591005666118,0.044677866061412254,0.042008761873962443,0.039435964817582519,0.036961551088488531,0.034587011194218045,0.032313277457930535,0.030140754093379112,0.028069349406665622,0.026098509686722324,0.024227254357319927,0.022454211978800521,0.020777656707150222,0.01919554484091637],[0.018815447586466555,0.020366231538771852,0.022009588791768921,0.023747522578910298,0.02558172457020871,0.027513539048997407,0.029543927174795367,0.031673431694456605,0.03390214248621843,0.036229663340296314,0.038655080394766256,0.041176932656117382,0.043793185039573197,0.046501204364642307,0.049297738736001212,0.05217890072843373,0.055140154776936783,0.05817630914911967,0.061281512846640976,0.064449257745714722,0.067672386243852259,0.070943104631279605,0.074253002351280656,0.077593077254578424,0.080953766889399106,0.084324985801785865,0.08769616875085931,0.091056319671955155,0.094394066147878819,0.09769771907592599,0.10095533714689815,0.10415479568318162,0.1072838593171566,0.11033025792983915,0.11328176521378314,0.1161262791748747,0.11885190384565765,0.12144703144906399,0.12390042422660665,0.12620129512981426,0.12833938656840524,0.13030504641371082,0.13208930047131121,0.13368392066271903,0.13508148819204449,0.13627545101954533,0.13726017501928109,0.13803098826207802,0.13858421793683645,0.13891721950192223,0.13902839774289066,0.13891721950192223,0.13858421793683645,0.13803098826207802,0.13726017501928109,0.1362754510195453,0.13508148819204446,0.133683920662719,0.13208930047131121,0.13030504641371082,0.12833938656840524,0.12620129512981426,0.12390042422660665,0.12144703144906399,0.11885190384565765,0.1161262791748747,0.11328176521378312,0.11033025792983912,0.10728385931715659,0.10415479568318159,0.10095533714689812,0.097697719075926018,0.094394066147878819,0.091056319671955155,0.08769616875085931,0.084324985801785865,0.080953766889399106,0.077593077254578424,0.074253002351280656,0.070943104631279605,0.067672386243852245,0.064449257745714708,0.061281512846640955,0.058176309149119636,0.055140154776936783,0.05217890072843373,0.049297738736001212,0.046501204364642307,0.043793185039573197,0.041176932656117382,0.038655080394766256,0.036229663340296314,0.033902142486218416,0.031673431694456591,0.029543927174795356,0.0275135390489974,0.025581724570208721,0.023747522578910298,0.022009588791768921,0.020366231538771852,0.018815447586466555],[0.01841339175340518,0.019931037948504489,0.021539279301848638,0.023240076241015307,0.025035084287751662,0.026925619000219621,0.028912620999506148,0.030996621434838497,0.0331777082639007,0.035455493743273642,0.037829083538791879,0.040297047876024492,0.042857395156681383,0.045507548467100381,0.048244325399727388,0.051063921597366627,0.053961898412739503,0.05693317505242089,0.059972025544487217,0.063072080833283542,0.066226336262766861,0.069427164662197755,0.072666335194921036,0.075935038073101591,0.079223915179170074,0.08252309656908903,0.085822242764172788,0.08911059266796173,0.092377016873513768,0.095610076055436782,0.098798084071091266,0.10192917532771055,0.10499137590778908,0.10797267788503787,0.11086111620852374,0.11364484748426988,0.11631222994249912,0.11885190384565765,0.12125287156807109,0.12350457656313303,0.1255969804287575,0.12752063728673113,0.1292667647067256,0.13082731043104853,0.13219501419153831,0.13336346395499699,0.13432714598768786,0.13508148819204452,0.13562289623902943,0.13594878209660702,0.13605758463749787,0.13594878209660702,0.13562289623902943,0.13508148819204452,0.13432714598768786,0.13336346395499696,0.13219501419153828,0.1308273104310485,0.12926676470672563,0.12752063728673113,0.1255969804287575,0.12350457656313303,0.12125287156807109,0.11885190384565765,0.11631222994249912,0.11364484748426988,0.11086111620852372,0.10797267788503785,0.10499137590778906,0.10192917532771052,0.098798084071091252,0.095610076055436796,0.092377016873513768,0.08911059266796173,0.085822242764172788,0.08252309656908903,0.079223915179170074,0.075935038073101591,0.072666335194921036,0.069427164662197755,0.066226336262766861,0.063072080833283528,0.059972025544487197,0.056933175052420855,0.053961898412739503,0.051063921597366627,0.048244325399727388,0.045507548467100381,0.042857395156681383,0.040297047876024492,0.037829083538791879,0.035455493743273642,0.033177708263900686,0.030996621434838483,0.028912620999506138,0.02692561900021961,0.025035084287751672,0.023240076241015307,0.021539279301848638,0.019931037948504489,0.01841339175340518],[0.017991118376101546,0.019473960468136136,0.021045320104255621,0.022707112753651681,0.024460955972075381,0.026308135148060175,0.028249569331477438,0.030285777490736188,0.032416845566391364,0.034642394707123977,0.036961551088488538,0.039372917724998506,0.04187454869158614,0.044463926170819332,0.04713794073713469,0.04989287527846667,0.052724392938809143,0.055627529442314388,0.058596690130481965,0.061625652008886596,0.064707571058906316,0.067834995023320646,0.07099988182283315,0.074193623704025422,0.077407077158562709,0.080630598589332608,0.083854085632388664,0.08706702397494949,0.090258539440196822,0.093417455040206362,0.096532352630053914,0.099591638730008675,0.10258361401980673,0.10549654595032244,0.1083187438645276,0.11103863597239759,0.11364484748426988,0.1161262791748747,0.11847218562652832,0.12067225238537123,0.12271667125948228,0.12459621299249314,0.12630229656110389,0.12782705436963859,0.12916339264929638,0.13030504641371085,0.13124662837532078,0.13198367128824096,0.13251266325199898,0.13283107558576643,0.1329373829635164,0.13283107558576643,0.13251266325199898,0.13198367128824096,0.13124662837532078,0.13030504641371082,0.12916339264929638,0.12782705436963857,0.12630229656110392,0.12459621299249314,0.12271667125948228,0.12067225238537123,0.11847218562652832,0.1161262791748747,0.11364484748426988,0.11103863597239759,0.10831874386452758,0.10549654595032243,0.10258361401980672,0.099591638730008647,0.0965323526300539,0.09341745504020639,0.090258539440196822,0.08706702397494949,0.083854085632388664,0.080630598589332608,0.077407077158562709,0.074193623704025422,0.07099988182283315,0.067834995023320646,0.064707571058906302,0.061625652008886575,0.058596690130481945,0.055627529442314354,0.052724392938809143,0.04989287527846667,0.04713794073713469,0.044463926170819332,0.04187454869158614,0.039372917724998506,0.036961551088488538,0.034642394707123977,0.03241684556639135,0.030285777490736174,0.028249569331477428,0.026308135148060165,0.024460955972075392,0.022707112753651681,0.021045320104255621,0.019473960468136136,0.017991118376101546],[0.017550425814864771,0.018996945680243543,0.020529814851891103,0.022150901879568859,0.023861784696989276,0.025663717207085341,0.027557595947595884,0.029543927174795374,0.031622794724124298,0.033793829024229179,0.036056177654999993,0.038408477850118743,0.040848831349964837,0.04337478201106048,0.045983296573241614,0.048670748975126833,0.05143290859202599,0.054264932748060435,0.057161363825925945,0.060116131263486042,0.063122558686399266,0.066173376380534055,0.06926073925737844,0.072376250410489826,0.075510990301829381,0.078655551554258463,0.081800079261300992,0.084934316658335285,0.088047655931574736,0.091129193873486711,0.094167792026680908,0.097152140893787708,0.10007082772946889,0.10291240737346569,0.10566547553146956,0.10831874386452758,0.11086111620852372,0.11328176521378312,0.11557020867169789,0.11771638478102261,0.11971072560156089,0.12154422794763889,0.1232085209881781,0.12469592984430962,0.12599953450914536,0.12711322345720055,0.12803174136255777,0.12875073040454862,0.1292667647067256,0.12957737752831353,0.12968108090615646,0.12957737752831353,0.1292667647067256,0.12875073040454862,0.12803174136255777,0.12711322345720055,0.12599953450914536,0.12469592984430959,0.12320852098817812,0.12154422794763889,0.11971072560156089,0.11771638478102261,0.11557020867169789,0.11328176521378312,0.11086111620852372,0.10831874386452758,0.10566547553146954,0.10291240737346566,0.10007082772946888,0.097152140893787681,0.094167792026680894,0.091129193873486725,0.088047655931574736,0.084934316658335285,0.081800079261300992,0.078655551554258463,0.075510990301829381,0.072376250410489826,0.06926073925737844,0.066173376380534055,0.063122558686399252,0.060116131263486021,0.057161363825925932,0.054264932748060393,0.05143290859202599,0.048670748975126833,0.045983296573241614,0.04337478201106048,0.040848831349964837,0.038408477850118743,0.036056177654999993,0.033793829024229179,0.031622794724124284,0.02954392717479536,0.027557595947595874,0.025663717207085334,0.023861784696989283,0.022150901879568859,0.020529814851891103,0.018996945680243543,0.017550425814864771],[0.017093157078531651,0.018501988495897823,0.019994919425791177,0.021573769733719127,0.023240076241015303,0.024995060180715355,0.02683959473165598,0.028774172959823891,0.030798876516363507,0.032913345458942762,0.035116749576888061,0.037407761610167053,0.039784532757490644,0.042244670869134603,0.044785221715213486,0.047402653709803247,0.050092846455306039,0.052851083449663869,0.055672049271425474,0.058549831524319161,0.061477927784042687,0.064449257745714708,0.067456180721203504,0.070490518581823688,0.07354358418423336,0.07660621525642701,0.079668813657244611,0.082721389857620314,0.085753612425757103,0.088754862232467979,0.091714291028041323,0.094620883979158701,0.097463525694614167,0.10023106921283788,0.10291240737346569,0.10549654595032243,0.10797267788503785,0.11033025792983912,0.11255907698551949,0.11464933540670311,0.11659171454172759,0.11837744577901889,0.11999837638587341,0.12144703144906402,0.12271667125948225,0.1238013435247904,0.12469592984430959,0.12539618593849983,0.12589877519063927,0.12620129512981426,0.12630229656110389,0.12620129512981426,0.12589877519063927,0.12539618593849983,0.12469592984430959,0.12380134352479039,0.12271667125948223,0.12144703144906399,0.11999837638587342,0.11837744577901889,0.11659171454172759,0.11464933540670311,0.11255907698551949,0.11033025792983912,0.10797267788503785,0.10549654595032243,0.10291240737346566,0.10023106921283786,0.097463525694614153,0.094620883979158688,0.091714291028041309,0.088754862232467993,0.085753612425757103,0.082721389857620314,0.079668813657244611,0.07660621525642701,0.07354358418423336,0.070490518581823688,0.067456180721203504,0.064449257745714708,0.06147792778404268,0.058549831524319147,0.055672049271425453,0.052851083449663834,0.050092846455306039,0.047402653709803247,0.044785221715213486,0.042244670869134603,0.039784532757490644,0.037407761610167053,0.035116749576888061,0.032913345458942762,0.030798876516363493,0.028774172959823877,0.026839594731655973,0.024995060180715348,0.02324007624101531,0.021573769733719127,0.019994919425791177,0.018501988495897823,0.017093157078531651],[0.016621187095070565,0.017991118376101543,0.019442827044767609,0.020978082717117312,0.022598379780337331,0.024304905747224683,0.02609850968672231,0.027979671050459752,0.029948469235059987,0.032004554236786588,0.03414711876843856,0.036374872217800724,0.038686016832007036,0.041078226512494001,0.043548628600488179,0.046093789022920648,0.048709701153100665,0.05139177871929506,0.054134853067519959,0.056933175052420869,0.059780421792250266,0.062669708480908123,0.065593605402140834,0.068544160238752483,0.071512925713616685,0.074490992540021825,0.077469027597160955,0.080437317183180632,0.083385815133989058,0.086304195531899205,0.089181909665091347,0.092008246837784399,0.094772398572877226,0.097463525694614167,0.10007082772946889,0.10258361401980672,0.10499137590778906,0.10728385931715659,0.10945113703860511,0.11148368001097241,0.11337242688578768,0.11510885116716334,0.11668502523266075,0.11809368056361502,0.11932826354529345,0.12038298623787105,0.12125287156807106,0.12193379244784333,0.12242250438990306,0.12271667125948225,0.12281488387629855,0.12271667125948225,0.12242250438990306,0.12193379244784333,0.12125287156807106,0.12038298623787104,0.11932826354529344,0.11809368056361501,0.11668502523266076,0.11510885116716334,0.11337242688578768,0.11148368001097241,0.10945113703860511,0.10728385931715659,0.10499137590778906,0.10258361401980672,0.10007082772946888,0.097463525694614153,0.094772398572877212,0.092008246837784385,0.089181909665091333,0.086304195531899219,0.083385815133989058,0.080437317183180632,0.077469027597160955,0.074490992540021825,0.071512925713616685,0.068544160238752483,0.065593605402140834,0.062669708480908123,0.059780421792250259,0.056933175052420855,0.054134853067519945,0.051391778719295025,0.048709701153100665,0.046093789022920648,0.043548628600488179,0.041078226512494001,0.038686016832007036,0.036374872217800724,0.03414711876843856,0.032004554236786588,0.029948469235059973,0.027979671050459738,0.026098509686722299,0.024304905747224676,0.022598379780337338,0.020978082717117312,0.019442827044767609,0.017991118376101543,0.016621187095070565],[0.016136410051965418,0.017466385628757172,0.018875753456674579,0.020366231538771849,0.021939270676624267,0.023596023747780536,0.025337315057059995,0.027163610072304993,0.029074985874439876,0.03107110266801091,0.0331511767113256,0.035313955034436441,0.037557692318116065,0.039880130307281547,0.042278480127730174,0.044749407865291357,0.047289023751392177,0.049892875278466663,0.052555944542581508,0.055272650079166354,0.058036853420974283,0.060841870565609864,0.063680488493488369,0.06654498682637193,0.069427164662197755,0.072318372564386682,0.075209549623898711,0.07809126545075426,0.080953766889399092,0.083787029190036,0.08658081130679568,0.089324714934305743,0.092008246837784399,0.094620883979158701,0.097152140893787708,0.099591638730008647,0.10192917532771052,0.10415479568318159,0.10625886212619483,0.10823212352219261,0.1100657828079019,0.11175156217300976,0.11328176521378311,0.11464933540670311,0.11584791028114452,0.11687187070955415,0.11771638478102259,0.11837744577901887,0.11885190384565762,0.11913749098236946,0.11923283910932089,0.11913749098236946,0.11885190384565762,0.11837744577901887,0.11771638478102259,0.11687187070955414,0.11584791028114449,0.11464933540670309,0.11328176521378312,0.11175156217300976,0.1100657828079019,0.10823212352219261,0.10625886212619483,0.10415479568318159,0.10192917532771052,0.099591638730008647,0.097152140893787681,0.094620883979158688,0.092008246837784385,0.08932471493430573,0.086580811306795666,0.083787029190036028,0.080953766889399092,0.07809126545075426,0.075209549623898711,0.072318372564386682,0.069427164662197755,0.06654498682637193,0.063680488493488369,0.060841870565609864,0.058036853420974276,0.05527265007916634,0.052555944542581487,0.049892875278466628,0.047289023751392177,0.044749407865291357,0.042278480127730174,0.039880130307281547,0.037557692318116065,0.035313955034436441,0.0331511767113256,0.03107110266801091,0.029074985874439865,0.027163610072304979,0.025337315057059988,0.023596023747780529,0.021939270676624278,0.020366231538771849,0.018875753456674579,0.017466385628757172,0.016136410051965418],[0.015640726924298663,0.016929847908804928,0.018295922349238672,0.019740615474516339,0.021265333520051326,0.022871193948950888,0.024558995744789439,0.026329190077027279,0.028181851658793586,0.03011665113257422,0.03213282883189119,0.03422917027590705,0.036403983758638687,0.038655080394766263,0.04097975697956889,0.043374782011060473,0.045836385207756361,0.048360250835565541,0.050941515132046401,0.053574768085746502,0.056254059792713612,0.058972911571760794,0.061724331975021959,0.064500837781174533,0.06729448000594726,0.070096874908771603,0.072899239916353734,0.075692434324287586,0.078467004577402993,0.081213233869201054,0.083921195741358909,0.08658081130679568,0.089181909665091347,0.091714291028041323,0.094167792026680908,0.0965323526300539,0.098798084071091252,0.10095533714689812,0.1029947702401184,0.10490741639534563,0.10668474878015884,0.10831874386452756,0.10980194166517791,0.11112750242301618,0.11228925911171536,0.11328176521378312,0.11410033724641168,0.11474109157260116,0.11520097509275398,0.11547778947736725,0.11557020867169786,0.11547778947736725,0.11520097509275398,0.11474109157260116,0.11410033724641168,0.11328176521378309,0.11228925911171535,0.11112750242301617,0.10980194166517793,0.10831874386452756,0.10668474878015884,0.10490741639534563,0.1029947702401184,0.10095533714689812,0.098798084071091252,0.0965323526300539,0.094167792026680894,0.091714291028041309,0.089181909665091333,0.086580811306795666,0.083921195741358895,0.081213233869201082,0.078467004577402993,0.075692434324287586,0.072899239916353734,0.070096874908771603,0.06729448000594726,0.064500837781174533,0.061724331975021959,0.058972911571760794,0.056254059792713605,0.053574768085746488,0.050941515132046387,0.048360250835565506,0.045836385207756361,0.043374782011060473,0.04097975697956889,0.038655080394766263,0.036403983758638687,0.03422917027590705,0.03213282883189119,0.03011665113257422,0.028181851658793576,0.026329190077027265,0.024558995744789432,0.022871193948950878,0.021265333520051336,0.019740615474516339,0.018295922349238672,0.016929847908804928,0.015640726924298663],[0.015136033303221486,0.016383557043505918,0.01770555111227021,0.019103627004968426,0.020579145580731501,0.022133188244463975,0.023766528198207515,0.025479602053125373,0.027272482111509955,0.029144849643526833,0.031095969495550116,0.03312466637550477,0.035229303165229757,0.037407761610167074,0.039657425732371514,0.041975168303683058,0.044357340701733299,0.046799766452164882,0.049297738736001233,0.051846022111570633,0.054438858665906024,0.057069978771343607,0.059732616579451205,0.062419530336843429,0.065123027556384716,0.067834995023320674,0.07054693355967151,0.07324999741248886,0.075935038073101618,0.078592652276080976,0.081213233869201096,0.083787029190036041,0.086304195531899233,0.088754862232468007,0.091129193873486738,0.09341745504020639,0.095610076055436796,0.097697719075926018,0.099671343918817282,0.10152227297364418,0.10324225455107544,0.10482352402365235,0.10625886212619487,0.10754164980436304,0.10866591902890101,0.10962639903007088,0.1104185574512823,0.1110386359723976,0.11148368001097243,0.1117515621730098,0.11184099919278614,0.1117515621730098,0.11148368001097243,0.1110386359723976,0.1104185574512823,0.10962639903007086,0.10866591902890098,0.10754164980436302,0.10625886212619488,0.10482352402365235,0.10324225455107544,0.10152227297364418,0.099671343918817282,0.097697719075926018,0.095610076055436796,0.09341745504020639,0.091129193873486725,0.088754862232467993,0.086304195531899219,0.083787029190036028,0.081213233869201082,0.07859265227608099,0.075935038073101618,0.07324999741248886,0.07054693355967151,0.067834995023320674,0.065123027556384716,0.062419530336843429,0.059732616579451205,0.057069978771343607,0.054438858665906011,0.051846022111570619,0.049297738736001212,0.046799766452164854,0.044357340701733299,0.041975168303683058,0.039657425732371514,0.037407761610167074,0.035229303165229757,0.03312466637550477,0.031095969495550116,0.029144849643526833,0.027272482111509944,0.025479602053125362,0.023766528198207508,0.022133188244463965,0.020579145580731512,0.019103627004968426,0.01770555111227021,0.016383557043505918,0.015136033303221486],[0.014624207630993185,0.015829546297804243,0.017106837075463652,0.018457636966631524,0.019883260812923798,0.021384753451487718,0.02296286193850185,0.024618008121102587,0.026350261856676941,0.028159315193254715,0.030044457836464162,0.032004554236786595,0.034038022635287969,0.036142816406286957,0.038316408031254613,0.040555776029397028,0.04285739515668139,0.045217230166425565,0.047630733400956235,0.050092846455306046,0.052598006120603516,0.055140154776936776,0.057712755363353983,0.060308811006698319,0.062920889341645539,0.065541151502176667,0.068161385710411748,0.070773045332951021,0.073367291218370864,0.075935038073101604,0.078467004577403021,0.080953766889399106,0.083385815133989072,0.085753612425757117,0.08804765593157475,0.090258539440196822,0.092377016873513768,0.094394066147878819,0.096300952774640208,0.098089292577134279,0.099751112897289385,0.10127891166888656,0.10266571374653462,0.10390512389952485,0.10499137590778909,0.10591937723291403,0.10668474878015885,0.10728385931715663,0.10771385417080621,0.10797267788503788,0.10805909058781833,0.10797267788503788,0.10771385417080621,0.10728385931715663,0.10668474878015885,0.10591937723291402,0.10499137590778908,0.10390512389952483,0.10266571374653463,0.10127891166888656,0.099751112897289385,0.098089292577134279,0.096300952774640208,0.094394066147878819,0.092377016873513768,0.090258539440196822,0.088047655931574736,0.085753612425757103,0.083385815133989058,0.080953766889399092,0.078467004577402993,0.075935038073101618,0.073367291218370864,0.070773045332951021,0.068161385710411748,0.065541151502176667,0.062920889341645539,0.060308811006698319,0.057712755363353983,0.055140154776936776,0.052598006120603509,0.050092846455306032,0.047630733400956221,0.045217230166425537,0.04285739515668139,0.040555776029397028,0.038316408031254613,0.036142816406286957,0.034038022635287969,0.032004554236786595,0.030044457836464162,0.028159315193254715,0.026350261856676931,0.024618008121102573,0.02296286193850184,0.021384753451487711,0.019883260812923804,0.018457636966631524,0.017106837075463652,0.015829546297804243,0.014624207630993185],[0.014107099941119392,0.015269818186418567,0.016501944337043228,0.017804980340496372,0.01918019454598029,0.020628594845507338,0.022150901879568859,0.023747522578910302,0.025418524330781987,0.027163610072304993,0.028982094624908104,0.030872882591770349,0.032834448144489367,0.03486481702546728,0.036961551088488538,0.039121735691433353,0.041341970241863306,0.043618362178234678,0.045946524646714809,0.048321578106051442,0.050738156060806075,0.053190415086729115,0.055672049271425467,0.058176309149119663,0.060696025160744058,0.063223635620281535,0.065751219115907936,0.06827053122067224,0.070773045332951021,0.073249997412488846,0.0756924343242876,0.078091265450754288,0.080437317183180645,0.082721389857620328,0.084934316658335299,0.08706702397494949,0.08911059266796173,0.091056319671955155,0.092895779347233295,0.094620883979158715,0.096223942820509362,0.097697719075926018,0.099035484239111446,0.10023106921283791,0.10127891166888656,0.1021740991395078,0.10291240737346569,0.10349033353770404,0.10390512389952482,0.10415479568318164,0.10423815285815245,0.10415479568318164,0.10390512389952482,0.10349033353770404,0.10291240737346569,0.10217409913950778,0.10127891166888654,0.10023106921283789,0.09903548423911146,0.097697719075926018,0.096223942820509362,0.094620883979158715,0.092895779347233295,0.091056319671955155,0.08911059266796173,0.08706702397494949,0.084934316658335285,0.082721389857620314,0.080437317183180632,0.07809126545075426,0.075692434324287586,0.07324999741248886,0.070773045332951021,0.06827053122067224,0.065751219115907936,0.063223635620281535,0.060696025160744058,0.058176309149119663,0.055672049271425467,0.053190415086729115,0.050738156060806068,0.048321578106051429,0.045946524646714795,0.04361836217823465,0.041341970241863306,0.039121735691433353,0.036961551088488538,0.03486481702546728,0.032834448144489367,0.030872882591770349,0.028982094624908104,0.027163610072304993,0.025418524330781976,0.023747522578910291,0.022150901879568849,0.020628594845507331,0.019180194545980297,0.017804980340496372,0.016501944337043228,0.015269818186418567,0.014107099941119392],[0.013586521193461716,0.014706332929943137,0.015892991288383319,0.017147942791573351,0.018472408984224021,0.019867360565220551,0.021333491582053162,0.022871193948950898,0.024480532566446708,0.026161221333845405,0.027912600356964769,0.029733614661204388,0.031622794724124298,0.033578239141976961,0.035597599740767115,0.037678069434197992,0.039816373118142755,0.042008761873962457,0.044251010731052323,0.046538420212488323,0.048865821856693366,0.051227587872857097,0.053617645048713518,0.056029492986577376,0.058456226697710577,0.060890563536653841,0.06332487440670552,0.065751219115907936,0.068161385710411748,0.070546933559671496,0.072899239916353747,0.075209549623898725,0.077469027597160969,0.079668813657244625,0.081800079261301006,0.083854085632388664,0.085822242764172788,0.08769616875085931,0.089467748874839187,0.091129193873486711,0.092673096802740954,0.094092487918718992,0.095380887009769252,0.096532352630053928,0.09754152771181665,0.09840368106668626,0.099114744326310414,0.099671343918817268,0.10007082772946889,0.10031128615070507,0.10039156728779881,0.10031128615070507,0.10007082772946889,0.099671343918817268,0.099114744326310414,0.098403681066686247,0.097541527711816636,0.096532352630053914,0.095380887009769266,0.094092487918718992,0.092673096802740954,0.091129193873486711,0.089467748874839187,0.08769616875085931,0.085822242764172788,0.083854085632388664,0.081800079261300992,0.079668813657244611,0.077469027597160955,0.075209549623898711,0.072899239916353734,0.07054693355967151,0.068161385710411748,0.065751219115907936,0.06332487440670552,0.060890563536653841,0.058456226697710577,0.056029492986577376,0.053617645048713518,0.051227587872857097,0.048865821856693359,0.046538420212488309,0.044251010731052309,0.042008761873962429,0.039816373118142755,0.037678069434197992,0.035597599740767115,0.033578239141976961,0.031622794724124298,0.029733614661204388,0.027912600356964769,0.026161221333845405,0.024480532566446698,0.022871193948950888,0.021333491582053155,0.019867360565220545,0.018472408984224028,0.017147942791573351,0.015892991288383319,0.014706332929943137,0.013586521193461716],[0.013064233284684923,0.014140997641948178,0.015282038928612808,0.016488748060787893,0.017762299625024486,0.01910362700496842,0.020513397567798811,0.021991988161926147,0.023539461193001633,0.025155541558504801,0.02683959473165598,0.028590606292789318,0.030407163210290657,0.032287437173456141,0.034229170275907064,0.036229663340296328,0.038285767162811166,0.040393876939324981,0.042549930113954922,0.044749407865291364,0.046987340415802249,0.049258316316082906,0.051556495817996144,0.053875628409685822,0.056209074541379203,0.058549831524319168,0.060890563536653841,0.063223635620281535,0.065541151502176667,0.06783499502332066,0.070096874908771617,0.072318372564386696,0.074490992540021839,0.076606215256427024,0.078655551554258477,0.080630598589332608,0.08252309656908903,0.084324985801785865,0.086028463512719103,0.08762603987115071,0.089110592667961744,0.090475420087527389,0.091714291028041336,0.092821492442479392,0.093791873197457618,0.094620883979158729,0.095304612813907744,0.095839815815406723,0.096223942820509334,0.096455157630066943,0.096532352630053914,0.096455157630066943,0.096223942820509334,0.095839815815406723,0.095304612813907744,0.094620883979158715,0.093791873197457604,0.092821492442479378,0.09171429102804135,0.090475420087527389,0.089110592667961744,0.08762603987115071,0.086028463512719103,0.084324985801785865,0.08252309656908903,0.080630598589332608,0.078655551554258463,0.07660621525642701,0.074490992540021825,0.072318372564386682,0.070096874908771603,0.067834995023320674,0.065541151502176667,0.063223635620281535,0.060890563536653841,0.058549831524319168,0.056209074541379203,0.053875628409685822,0.051556495817996144,0.049258316316082906,0.046987340415802242,0.04474940786529135,0.042549930113954915,0.040393876939324953,0.038285767162811166,0.036229663340296328,0.034229170275907064,0.032287437173456141,0.030407163210290657,0.028590606292789318,0.02683959473165598,0.025155541558504801,0.023539461193001623,0.021991988161926136,0.020513397567798804,0.019103627004968413,0.017762299625024493,0.016488748060787893,0.015282038928612808,0.014140997641948178,0.013064233284684923],[0.012541939804212972,0.013575656323034577,0.01467108005128704,0.015829546297804239,0.017052182690476543,0.018339885297312321,0.019693294804894967,0.021112772995655688,0.022598379780337338,0.024149851054711482,0.025766577659671622,0.027447585730919103,0.029191518728268202,0.030996621434838494,0.032860726212830794,0.034781241794998828,0.036755144879186998,0.038778974777318426,0.04084883134996483,0.042960376433158178,0.045108838935530991,0.047289023751392177,0.049495324599223914,0.051721740855664937,0.053961898412739503,0.056209074541379203,0.058456226697710577,0.060696025160744058,0.062920889341645539,0.065123027556384702,0.067294480005947274,0.069427164662197768,0.071512925713616698,0.073543584184233374,0.075510990301829395,0.077407077158562709,0.079223915179170074,0.080953766889399106,0.082589141460778587,0.084122848497652447,0.085548050528881245,0.086858313669956541,0.088047655931574723,0.08911059266796173,0.090042178682302965,0.090838046537275188,0.091494440655549208,0.092008246837784427,0.092377016873513754,0.092598987972783209,0.09267309680274094,0.092598987972783209,0.092377016873513754,0.092008246837784427,0.091494440655549208,0.090838046537275174,0.090042178682302951,0.089110592667961716,0.088047655931574736,0.086858313669956541,0.085548050528881245,0.084122848497652447,0.082589141460778587,0.080953766889399106,0.079223915179170074,0.077407077158562709,0.075510990301829381,0.07354358418423336,0.071512925713616685,0.069427164662197755,0.06729448000594726,0.065123027556384716,0.062920889341645539,0.060696025160744058,0.058456226697710577,0.056209074541379203,0.053961898412739503,0.051721740855664937,0.049495324599223914,0.047289023751392177,0.045108838935530984,0.042960376433158171,0.040848831349964816,0.038778974777318405,0.036755144879186998,0.034781241794998828,0.032860726212830794,0.030996621434838494,0.029191518728268202,0.027447585730919103,0.025766577659671622,0.024149851054711482,0.022598379780337328,0.021112772995655678,0.01969329480489496,0.018339885297312314,0.01705218269047655,0.015829546297804239,0.01467108005128704,0.013575656323034577,0.012541939804212972],[0.012021277595150495,0.013012080726199879,0.01406202937267753,0.015172403409819481,0.016344283653520707,0.01757852897269948,0.018875753456674579,0.020236303868953278,0.021660237633162393,0.023147301609014716,0.024696911925846457,0.026308135148060172,0.027979671050459756,0.029709837281695361,0.031496556190612812,0.033337344083032683,0.03522930316522975,0.037169116415061383,0.039153045602280973,0.041176932656117396,0.043236204550814221,0.045325881848690873,0.047440591005666104,0.049574580506400498,0.051721740855664937,0.053875628409685822,0.056029492986577376,0.058176309149119663,0.060308811006698319,0.062419530336843415,0.064500837781174533,0.066544986826371944,0.068544160238752497,0.070490518581823702,0.07237625041048984,0.074193623704025422,0.075935038073101591,0.077593077254578424,0.0791605613919205,0.080630598589332594,0.081996635224336908,0.083252504506716105,0.084392472781619918,0.085411283091162263,0.086304195531899219,0.08706702397494949,0.08769616875085931,0.088188644942196096,0.088542105972744714,0.088754862232467993,0.088825894531385133,0.088754862232467993,0.088542105972744714,0.088188644942196096,0.08769616875085931,0.087067023974949476,0.086304195531899205,0.085411283091162249,0.084392472781619932,0.083252504506716105,0.081996635224336908,0.080630598589332594,0.0791605613919205,0.077593077254578424,0.075935038073101591,0.074193623704025422,0.072376250410489826,0.070490518581823688,0.068544160238752483,0.06654498682637193,0.064500837781174533,0.062419530336843429,0.060308811006698319,0.058176309149119663,0.056029492986577376,0.053875628409685822,0.051721740855664937,0.049574580506400498,0.047440591005666104,0.045325881848690873,0.043236204550814214,0.041176932656117382,0.039153045602280959,0.037169116415061362,0.03522930316522975,0.033337344083032683,0.031496556190612812,0.029709837281695361,0.027979671050459756,0.026308135148060172,0.024696911925846457,0.023147301609014716,0.021660237633162382,0.020236303868953268,0.018875753456674572,0.017578528972699473,0.016344283653520711,0.015172403409819481,0.01406202937267753,0.013012080726199879,0.012021277595150495],[0.011503809168561334,0.012451962145895727,0.013456714658285983,0.014519291487404298,0.015640726924298663,0.016821842866979374,0.018063226970650274,0.019365211072021962,0.020727850122861366,0.022150901879568849,0.023633807604802045,0.025175674043671933,0.026775256940531494,0.028430946362598634,0.030140754093379116,0.031902303351898774,0.033712821082984332,0.035569133049169366,0.037467661936225437,0.039404428661872666,0.041375057051015816,0.043374782011060459,0.045398461307732389,0.047440591005666104,0.049495324599223914,0.051556495817996144,0.053617645048713518,0.055672049271425467,0.057712755363353983,0.059732616579451191,0.061724331975021973,0.063680488493488382,0.065593605402140848,0.067456180721203518,0.069260739257378454,0.07099988182283315,0.072666335194921036,0.074253002351280656,0.075753012499786387,0.077159770413482473,0.078467004577403007,0.079668813657244611,0.08075971080930755,0.081734665366938422,0.082589141460778573,0.083319133158228531,0.083921195741358923,0.084392472781619918,0.084730718713615927,0.084934316658335271,0.085002291297892441,0.084934316658335271,0.084730718713615927,0.084392472781619918,0.083921195741358923,0.083319133158228517,0.082589141460778559,0.081734665366938408,0.080759710809307564,0.079668813657244611,0.078467004577403007,0.077159770413482473,0.075753012499786387,0.074253002351280656,0.072666335194921036,0.07099988182283315,0.06926073925737844,0.067456180721203504,0.065593605402140834,0.063680488493488369,0.061724331975021959,0.059732616579451205,0.057712755363353983,0.055672049271425467,0.053617645048713518,0.051556495817996144,0.049495324599223914,0.047440591005666104,0.045398461307732389,0.043374782011060459,0.041375057051015809,0.039404428661872652,0.037467661936225423,0.035569133049169345,0.033712821082984332,0.031902303351898774,0.030140754093379116,0.028430946362598634,0.026775256940531494,0.025175674043671933,0.023633807604802045,0.022150901879568849,0.020727850122861356,0.019365211072021955,0.01806322697065027,0.016821842866979367,0.015640726924298669,0.014519291487404298,0.013456714658285983,0.012451962145895727,0.011503809168561334],[0.010991016008249595,0.011896904170983703,0.012856868891034025,0.013872080354272774,0.014943526747247476,0.016071993331088243,0.017258041565713103,0.01850198849589782,0.019803886623882407,0.021163504504304504,0.022580308306066572,0.024053444591960047,0.02558172457020871,0.02716361007230499,0.028797201508382976,0.030480228044725551,0.032210040237713254,0.03398360534451314,0.035797505513057673,0.037647939032418289,0.039530724799638393,0.041441310130627122,0.043374782011060459,0.045325881848690873,0.047289023751392177,0.049258316316082906,0.051227587872857097,0.053190415086729115,0.055140154776936776,0.057069978771343594,0.058972911571760808,0.060841870565609878,0.062669708480908137,0.064449257745714708,0.066173376380534055,0.067834995023320646,0.069427164662197755,0.070943104631279605,0.072376250410489812,0.073720300761344087,0.074969263727580282,0.076117501032446022,0.077159770413482459,0.078091265450754274,0.078907652465564096,0.079605104093542128,0.080180329168314635,0.080630598589332581,0.080953766889399079,0.081148289263411735,0.081213233869201068,0.081148289263411735,0.080953766889399079,0.080630598589332581,0.080180329168314635,0.079605104093542128,0.078907652465564082,0.07809126545075426,0.077159770413482473,0.076117501032446022,0.074969263727580282,0.073720300761344087,0.072376250410489812,0.070943104631279605,0.069427164662197755,0.067834995023320646,0.066173376380534055,0.064449257745714708,0.062669708480908123,0.060841870565609864,0.058972911571760794,0.057069978771343607,0.055140154776936776,0.053190415086729115,0.051227587872857097,0.049258316316082906,0.047289023751392177,0.045325881848690873,0.043374782011060459,0.041441310130627122,0.039530724799638386,0.037647939032418275,0.035797505513057659,0.033983605344513119,0.032210040237713254,0.030480228044725551,0.028797201508382976,0.02716361007230499,0.02558172457020871,0.024053444591960047,0.022580308306066572,0.021163504504304504,0.019803886623882397,0.018501988495897813,0.017258041565713096,0.016071993331088236,0.014943526747247481,0.013872080354272774,0.012856868891034025,0.011896904170983703,0.010991016008249595],[0.010484292791926746,0.011348416429606493,0.01226412351140615,0.013232530273649647,0.014254579344124031,0.015331019780750795,0.016462387158236329,0.017648983904514026,0.018890860101292078,0.020187794973626442,0.021539279301848624,0.022944498995107754,0.024402320068971355,0.025911275269731065,0.027469552585073932,0.029074985874439879,0.030725047842570543,0.032416845566391357,0.034147118768438567,0.035912241009586301,0.037708223949943401,0.039530724799638386,0.041375057051015809,0.043236204550814214,0.045108838935530984,0.046987340415802242,0.048865821856693359,0.050738156060806068,0.052598006120603509,0.054438858665906004,0.056254059792713612,0.058036853420974283,0.059780421792250266,0.061477927784042687,0.063122558686399266,0.064707571058906302,0.066226336262766861,0.067672386243852245,0.069039459128786271,0.070321544187608068,0.071512925713616698,0.072608225373792745,0.073602442591804651,0.074490992540021839,0.075269741337072885,0.075935038073101591,0.076483743315696656,0.076913253785125521,0.077221522927525404,0.077407077158562695,0.077469027597160955,0.077407077158562695,0.077221522927525404,0.076913253785125521,0.076483743315696656,0.075935038073101577,0.075269741337072871,0.074490992540021825,0.073602442591804665,0.072608225373792745,0.071512925713616698,0.070321544187608068,0.069039459128786271,0.067672386243852245,0.066226336262766861,0.064707571058906302,0.063122558686399252,0.06147792778404268,0.059780421792250259,0.058036853420974276,0.056254059792713605,0.054438858665906011,0.052598006120603509,0.050738156060806068,0.048865821856693359,0.046987340415802242,0.045108838935530984,0.043236204550814214,0.041375057051015809,0.039530724799638386,0.037708223949943394,0.035912241009586288,0.034147118768438553,0.032416845566391336,0.030725047842570543,0.029074985874439879,0.027469552585073932,0.025911275269731065,0.024402320068971355,0.022944498995107754,0.021539279301848624,0.020187794973626442,0.018890860101292071,0.017648983904514016,0.016462387158236325,0.01533101978075079,0.014254579344124036,0.013232530273649647,0.01226412351140615,0.011348416429606493,0.010484292791926746],[0.0099849425435298653,0.010807909341956396,0.011680002746817584,0.012602285829870444,0.013575656323034571,0.014600827607789888,0.015678309750268387,0.016808390774240334,0.017991118376101539,0.019226282296068622,0.020513397567798804,0.021851688874298125,0.0232400762410153,0.02467716229721055,0.026161221333845401,0.027690190380201381,0.029261662512087606,0.030872882591770352,0.032520745623634023,0.03420179789010052,0.035912241009586295,0.037647939032418275,0.039404428661872652,0.041176932656117382,0.042960376433158171,0.04474940786529135,0.046538420212488309,0.048321578106051429,0.050092846455306032,0.051846022111570605,0.053574768085746502,0.055272650079166347,0.056933175052420862,0.058549831524319154,0.060116131263486035,0.061625652008886575,0.063072080833283528,0.064449257745714708,0.065751219115907922,0.06697224049544355,0.068106878407671559,0.069150010681049812,0.070096874908771603,0.070943104631279633,0.071684762857420106,0.072318372564386682,0.072840943845957934,0.073249997412488832,0.073543584184233332,0.073720300761344087,0.073779300598741465,0.073720300761344087,0.073543584184233332,0.073249997412488832,0.072840943845957934,0.072318372564386682,0.071684762857420092,0.070943104631279619,0.070096874908771617,0.069150010681049812,0.068106878407671559,0.06697224049544355,0.065751219115907922,0.064449257745714708,0.063072080833283528,0.061625652008886575,0.060116131263486021,0.058549831524319147,0.056933175052420855,0.05527265007916634,0.053574768085746488,0.051846022111570619,0.050092846455306032,0.048321578106051429,0.046538420212488309,0.04474940786529135,0.042960376433158171,0.041176932656117382,0.039404428661872652,0.037647939032418275,0.035912241009586288,0.034201797890100506,0.032520745623634009,0.030872882591770331,0.029261662512087606,0.027690190380201381,0.026161221333845401,0.02467716229721055,0.0232400762410153,0.021851688874298125,0.020513397567798804,0.019226282296068622,0.017991118376101532,0.016808390774240328,0.01567830975026838,0.014600827607789883,0.013575656323034577,0.012602285829870444,0.011680002746817584,0.010807909341956396,0.0099849425435298653],[0.0094941727206312582,0.010276689885206171,0.011105919034816123,0.011982870990187581,0.012908399358826471,0.01388318245880589,0.014907705286001875,0.0159822417075309,0.017106837075463645,0.018281291464493487,0.019505143744854084,0.020777656707150212,0.022097803458650228,0.023464255310771263,0.024875371374784572,0.026329190077027276,0.027823422796018165,0.029355449811773973,0.030922318742291215,0.032520745623634023,0.03414711876843856,0.035797505513057659,0.037467661936225423,0.039153045602280959,0.040848831349964816,0.042549930113954915,0.044251010731052309,0.045946524646714795,0.047630733400956221,0.049297738736001205,0.050941515132046394,0.052555944542581501,0.054134853067519952,0.05567204927142546,0.057161363825925939,0.058596690130481945,0.059972025544487197,0.061281512846640955,0.062519481525009968,0.063680488493488369,0.064759357827698982,0.065751219115907922,0.066651544028323476,0.067456180721203504,0.06816138571041172,0.068763852872259085,0.06926073925737844,0.069649687435668267,0.069928844126583942,0.070096874908771603,0.070152974845681393,0.070096874908771603,0.069928844126583942,0.069649687435668267,0.06926073925737844,0.068763852872259071,0.06816138571041172,0.067456180721203504,0.066651544028323489,0.065751219115907922,0.064759357827698982,0.063680488493488369,0.062519481525009968,0.061281512846640955,0.059972025544487197,0.058596690130481945,0.057161363825925932,0.055672049271425453,0.054134853067519945,0.052555944542581487,0.050941515132046387,0.049297738736001212,0.047630733400956221,0.045946524646714795,0.044251010731052309,0.042549930113954915,0.040848831349964816,0.039153045602280959,0.037467661936225423,0.035797505513057659,0.034147118768438553,0.032520745623634009,0.030922318742291205,0.029355449811773952,0.027823422796018165,0.026329190077027276,0.024875371374784572,0.023464255310771263,0.022097803458650228,0.020777656707150212,0.019505143744854084,0.018281291464493487,0.017106837075463639,0.015982241707530893,0.01490770528600187,0.013883182458805885,0.012908399358826476,0.011982870990187581,0.011105919034816123,0.010276689885206171,0.0094941727206312582],[0.0090130922304875443,0.0097559583636185575,0.010543169532570867,0.011375685338639309,0.012254316136070215,0.013179705871791274,0.014152314966387913,0.015172403409819476,0.01624001425611583,0.017354957710412188,0.01851679600891,0.019724829297449474,0.020978082717117305,0.022275294905486735,0.023614908119520286,0.024995060180715355,0.026413578434634547,0.027867975905474698,0.029355449811773963,0.030872882591770342,0.032416845566391343,0.033983605344513119,0.035569133049169345,0.037169116415061362,0.038778974777318405,0.040393876939324953,0.042008761873962429,0.04361836217823465,0.045217230166425537,0.04679976645216484,0.048360250835565513,0.049892875278466635,0.051391778719295032,0.052851083449663848,0.054264932748060407,0.055627529442314354,0.056933175052420855,0.058176309149119636,0.059351548551742669,0.060453725981524979,0.06147792778404268,0.062419530336843401,0.063274234765737278,0.0640380996056093,0.064707571058906288,0.065279510526972881,0.065751219115907908,0.066120458849264388,0.066385470354322976,0.06654498682637193,0.06659824411590845,0.06654498682637193,0.066385470354322976,0.066120458849264388,0.065751219115907908,0.065279510526972881,0.064707571058906274,0.064038099605609286,0.063274234765737292,0.062419530336843401,0.06147792778404268,0.060453725981524979,0.059351548551742669,0.058176309149119636,0.056933175052420855,0.055627529442314354,0.054264932748060393,0.052851083449663834,0.051391778719295025,0.049892875278466628,0.048360250835565506,0.046799766452164854,0.045217230166425537,0.04361836217823465,0.042008761873962429,0.040393876939324953,0.038778974777318405,0.037169116415061362,0.035569133049169345,0.033983605344513119,0.032416845566391336,0.030872882591770331,0.029355449811773952,0.027867975905474681,0.026413578434634547,0.024995060180715355,0.023614908119520286,0.022275294905486735,0.020978082717117305,0.019724829297449474,0.01851679600891,0.017354957710412188,0.016240014256115824,0.015172403409819469,0.014152314966387908,0.013179705871791271,0.012254316136070219,0.011375685338639309,0.010543169532570867,0.0097559583636185575,0.0090130922304875443],[0.0085427093584435534,0.0092468061662075839,0.0099929336935985266,0.010782001461428119,0.011614777532490659,0.012491872246867534,0.013413721996325671,0.014380573202248762,0.015392466671726591,0.016449222515069122,0.017550425814864767,0.018695413241533902,0.019883260812923801,0.021112772995655688,0.022382473343501793,0.023690596862904468,0.025035084287751665,0.026413578434634565,0.027823422796018175,0.029261662512087616,0.03072504784257055,0.032210040237713254,0.033712821082984332,0.03522930316522975,0.036755144879186998,0.038285767162811166,0.039816373118142755,0.041341970241863306,0.04285739515668139,0.044357340701733285,0.045836385207756368,0.047289023751392191,0.048709701153100679,0.050092846455306046,0.051432908592026004,0.052724392938809143,0.053961898412739503,0.055140154776936783,0.056254059792713633,0.057298715855614836,0.058269465749164903,0.059161927152426269,0.059972025544487217,0.060696025160744072,0.061330557672232819,0.061872648280136368,0.062319738942708612,0.062669708480908165,0.062920889341645539,0.063072080833283556,0.063122558686399266,0.063072080833283556,0.062920889341645539,0.062669708480908165,0.062319738942708612,0.061872648280136361,0.061330557672232812,0.060696025160744058,0.059972025544487224,0.059161927152426269,0.058269465749164903,0.057298715855614836,0.056254059792713633,0.055140154776936783,0.053961898412739503,0.052724392938809143,0.05143290859202599,0.050092846455306039,0.048709701153100665,0.047289023751392177,0.045836385207756361,0.044357340701733299,0.04285739515668139,0.041341970241863306,0.039816373118142755,0.038285767162811166,0.036755144879186998,0.03522930316522975,0.033712821082984332,0.032210040237713254,0.030725047842570543,0.029261662512087606,0.027823422796018165,0.026413578434634547,0.025035084287751665,0.023690596862904468,0.022382473343501793,0.021112772995655688,0.019883260812923801,0.018695413241533902,0.017550425814864767,0.016449222515069122,0.015392466671726586,0.014380573202248755,0.013413721996325666,0.012491872246867531,0.011614777532490664,0.010782001461428119,0.0099929336935985266,0.0092468061662075839,0.0085427093584435534],[0.0080839305832440186,0.0087502144844073346,0.0094562718819605172,0.010202963451691261,0.010991016008249596,0.011821007113933748,0.01269334972447039,0.013608277027397159,0.01456582763829458,0.015565831328291937,0.016607895462756317,0.017691392335646171,0.018815447586466558,0.019978929886918871,0.021180442082035712,0.022418313965703162,0.023690596862904468,0.024995060180715369,0.026329190077027286,0.027690190380201391,0.029074985874439883,0.030480228044725551,0.031902303351898774,0.033337344083032683,0.034781241794998828,0.036229663340296328,0.037678069434197992,0.039121735691433353,0.040555776029397028,0.041975168303683051,0.04337478201106048,0.044749407865291364,0.046093789022920655,0.047402653709803254,0.04867074897512684,0.04989287527846667,0.051063921597366627,0.05217890072843373,0.053232984444271166,0.054221538162010779,0.055140154776936796,0.055984687316845652,0.056751280079426938,0.057436397926065474,0.058036853420974303,0.058549831524319182,0.058972911571760836,0.059304086300333195,0.059541777711434929,0.059684849595528798,0.059732616579451212,0.059684849595528798,0.059541777711434929,0.059304086300333195,0.058972911571760836,0.058549831524319168,0.058036853420974296,0.057436397926065468,0.056751280079426945,0.055984687316845652,0.055140154776936796,0.054221538162010779,0.053232984444271166,0.05217890072843373,0.051063921597366627,0.04989287527846667,0.048670748975126833,0.047402653709803247,0.046093789022920648,0.044749407865291357,0.043374782011060473,0.041975168303683058,0.040555776029397028,0.039121735691433353,0.037678069434197992,0.036229663340296328,0.034781241794998828,0.033337344083032683,0.031902303351898774,0.030480228044725551,0.029074985874439879,0.027690190380201381,0.026329190077027276,0.024995060180715355,0.023690596862904468,0.022418313965703162,0.021180442082035712,0.019978929886918871,0.018815447586466558,0.017691392335646171,0.016607895462756317,0.015565831328291937,0.014565827638294573,0.013608277027397152,0.012693349724470386,0.011821007113933742,0.010991016008249602,0.010202963451691261,0.0094562718819605172,0.0087502144844073346,0.0080839305832440186],[0.0076375602454110186,0.0082670539531167833,0.0089341249843435961,0.0096395864909502686,0.010384125155067441,0.011168286647740003,0.011992461122521192,0.012856868891034027,0.013761546436622795,0.01470633292994313,0.015690857416465871,0.016714526850189523,0.017776515150176406,0.018875753456674579,0.020010921761412597,0.021180442082035712,0.022382473343501793,0.023614908119520304,0.024875371374784579,0.026161221333845408,0.027469552585073935,0.028797201508382976,0.030140754093379116,0.031496556190612812,0.032860726212830794,0.034229170275907064,0.035597599740767115,0.036961551088488538,0.038316408031254613,0.039657425732371507,0.040979756979568897,0.042278480127730181,0.043548628600488186,0.044785221715213493,0.045983296573241628,0.04713794073713469,0.048244325399727388,0.049297738736001212,0.050293619118757349,0.051227587872857104,0.052095481240654627,0.052893381233281161,0.053617645048713525,0.054264932748060428,0.054832232896154222,0.055316885891195267,0.055716604730650009,0.056029492986577369,0.056254059792713619,0.056389231677595499,0.05643436111230455,0.056389231677595499,0.056254059792713619,0.056029492986577369,0.055716604730650009,0.05531688589119526,0.054832232896154215,0.054264932748060414,0.053617645048713532,0.052893381233281161,0.052095481240654627,0.051227587872857104,0.050293619118757349,0.049297738736001212,0.048244325399727388,0.04713794073713469,0.045983296573241614,0.044785221715213486,0.043548628600488179,0.042278480127730174,0.04097975697956889,0.039657425732371514,0.038316408031254613,0.036961551088488538,0.035597599740767115,0.034229170275907064,0.032860726212830794,0.031496556190612812,0.030140754093379116,0.028797201508382976,0.027469552585073932,0.026161221333845401,0.024875371374784572,0.023614908119520286,0.022382473343501793,0.021180442082035712,0.020010921761412597,0.018875753456674579,0.017776515150176406,0.016714526850189523,0.015690857416465871,0.01470633292994313,0.013761546436622788,0.012856868891034021,0.011992461122521189,0.011168286647739998,0.010384125155067446,0.0096395864909502686,0.0089341249843435961,0.0082670539531167833,0.0076375602454110186],[0.0072043010272956369,0.0077980851703177033,0.0084273149716058825,0.0090927574549980999,0.0097950603489076471,0.01053473836985956,0.011312159538995937,0.012127531670226073,0.012980889177287638,0.013872080354272776,0.014800755289952028,0.015766354580303624,0.016768099005844285,0.017804980340496372,0.018875753456674579,0.019978929886918871,0.021112772995655688,0.022275294905486749,0.02346425531077127,0.024677162297210557,0.025911275269731068,0.02716361007230499,0.028430946362598634,0.029709837281695361,0.030996621434838494,0.032287437173456141,0.033578239141976961,0.03486481702546728,0.036142816406286957,0.037407761610167067,0.03865508039476627,0.039880130307281554,0.041078226512494008,0.04224467086913461,0.043374782011060486,0.044463926170819332,0.045507548467100381,0.046501204364642307,0.047440591005666118,0.048321578106051442,0.049140238107452223,0.04989287527846667,0.050576053463894079,0.051186622191016405,0.051721740855664944,0.052178900728433744,0.052555944542581522,0.052851083449663869,0.053062911156439206,0.053190415086729136,0.053232984444271166,0.053190415086729136,0.053062911156439206,0.052851083449663869,0.052555944542581522,0.052178900728433737,0.051721740855664937,0.051186622191016398,0.050576053463894086,0.04989287527846667,0.049140238107452223,0.048321578106051442,0.047440591005666118,0.046501204364642307,0.045507548467100381,0.044463926170819332,0.04337478201106048,0.042244670869134603,0.041078226512494001,0.039880130307281547,0.038655080394766263,0.037407761610167074,0.036142816406286957,0.03486481702546728,0.033578239141976961,0.032287437173456141,0.030996621434838494,0.029709837281695361,0.028430946362598634,0.02716361007230499,0.025911275269731065,0.02467716229721055,0.023464255310771263,0.022275294905486735,0.021112772995655688,0.019978929886918871,0.018875753456674579,0.017804980340496372,0.016768099005844285,0.015766354580303624,0.014800755289952028,0.013872080354272776,0.012980889177287631,0.012127531670226068,0.011312159538995933,0.010534738369859555,0.0097950603489076523,0.0090927574549980999,0.0084273149716058825,0.0077980851703177033,0.0072043010272956369],[0.006784755196771599,0.0073439600432744986,0.0079365463536019715,0.0085632364836009875,0.0092246404409185804,0.0099212429673228766,0.01065339065207312,0.011421279206938664,0.012224941041557115,0.013064233284684921,0.013938826402336273,0.014848193567643525,0.015791600939333447,0.016768099005844285,0.017776515150176406,0.018815447586466558,0.019883260812923801,0.020978082717117319,0.022097803458650235,0.023240076241015307,0.024402320068971358,0.02558172457020871,0.026775256940531494,0.027979671050459756,0.029191518728268202,0.030407163210290657,0.031622794724124298,0.032834448144489367,0.034038022635287969,0.03522930316522975,0.036403983758638694,0.037557692318116072,0.038686016832007043,0.039784532757490651,0.040848831349964844,0.04187454869158614,0.042857395156681383,0.043793185039573197,0.044677866061412254,0.045507548467100381,0.046278533421483671,0.046987340415802256,0.047630733400956235,0.048205745373475724,0.048709701153100679,0.049140238107452217,0.049495324599223928,0.049773275954394902,0.049972767775866393,0.050092846455306046,0.050132936766456603,0.050092846455306046,0.049972767775866393,0.049773275954394902,0.049495324599223928,0.04914023810745221,0.048709701153100672,0.048205745373475717,0.047630733400956242,0.046987340415802256,0.046278533421483671,0.045507548467100381,0.044677866061412254,0.043793185039573197,0.042857395156681383,0.04187454869158614,0.040848831349964837,0.039784532757490644,0.038686016832007036,0.037557692318116065,0.036403983758638687,0.035229303165229757,0.034038022635287969,0.032834448144489367,0.031622794724124298,0.030407163210290657,0.029191518728268202,0.027979671050459756,0.026775256940531494,0.02558172457020871,0.024402320068971355,0.0232400762410153,0.022097803458650228,0.020978082717117305,0.019883260812923801,0.018815447586466558,0.017776515150176406,0.016768099005844285,0.015791600939333447,0.014848193567643525,0.013938826402336273,0.013064233284684921,0.01222494104155711,0.011421279206938658,0.010653390652073116,0.0099212429673228731,0.0092246404409185839,0.0085632364836009875,0.0079365463536019715,0.0073439600432744986,0.006784755196771599],[0.0063794265608507874,0.0069052239031682479,0.0074624084644474018,0.0080516594462132721,0.0086735504135942894,0.0093285371493594775,0.010016945537149735,0.010738959596700997,0.011494609801463957,0.012283761815478149,0.013106105791475574,0.013961146375797184,0.014848193567643525,0.015766354580303624,0.016714526850189523,0.017691392335646171,0.018695413241533902,0.019724829297449484,0.020777656707150219,0.021851688874298131,0.022944498995107757,0.024053444591960047,0.025175674043671933,0.026308135148060172,0.027447585730919103,0.028590606292789318,0.029733614661204388,0.030872882591770349,0.032004554236786595,0.033124666375504763,0.034229170275907057,0.035313955034436448,0.036374872217800731,0.03740776161016706,0.03840847785011875,0.039372917724998506,0.040297047876024492,0.041176932656117382,0.042008761873962443,0.042788878152650867,0.043513803629453542,0.04418026572497976,0.044785221715213486,0.045325881848690887,0.045799730763322839,0.046204546972951878,0.046538420212488309,0.046799766452164861,0.046987340415802235,0.047100245464664382,0.04713794073713469,0.047100245464664382,0.046987340415802235,0.046799766452164861,0.046538420212488309,0.046204546972951871,0.045799730763322832,0.04532588184869088,0.044785221715213493,0.04418026572497976,0.043513803629453542,0.042788878152650867,0.042008761873962443,0.041176932656117382,0.040297047876024492,0.039372917724998506,0.038408477850118743,0.037407761610167053,0.036374872217800724,0.035313955034436441,0.03422917027590705,0.03312466637550477,0.032004554236786595,0.030872882591770349,0.029733614661204388,0.028590606292789318,0.027447585730919103,0.026308135148060172,0.025175674043671933,0.024053444591960047,0.022944498995107754,0.021851688874298125,0.020777656707150212,0.019724829297449474,0.018695413241533902,0.017691392335646171,0.016714526850189523,0.015766354580303624,0.014848193567643525,0.013961146375797184,0.013106105791475574,0.012283761815478149,0.011494609801463952,0.010738959596700992,0.010016945537149732,0.009328537149359474,0.0086735504135942929,0.0080516594462132721,0.0074624084644474018,0.0069052239031682479,0.0063794265608507874],[0.0059887230707933534,0.0064823183249220345,0.0070053785098765477,0.0075585412299625163,0.0081423449227157416,0.0087572174568103251,0.0094034647573729251,0.010081259573980258,0.010790630513757976,0.01153145146805697,0.012303431565987108,0.013106105791475574,0.013938826402336273,0.014800755289952028,0.015690857416465871,0.016607895462756317,0.017550425814864767,0.018516796008910014,0.019505143744854091,0.020513397567798807,0.021539279301848627,0.022580308306066572,0.023633807604802045,0.024696911925846457,0.025766577659671622,0.02683959473165598,0.027912600356964769,0.028982094624908104,0.030044457836464162,0.031095969495550109,0.032132828831891197,0.033151176711325607,0.034147118768438567,0.035116749576888068,0.036056177655,0.036961551088488538,0.037829083538791879,0.038655080394766256,0.039435964817582519,0.040168303423806673,0.04084883134996483,0.041474476443487916,0.042042382329850872,0.042549930113954922,0.042994758485291842,0.043374782011060473,0.043688207419012137,0.043933547692167868,0.044109633820411574,0.044215624079015574,0.044251010731052316,0.044215624079015574,0.044109633820411574,0.043933547692167868,0.043688207419012137,0.043374782011060466,0.042994758485291835,0.042549930113954915,0.042042382329850879,0.041474476443487916,0.04084883134996483,0.040168303423806673,0.039435964817582519,0.038655080394766256,0.037829083538791879,0.036961551088488538,0.036056177654999993,0.035116749576888061,0.03414711876843856,0.0331511767113256,0.03213282883189119,0.031095969495550116,0.030044457836464162,0.028982094624908104,0.027912600356964769,0.02683959473165598,0.025766577659671622,0.024696911925846457,0.023633807604802045,0.022580308306066572,0.021539279301848624,0.020513397567798804,0.019505143744854084,0.01851679600891,0.017550425814864767,0.016607895462756317,0.015690857416465871,0.014800755289952028,0.013938826402336273,0.013106105791475574,0.012303431565987108,0.01153145146805697,0.010790630513757971,0.010081259573980253,0.0094034647573729216,0.0087572174568103216,0.0081423449227157451,0.0075585412299625163,0.0070053785098765477,0.0064823183249220345,0.0059887230707933534],[0.005612960016569659,0.0060755845849529491,0.0065658253040016389,0.007084279771472639,0.0076314526405823584,0.0082077449333402795,0.0088134433795690539,0.0094487098896551738,0.010113571275767206,0.010807909341956395,0.01153145146805697,0.012283761815478149,0.013064233284684921,0.013872080354272776,0.01470633292994313,0.015565831328291937,0.016449222515069122,0.017354957710412202,0.018281291464493494,0.019226282296068629,0.020187794973626445,0.021163504504304504,0.022150901879568849,0.023147301609014716,0.024149851054711482,0.025155541558504801,0.026161221333845405,0.027163610072304993,0.028159315193254715,0.029144849643526829,0.030116651132574227,0.031071102668010917,0.032004554236786595,0.032913345458942769,0.033793829024229186,0.034642394707123977,0.035455493743273642,0.036229663340296314,0.036961551088488531,0.037647939032418289,0.038285767162811166,0.038872156089631731,0.039404428661872666,0.039880130307281554,0.040297047876024499,0.040653226785999134,0.040946986284011236,0.041176932656117389,0.041341970241863292,0.041441310130627143,0.041474476443487916,0.041441310130627143,0.041341970241863292,0.041176932656117389,0.040946986284011236,0.040653226785999128,0.040297047876024492,0.039880130307281547,0.039404428661872673,0.038872156089631731,0.038285767162811166,0.037647939032418289,0.036961551088488531,0.036229663340296314,0.035455493743273642,0.034642394707123977,0.033793829024229179,0.032913345458942762,0.032004554236786588,0.03107110266801091,0.03011665113257422,0.029144849643526833,0.028159315193254715,0.027163610072304993,0.026161221333845405,0.025155541558504801,0.024149851054711482,0.023147301609014716,0.022150901879568849,0.021163504504304504,0.020187794973626442,0.019226282296068622,0.018281291464493487,0.017354957710412188,0.016449222515069122,0.015565831328291937,0.01470633292994313,0.013872080354272776,0.013064233284684921,0.012283761815478149,0.01153145146805697,0.010807909341956395,0.010113571275767202,0.0094487098896551686,0.0088134433795690522,0.0082077449333402761,0.007631452640582361,0.007084279771472639,0.0065658253040016389,0.0060755845849529491,0.005612960016569659],[0.0052523637458022025,0.0056852676866321235,0.006144013619588367,0.0066291607506484751,0.0071411813123333006,0.007680450563589577,0.0082472368137088154,0.008841691571385462,0.009463839926280181,0.010113571275767202,0.010790630513757971,0.011494609801463952,0.01222494104155711,0.012980889177287631,0.013761546436622788,0.014565827638294573,0.015392466671726586,0.016240014256115834,0.017106837075463642,0.017991118376101539,0.018890860101292074,0.019803886623882397,0.020727850122861356,0.021660237633162382,0.022598379780337328,0.023539461193001623,0.024480532566446698,0.025418524330781976,0.026350261856676931,0.027272482111509937,0.028181851658793583,0.029074985874439869,0.02994846923505998,0.0307988765163635,0.031622794724124284,0.03241684556639135,0.033177708263900686,0.033902142486218416,0.034587011194218045,0.035229303165229736,0.035826154975725222,0.036374872217800724,0.036872949730034944,0.037318090630520301,0.037708223949943394,0.038041520675422914,0.038316408031254599,0.038531581840575133,0.038686016832007022,0.038778974777318412,0.038810010369721995,0.038778974777318412,0.038686016832007022,0.038531581840575133,0.038316408031254599,0.038041520675422907,0.037708223949943387,0.037318090630520294,0.036872949730034951,0.036374872217800724,0.035826154975725222,0.035229303165229736,0.034587011194218045,0.033902142486218416,0.033177708263900686,0.03241684556639135,0.031622794724124284,0.030798876516363493,0.029948469235059973,0.029074985874439865,0.028181851658793576,0.027272482111509944,0.026350261856676931,0.025418524330781976,0.024480532566446698,0.023539461193001623,0.022598379780337328,0.021660237633162382,0.020727850122861356,0.019803886623882397,0.018890860101292071,0.017991118376101532,0.017106837075463639,0.016240014256115824,0.015392466671726586,0.014565827638294573,0.013761546436622788,0.012980889177287631,0.01222494104155711,0.011494609801463952,0.010790630513757971,0.010113571275767202,0.0094638399262801758,0.0088416915713854585,0.0082472368137088137,0.0076804505635895744,0.0071411813123333032,0.0066291607506484751,0.006144013619588367,0.0056852676866321235,0.0052523637458022025],[0.0049070758405529522,0.0053115208813261563,0.0057401090739014771,0.0061933628623203202,0.0066717234347612566,0.0071755413808255739,0.0077050673712790278,0.0082604429547062392,0.008841691571385462,0.0094487098896551686,0.010081259573980253,0.010738959596700992,0.011421279206938658,0.012127531670226068,0.012856868891034021,0.013608277027397152,0.014380573202248755,0.015172403409819478,0.015982241707530896,0.016808390774240331,0.017648983904514019,0.018501988495897813,0.019365211072021955,0.020236303868953268,0.021112772995655678,0.021991988161926136,0.022871193948950888,0.023747522578910291,0.024618008121102573,0.025479602053125359,0.026329190077027272,0.027163610072304986,0.027979671050459745,0.028774172959823881,0.029543927174795363,0.030285777490736174,0.030996621434838483,0.031673431694456591,0.032313277457930535,0.032913345458942762,0.033470960514071689,0.033983605344513133,0.034448939476971238,0.034864817025467267,0.035229303165229743,0.035540689121817973,0.035797505513057666,0.03599853389805488,0.036142816406286936,0.036229663340296314,0.036258658667553033,0.036229663340296314,0.036142816406286936,0.03599853389805488,0.035797505513057666,0.035540689121817966,0.035229303165229736,0.03486481702546726,0.034448939476971238,0.033983605344513133,0.033470960514071689,0.032913345458942762,0.032313277457930535,0.031673431694456591,0.030996621434838483,0.030285777490736174,0.02954392717479536,0.028774172959823877,0.027979671050459738,0.027163610072304979,0.026329190077027265,0.025479602053125362,0.024618008121102573,0.023747522578910291,0.022871193948950888,0.021991988161926136,0.021112772995655678,0.020236303868953268,0.019365211072021955,0.018501988495897813,0.017648983904514016,0.016808390774240328,0.015982241707530893,0.015172403409819469,0.014380573202248755,0.013608277027397152,0.012856868891034021,0.012127531670226068,0.011421279206938658,0.010738959596700992,0.010081259573980253,0.0094487098896551686,0.0088416915713854585,0.0082604429547062357,0.0077050673712790252,0.0071755413808255713,0.0066717234347612592,0.0061933628623203202,0.0057401090739014771,0.0053115208813261563,0.0049070758405529522],[0.0045771576844913587,0.0049544106119946947,0.0053541834712027021,0.0057769635805992488,0.0062231624658928147,0.0066931071454421507,0.0071870314366283255,0.0077050673712790287,0.0082472368137088171,0.0088134433795690522,0.0094034647573729216,0.010016945537149732,0.010653390652073116,0.011312159538995933,0.011992461122521189,0.012693349724470386,0.013413721996325666,0.014152314966387919,0.014907705286001875,0.015678309750268387,0.016462387158236325,0.017258041565713096,0.01806322697065027,0.018875753456674572,0.01969329480489496,0.020513397567798804,0.021333491582053155,0.022150901879568849,0.02296286193850184,0.023766528198207505,0.024558995744789435,0.025337315057059991,0.026098509686722306,0.026839594731655977,0.027557595947595877,0.028249569331477428,0.028912620999506138,0.029543927174795356,0.030140754093379112,0.030700477633690441,0.031220602473310571,0.03169878057801364,0.032132828831891197,0.032520745623634023,0.032860726212830781,0.033151176711325607,0.033390726528133345,0.033578239141976947,0.033712821082984325,0.033793829024229179,0.033820874904358166,0.033793829024229179,0.033712821082984325,0.033578239141976947,0.033390726528133345,0.0331511767113256,0.032860726212830781,0.032520745623634016,0.032132828831891197,0.03169878057801364,0.031220602473310571,0.030700477633690441,0.030140754093379112,0.029543927174795356,0.028912620999506138,0.028249569331477428,0.027557595947595874,0.026839594731655973,0.026098509686722299,0.025337315057059988,0.024558995744789432,0.023766528198207508,0.02296286193850184,0.022150901879568849,0.021333491582053155,0.020513397567798804,0.01969329480489496,0.018875753456674572,0.01806322697065027,0.017258041565713096,0.016462387158236325,0.01567830975026838,0.01490770528600187,0.014152314966387908,0.013413721996325666,0.012693349724470386,0.011992461122521189,0.011312159538995933,0.010653390652073116,0.010016945537149732,0.0094034647573729216,0.0088134433795690522,0.0082472368137088137,0.0077050673712790252,0.0071870314366283237,0.0066931071454421481,0.0062231624658928165,0.0057769635805992488,0.0053541834712027021,0.0049544106119946947,0.0045771576844913587],[0.0042625953530344707,0.0046139218063797347,0.0049862205230490784,0.0053799453308649115,0.0057954794736858779,0.0062331274957362435,0.0066931071454421499,0.0071755413808255748,0.007680450563589577,0.0082077449333402761,0.0087572174568103216,0.009328537149359474,0.0099212429673228731,0.010534738369859555,0.011168286647739998,0.011821007113933742,0.012491872246867531,0.01317970587179128,0.013883182458805888,0.014600827607789886,0.015331019780750792,0.016071993331088236,0.016821842866979367,0.017578528972699473,0.018339885297312314,0.019103627004968413,0.019867360565220545,0.020628594845507331,0.021384753451487711,0.022133188244463961,0.022871193948950885,0.023596023747780533,0.02430490574722468,0.024995060180715352,0.025663717207085338,0.026308135148060165,0.02692561900021961,0.0275135390489974,0.028069349406665622,0.028590606292789308,0.029074985874439869,0.02952030148459164,0.029924520040626984,0.030285777490736174,0.030602393124176619,0.030872882591770342,0.031095969495550102,0.03127059542096082,0.031395928301294868,0.031471369021871129,0.031496556190612805,0.031471369021871129,0.031395928301294868,0.03127059542096082,0.031095969495550102,0.030872882591770338,0.030602393124176615,0.030285777490736167,0.029924520040626991,0.02952030148459164,0.029074985874439869,0.028590606292789308,0.028069349406665622,0.0275135390489974,0.02692561900021961,0.026308135148060165,0.025663717207085334,0.024995060180715348,0.024304905747224676,0.023596023747780529,0.022871193948950878,0.022133188244463965,0.021384753451487711,0.020628594845507331,0.019867360565220545,0.019103627004968413,0.018339885297312314,0.017578528972699473,0.016821842866979367,0.016071993331088236,0.01533101978075079,0.014600827607789883,0.013883182458805885,0.013179705871791271,0.012491872246867531,0.011821007113933742,0.011168286647739998,0.010534738369859555,0.0099212429673228731,0.009328537149359474,0.0087572174568103216,0.0082077449333402761,0.0076804505635895744,0.0071755413808255713,0.0066931071454421481,0.0062331274957362409,0.0057954794736858797,0.0053799453308649115,0.0049862205230490784,0.0046139218063797347,0.0042625953530344707],[0.0039633047599361105,0.004289963447780717,0.0046361218685755292,0.005002201985425129,0.0053885601333985029,0.0057954794736858823,0.0062231624658928191,0.0066717234347612618,0.0071411813123333067,0.007631452640582361,0.0081423449227157451,0.0086735504135942929,0.0092246404409185839,0.0097950603489076523,0.010384125155067446,0.010991016008249602,0.011614777532490664,0.012254316136070227,0.01290839935882648,0.01357565632303458,0.014254579344124038,0.014943526747247481,0.015640726924298669,0.016344283653520711,0.01705218269047655,0.017762299625024493,0.018472408984224028,0.019180194545980297,0.019883260812923804,0.020579145580731505,0.02126533352005134,0.021939270676624281,0.022598379780337342,0.023240076241015314,0.023861784696989286,0.024460955972075392,0.025035084287751672,0.025581724570208721,0.026098509686722324,0.026583167442578225,0.02703353716866656,0.02744758573091912,0.027823422796018182,0.028159315193254732,0.028453700220018158,0.028705197748082514,0.028912620999506158,0.029074985874439893,0.029191518728268206,0.029261662512087627,0.029285081208326794,0.029261662512087627,0.029191518728268206,0.029074985874439893,0.028912620999506158,0.028705197748082511,0.028453700220018155,0.028159315193254725,0.027823422796018186,0.02744758573091912,0.02703353716866656,0.026583167442578225,0.026098509686722324,0.025581724570208721,0.025035084287751672,0.024460955972075392,0.023861784696989283,0.02324007624101531,0.022598379780337338,0.021939270676624278,0.021265333520051336,0.020579145580731512,0.019883260812923804,0.019180194545980297,0.018472408984224028,0.017762299625024493,0.01705218269047655,0.016344283653520711,0.015640726924298669,0.014943526747247481,0.014254579344124036,0.013575656323034577,0.012908399358826476,0.012254316136070219,0.011614777532490664,0.010991016008249602,0.010384125155067446,0.0097950603489076523,0.0092246404409185839,0.0086735504135942929,0.0081423449227157451,0.007631452640582361,0.0071411813123333032,0.0066717234347612592,0.0062231624658928165,0.0057954794736858797,0.0053885601333985046,0.005002201985425129,0.0046361218685755292,0.004289963447780717,0.0039633047599361105],[0.0036791369954507149,0.0039823743531940169,0.0043037133188741422,0.0046435456009674319,0.0050022019854251273,0.0053799453308649142,0.0057769635805992505,0.0061933628623203237,0.0066291607506484777,0.007084279771472639,0.0075585412299625163,0.0080516594462132721,0.0085632364836009875,0.0090927574549980999,0.0096395864909502686,0.010202963451691261,0.010782001461428119,0.011375685338639316,0.011982870990187584,0.012602285829870448,0.013232530273649649,0.013872080354272774,0.014519291487404298,0.015172403409819481,0.015829546297804239,0.016488748060787893,0.017147942791573351,0.017804980340496372,0.018457636966631524,0.019103627004968423,0.019740615474516342,0.020366231538771856,0.020978082717117316,0.02157376973371913,0.022150901879568863,0.022707112753651681,0.023240076241015307,0.023747522578910298,0.024227254357319927,0.024677162297210554,0.02509524064880048,0.025479602053125369,0.025828491713200331,0.026140300726137187,0.026413578434634558,0.026647043665247026,0.026839594731655987,0.026990318093676739,0.027098495576781047,0.027163610072305,0.027185349655036491,0.027163610072305,0.027098495576781047,0.026990318093676739,0.026839594731655987,0.026647043665247023,0.026413578434634554,0.026140300726137183,0.025828491713200334,0.025479602053125369,0.02509524064880048,0.024677162297210554,0.024227254357319927,0.023747522578910298,0.023240076241015307,0.022707112753651681,0.022150901879568859,0.021573769733719127,0.020978082717117312,0.020366231538771849,0.019740615474516339,0.019103627004968426,0.018457636966631524,0.017804980340496372,0.017147942791573351,0.016488748060787893,0.015829546297804239,0.015172403409819481,0.014519291487404298,0.013872080354272774,0.013232530273649647,0.012602285829870444,0.011982870990187581,0.011375685338639309,0.010782001461428119,0.010202963451691261,0.0096395864909502686,0.0090927574549980999,0.0085632364836009875,0.0080516594462132721,0.0075585412299625163,0.007084279771472639,0.0066291607506484751,0.0061933628623203202,0.0057769635805992488,0.0053799453308649115,0.005002201985425129,0.0046435456009674319,0.0043037133188741422,0.0039823743531940169,0.0036791369954507149],[0.0034098837935359152,0.0036909290911266526,0.003988751252318022,0.0043037133188741422,0.0046361218685755266,0.0049862205230490802,0.0053541834712027038,0.0057401090739014797,0.0061440136195883696,0.0065658253040016389,0.0070053785098765477,0.0074624084644474018,0.0079365463536019715,0.0084273149716058825,0.0089341249843435961,0.0094562718819605172,0.0099929336935985266,0.010543169532570874,0.011105919034816126,0.011680002746817587,0.012264123511406154,0.012856868891034025,0.013456714658285983,0.01406202937267753,0.01467108005128704,0.015282038928612808,0.015892991288383319,0.016501944337043228,0.017106837075463652,0.017705551112270207,0.018295922349238675,0.018875753456674582,0.019442827044767613,0.01999491942579118,0.020529814851891107,0.021045320104255621,0.021539279301848638,0.022009588791768921,0.022454211978800521,0.022871193948950898,0.023258675740816071,0.023614908119520307,0.023938264710778773,0.024227254357319934,0.024480532566446708,0.024696911925846471,0.024875371374784586,0.025015064229412538,0.025115324873938413,0.02517567404367195,0.025195822641271334,0.02517567404367195,0.025115324873938413,0.025015064229412538,0.024875371374784586,0.024696911925846467,0.024480532566446705,0.024227254357319931,0.023938264710778777,0.023614908119520307,0.023258675740816071,0.022871193948950898,0.022454211978800521,0.022009588791768921,0.021539279301848638,0.021045320104255621,0.020529814851891103,0.019994919425791177,0.019442827044767609,0.018875753456674579,0.018295922349238672,0.01770555111227021,0.017106837075463652,0.016501944337043228,0.015892991288383319,0.015282038928612808,0.01467108005128704,0.01406202937267753,0.013456714658285983,0.012856868891034025,0.01226412351140615,0.011680002746817584,0.011105919034816123,0.010543169532570867,0.0099929336935985266,0.0094562718819605172,0.0089341249843435961,0.0084273149716058825,0.0079365463536019715,0.0074624084644474018,0.0070053785098765477,0.0065658253040016389,0.006144013619588367,0.0057401090739014771,0.0053541834712027021,0.0049862205230490784,0.0046361218685755292,0.0043037133188741422,0.003988751252318022,0.0036909290911266526,0.0034098837935359152],[0.0031552830685064662,0.0034153439745855732,0.0036909290911266526,0.0039823743531940169,0.0042899634477807152,0.0046139218063797364,0.0049544106119946956,0.0053115208813261589,0.0056852676866321261,0.0060755845849529491,0.0064823183249220345,0.0069052239031682479,0.0073439600432744986,0.0077980851703177033,0.0082670539531167833,0.0087502144844073346,0.0092468061662075839,0.0097559583636185644,0.010276689885206174,0.0108079093419564,0.011348416429606495,0.011896904170983703,0.012451962145895727,0.013012080726199879,0.013575656323034577,0.014140997641948178,0.014706332929943137,0.015269818186418567,0.015829546297804243,0.016383557043505914,0.016929847908804932,0.017466385628757176,0.017991118376101546,0.018501988495897827,0.018996945680243547,0.019473960468136136,0.019931037948504489,0.020366231538771852,0.020777656707150222,0.021163504504304514,0.021522054769138883,0.021851688874298138,0.022150901879568859,0.022418313965703162,0.022652681027241835,0.022852904310622518,0.023018038993134829,0.023147301609014723,0.023240076241015303,0.023295919408990597,0.023314563601200315,0.023295919408990597,0.023240076241015303,0.023147301609014723,0.023018038993134829,0.022852904310622514,0.022652681027241831,0.022418313965703159,0.022150901879568863,0.021851688874298138,0.021522054769138883,0.021163504504304514,0.020777656707150222,0.020366231538771852,0.019931037948504489,0.019473960468136136,0.018996945680243543,0.018501988495897823,0.017991118376101543,0.017466385628757172,0.016929847908804928,0.016383557043505918,0.015829546297804243,0.015269818186418567,0.014706332929943137,0.014140997641948178,0.013575656323034577,0.013012080726199879,0.012451962145895727,0.011896904170983703,0.011348416429606493,0.010807909341956396,0.010276689885206171,0.0097559583636185575,0.0092468061662075839,0.0087502144844073346,0.0082670539531167833,0.0077980851703177033,0.0073439600432744986,0.0069052239031682479,0.0064823183249220345,0.0060755845849529491,0.0056852676866321235,0.0053115208813261563,0.0049544106119946947,0.0046139218063797347,0.004289963447780717,0.0039823743531940169,0.0036909290911266526,0.0034153439745855732,0.0031552830685064662],[0.0029150244650281948,0.0031552830685064662,0.0034098837935359152,0.0036791369954507149,0.0039633047599361097,0.0042625953530344724,0.0045771576844913604,0.0049070758405529548,0.0052523637458022042,0.005612960016569659,0.0059887230707933534,0.0063794265608507874,0.006784755196771599,0.0072043010272956369,0.0076375602454110186,0.0080839305832440186,0.0085427093584435534,0.0090130922304875512,0.0094941727206312616,0.0099849425435298688,0.010484292791926746,0.010991016008249595,0.011503809168561334,0.012021277595150495,0.012541939804212972,0.013064233284684923,0.013586521193461716,0.014107099941119392,0.014624207630993185,0.015136033303221483,0.015640726924298666,0.016136410051965418,0.016621187095070565,0.017093157078531655,0.017550425814864774,0.017991118376101546,0.01841339175340518,0.018815447586466555,0.01919554484091637,0.019552012309622557,0.019883260812923801,0.020187794973626452,0.020464224444986568,0.0207112744739067,0.020927795687169945,0.021112772995655688,0.021265333520051336,0.021384753451487722,0.021470463771653604,0.021522054769138883,0.021539279301848634,0.021522054769138883,0.021470463771653604,0.021384753451487722,0.021265333520051336,0.021112772995655685,0.020927795687169942,0.020711274473906697,0.020464224444986572,0.020187794973626452,0.019883260812923801,0.019552012309622557,0.01919554484091637,0.018815447586466555,0.01841339175340518,0.017991118376101546,0.017550425814864771,0.017093157078531651,0.016621187095070565,0.016136410051965418,0.015640726924298663,0.015136033303221486,0.014624207630993185,0.014107099941119392,0.013586521193461716,0.013064233284684923,0.012541939804212972,0.012021277595150495,0.011503809168561334,0.010991016008249595,0.010484292791926746,0.0099849425435298653,0.0094941727206312582,0.0090130922304875443,0.0085427093584435534,0.0080839305832440186,0.0076375602454110186,0.0072043010272956369,0.006784755196771599,0.0063794265608507874,0.0059887230707933534,0.005612960016569659,0.0052523637458022025,0.0049070758405529522,0.0045771576844913587,0.0042625953530344707,0.0039633047599361105,0.0036791369954507149,0.0034098837935359152,0.0031552830685064662,0.0029150244650281948]],"type":"surface","frame":null}],"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- # Examples of joint pdfs: normal <img src="12-multivariate-pdf_files/figure-html/multivar-contour-1.png" width="864" style="display: block; margin: auto;" /> --- # Examples of joint pdfs: uniform `\(f(x,y) = 1\)` if `\(x \in [0,1], y \in [0,1]\)`, `\(f(x,y) = 0\)` <div class="plotly html-widget html-fill-item" id="htmlwidget-f30d7598595affc4f25a" style="width:864px;height:504px;"></div> <script type="application/json" data-for="htmlwidget-f30d7598595affc4f25a">{"x":{"visdat":{"d4317e222ff4":["function () ","plotlyVisDat"]},"cur_data":"d4317e222ff4","attrs":{"d4317e222ff4":{"x":{},"y":{},"z":{},"alpha_stroke":1,"sizes":[10,100],"spans":[1,20],"type":"surface","inherit":true}},"layout":{"margin":{"b":40,"l":60,"t":25,"r":10},"scene":{"xaxis":{"title":"x"},"yaxis":{"title":"y"},"zaxis":{"title":"z_mat"}},"hovermode":"closest","showlegend":false,"legend":{"yanchor":"top","y":0.5}},"source":"A","config":{"modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"data":[{"colorbar":{"title":"z_mat","ticklen":2,"len":0.5,"lenmode":"fraction","y":1,"yanchor":"top"},"colorscale":[["0","rgba(68,1,84,1)"],["0.0416666666666667","rgba(70,19,97,1)"],["0.0833333333333333","rgba(72,32,111,1)"],["0.125","rgba(71,45,122,1)"],["0.166666666666667","rgba(68,58,128,1)"],["0.208333333333333","rgba(64,70,135,1)"],["0.25","rgba(60,82,138,1)"],["0.291666666666667","rgba(56,93,140,1)"],["0.333333333333333","rgba(49,104,142,1)"],["0.375","rgba(46,114,142,1)"],["0.416666666666667","rgba(42,123,142,1)"],["0.458333333333333","rgba(38,133,141,1)"],["0.5","rgba(37,144,140,1)"],["0.541666666666667","rgba(33,154,138,1)"],["0.583333333333333","rgba(39,164,133,1)"],["0.625","rgba(47,174,127,1)"],["0.666666666666667","rgba(53,183,121,1)"],["0.708333333333333","rgba(79,191,110,1)"],["0.75","rgba(98,199,98,1)"],["0.791666666666667","rgba(119,207,85,1)"],["0.833333333333333","rgba(147,214,70,1)"],["0.875","rgba(172,220,52,1)"],["0.916666666666667","rgba(199,225,42,1)"],["0.958333333333333","rgba(226,228,40,1)"],["1","rgba(253,231,37,1)"]],"showscale":true,"x":[-0.5,-0.47999999999999998,-0.46000000000000002,-0.44,-0.41999999999999998,-0.40000000000000002,-0.38,-0.35999999999999999,-0.33999999999999997,-0.32000000000000001,-0.29999999999999999,-0.28000000000000003,-0.26000000000000001,-0.23999999999999999,-0.21999999999999997,-0.20000000000000001,-0.17999999999999999,-0.15999999999999998,-0.14000000000000001,-0.12,-0.099999999999999978,-0.080000000000000016,-0.059999999999999998,-0.03999999999999998,-0.020000000000000018,0,0.020000000000000018,0.040000000000000036,0.060000000000000053,0.07999999999999996,0.099999999999999978,0.12,0.14000000000000001,0.16000000000000003,0.18000000000000005,0.20000000000000007,0.21999999999999997,0.23999999999999999,0.26000000000000001,0.28000000000000003,0.30000000000000004,0.32000000000000006,0.33999999999999997,0.35999999999999999,0.38,0.40000000000000002,0.42000000000000004,0.44000000000000006,0.45999999999999996,0.47999999999999998,0.5,0.52000000000000002,0.54000000000000004,0.56000000000000005,0.58000000000000007,0.60000000000000009,0.62000000000000011,0.64000000000000012,0.65999999999999992,0.67999999999999994,0.69999999999999996,0.71999999999999997,0.73999999999999999,0.76000000000000001,0.78000000000000003,0.80000000000000004,0.82000000000000006,0.84000000000000008,0.8600000000000001,0.88000000000000012,0.90000000000000013,0.91999999999999993,0.93999999999999995,0.95999999999999996,0.97999999999999998,1,1.02,1.04,1.0600000000000001,1.0800000000000001,1.1000000000000001,1.1200000000000001,1.1400000000000001,1.1600000000000001,1.1799999999999999,1.2,1.22,1.24,1.26,1.28,1.3,1.3200000000000001,1.3400000000000001,1.3600000000000001,1.3800000000000001,1.4000000000000001,1.4199999999999999,1.4399999999999999,1.46,1.48,1.5],"y":[-0.5,-0.47999999999999998,-0.46000000000000002,-0.44,-0.41999999999999998,-0.40000000000000002,-0.38,-0.35999999999999999,-0.33999999999999997,-0.32000000000000001,-0.29999999999999999,-0.28000000000000003,-0.26000000000000001,-0.23999999999999999,-0.21999999999999997,-0.20000000000000001,-0.17999999999999999,-0.15999999999999998,-0.14000000000000001,-0.12,-0.099999999999999978,-0.080000000000000016,-0.059999999999999998,-0.03999999999999998,-0.020000000000000018,0,0.020000000000000018,0.040000000000000036,0.060000000000000053,0.07999999999999996,0.099999999999999978,0.12,0.14000000000000001,0.16000000000000003,0.18000000000000005,0.20000000000000007,0.21999999999999997,0.23999999999999999,0.26000000000000001,0.28000000000000003,0.30000000000000004,0.32000000000000006,0.33999999999999997,0.35999999999999999,0.38,0.40000000000000002,0.42000000000000004,0.44000000000000006,0.45999999999999996,0.47999999999999998,0.5,0.52000000000000002,0.54000000000000004,0.56000000000000005,0.58000000000000007,0.60000000000000009,0.62000000000000011,0.64000000000000012,0.65999999999999992,0.67999999999999994,0.69999999999999996,0.71999999999999997,0.73999999999999999,0.76000000000000001,0.78000000000000003,0.80000000000000004,0.82000000000000006,0.84000000000000008,0.8600000000000001,0.88000000000000012,0.90000000000000013,0.91999999999999993,0.93999999999999995,0.95999999999999996,0.97999999999999998,1,1.02,1.04,1.0600000000000001,1.0800000000000001,1.1000000000000001,1.1200000000000001,1.1400000000000001,1.1600000000000001,1.1799999999999999,1.2,1.22,1.24,1.26,1.28,1.3,1.3200000000000001,1.3400000000000001,1.3600000000000001,1.3800000000000001,1.4000000000000001,1.4199999999999999,1.4399999999999999,1.46,1.48,1.5],"z":[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],"type":"surface","frame":null}],"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- # Examples of joint pdfs: uniform `\(f(x,y) = 1\)` if `\(x \in [0,1], y \in [0,1]\)`, `\(f(x,y) = 0\)` <img src="12-multivariate-pdf_files/figure-html/joint-pdf-uniform-2d-1.png" width="864" style="display: block; margin: auto;" /> --- # Examples of joint pdfs: exponential `\(f(x,y) = \frac{2 \exp(-2x)}{\sqrt{2\pi}}\exp\left(-\frac{(y)^2}{2}\right)\)` if `\(x \in [0,\infty), y \in \Re\)`, `\(f(x,y) = 0\)` otherwise <div class="plotly html-widget html-fill-item" id="htmlwidget-b85bf888dc62471906a9" style="width:864px;height:504px;"></div> <script type="application/json" data-for="htmlwidget-b85bf888dc62471906a9">{"x":{"visdat":{"d4319ed3900":["function () ","plotlyVisDat"]},"cur_data":"d4319ed3900","attrs":{"d4319ed3900":{"x":{},"y":{},"z":{},"alpha_stroke":1,"sizes":[10,100],"spans":[1,20],"type":"surface","inherit":true}},"layout":{"margin":{"b":40,"l":60,"t":25,"r":10},"scene":{"xaxis":{"title":"x"},"yaxis":{"title":"y"},"zaxis":{"title":"z_mat"}},"hovermode":"closest","showlegend":false,"legend":{"yanchor":"top","y":0.5}},"source":"A","config":{"modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"data":[{"colorbar":{"title":"z_mat","ticklen":2,"len":0.5,"lenmode":"fraction","y":1,"yanchor":"top"},"colorscale":[["0","rgba(68,1,84,1)"],["0.0416666666666667","rgba(70,19,97,1)"],["0.0833333333333333","rgba(72,32,111,1)"],["0.125","rgba(71,45,122,1)"],["0.166666666666667","rgba(68,58,128,1)"],["0.208333333333333","rgba(64,70,135,1)"],["0.25","rgba(60,82,138,1)"],["0.291666666666667","rgba(56,93,140,1)"],["0.333333333333333","rgba(49,104,142,1)"],["0.375","rgba(46,114,142,1)"],["0.416666666666667","rgba(42,123,142,1)"],["0.458333333333333","rgba(38,133,141,1)"],["0.5","rgba(37,144,140,1)"],["0.541666666666667","rgba(33,154,138,1)"],["0.583333333333333","rgba(39,164,133,1)"],["0.625","rgba(47,174,127,1)"],["0.666666666666667","rgba(53,183,121,1)"],["0.708333333333333","rgba(79,191,110,1)"],["0.75","rgba(98,199,98,1)"],["0.791666666666667","rgba(119,207,85,1)"],["0.833333333333333","rgba(147,214,70,1)"],["0.875","rgba(172,220,52,1)"],["0.916666666666667","rgba(199,225,42,1)"],["0.958333333333333","rgba(226,228,40,1)"],["1","rgba(253,231,37,1)"]],"showscale":true,"x":[0,0.029999999999999999,0.059999999999999998,0.089999999999999997,0.12,0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3],"y":[-2,-1.96,-1.9199999999999999,-1.8799999999999999,-1.8400000000000001,-1.8,-1.76,-1.72,-1.6799999999999999,-1.6400000000000001,-1.6000000000000001,-1.5600000000000001,-1.52,-1.48,-1.4399999999999999,-1.3999999999999999,-1.3599999999999999,-1.3199999999999998,-1.28,-1.24,-1.2,-1.1600000000000001,-1.1200000000000001,-1.0800000000000001,-1.04,-1,-0.95999999999999996,-0.91999999999999993,-0.87999999999999989,-0.84000000000000008,-0.80000000000000004,-0.76000000000000001,-0.71999999999999997,-0.67999999999999994,-0.6399999999999999,-0.59999999999999987,-0.56000000000000005,-0.52000000000000002,-0.47999999999999998,-0.43999999999999995,-0.39999999999999991,-0.35999999999999988,-0.32000000000000006,-0.28000000000000003,-0.23999999999999999,-0.19999999999999996,-0.15999999999999992,-0.11999999999999988,-0.080000000000000071,-0.040000000000000036,0,0.040000000000000036,0.080000000000000071,0.12000000000000011,0.16000000000000014,0.20000000000000018,0.24000000000000021,0.28000000000000025,0.31999999999999984,0.35999999999999988,0.39999999999999991,0.43999999999999995,0.47999999999999998,0.52000000000000002,0.56000000000000005,0.60000000000000009,0.64000000000000012,0.68000000000000016,0.7200000000000002,0.76000000000000023,0.80000000000000027,0.83999999999999986,0.87999999999999989,0.91999999999999993,0.95999999999999996,1,1.04,1.0800000000000001,1.1200000000000001,1.1600000000000001,1.2000000000000002,1.2400000000000002,1.2800000000000002,1.3200000000000003,1.3599999999999999,1.3999999999999999,1.4399999999999999,1.48,1.52,1.5600000000000001,1.6000000000000001,1.6400000000000001,1.6800000000000002,1.7200000000000002,1.7600000000000002,1.8000000000000003,1.8399999999999999,1.8799999999999999,1.9199999999999999,1.96,2],"z":[[0.10798193302637613,0.11688188866690294,0.12631312287039731,0.13628713220208916,0.14681362516331378,0.1579003166017883,0.16955272261604445,0.18177395803256574,0.19456453866293502,0.20792219065752837,0.22184166935891109,0.23631459011916453,0.2513292735781763,0.26687060790200462,0.28291993044967756,0.29945493127148975,0.31644958074076612,0.33387408348342773,0.35169486059532473,0.36987456192661061,0.3883721099664259,0.40714277658151876,0.42613829355143568,0.44530699750352226,0.46459400948673241,0.48394144903828673,0.50328868219623424,0.52257260249910631,0.54172794359667609,0.56068762167924113,0.57938310552296546,0.59774481155190551,0.6157025209397059,0.63318581542178565,0.65012452816816435,0.66644920578359934,0.68209157726070513,0.69698502551794894,0.71106505701199418,0.72426976482618444,0.73654028060664678,0.74782121074625685,0.75806105230540333,0.76721258430695716,0.77523323025002833,0.78208538795091187,0.78773672313708165,0.7921604235873122,0.7953354110232177,0.79724650840921008,0.79788456080286541,0.79724650840921008,0.7953354110232177,0.7921604235873122,0.78773672313708165,0.78208538795091176,0.77523323025002822,0.76721258430695705,0.75806105230540344,0.74782121074625685,0.73654028060664678,0.72426976482618444,0.71106505701199418,0.69698502551794894,0.68209157726070513,0.66644920578359934,0.65012452816816424,0.63318581542178554,0.61570252093970579,0.5977448115519054,0.57938310552296535,0.56068762167924124,0.54172794359667609,0.52257260249910631,0.50328868219623424,0.48394144903828673,0.46459400948673241,0.44530699750352226,0.42613829355143568,0.40714277658151876,0.38837210996642585,0.3698745619266105,0.35169486059532462,0.33387408348342751,0.31644958074076612,0.29945493127148975,0.28291993044967756,0.26687060790200462,0.2513292735781763,0.23631459011916453,0.22184166935891109,0.20792219065752837,0.19456453866293494,0.18177395803256566,0.1695527226160444,0.15790031660178824,0.14681362516331384,0.13628713220208916,0.12631312287039731,0.11688188866690294,0.10798193302637613],[0.10169355479211069,0.11007521736483193,0.11895721924560962,0.12835038749183533,0.13826386522574091,0.14870491801728836,0.1596787407324386,0.17118826680430207,0.18323398200593352,0.19581374490640244,0.20892261627334602,0.2225526997427279,0.23669299610741926,0.2513292735781763,0.26644395634162865,0.28201603367839778,0.29802099180925867,0.31443077050763885,0.33121374635253337,0.34833474429749278,0.36575507899966164,0.38343262708949,0.40132193126885546,0.41937433680570685,0.43753816065030859,0.45575889303562755,0.47397943104676771,0.49214034325647787,0.51018016413087786,0.52803571651721226,0.54564246013942908,0.56293486365358492,0.57984679745942824,0.59631194413286015,0.61226422304197103,0.62763822544238446,0.64236965612067254,0.65639577747211686,0.6696558517649579,0.68209157726070513,0.69364751383153034,0.7042714937428568,0.71391501335278296,0.72253360161980762,0.73008716150542841,0.73654028060664678,0.74186250765237816,0.74602859184360593,0.74901868240531733,0.75081848614367053,0.75141938125858365,0.75081848614367053,0.74901868240531733,0.74602859184360593,0.74186250765237816,0.73654028060664667,0.73008716150542829,0.72253360161980751,0.71391501335278307,0.7042714937428568,0.69364751383153034,0.68209157726070513,0.6696558517649579,0.65639577747211686,0.64236965612067254,0.62763822544238446,0.61226422304197092,0.59631194413286004,0.57984679745942813,0.5629348636535848,0.54564246013942896,0.52803571651721237,0.51018016413087786,0.49214034325647787,0.47397943104676771,0.45575889303562755,0.43753816065030859,0.41937433680570685,0.40132193126885546,0.38343262708949,0.36575507899966159,0.34833474429749267,0.33121374635253326,0.31443077050763862,0.29802099180925867,0.28201603367839778,0.26644395634162865,0.2513292735781763,0.23669299610741926,0.2225526997427279,0.20892261627334602,0.19581374490640244,0.18323398200593344,0.17118826680430199,0.15967874073243854,0.1487049180172883,0.13826386522574097,0.12835038749183533,0.11895721924560962,0.11007521736483193,0.10169355479211069],[0.095771383197316359,0.10366493574077573,0.11202969009932075,0.12087584281160589,0.13021200454587531,0.1400450177582355,0.15037977478920522,0.16121903824204947,0.17256326560060259,0.18441044014116315,0.19675591026986866,0.20959223947112549,0.22290906908176208,0.23669299610741923,0.25092746827041584,0.26559269842041605,0.28066560034956167,0.2961197479316624,0.31192535935038523,0.32804930799451681,0.34445516138018639,0.36110324921191672,0.37795076141854356,0.39495187669903015,0.41205792179014789,0.4292175613265713,0.44637701780828676,0.4634803208249289,0.4804695843166516,0.4972853102816569,0.5138667169769715,0.53015208930703106,0.54607914875969876,0.56158543993699961,0.5766087304434443,0.5910874206433927,0.60496095958515939,0.61817026321769841,0.63065813089938838,0.64236965612067243,0.65325262733542488,0.6632579148214236,0.67233983956897625,0.68045652032842541,0.68757019513100781,0.69364751383153034,0.69865979850288307,0.7025832688381074,0.70539923008133221,0.7070942214095256,0.70766012311715476,0.7070942214095256,0.70539923008133221,0.7025832688381074,0.69865979850288307,0.69364751383153023,0.6875701951310077,0.6804565203284253,0.67233983956897636,0.6632579148214236,0.65325262733542488,0.64236965612067243,0.63065813089938838,0.61817026321769841,0.60496095958515939,0.5910874206433927,0.57660873044344418,0.5615854399369995,0.54607914875969865,0.53015208930703095,0.51386671697697139,0.49728531028165701,0.4804695843166516,0.4634803208249289,0.44637701780828676,0.4292175613265713,0.41205792179014789,0.39495187669903015,0.37795076141854356,0.36110324921191672,0.34445516138018634,0.3280493079945167,0.31192535935038512,0.29611974793166224,0.28066560034956167,0.26559269842041605,0.25092746827041584,0.23669299610741923,0.22290906908176208,0.20959223947112549,0.19675591026986866,0.18441044014116315,0.17256326560060253,0.16121903824204939,0.15037977478920517,0.14004501775823547,0.13021200454587536,0.12087584281160589,0.11202969009932075,0.10366493574077573,0.095771383197316359],[0.090194092027539002,0.097627959856952773,0.10550558884397473,0.11383658172707499,0.12262904772821634,0.1318894308298825,0.14162233846486022,0.15183037235492486,0.16251396334212634,0.17367121214760853,0.18529773806524716,0.19738653764840264,0.20992785547548473,0.22290906908176208,0.23631459011916456,0.25012578375128519,0.26432090820634813,0.27887507629594738,0.29376024056171474,0.30894520353609167,0.32439565439789836,0.34007423306981743,0.35594062254514636,0.3719516699476858,0.38806153652439351,0.40422187644888707,0.42038204397894907,0.43648932816716712,0.45248921397538927,0.46832566829570305,0.48394144903828668,0.49927843511495107,0.5142779748317613,0.52888124990997354,0.54302965208667608,0.55666516900974139,0.56973077594039712,0.58217082961486799,0.59393146049757661,0.60496095958515927,0.61521015589523143,0.62463278079785933,0.63318581542178554,0.6408298174914604,0.6475292241239845,0.65325262733542488,0.65797301927113283,0.66166800448141705,0.66431997690823397,0.66591625962585932,0.66644920578359934,0.66591625962585932,0.66431997690823397,0.66166800448141705,0.65797301927113283,0.65325262733542477,0.64752922412398439,0.6408298174914604,0.63318581542178565,0.62463278079785933,0.61521015589523143,0.60496095958515927,0.59393146049757661,0.58217082961486799,0.56973077594039712,0.55666516900974139,0.54302965208667597,0.52888124990997343,0.51427797483176119,0.49927843511495096,0.48394144903828656,0.4683256682957031,0.45248921397538927,0.43648932816716712,0.42038204397894907,0.40422187644888707,0.38806153652439351,0.3719516699476858,0.35594062254514636,0.34007423306981743,0.3243956543978983,0.30894520353609156,0.29376024056171463,0.27887507629594716,0.26432090820634813,0.25012578375128519,0.23631459011916456,0.22290906908176208,0.20992785547548473,0.19738653764840264,0.18529773806524716,0.17367121214760853,0.16251396334212628,0.1518303723549248,0.14162233846486016,0.13188943082988244,0.12262904772821639,0.11383658172707499,0.10550558884397473,0.097627959856952773,0.090194092027539002],[0.084941597010370087,0.091942550079464891,0.099361421668177394,0.10720725529502399,0.11548768793764425,0.12420878831019633,0.13337489552946968,0.14298845980475863,0.15304988688782531,0.16355738810520368,0.17450683786323382,0.18589164056425769,0.19770260889821148,0.20992785547548476,0.22255269974272793,0.23555959207192376,0.24892805683351646,0.26263465615612469,0.27665297593819999,0.29095363551125819,0.30550432216079393,0.32026985149101778,0.33521225437491692,0.35029089096416477,0.36546259194688235,0.380681826938436,0.39590089957502811,0.41107016855585427,0.42613829355143584,0.44105250456803441,0.45575889303562755,0.47020272257470552,0.48432875710008572,0.49808160364292076,0.51140606701982538,0.52424751325505603,0.53655223847210032,0.54826783981860139,0.55934358487651192,0.56973077594039712,0.57938310552296568,0.58825699946952836,0.59631194413286015,0.60351079417672449,0.60982005773929471,0.61521015589523143,0.61965565360489838,0.62313545962806238,0.62563299320368193,0.62713631565271499,0.62763822544238446,0.62713631565271499,0.62563299320368193,0.62313545962806238,0.61965565360489838,0.61521015589523143,0.6098200577392946,0.60351079417672449,0.59631194413286026,0.58825699946952836,0.57938310552296568,0.56973077594039712,0.55934358487651192,0.54826783981860139,0.53655223847210032,0.52424751325505603,0.51140606701982527,0.4980816036429207,0.48432875710008561,0.47020272257470541,0.4557588930356275,0.44105250456803446,0.42613829355143584,0.41107016855585427,0.39590089957502811,0.380681826938436,0.36546259194688235,0.35029089096416477,0.33521225437491692,0.32026985149101778,0.30550432216079387,0.29095363551125808,0.27665297593819993,0.26263465615612447,0.24892805683351646,0.23555959207192376,0.22255269974272793,0.20992785547548476,0.19770260889821148,0.18589164056425769,0.17450683786323382,0.16355738810520368,0.15304988688782525,0.14298845980475858,0.13337489552946966,0.12420878831019629,0.1154876879376443,0.10720725529502399,0.099361421668177394,0.091942550079464891,0.084941597010370087],[0.079994983490372387,0.086588232792133679,0.093575062933598935,0.10096399077976574,0.1087622085653188,0.11697543159001672,0.12560774628015892,0.13466146015595862,0.14413695534003482,0.15403254732315508,0.16434435076753048,0.17506615417320895,0.18618930525741326,0.19770260889821145,0.20959223947112551,0.22184166935891117,0.23443161533984996,0.24734000445793225,0.26054196084913328,0.27400981484190157,0.28771313546773208,0.30161878731053493,0.31569101239311814,0.32989153754767753,0.34417970744734627,0.35851264319067583,0.37284542603386084,0.38713130556040259,0.40132193126885563,0.41536760625067959,0.42921756132657124,0.4428202477156114,0.45612364603180106,0.46907558914166986,0.48162409617908086,0.49371771480335008,0.5053058686082621,0.51633920644600861,0.52676995032456986,0.53655223847210021,0.5456424601394293,0.55399957873308991,0.56158543993699961,0.5683650615909025,0.57430690224716652,0.57938310552296557,0.58356971760005982,0.58684687549642855,0.58919896403938288,0.59061473980442325,0.5910874206433927,0.59061473980442325,0.58919896403938288,0.58684687549642855,0.58356971760005982,0.57938310552296546,0.57430690224716641,0.56836506159090239,0.56158543993699961,0.55399957873308991,0.5456424601394293,0.53655223847210021,0.52676995032456986,0.51633920644600861,0.5053058686082621,0.49371771480335008,0.48162409617908081,0.4690755891416698,0.456123646031801,0.44282024771561129,0.42921756132657118,0.4153676062506797,0.40132193126885563,0.38713130556040259,0.37284542603386084,0.35851264319067583,0.34417970744734627,0.32989153754767753,0.31569101239311814,0.30161878731053493,0.28771313546773208,0.27400981484190146,0.26054196084913323,0.24734000445793211,0.23443161533984996,0.22184166935891117,0.20959223947112551,0.19770260889821145,0.18618930525741326,0.17506615417320895,0.16434435076753048,0.15403254732315508,0.14413695534003476,0.13466146015595856,0.12560774628015889,0.11697543159001668,0.10876220856531883,0.10096399077976574,0.093575062933598935,0.086588232792133679,0.079994983490372387],[0.075336438315890222,0.081545726669368115,0.08812567549877752,0.095084305685510462,0.10242839062111023,0.11016331277218828,0.1182929205901025,0.12681938721555025,0.13574307251806159,0.14506239008658484,0.1547736808477895,0.16487109503132027,0.17534648422412311,0.18618930525741326,0.19738653764840267,0.20892261627334607,0.2207793808779358,0.23293604393505055,0.24536917823820958,0.25805272547208974,0.2709580268298305,0.28405387655175263,0.29730659904314416,0.31068014999197918,0.32413624165331323,0.33763449219852298,0.35113259874779945,0.3645865334169538,0.37795076141854367,0.3911784799666771,0.40422187644888702,0.41703240405155423,0.42956107276188604,0.44175875342376136,0.45357649230102742,0.46496583340405812,0.47587914566724354,0.48626995192988642,0.4960932565736163,0.50530586860826199,0.51386671697697162,0.52173715487143868,0.52888124990997343,0.53526605713473907,0.54086187192901747,0.54564246013942919,0.54958526290951204,0.55267157398726774,0.55488668755687187,0.55622001495989504,0.55666516900974128,0.55622001495989504,0.55488668755687187,0.55267157398726774,0.54958526290951204,0.54564246013942908,0.54086187192901736,0.53526605713473896,0.52888124990997354,0.52173715487143868,0.51386671697697162,0.50530586860826199,0.4960932565736163,0.48626995192988642,0.47587914566724354,0.46496583340405812,0.45357649230102737,0.44175875342376131,0.42956107276188599,0.41703240405155412,0.40422187644888696,0.39117847996667721,0.37795076141854367,0.3645865334169538,0.35113259874779945,0.33763449219852298,0.32413624165331323,0.31068014999197918,0.29730659904314416,0.28405387655175263,0.27095802682983045,0.25805272547208968,0.2453691782382095,0.23293604393505041,0.2207793808779358,0.20892261627334607,0.19738653764840267,0.18618930525741326,0.17534648422412311,0.16487109503132027,0.1547736808477895,0.14506239008658484,0.13574307251806153,0.12681938721555019,0.11829292059010246,0.11016331277218824,0.10242839062111027,0.095084305685510462,0.08812567549877752,0.081545726669368115,0.075336438315890222],[0.070949185692462877,0.076796873242566094,0.082993635682903064,0.089547026795096893,0.096463425519075108,0.10374790087099561,0.11140407718585646,0.11943400105049291,0.12783801137726511,0.13661461414050893,0.14576036335473586,0.15526974991369569,0.16513509993096911,0.17534648422412308,0.18589164056425767,0.19675591026986874,0.2079221906575284,0.21937090477145296,0.23107998969945784,0.24302490464436677,0.25517865975830367,0.26751186656355908,0.27999281057938591,0.29258754655108071,0.30526001643838385,0.31797219006729666,0.3306842280859465,0.34335466659451558,0.35594062254514647,0.36839801873401307,0.38068182693843589,0.39274632749112992,0.40454538333554713,0.41603272637488775,0.42716225371665667,0.43788833122838428,0.44816610166178239,0.4579517944752845,0.46720303439134281,0.47587914566724354,0.48394144903828679,0.49135354831107342,0.49808160364292065,0.50409458864097734,0.50936452855073477,0.5138667169769715,0.51757990878875337,0.52048648710139178,0.5225726024991062,0.52382828295892936,0.52424751325505603,0.52382828295892936,0.5225726024991062,0.52048648710139178,0.51757990878875337,0.5138667169769715,0.50936452855073466,0.50409458864097723,0.4980816036429207,0.49135354831107342,0.48394144903828679,0.47587914566724354,0.46720303439134281,0.4579517944752845,0.44816610166178239,0.43788833122838428,0.42716225371665661,0.4160327263748877,0.40454538333554707,0.39274632749112981,0.38068182693843583,0.36839801873401312,0.35594062254514647,0.34335466659451558,0.3306842280859465,0.31797219006729666,0.30526001643838385,0.29258754655108071,0.27999281057938591,0.26751186656355908,0.25517865975830362,0.24302490464436671,0.23107998969945776,0.2193709047714528,0.2079221906575284,0.19675591026986874,0.18589164056425767,0.17534648422412308,0.16513509993096911,0.15526974991369569,0.14576036335473586,0.13661461414050893,0.12783801137726505,0.11943400105049286,0.11140407718585642,0.10374790087099557,0.096463425519075149,0.089547026795096893,0.082993635682903064,0.076796873242566094,0.070949185692462877],[0.06681742677184456,0.072324571510013938,0.078160462599370262,0.08433221392354065,0.09084583294191069,0.097706093474118058,0.10491640879032176,0.11247870629341813,0.12039330515904796,0.1286587983668285,0.13727194060984343,0.14622754360721457,0.15551838036487742,0.16513509993096911,0.17506615417320895,0.18529773806524721,0.19581374490640249,0.20659573781404203,0.21762293871996291,0.2288722359717586,0.24031821148793253,0.25193318824248201,0.26368729866223828,0.27554857431023821,0.28748305700301463,0.2994549312714897,0.31142667782702871,0.32335924743935918,0.33521225437491697,0.34694418828639911,0.35851264319067577,0.36987456192661056,0.38098649425066267,0.39180486651022955,0.40228626063626366,0.41238770002128433,0.42206693969977949,0.43128275812808609,0.43999524777270865,0.44816610166178239,0.45575889303562761,0.46273934525014365,0.4690755891416698,0.47473840515381371,0.47970144765494349,0.48394144903828673,0.48743840139301831,0.4901757137619463,0.49214034325647776,0.49332289857905398,0.49371771480335008,0.49332289857905398,0.49214034325647776,0.4901757137619463,0.48743840139301831,0.48394144903828668,0.47970144765494338,0.47473840515381366,0.46907558914166986,0.46273934525014365,0.45575889303562761,0.44816610166178239,0.43999524777270865,0.43128275812808609,0.42206693969977949,0.41238770002128433,0.4022862606362636,0.3918048665102295,0.38098649425066261,0.3698745619266105,0.35851264319067572,0.34694418828639922,0.33521225437491697,0.32335924743935918,0.31142667782702871,0.2994549312714897,0.28748305700301463,0.27554857431023821,0.26368729866223828,0.25193318824248201,0.2403182114879325,0.22887223597175851,0.21762293871996283,0.20659573781404189,0.19581374490640249,0.18529773806524721,0.17506615417320895,0.16513509993096911,0.15551838036487742,0.14622754360721457,0.13727194060984343,0.1286587983668285,0.12039330515904791,0.11247870629341808,0.10491640879032171,0.097706093474118016,0.090845832941910717,0.08433221392354065,0.078160462599370262,0.072324571510013938,0.06681742677184456],[0.062926282759085878,0.068112716354808908,0.073608751604625058,0.079421088111830337,0.085555383488611095,0.092016133548991796,0.098806552789751728,0.10592845637058063,0.11338214487977692,0.12116629323544613,0.12927784512263388,0.13771191440241881,0.14646169494810657,0.15551838036487742,0.1648710950313203,0.17450683786323384,0.1844104401411632,0.19456453866293502,0.20494956538083939,0.21554375456032734,0.22632316835373362,0.23726174151957377,0.24833134583673333,0.25950187456508617,0.27074134709181807,0.28201603367839778,0.29329059998946377,0.30452827084488177,0.3156910123931182,0.32673973166130643,0.33763449219852293,0.34833474429749273,0.3587995680598734,0.36898792736504515,0.37885893261546238,0.3883721099664259,0.39748767460769402,0.40616680555142531,0.41437191929795092,0.42206693969977943,0.42921756132657135,0.43579150365058217,0.44175875342376136,0.44709179270421145,0.45176581011044675,0.45575889303562761,0.45905219873894765,0.46163010244534552,0.46348032082492885,0.46459400948673241,0.46496583340405812,0.46459400948673241,0.46348032082492885,0.46163010244534552,0.45905219873894765,0.4557588930356275,0.45176581011044664,0.4470917927042114,0.44175875342376142,0.43579150365058217,0.42921756132657135,0.42206693969977943,0.41437191929795092,0.40616680555142531,0.39748767460769402,0.3883721099664259,0.37885893261546233,0.3689879273650451,0.35879956805987329,0.34833474429749267,0.33763449219852287,0.32673973166130649,0.3156910123931182,0.30452827084488177,0.29329059998946377,0.28201603367839778,0.27074134709181807,0.25950187456508617,0.24833134583673333,0.23726174151957377,0.22632316835373359,0.21554375456032729,0.20494956538083933,0.19456453866293491,0.1844104401411632,0.17450683786323384,0.1648710950313203,0.15551838036487742,0.14646169494810657,0.13771191440241881,0.12927784512263388,0.12116629323544613,0.11338214487977688,0.10592845637058057,0.0988065527897517,0.092016133548991755,0.085555383488611123,0.079421088111830337,0.073608751604625058,0.068112716354808908,0.062926282759085878],[0.059261741332801064,0.064146140549042843,0.069322111622648536,0.074795964002391413,0.080573025826773365,0.086657531093992199,0.093052507103107987,0.099759663307139299,0.10677928278948483,0.11411011763501223,0.12174928951469403,0.12969219683618793,0.13793242983076209,0.14646169494810657,0.15526974991369569,0.16434435076753051,0.17367121214760856,0.18323398200593352,0.19301423184918071,0.20299146348050445,0.21314313308396332,0.22344469333956796,0.23386965408627991,0.24438966186402658,0.25497459846589721,0.26559269842041605,0.27621068510372182,0.28679392495544781,0.29730659904314427,0.30771189099145285,0.3179721900672966,0.32804930799451676,0.33790470786413651,0.34749974331316041,0.35679590596882721,0.36575507899966164,0.37433979448240257,0.38251349218754227,0.39024077730804468,0.39748767460769402,0.40422187644888713,0.41041298217546895,0.4160327263748877,0.42105519362542732,0.42545701744797509,0.4292175613265713,0.43231907983620887,0.43474685811788977,0.43648932816716707,0.43753816065030854,0.43788833122838422,0.43753816065030854,0.43648932816716707,0.43474685811788977,0.43231907983620887,0.42921756132657124,0.42545701744797504,0.42105519362542726,0.41603272637488775,0.41041298217546895,0.40422187644888713,0.39748767460769402,0.39024077730804468,0.38251349218754227,0.37433979448240257,0.36575507899966164,0.35679590596882715,0.3474997433131603,0.33790470786413646,0.3280493079945167,0.31797219006729655,0.30771189099145291,0.29730659904314427,0.28679392495544781,0.27621068510372182,0.26559269842041605,0.25497459846589721,0.24438966186402658,0.23386965408627991,0.22344469333956796,0.21314313308396329,0.2029914634805044,0.19301423184918065,0.18323398200593341,0.17367121214760856,0.16434435076753051,0.15526974991369569,0.14646169494810657,0.13793242983076209,0.12969219683618793,0.12174928951469403,0.11411011763501223,0.10677928278948477,0.099759663307139243,0.093052507103107959,0.086657531093992157,0.080573025826773392,0.074795964002391413,0.069322111622648536,0.064146140549042843,0.059261741332801064],[0.0558106061856758,0.060410560135399007,0.065285106119378836,0.070440186152696427,0.075880818087222857,0.081610989352296104,0.087633550950803496,0.093950112784969744,0.10056094145269978,0.10746486171178107,0.11465916285401952,0.12213951126294913,0.1298998704457098,0.13793242983076212,0.1462275436072146,0.15477368084778959,0.1635573881052037,0.17256326560060264,0.18177395803256574,0.19117016092630137,0.20073064331550422,0.21043228740481373,0.22025014570007503,0.23015751591818728,0.24012603380006683,0.25012578375128519,0.26012542702769242,0.27009234697046342,0.27999281057938602,0.28979214549789278,0.2994549312714897,0.30894520353609167,0.31822666959759044,0.32726293368196469,0.33601772996950208,0.34445516138018645,0.35253994195274346,0.36023764055968299,0.36751492362706545,0.37433979448240262,0.38068182693843605,0.38651239073540117,0.39180486651022955,0.39653484803787614,0.40068032959703792,0.40422187644888713,0.40714277658151893,0.40942917206261209,0.41107016855585421,0.412057921790148,0.41238770002128439,0.412057921790148,0.41107016855585421,0.40942917206261209,0.40714277658151893,0.40422187644888707,0.40068032959703787,0.39653484803787609,0.39180486651022961,0.38651239073540117,0.38068182693843605,0.37433979448240262,0.36751492362706545,0.36023764055968299,0.35253994195274346,0.34445516138018645,0.33601772996950202,0.32726293368196463,0.31822666959759038,0.30894520353609162,0.29945493127148964,0.28979214549789284,0.27999281057938602,0.27009234697046342,0.26012542702769242,0.25012578375128519,0.24012603380006683,0.23015751591818728,0.22025014570007503,0.21043228740481373,0.20073064331550419,0.19117016092630132,0.18177395803256569,0.17256326560060253,0.1635573881052037,0.15477368084778959,0.1462275436072146,0.13793242983076212,0.1298998704457098,0.12213951126294913,0.11465916285401952,0.10746486171178107,0.10056094145269974,0.093950112784969703,0.087633550950803468,0.081610989352296076,0.075880818087222884,0.070440186152696427,0.065285106119378836,0.060410560135399007,0.0558106061856758],[0.052560449503507155,0.056892522989477251,0.061483197514514983,0.066338069057681803,0.071461863253904648,0.07685833532271423,0.082530170237514952,0.088478884147124584,0.094704728123994747,0.10120659536669128,0.1079819330263761,0.11502665985675936,0.12233509090295822,0.1298998704457098,0.13771191440241884,0.14576036335473591,0.15403254732315511,0.16251396334212637,0.17118826680430207,0.18003727743998396,0.18904100067809201,0.198177664998861,0.20742377573709397,0.21675418562960094,0.22614218222315549,0.23555959207192373,0.24497690145813825,0.25436339316931356,0.26368729866223839,0.27291596474120172,0.28201603367839778,0.29095363551125814,0.29969459106764357,0.30820462409840838,0.31644958074076618,0.32439565439789836,0.33200961400294354,0.33925903354118009,0.34611252063489406,0.35253994195274341,0.35851264319067588,0.36400366138545792,0.36898792736504515,0.37344245621229138,0.37734652371933747,0.380681826938436,0.38343262708949011,0.38558587326333099,0.38713130556040254,0.38806153652439351,0.3883721099664259,0.38806153652439351,0.38713130556040254,0.38558587326333099,0.38343262708949011,0.38068182693843594,0.37734652371933741,0.37344245621229133,0.36898792736504521,0.36400366138545792,0.35851264319067588,0.35253994195274341,0.34611252063489406,0.33925903354118009,0.33200961400294354,0.32439565439789836,0.31644958074076612,0.30820462409840832,0.29969459106764351,0.29095363551125808,0.28201603367839773,0.27291596474120178,0.26368729866223839,0.25436339316931356,0.24497690145813825,0.23555959207192373,0.22614218222315549,0.21675418562960094,0.20742377573709397,0.198177664998861,0.18904100067809199,0.18003727743998391,0.17118826680430202,0.16251396334212626,0.15403254732315511,0.14576036335473591,0.13771191440241884,0.1298998704457098,0.12233509090295822,0.11502665985675936,0.1079819330263761,0.10120659536669128,0.094704728123994719,0.088478884147124542,0.082530170237514924,0.076858335322714202,0.071461863253904676,0.066338069057681803,0.061483197514514983,0.056892522989477251,0.052560449503507155],[0.049499567211648859,0.053579360377616188,0.057902694830525438,0.062474840664987374,0.067300248316374864,0.072382454317257733,0.077723987280361895,0.083326275060871549,0.089189554109916983,0.095312782081161784,0.10169355479211065,0.10832802866975499,0.1152108498252111,0.1223350909029582,0.12969219683618793,0.13727194060984346,0.14506239008658486,0.15304988688782531,0.16121903824204944,0.16955272261604445,0.17803210983190296,0.18663669624446777,0.19534435541132808,0.20413140453189477,0.21297268676511419,0.22184166935891111,0.230710557340638,0.23955042232900539,0.24833134583673339,0.2570225762421931,0.265592698420416,0.27400981484190151,0.28224173677454145,0.29025618406254622,0.29802099180925867,0.30550432216079387,0.31267487927696852,0.3195021254871524,0.3259564965633896,0.33200961400294349,0.33763449219852304,0.34280573838763456,0.34749974331316036,0.35169486059532473,0.35537157291017946,0.35851264319067583,0.36110324921191678,0.36313110009051608,0.36458653341695374,0.36546259194688235,0.36575507899966164,0.36546259194688235,0.36458653341695374,0.36313110009051608,0.36110324921191678,0.35851264319067577,0.3553715729101794,0.35169486059532468,0.34749974331316041,0.34280573838763456,0.33763449219852304,0.33200961400294349,0.3259564965633896,0.3195021254871524,0.31267487927696852,0.30550432216079387,0.29802099180925862,0.29025618406254616,0.2822417367745414,0.27400981484190146,0.26559269842041594,0.25702257624219316,0.24833134583673339,0.23955042232900539,0.230710557340638,0.22184166935891111,0.21297268676511419,0.20413140453189477,0.19534435541132808,0.18663669624446777,0.17803210983190293,0.1695527226160444,0.16121903824204939,0.1530498868878252,0.14506239008658486,0.13727194060984346,0.12969219683618793,0.1223350909029582,0.1152108498252111,0.10832802866975499,0.10169355479211065,0.095312782081161784,0.089189554109916955,0.083326275060871521,0.077723987280361881,0.072382454317257719,0.067300248316374892,0.062474840664987374,0.057902694830525438,0.053579360377616188,0.049499567211648859],[0.04661693682770067,0.050459141335768093,0.054530704390340884,0.058836589179612098,0.063380986965774905,0.068167228329775439,0.073197694629398111,0.07847373056801453,0.083995558826913091,0.089762197761282483,0.095771383197316345,0.10201949539427295,0.10850149224948487,0.11521084982521111,0.12213951126294913,0.12927784512263393,0.13661461414050896,0.14413695534003484,0.15183037235492486,0.15967874073243862,0.16766432687886185,0.17576782118837633,0.18396838576226512,0.19224371697887749,0.20057012301753208,0.20892261627334607,0.21727502042686805,0.22560009175458559,0.23386965408628002,0.24205474663535101,0.25012578375128514,0.25805272547208974,0.26580525759148438,0.27335297980360773,0.28066560034956173,0.28771313546773214,0.29446611184578558,0.30089577018858421,0.30697426795477645,0.31267487927696858,0.31797219006729677,0.32284228632263468,0.32726293368196463,0.33121374635253342,0.33467634361085602,0.33763449219852304,0.3400742330698176,0.34198399110668004,0.34335466659451558,0.34417970744734627,0.34445516138018639,0.34417970744734627,0.34335466659451558,0.34198399110668004,0.3400742330698176,0.33763449219852298,0.33467634361085596,0.33121374635253337,0.32726293368196469,0.32284228632263468,0.31797219006729677,0.31267487927696858,0.30697426795477645,0.30089577018858421,0.29446611184578558,0.28771313546773214,0.28066560034956167,0.27335297980360768,0.26580525759148432,0.25805272547208968,0.25012578375128508,0.24205474663535106,0.23386965408628002,0.22560009175458559,0.21727502042686805,0.20892261627334607,0.20057012301753208,0.19224371697887749,0.18396838576226512,0.17576782118837633,0.16766432687886182,0.1596787407324386,0.15183037235492483,0.14413695534003476,0.13661461414050896,0.12927784512263393,0.12213951126294913,0.11521084982521111,0.10850149224948487,0.10201949539427295,0.095771383197316345,0.089762197761282483,0.083995558826913064,0.078473730568014488,0.073197694629398097,0.068167228329775412,0.063380986965774933,0.058836589179612098,0.054530704390340884,0.050459141335768093,0.04661693682770067],[0.043902177768665909,0.047520629705141322,0.05135508338618993,0.055410212966425447,0.05968996562793235,0.064197477993721955,0.068934992742097384,0.073903776267002202,0.079104038281776146,0.084534854308151303,0.090194092027538988,0.096078342496487876,0.1021828572415311,0.10850149224948487,0.11502665985675939,0.1217492895146941,0.12865879836682856,0.13574307251806161,0.14298845980475863,0.15037977478920525,0.15790031660178835,0.16553190014059088,0.17325490101164676,0.18104831445511488,0.18888982835454149,0.19675591026986874,0.2046219082718175,0.21246216518782104,0.22025014570007509,0.22795857556689486,0.23555959207192373,0.2430249046443668,0.25032596443988536,0.25743414152860922,0.26432090820634818,0.27095802682983056,0.27731774047881347,0.28337296466912532,0.28909747828279619,0.29446611184578558,0.29945493127148981,0.30404141519990857,0.30820462409840838,0.31192535935038535,0.31518631064235958,0.31797219006729671,0.32026985149101783,0.3220683938778624,0.32335924743935918,0.32413624165331328,0.32439565439789841,0.32413624165331328,0.32335924743935918,0.3220683938778624,0.32026985149101783,0.31797219006729671,0.31518631064235952,0.31192535935038529,0.30820462409840843,0.30404141519990857,0.29945493127148981,0.29446611184578558,0.28909747828279619,0.28337296466912532,0.27731774047881347,0.27095802682983056,0.26432090820634813,0.25743414152860916,0.25032596443988531,0.24302490464436674,0.23555959207192367,0.22795857556689492,0.22025014570007509,0.21246216518782104,0.2046219082718175,0.19675591026986874,0.18888982835454149,0.18104831445511488,0.17325490101164676,0.16553190014059088,0.15790031660178833,0.1503797747892052,0.14298845980475858,0.13574307251806153,0.12865879836682856,0.1217492895146941,0.11502665985675939,0.10850149224948487,0.1021828572415311,0.096078342496487876,0.090194092027538988,0.084534854308151303,0.079104038281776104,0.073903776267002175,0.06893499274209737,0.064197477993721927,0.059689965627932377,0.055410212966425447,0.05135508338618993,0.047520629705141322,0.043902177768665909],[0.041345513969640424,0.044753243669892209,0.048364396152375359,0.052183373370129543,0.056213892639249551,0.060458907920042625,0.064920531287394917,0.069599955386208001,0.074497377717067464,0.079611927639128527,0.08494159701037006,0.090483175408752614,0.096232190890376407,0.10218285724153109,0.10832802866975502,0.11465916285401954,0.12116629323544618,0.12783801137726514,0.13466146015595862,0.14162233846486025,0.14870491801728838,0.15589207272921798,0.16316532104241868,0.17050488141903566,0.17788974109912356,0.18529773806524721,0.19270565600472714,0.20008933190240788,0.20742377573709403,0.21468330159528645,0.22184166935891114,0.2288722359717586,0.23574811514475585,0.24244234422535213,0.24892805683351649,0.25517865975830367,0.26116801251666749,0.26687060790200462,0.27226175179538004,0.27731774047881347,0.28201603367839784,0.28633542157603675,0.29025618406254627,0.29376024056171479,0.29683128883424187,0.29945493127148975,0.30161878731053504,0.30331259074261319,0.30452827084488177,0.30526001643838391,0.30550432216079393,0.30526001643838391,0.30452827084488177,0.30331259074261319,0.30161878731053504,0.29945493127148975,0.29683128883424187,0.29376024056171474,0.29025618406254627,0.28633542157603675,0.28201603367839784,0.27731774047881347,0.27226175179538004,0.26687060790200462,0.26116801251666749,0.25517865975830367,0.24892805683351643,0.24244234422535207,0.23574811514475583,0.22887223597175857,0.22184166935891109,0.21468330159528648,0.20742377573709403,0.20008933190240788,0.19270565600472714,0.18529773806524721,0.17788974109912356,0.17050488141903566,0.16316532104241868,0.15589207272921798,0.14870491801728838,0.14162233846486019,0.13466146015595856,0.12783801137726505,0.12116629323544618,0.11465916285401954,0.10832802866975502,0.10218285724153109,0.096232190890376407,0.090483175408752614,0.08494159701037006,0.079611927639128527,0.074497377717067423,0.069599955386207973,0.064920531287394889,0.060458907920042597,0.056213892639249571,0.052183373370129543,0.048364396152375359,0.044753243669892209,0.041345513969640424],[0.038937738679419451,0.042147017651158261,0.04554787298452561,0.049144450282772756,0.052940250382357876,0.056938055218331972,0.061139853867915088,0.065546769521776696,0.070158988178963641,0.07497568990080683,0.079994983490372359,0.085213845486045658,0.090628064369665709,0.096232190890376393,0.10201949539427295,0.10798193302637613,0.11411011763501228,0.12039330515904798,0.12681938721555025,0.13337489552946971,0.14004501775823552,0.14681362516331375,0.15366331246863763,0.16057545012343574,0.16753024905563885,0.17450683786323382,0.18148335224633849,0.18843703633425507,0.19534435541132816,0.20218111939521152,0.20892261627334605,0.21554375456032734,0.22201921370266675,0.22832360123046061,0.23443161533984999,0.24031821148793256,0.24595877149488457,0.25132927357817625,0.25640646169240655,0.26116801251666749,0.26559269842041611,0.26966054474920548,0.27335297980360768,0.27665297593819999,0.27954518028219122,0.28201603367839778,0.28405387655175268,0.2856490405509472,0.28679392495544781,0.28748305700301469,0.28771313546773208,0.28748305700301469,0.28679392495544781,0.2856490405509472,0.28405387655175268,0.28201603367839778,0.27954518028219116,0.27665297593819999,0.27335297980360773,0.26966054474920548,0.26559269842041611,0.26116801251666749,0.25640646169240655,0.25132927357817625,0.24595877149488457,0.24031821148793256,0.23443161533984994,0.22832360123046055,0.2220192137026667,0.21554375456032729,0.20892261627334599,0.20218111939521155,0.19534435541132816,0.18843703633425507,0.18148335224633849,0.17450683786323382,0.16753024905563885,0.16057545012343574,0.15366331246863763,0.14681362516331375,0.14004501775823552,0.13337489552946966,0.12681938721555019,0.12039330515904789,0.11411011763501228,0.10798193302637613,0.10201949539427295,0.096232190890376393,0.090628064369665709,0.085213845486045658,0.079994983490372359,0.07497568990080683,0.070158988178963599,0.065546769521776654,0.061139853867915074,0.056938055218331951,0.052940250382357897,0.049144450282772756,0.04554787298452561,0.042147017651158261,0.038937738679419451],[0.036670181306248814,0.039692566420210157,0.042895371357026355,0.046282500298809773,0.049857250209174607,0.053622241015886606,0.057579345961326175,0.061729622826630262,0.066073246779104491,0.070609445629590595,0.075336438315890195,0.080251377449086017,0.085350296770741491,0.090628064369665695,0.096078342496487862,0.10169355479211067,0.10746486171178107,0.11338214487977692,0.11943400105049289,0.12560774628015892,0.1318894308298825,0.13826386522574086,0.14471465779603718,0.15122426389057822,0.15777404686313673,0.16434435076753048,0.17091458458157888,0.17746331763332782,0.18396838576226515,0.19040700760677265,0.19675591026986869,0.20299146348050442,0.20908982123943357,0.21502706981908068,0.2207793808779358,0.22632316835373362,0.23163524771783475,0.23669299610741917,0.24147451180373677,0.24595877149488454,0.25012578375128519,0.25395673715180989,0.25743414152860911,0.26054196084913328,0.26326573632418249,0.26559269842041605,0.26751186656355913,0.26901413544325092,0.2700923469704633,0.27074134709181807,0.27095802682983045,0.27074134709181807,0.2700923469704633,0.26901413544325092,0.26751186656355913,0.265592698420416,0.26326573632418243,0.26054196084913323,0.25743414152860916,0.25395673715180989,0.25012578375128519,0.24595877149488454,0.24147451180373677,0.23669299610741917,0.23163524771783475,0.22632316835373362,0.22077938087793575,0.21502706981908065,0.20908982123943351,0.2029914634805044,0.19675591026986863,0.19040700760677268,0.18396838576226515,0.17746331763332782,0.17091458458157888,0.16434435076753048,0.15777404686313673,0.15122426389057822,0.14471465779603718,0.13826386522574086,0.13188943082988247,0.12560774628015889,0.11943400105049284,0.11338214487977685,0.10746486171178107,0.10169355479211067,0.096078342496487862,0.090628064369665695,0.085350296770741491,0.080251377449086017,0.075336438315890195,0.070609445629590595,0.066073246779104464,0.061729622826630234,0.057579345961326155,0.053622241015886585,0.049857250209174621,0.046282500298809773,0.042895371357026355,0.039692566420210157,0.036670181306248814],[0.034534676194329261,0.037381051301491039,0.040397339398973081,0.043587217307021454,0.046953789989036522,0.050499524800068633,0.054226185893354456,0.058134769449653061,0.062225440435320328,0.066497471629993782,0.070949185692462877,0.075577901052832006,0.080379882429574598,0.085350296770741518,0.090483175408752628,0.095771383197316387,0.10120659536669131,0.10677928278948486,0.11247870629341813,0.11829292059010255,0.12420878831019637,0.13021200454587531,0.13628713220208916,0.1424176483495318,0.14858600165576138,0.15477368084778956,0.16096129403121631,0.16712865855926443,0.17325490101164681,0.17931856670996479,0.18529773806524721,0.19117016092630137,0.19691337797676914,0.20250486811615426,0.20792219065752846,0.2131431330839634,0.21814586102865863,0.22290906908176208,0.22741213098133037,0.23163524771783481,0.23555959207192381,0.23916744811435195,0.24244234422535213,0.24536917823820967,0.24793433337805759,0.25012578375128525,0.25193318824248212,0.25334797179328317,0.25436339316931356,0.25497459846589732,0.25517865975830373,0.25497459846589732,0.25436339316931356,0.25334797179328317,0.25193318824248212,0.25012578375128519,0.24793433337805756,0.24536917823820964,0.24244234422535216,0.23916744811435195,0.23555959207192381,0.23163524771783481,0.22741213098133037,0.22290906908176208,0.21814586102865863,0.2131431330839634,0.20792219065752843,0.20250486811615423,0.19691337797676911,0.19117016092630132,0.18529773806524719,0.17931856670996482,0.17325490101164681,0.16712865855926443,0.16096129403121631,0.15477368084778956,0.14858600165576138,0.1424176483495318,0.13628713220208916,0.13021200454587531,0.12420878831019634,0.1182929205901025,0.11247870629341811,0.10677928278948479,0.10120659536669131,0.095771383197316387,0.090483175408752628,0.085350296770741518,0.080379882429574598,0.075577901052832006,0.070949185692462877,0.066497471629993782,0.062225440435320301,0.058134769449653033,0.054226185893354435,0.050499524800068613,0.046953789989036536,0.043587217307021454,0.040397339398973081,0.037381051301491039,0.034534676194329261],[0.032523533218635547,0.035204148343837581,0.038044781497118471,0.04104889537738235,0.044219414129037744,0.047558661419562831,0.051068298665907723,0.054749264035780343,0.058601712888643895,0.062624960354152895,0.066817426771844546,0.071176586734296832,0.07569892248584506,0.080379882429574584,0.085213845486045672,0.090194092027539016,0.095312782081161826,0.1005609414526998,0.10592845637058063,0.11140407718585649,0.11697543159001675,0.12262904772821633,0.1283503874918353,0.13412389017206236,0.13993302654648654,0.14576036335473591,0.15158763799842553,0.1573958431766268,0.16316532104241874,0.16887586634060597,0.17450683786323384,0.18003727743998396,0.18544603556679085,0.19071190266994981,0.19581374490640252,0.20073064331550422,0.20544203506498901,0.20992785547548473,0.21416867946503268,0.2181458610286586,0.2218416693589112,0.22523942022194765,0.22832360123046061,0.23107998969945789,0.23349576183330803,0.23555959207192376,0.23726174151957388,0.23859413449041672,0.23955042232900542,0.24012603380006686,0.24031821148793259,0.24012603380006686,0.23955042232900542,0.23859413449041672,0.23726174151957388,0.23555959207192373,0.233495761833308,0.23107998969945787,0.22832360123046064,0.22523942022194765,0.2218416693589112,0.2181458610286586,0.21416867946503268,0.20992785547548473,0.20544203506498901,0.20073064331550422,0.19581374490640249,0.19071190266994978,0.18544603556679082,0.18003727743998393,0.17450683786323379,0.168875866340606,0.16316532104241874,0.1573958431766268,0.15158763799842553,0.14576036335473591,0.13993302654648654,0.13412389017206236,0.1283503874918353,0.12262904772821633,0.11697543159001673,0.11140407718585646,0.1059284563705806,0.10056094145269973,0.095312782081161826,0.090194092027539016,0.085213845486045672,0.080379882429574584,0.07569892248584506,0.071176586734296832,0.066817426771844546,0.062624960354152895,0.058601712888643874,0.054749264035780315,0.051068298665907702,0.047558661419562817,0.044219414129037758,0.04104889537738235,0.038044781497118471,0.035204148343837581,0.032523533218635547],[0.030629510092160125,0.0331540183452649,0.035829225901948432,0.038658393809229107,0.041644275922601968,0.044789060589685792,0.04809431247403969,0.051560915108737553,0.055189014805811773,0.058977966578660862,0.062926282759085864,0.067031585007943872,0.071290560427712063,0.075698922485845047,0.080251377449086031,0.084941597010370073,0.089762197761282511,0.094704728123994761,0.099759663307139299,0.10491640879032177,0.11016331277218831,0.11548768793764422,0.12087584281160588,0.12631312287039728,0.13178396147858418,0.13727194060984346,0.14275986119672515,0.14822982283733549,0.15366331246863768,0.15904130149789669,0.16434435076753051,0.16955272261604445,0.17464649919060676,0.17960570606692991,0.18441044014116323,0.18904100067809201,0.19347802233157824,0.19770260889821142,0.20169646652474094,0.20544203506498898,0.2089226162733461,0.21212249753010912,0.21502706981908071,0.21762293871996297,0.21989802723684415,0.22184166935891117,0.22344469333956804,0.22469949378430479,0.22560009175458556,0.22614218222315549,0.22632316835373364,0.22614218222315549,0.22560009175458556,0.22469949378430479,0.22344469333956804,0.22184166935891114,0.2198980272368441,0.21762293871996291,0.21502706981908074,0.21212249753010912,0.2089226162733461,0.20544203506498898,0.20169646652474094,0.19770260889821142,0.19347802233157824,0.18904100067809201,0.18441044014116317,0.17960570606692988,0.17464649919060674,0.16955272261604443,0.16434435076753048,0.15904130149789672,0.15366331246863768,0.14822982283733549,0.14275986119672515,0.13727194060984346,0.13178396147858418,0.12631312287039728,0.12087584281160588,0.11548768793764422,0.1101633127721883,0.10491640879032174,0.099759663307139271,0.094704728123994705,0.089762197761282511,0.084941597010370073,0.080251377449086031,0.075698922485845047,0.071290560427712063,0.067031585007943872,0.062926282759085864,0.058977966578660862,0.055189014805811745,0.051560915108737532,0.048094312474039676,0.044789060589685778,0.041644275922601982,0.038658393809229107,0.035829225901948432,0.0331540183452649,0.030629510092160125],[0.028845786285857218,0.031223278623372024,0.033742694220233148,0.036407104214864858,0.039219102090702999,0.0421807487559221,0.045293517755169106,0.048558241168557267,0.051975056787569522,0.055543357186699956,0.05926174133280105,0.063127969390419175,0.067138921390163947,0.071290560427712063,0.075577901052832006,0.079994983490372387,0.084534854308151317,0.08918955410991701,0.09395011278496973,0.098806552789751756,0.10374790087099564,0.10876220856531878,0.11383658172707496,0.11895721924560961,0.12410946101576342,0.12927784512263393,0.13444617409448595,0.13959758996767907,0.14471465779603723,0.14977945712579857,0.15477368084778953,0.15967874073243862,0.16447587885236367,0.16914628400319193,0.17367121214760858,0.17803210983190298,0.18221073945990163,0.18618930525741323,0.1899505787222637,0.19347802233157824,0.19675591026986877,0.19976944494916918,0.20250486811615423,0.20494956538083944,0.20709216305680295,0.2089226162733461,0.21043228740481379,0.21161401396039259,0.21246216518782099,0.21297268676511422,0.21314313308396338,0.21297268676511422,0.21246216518782099,0.21161401396039259,0.21043228740481379,0.20892261627334607,0.20709216305680292,0.20494956538083942,0.20250486811615426,0.19976944494916918,0.19675591026986877,0.19347802233157824,0.1899505787222637,0.18618930525741323,0.18221073945990163,0.17803210983190298,0.17367121214760856,0.1691462840031919,0.16447587885236362,0.1596787407324386,0.1547736808477895,0.1497794571257986,0.14471465779603723,0.13959758996767907,0.13444617409448595,0.12927784512263393,0.12410946101576342,0.11895721924560961,0.11383658172707496,0.10876220856531878,0.10374790087099563,0.098806552789751728,0.093950112784969703,0.089189554109916955,0.084534854308151317,0.079994983490372387,0.075577901052832006,0.071290560427712063,0.067138921390163947,0.063127969390419175,0.05926174133280105,0.055543357186699956,0.051975056787569501,0.048558241168557247,0.045293517755169092,0.042180748755922079,0.039219102090703013,0.036407104214864858,0.033742694220233148,0.031223278623372024,0.028845786285857218],[0.02716593846737124,0.029404976429710995,0.031777672684193792,0.034286919520065337,0.036935159388043939,0.039724333178355352,0.042655828623086721,0.045730429345777791,0.048948265113560249,0.052308763874635809,0.055810606185675772,0.059451682649088844,0.063229054988357292,0.067138921390163947,0.071176586734296832,0.075336438315890222,0.079611927639128527,0.083995558826913105,0.08847888414712457,0.093052507103108001,0.097706093474118072,0.10242839062111021,0.10720725529502396,0.11202969009932073,0.11688188866690293,0.12174928951469408,0.12661663843828025,0.13146805920539648,0.13628713220208916,0.14105698058057967,0.14576036335473588,0.15037977478920522,0.15489754933325564,0.15929597126177489,0.1635573881052037,0.16766432687886185,0.17159961206149532,0.17534648422412308,0.17888871817443078,0.18221073945990163,0.18529773806524724,0.18813577814693855,0.19071190266994978,0.19301423184918073,0.1950320543501432,0.19675591026986874,0.19817766499886103,0.19929057315729981,0.20008933190240782,0.20057012301753208,0.20073064331550419,0.20057012301753208,0.20008933190240782,0.19929057315729981,0.19817766499886103,0.19675591026986872,0.19503205435014317,0.19301423184918071,0.19071190266994981,0.18813577814693855,0.18529773806524724,0.18221073945990163,0.17888871817443078,0.17534648422412308,0.17159961206149532,0.16766432687886185,0.16355738810520368,0.15929597126177486,0.15489754933325561,0.1503797747892052,0.14576036335473586,0.14105698058057969,0.13628713220208916,0.13146805920539648,0.12661663843828025,0.12174928951469408,0.11688188866690293,0.11202969009932073,0.10720725529502396,0.10242839062111021,0.097706093474118058,0.093052507103107973,0.088478884147124542,0.08399555882691305,0.079611927639128527,0.075336438315890222,0.071176586734296832,0.067138921390163947,0.063229054988357292,0.059451682649088844,0.055810606185675772,0.052308763874635809,0.048948265113560228,0.045730429345777771,0.042655828623086707,0.039724333178355338,0.036935159388043953,0.034286919520065337,0.031777672684193792,0.029404976429710995,0.02716593846737124],[0.025583917370102276,0.027692563912382603,0.029927085093822688,0.032290204769855009,0.034784223153941085,0.037410968107659121,0.04017174654787091,0.043067296463433866,0.046097740064430216,0.049262538612764993,0.052560449503507134,0.055989486180817928,0.059546881480083115,0.063229054988357292,0.067031585007943872,0.070949185692462877,0.074975689900806844,0.079104038281776146,0.083326275060871549,0.087633550950803496,0.09201613354899181,0.096463425519075094,0.10096399077976571,0.10550558884397472,0.11007521736483193,0.11465916285401953,0.11924305944283246,0.1238119554587966,0.12835038749183533,0.13284246152527202,0.13727194060984346,0.14162233846486022,0.14587701830117666,0.15001929607719533,0.15403254732315511,0.15790031660178833,0.16160642861633215,0.16513509993096909,0.16847105023502693,0.17159961206149532,0.17450683786323384,0.17717960335706126,0.17960570606692988,0.18177395803256574,0.18367427169904044,0.18529773806524724,0.18663669624446785,0.18768479367722207,0.18843703633425504,0.18888982835454149,0.18904100067809201,0.18888982835454149,0.18843703633425504,0.18768479367722207,0.18663669624446785,0.18529773806524721,0.18367427169904044,0.18177395803256571,0.17960570606692991,0.17717960335706126,0.17450683786323384,0.17159961206149532,0.16847105023502693,0.16513509993096909,0.16160642861633215,0.15790031660178833,0.15403254732315508,0.1500192960771953,0.14587701830117664,0.14162233846486019,0.13727194060984343,0.13284246152527204,0.12835038749183533,0.1238119554587966,0.11924305944283246,0.11465916285401953,0.11007521736483193,0.10550558884397472,0.10096399077976571,0.096463425519075094,0.092016133548991796,0.087633550950803482,0.083326275060871521,0.07910403828177609,0.074975689900806844,0.070949185692462877,0.067031585007943872,0.063229054988357292,0.059546881480083115,0.055989486180817928,0.052560449503507134,0.049262538612764993,0.046097740064430202,0.043067296463433845,0.040171746547870896,0.037410968107659107,0.034784223153941099,0.032290204769855009,0.029927085093822688,0.027692563912382603,0.025583917370102276],[0.024094026009312326,0.026079874536696995,0.028184267334920046,0.030409769634422379,0.032758547694661751,0.035232322930844794,0.037832326150920297,0.040559252366620356,0.043413216671066054,0.046393711699826666,0.049499567211648846,0.052728912338699731,0.056079141063487006,0.059546881480083108,0.063127969390419175,0.06681742677184456,0.070609445629590623,0.074497377717067451,0.078473730568014502,0.082530170237514952,0.086657531093992213,0.090845832941910662,0.095084305685510434,0.099361421668177366,0.10366493574077572,0.10798193302637611,0.11229888425933794,0.11660170848480735,0.12087584281160589,0.12510631881853129,0.12927784512263391,0.13337489552946968,0.13738180210106854,0.14128285239877716,0.14506239008658489,0.14870491801728838,0.15219520287007623,0.15551838036487739,0.15866006004703864,0.16160642861633215,0.16434435076753054,0.16686146651620498,0.16914628400319187,0.17118826680430207,0.1729779148180734,0.17450683786323382,0.17576782118837636,0.17675488217828497,0.17746331763332782,0.17788974109912353,0.17803210983190296,0.17788974109912353,0.17746331763332782,0.17675488217828497,0.17576782118837636,0.17450683786323382,0.17297791481807337,0.17118826680430205,0.1691462840031919,0.16686146651620498,0.16434435076753054,0.16160642861633215,0.15866006004703864,0.15551838036487739,0.15219520287007623,0.14870491801728838,0.14506239008658486,0.14128285239877714,0.13738180210106851,0.13337489552946966,0.12927784512263388,0.12510631881853132,0.12087584281160589,0.11660170848480735,0.11229888425933794,0.10798193302637611,0.10366493574077572,0.099361421668177366,0.095084305685510434,0.090845832941910662,0.086657531093992199,0.082530170237514924,0.078473730568014488,0.074497377717067409,0.070609445629590623,0.06681742677184456,0.063127969390419175,0.059546881480083108,0.056079141063487006,0.052728912338699731,0.049499567211648846,0.046393711699826666,0.043413216671066041,0.040559252366620335,0.037832326150920283,0.03523232293084478,0.032758547694661765,0.030409769634422379,0.028184267334920046,0.026079874536696995,0.024094026009312326],[0.022690899166826782,0.024561100878988169,0.02654294338108475,0.028638842516166239,0.030850838390560489,0.033180552172056677,0.035629142991928625,0.038197265387576056,0.040885027749618455,0.043691952260229358,0.046616936827700642,0.049658219535060291,0.05281334612746013,0.056079141063487006,0.059451682649088844,0.062926282759085878,0.066497471629993768,0.070158988178963627,0.073903776267002175,0.077723987280361909,0.081610989352296104,0.085555383488611067,0.089547026795096865,0.093575062933598907,0.097627959856952759,0.10169355479211067,0.10575910635652692,0.10981135360632112,0.11383658172707498,0.11782069399057644,0.12174928951469405,0.12560774628015892,0.12938130877867637,0.13305517959278662,0.13661461414050896,0.14004501775823552,0.14333204424469745,0.14646169494810654,0.14942041744864823,0.15219520287007621,0.15477368084778956,0.15714421118681751,0.15929597126177486,0.16121903824204944,0.16290446526901878,0.16434435076753051,0.16553190014059088,0.16646147917337137,0.16712865855926434,0.16753024905563885,0.16766432687886182,0.16753024905563885,0.16712865855926434,0.16646147917337137,0.16553190014059088,0.16434435076753048,0.16290446526901875,0.16121903824204942,0.15929597126177489,0.15714421118681751,0.15477368084778956,0.15219520287007621,0.14942041744864823,0.14646169494810654,0.14333204424469745,0.14004501775823552,0.13661461414050893,0.13305517959278659,0.12938130877867635,0.12560774628015889,0.12174928951469402,0.11782069399057647,0.11383658172707498,0.10981135360632112,0.10575910635652692,0.10169355479211067,0.097627959856952759,0.093575062933598907,0.089547026795096865,0.085555383488611067,0.08161098935229609,0.077723987280361881,0.073903776267002161,0.070158988178963586,0.066497471629993768,0.062926282759085878,0.059451682649088844,0.056079141063487006,0.05281334612746013,0.049658219535060291,0.046616936827700642,0.043691952260229358,0.040885027749618434,0.038197265387576035,0.035629142991928618,0.033180552172056663,0.030850838390560499,0.028638842516166239,0.02654294338108475,0.024561100878988169,0.022690899166826782],[0.021369484070453845,0.023130773713615983,0.024997202693240409,0.026971046164630058,0.02905422542756924,0.031248267240384795,0.033554263231800177,0.035972829821924339,0.038504069089198498,0.041147531041740175,0.043902177768665895,0.046766349959060288,0.049737736282750987,0.052813346127460144,0.055989486180817942,0.059261741332801078,0.062624960354152909,0.066073246779104519,0.069599955386207987,0.073197694629398125,0.076858335322714244,0.080573025826773351,0.084332213923540636,0.08812567549877752,0.091942550079464891,0.095771383197316373,0.09960017547014155,0.10341643821131205,0.10720725529502401,0.11095935092260775,0.11465916285401953,0.11829292059010253,0.12184672791646985,0.12530664915016917,0.12865879836682856,0.13188943082988255,0.13498503579578441,0.13793242983076209,0.14071884974648999,0.14333204424469748,0.14576036335473594,0.14799284475381791,0.15001929607719533,0.15183037235492489,0.15341764775286895,0.15477368084778959,0.15589207272921804,0.15676751729345426,0.15739584317662678,0.15777404686313676,0.15790031660178835,0.15777404686313676,0.15739584317662678,0.15676751729345426,0.15589207272921804,0.15477368084778956,0.15341764775286892,0.15183037235492489,0.15001929607719536,0.14799284475381791,0.14576036335473594,0.14333204424469748,0.14071884974648999,0.13793242983076209,0.13498503579578441,0.13188943082988255,0.12865879836682853,0.12530664915016915,0.12184672791646982,0.1182929205901025,0.1146591628540195,0.11095935092260777,0.10720725529502401,0.10341643821131205,0.09960017547014155,0.095771383197316373,0.091942550079464891,0.08812567549877752,0.084332213923540636,0.080573025826773351,0.07685833532271423,0.073197694629398111,0.069599955386207973,0.066073246779104478,0.062624960354152909,0.059261741332801078,0.055989486180817942,0.052813346127460144,0.049737736282750987,0.046766349959060288,0.043902177768665895,0.041147531041740175,0.038504069089198484,0.035972829821924318,0.033554263231800163,0.031248267240384785,0.02905422542756925,0.026971046164630058,0.024997202693240409,0.023130773713615983,0.021369484070453845],[0.020125022198546998,0.021783742317846352,0.023541478935310476,0.025400374711512064,0.027362239058446359,0.029428509822956941,0.031600215062259393,0.03387793529895012,0.036261766666884708,0.038751285379667821,0.041345513969640403,0.044042889756632161,0.046841236011861347,0.04973773628275098,0.052728912338699738,0.055810606185675793,0.058977966578660876,0.062225440435320321,0.065546769521776682,0.068934992742097384,0.072382454317257761,0.075880818087222829,0.079421088111830324,0.08299363568290305,0.086588232792133679,0.090194092027538988,0.093799912796547175,0.097393933697020554,0.10096399077976574,0.10449758136844065,0.1079819330263761,0.11140407718585646,0.11475092688502106,0.11800935799191414,0.12116629323544617,0.12420878831019636,0.12712411927707001,0.12989987044570978,0.1325240218980151,0.13498503579578439,0.13727194060984349,0.13937441241338544,0.14128285239877714,0.14298845980475863,0.14448329947957317,0.14576036335473591,0.14681362516331378,0.14763808780503057,0.14822982283733546,0.14858600165576138,0.14870491801728838,0.14858600165576138,0.14822982283733546,0.14763808780503057,0.14681362516331378,0.14576036335473588,0.14448329947957314,0.14298845980475861,0.14128285239877716,0.13937441241338544,0.13727194060984349,0.13498503579578439,0.1325240218980151,0.12989987044570978,0.12712411927707001,0.12420878831019636,0.12116629323544616,0.11800935799191413,0.11475092688502105,0.11140407718585645,0.10798193302637608,0.10449758136844067,0.10096399077976574,0.097393933697020554,0.093799912796547175,0.090194092027538988,0.086588232792133679,0.08299363568290305,0.079421088111830324,0.075880818087222829,0.072382454317257747,0.06893499274209737,0.065546769521776654,0.06222544043532028,0.058977966578660876,0.055810606185675793,0.052728912338699738,0.04973773628275098,0.046841236011861347,0.044042889756632161,0.041345513969640403,0.038751285379667821,0.036261766666884694,0.033877935298950106,0.031600215062259386,0.02942850982295693,0.027362239058446369,0.025400374711512064,0.023541478935310476,0.021783742317846352,0.020125022198546998],[0.018953032144187261,0.020515155923686031,0.022170529929396086,0.023921172043052302,0.025768786304698445,0.027714726827496521,0.029759961799270668,0.031905037935613112,0.034150045771979533,0.036494586201372983,0.03893773867941943,0.041478031529357168,0.044113414785220309,0.04684123601186134,0.049658219535060298,0.052560449503507141,0.055543357186699963,0.058601712888643888,0.061729622826630262,0.064920531287394903,0.068167228329775439,0.07146186325390462,0.074795964002391399,0.078160462599370248,0.081545726669368115,0.08494159701037006,0.088337431125083452,0.091722152542109789,0.095084305685510462,0.098412115978131584,0.10169355479211066,0.10491640879032176,0.10806835313623207,0.11113702798783165,0.11411011763501226,0.11697543159001673,0.11972098689827823,0.12233509090295817,0.12480642367149293,0.12712411927706999,0.12927784512263393,0.13125787850007065,0.13305517959278659,0.13466146015595859,0.13606924714509355,0.13727194060984346,0.13826386522574091,0.13904031490097496,0.13959758996767904,0.13993302654648651,0.14004501775823552,0.13993302654648651,0.13959758996767904,0.13904031490097496,0.13826386522574091,0.13727194060984343,0.13606924714509352,0.13466146015595859,0.13305517959278662,0.13125787850007065,0.12927784512263393,0.12712411927706999,0.12480642367149293,0.12233509090295817,0.11972098689827823,0.11697543159001673,0.11411011763501225,0.11113702798783162,0.10806835313623206,0.10491640879032173,0.10169355479211065,0.098412115978131598,0.095084305685510462,0.091722152542109789,0.088337431125083452,0.08494159701037006,0.081545726669368115,0.078160462599370248,0.074795964002391399,0.07146186325390462,0.068167228329775426,0.064920531287394889,0.061729622826630241,0.058601712888643853,0.055543357186699963,0.052560449503507141,0.049658219535060298,0.04684123601186134,0.044113414785220309,0.041478031529357168,0.03893773867941943,0.036494586201372983,0.034150045771979519,0.031905037935613098,0.029759961799270658,0.027714726827496514,0.025768786304698456,0.023921172043052302,0.022170529929396086,0.020515155923686031,0.018953032144187261],[0.017849293477277792,0.019320446249878314,0.020879418778273335,0.022528111431913727,0.024268129015276512,0.026100746784112134,0.028026876543375205,0.030047033170420449,0.032161301928329056,0.03436930695228619,0.036670181306248807,0.039062539017237823,0.041544449500011515,0.044113414785220316,0.046766349959060295,0.049499567211648873,0.05230876387463583,0.05518901480581178,0.058134769449653054,0.061139853867915102,0.064197477993721955,0.067300248316374864,0.070440186152696413,0.073608751604625058,0.076796873242566108,0.079994983490372387,0.083193059621544926,0.086380670208163354,0.089547026795096907,0.092681040503184098,0.095771383197316359,0.098806552789751756,0.10177494218656151,0.10466491132689988,0.1074648617117811,0.11016331277218833,0.11274897938650297,0.1152108498252111,0.11753826337730171,0.11972098689827824,0.1217492895146941,0.12361401472487704,0.12530664915016915,0.12681938721555028,0.1281451910727589,0.12927784512263393,0.13021200454587534,0.13094323731212379,0.13146805920539648,0.13178396147858418,0.13188943082988253,0.13178396147858418,0.13146805920539648,0.13094323731212379,0.13021200454587534,0.12927784512263393,0.1281451910727589,0.12681938721555025,0.12530664915016917,0.12361401472487704,0.1217492895146941,0.11972098689827824,0.11753826337730171,0.1152108498252111,0.11274897938650297,0.11016331277218833,0.10746486171178109,0.10466491132689987,0.10177494218656148,0.098806552789751728,0.095771383197316345,0.092681040503184112,0.089547026795096907,0.086380670208163354,0.083193059621544926,0.079994983490372387,0.076796873242566108,0.073608751604625058,0.070440186152696413,0.067300248316374864,0.064197477993721955,0.061139853867915088,0.058134769449653033,0.055189014805811745,0.05230876387463583,0.049499567211648873,0.046766349959060295,0.044113414785220316,0.041544449500011515,0.039062539017237823,0.036670181306248807,0.03436930695228619,0.032161301928329042,0.030047033170420435,0.028026876543375195,0.026100746784112124,0.024268129015276522,0.022528111431913727,0.020879418778273335,0.019320446249878314,0.017849293477277792],[0.016809831546436893,0.018195311051156196,0.019663496087230791,0.021216176355210212,0.022854863203034259,0.024580757621339943,0.026394718315695072,0.028297230179331466,0.030288373509995008,0.032367794331533681,0.034534676194329247,0.036787713838185493,0.039125089106392716,0.041544449500011515,0.044042889756632168,0.04661693682770067,0.049262538612765014,0.051975056787569529,0.054749264035780336,0.057579345961326196,0.060458907920042632,0.063380986965774891,0.066338069057681789,0.069322111622648536,0.072324571510013938,0.075336438315890222,0.078348272991930853,0.081350251589285771,0.084332213923540664,0.087283716881584039,0.090194092027539002,0.093052507103108015,0.095848030958890981,0.098569701398414616,0.10120659536669131,0.10374790087099565,0.10618298998403004,0.10850149224948485,0.11069336778782712,0.11274897938650297,0.11465916285401956,0.11641529492185028,0.11800935799191414,0.11943400105049293,0.12068259610170123,0.1217492895146941,0.12262904772821637,0.12331769681326385,0.1238119554587966,0.12410946101576344,0.12420878831019636,0.12410946101576344,0.1238119554587966,0.12331769681326385,0.12262904772821637,0.12174928951469408,0.12068259610170121,0.11943400105049291,0.11800935799191416,0.11641529492185028,0.11465916285401956,0.11274897938650297,0.11069336778782712,0.10850149224948485,0.10618298998403004,0.10374790087099565,0.1012065953666913,0.098569701398414603,0.095848030958890953,0.093052507103107987,0.090194092027538975,0.087283716881584053,0.084332213923540664,0.081350251589285771,0.078348272991930853,0.075336438315890222,0.072324571510013938,0.069322111622648536,0.066338069057681789,0.063380986965774891,0.060458907920042625,0.057579345961326175,0.054749264035780322,0.051975056787569494,0.049262538612765014,0.04661693682770067,0.044042889756632168,0.041544449500011515,0.039125089106392716,0.036787713838185493,0.034534676194329247,0.032367794331533681,0.030288373509994998,0.028297230179331452,0.026394718315695061,0.024580757621339933,0.022854863203034266,0.021216176355210212,0.019663496087230791,0.018195311051156196,0.016809831546436893],[0.01583090316595993,0.017135698625512442,0.018518383221226606,0.019980642429605708,0.021523899584537366,0.023149285736408676,0.024857609583668193,0.026649327781564223,0.028524515951665962,0.030482840731787707,0.032523533218635541,0.03464536416444957,0.036846621293724111,0.039125089106392716,0.041478031529357175,0.043902177768665909,0.04639371169982668,0.048948265113560256,0.051560915108737553,0.054226185893354456,0.056938055218331986,0.059689965627932336,0.062474840664987367,0.065285106119378822,0.068112716354808922,0.070949185692462877,0.073785624771377151,0.076612781744944999,0.079421088111830351,0.082200708918484605,0.08494159701037006,0.087633550950803496,0.090266276170968579,0.092829448863016611,0.09531278208116184,0.097706093474118086,0.099999374036891006,0.10218285724153107,0.1042470878855727,0.10618298998403003,0.10798193302637614,0.10963579592414908,0.11113702798783165,0.11247870629341815,0.11365458882945492,0.11465916285401954,0.11548768793764426,0.11613623322202722,0.11660170848480735,0.11688188866690295,0.11697543159001675,0.11688188866690295,0.11660170848480735,0.11613623322202722,0.11548768793764426,0.11465916285401953,0.11365458882945491,0.11247870629341812,0.11113702798783166,0.10963579592414908,0.10798193302637614,0.10618298998403003,0.1042470878855727,0.10218285724153107,0.099999374036891006,0.097706093474118086,0.095312782081161812,0.092829448863016598,0.090266276170968565,0.087633550950803482,0.084941597010370046,0.082200708918484619,0.079421088111830351,0.076612781744944999,0.073785624771377151,0.070949185692462877,0.068112716354808922,0.065285106119378822,0.062474840664987367,0.059689965627932336,0.056938055218331979,0.054226185893354442,0.051560915108737532,0.048948265113560221,0.04639371169982668,0.043902177768665909,0.041478031529357175,0.039125089106392716,0.036846621293724111,0.03464536416444957,0.032523533218635541,0.030482840731787707,0.028524515951665951,0.026649327781564213,0.024857609583668186,0.023149285736408669,0.021523899584537376,0.019980642429605708,0.018518383221226606,0.017135698625512442,0.01583090316595993],[0.01490898313630766,0.016137793223695976,0.017439956537072851,0.018817060398431271,0.020270445253146037,0.021801176284357418,0.023410015095582628,0.025097391748538592,0.026863377460937157,0.028707658284094988,0.030629510092160115,0.032627775223189298,0.034700841116839527,0.036846621293724104,0.039062539017237823,0.041345513969640417,0.043691952260229379,0.046097740064430223,0.04855824116855726,0.051068298665907723,0.053622241015886619,0.05621389263924953,0.058836589179612084,0.061483197514514976,0.064146140549042843,0.06681742677184456,0.069488684498038383,0.072151200666619966,0.074795964002391427,0.077413712294911244,0.079994983490372373,0.082530170237514952,0.085009577476539214,0.087423482611361708,0.089762197761282511,0.092016133548991824,0.094175863848569477,0.096232190890376379,0.098176210100072561,0.099999374036890992,0.1016935547921107,0.10325110421264413,0.10466491132689987,0.10592845637058064,0.10703586083868118,0.10798193302637613,0.1087622085653188,0.10937298551257399,0.10981135360632113,0.11007521736483193,0.11016331277218831,0.11007521736483193,0.10981135360632113,0.10937298551257399,0.1087622085653188,0.10798193302637611,0.10703586083868116,0.10592845637058063,0.10466491132689988,0.10325110421264413,0.1016935547921107,0.099999374036890992,0.098176210100072561,0.096232190890376379,0.094175863848569477,0.092016133548991824,0.089762197761282497,0.087423482611361694,0.0850095774765392,0.082530170237514938,0.079994983490372359,0.077413712294911258,0.074795964002391427,0.072151200666619966,0.069488684498038383,0.06681742677184456,0.064146140549042843,0.061483197514514976,0.058836589179612084,0.05621389263924953,0.053622241015886613,0.051068298665907709,0.048558241168557247,0.046097740064430195,0.043691952260229379,0.041345513969640417,0.039062539017237823,0.036846621293724104,0.034700841116839527,0.032627775223189298,0.030629510092160115,0.028707658284094988,0.026863377460937147,0.025097391748538582,0.023410015095582618,0.021801176284357411,0.020270445253146044,0.018817060398431271,0.017439956537072851,0.016137793223695976,0.01490898313630766],[0.014040751549580212,0.015198001308393088,0.016424332533865979,0.01772124010955526,0.019089986419374122,0.020531574615025847,0.02204672194769159,0.023635833434243615,0.025298976144997098,0.027035854414216704,0.028845786285857204,0.030727681514958569,0.032680021449381494,0.03470084111683952,0.036787713838185493,0.038937738679419444,0.041147531041740175,0.043413216671066061,0.045730429345777784,0.04809431247403969,0.050499524800068626,0.052940250382357855,0.055410212966425419,0.057902694830525424,0.060410560135398993,0.062926282759085864,0.065441978545678126,0.067949441843342881,0.070440186152696413,0.072905488652442285,0.075336438315890208,0.077723987280361895,0.080059005082386989,0.082332335325799713,0.084534854308151303,0.086657531093992213,0.088691488492241732,0.090628064369665681,0.092458872713964024,0.094175863848569463,0.095771383197316359,0.097238228000879445,0.098569701398414589,0.099759663307139299,0.10080257755952911,0.10169355479211067,0.10242839062111023,0.10300359868796602,0.10341643821131201,0.10366493574077573,0.10374790087099563,0.10366493574077573,0.10341643821131201,0.10300359868796602,0.10242839062111023,0.10169355479211066,0.10080257755952909,0.099759663307139285,0.098569701398414603,0.097238228000879445,0.095771383197316359,0.094175863848569463,0.092458872713964024,0.090628064369665681,0.088691488492241732,0.086657531093992213,0.084534854308151289,0.082332335325799699,0.080059005082386975,0.077723987280361881,0.075336438315890195,0.072905488652442299,0.070440186152696413,0.067949441843342881,0.065441978545678126,0.062926282759085864,0.060410560135398993,0.057902694830525424,0.055410212966425419,0.052940250382357855,0.050499524800068619,0.048094312474039676,0.045730429345777771,0.043413216671066027,0.041147531041740175,0.038937738679419444,0.036787713838185493,0.03470084111683952,0.032680021449381494,0.030727681514958569,0.028845786285857204,0.027035854414216704,0.025298976144997085,0.023635833434243605,0.022046721947691583,0.020531574615025836,0.019089986419374129,0.01772124010955526,0.016424332533865979,0.015198001308393088,0.014040751549580212],[0.013223081834262726,0.014312938613611619,0.015467853868188896,0.01668923542630979,0.017978272156371513,0.019335908791070017,0.020762820812129389,0.022259389650075432,0.023825678469352227,0.025461408822456448,0.027165938467371229,0.028938240650060298,0.030776885157800006,0.032680021449381494,0.03464536416444957,0.036670181306248814,0.038751285379667828,0.040885027749618462,0.043067296463433859,0.045293517755169106,0.047558661419562831,0.049857250209174593,0.052183373370129522,0.054530704390340863,0.056892522989477244,0.059261741332801057,0.061630934401900969,0.06399237440490585,0.066338069057681789,0.068659803516499057,0.070949185692462863,0.073197694629398111,0.075396731580633189,0.077537673377003735,0.079611927639128527,0.081610989352296104,0.083526498292788798,0.085350296770741477,0.08707448713719175,0.088691488492241732,0.090194092027539002,0.091575514439807063,0.092829448863016584,0.09395011278496973,0.09493229243944,0.095771383197316359,0.096463425519075108,0.097005136075871454,0.097393933697020527,0.097627959856952773,0.097706093474118072,0.097627959856952773,0.097393933697020527,0.097005136075871454,0.096463425519075108,0.095771383197316345,0.094932292439439986,0.093950112784969717,0.092829448863016598,0.091575514439807063,0.090194092027539002,0.088691488492241732,0.08707448713719175,0.085350296770741477,0.083526498292788798,0.081610989352296104,0.079611927639128513,0.077537673377003721,0.075396731580633175,0.073197694629398097,0.070949185692462849,0.068659803516499071,0.066338069057681789,0.06399237440490585,0.061630934401900969,0.059261741332801057,0.056892522989477244,0.054530704390340863,0.052183373370129522,0.049857250209174593,0.047558661419562824,0.045293517755169092,0.043067296463433845,0.040885027749618434,0.038751285379667828,0.036670181306248814,0.03464536416444957,0.032680021449381494,0.030776885157800006,0.028938240650060298,0.027165938467371229,0.025461408822456448,0.023825678469352216,0.022259389650075422,0.020762820812129382,0.01933590879107001,0.01797827215637152,0.01668923542630979,0.015467853868188896,0.014312938613611619,0.013223081834262726],[0.012453029496190787,0.013479417957667928,0.014567076183724232,0.01571733001713636,0.016931299091995901,0.018209873124049626,0.019553688258028366,0.020963103711673339,0.022438178971017776,0.023978651804078571,0.025583917370102266,0.027253008708552781,0.028984578895811509,0.030776885157800006,0.032627775223189291,0.034534676194329247,0.03649458620137299,0.038504069089198491,0.040559252366620349,0.042655828623086721,0.044789060589685792,0.046953789989036494,0.049144450282772735,0.051355083386189909,0.053579360377616181,0.055810606185675779,0.058041828191367689,0.060265748634384768,0.062474840664987374,0.064661367834701888,0.066817426771844532,0.06893499274209737,0.071005967750811805,0.073022230803101745,0.07497568990080683,0.07685833532271423,0.078662293706633787,0.080379882429574556,0.082003663765845045,0.083526498292788798,0.084941597010370073,0.086242571644142521,0.08742348261136168,0.08847888414712457,0.089403866111312708,0.090194092027538988,0.090845832941910676,0.091355996731769654,0.091722152542109775,0.091942550079464877,0.092016133548991796,0.091942550079464877,0.091722152542109775,0.091355996731769654,0.090845832941910676,0.090194092027538975,0.089403866111312694,0.088478884147124556,0.087423482611361694,0.086242571644142521,0.084941597010370073,0.083526498292788798,0.082003663765845045,0.080379882429574556,0.078662293706633787,0.07685833532271423,0.07497568990080683,0.073022230803101731,0.071005967750811791,0.068934992742097356,0.066817426771844518,0.064661367834701902,0.062474840664987374,0.060265748634384768,0.058041828191367689,0.055810606185675779,0.053579360377616181,0.051355083386189909,0.049144450282772735,0.046953789989036494,0.044789060589685785,0.042655828623086707,0.040559252366620335,0.038504069089198463,0.03649458620137299,0.034534676194329247,0.032627775223189291,0.030776885157800006,0.028984578895811509,0.027253008708552781,0.025583917370102266,0.023978651804078571,0.022438178971017766,0.020963103711673332,0.019553688258028359,0.018209873124049623,0.016931299091995908,0.01571733001713636,0.014567076183724232,0.013479417957667928,0.012453029496190787],[0.011727821515191012,0.012694437765890288,0.013718755707851275,0.01480202397277814,0.01594529699234894,0.017149412669298949,0.018414970102173894,0.019742307589502284,0.021131481153120461,0.022582243832247169,0.02409402600931233,0.025665917035177687,0.027296648424949794,0.028984578895811519,0.030727681514958582,0.032523533218635554,0.034369306952286204,0.036261766666884722,0.038197265387576063,0.040171746547870923,0.042180748755922114,0.044219414129037737,0.04628250029880978,0.048364396152375359,0.050459141335768093,0.052560449503507155,0.054661735255020515,0.056756144653766966,0.058836589179612112,0.060895782919767591,0.062926282759085891,0.064920531287394931,0.066870902100541516,0.068769747133564499,0.07060944562959065,0.072382454317257774,0.074081358343295184,0.07569892248584506,0.077228142158640656,0.078662293706633815,0.079994983490372415,0.081220195259552069,0.082332335325799741,0.083326275060871591,0.084197390268949054,0.084941597010370101,0.085555383488611123,0.086035837652219227,0.086380670208163368,0.086588232792133707,0.086657531093992241,0.086588232792133707,0.086380670208163368,0.086035837652219227,0.085555383488611123,0.084941597010370087,0.084197390268949054,0.083326275060871577,0.082332335325799755,0.081220195259552069,0.079994983490372415,0.078662293706633815,0.077228142158640656,0.07569892248584506,0.074081358343295184,0.072382454317257774,0.070609445629590636,0.068769747133564485,0.066870902100541502,0.064920531287394917,0.062926282759085878,0.060895782919767598,0.058836589179612112,0.056756144653766966,0.054661735255020515,0.052560449503507155,0.050459141335768093,0.048364396152375359,0.04628250029880978,0.044219414129037737,0.042180748755922107,0.04017174654787091,0.038197265387576049,0.036261766666884694,0.034369306952286204,0.032523533218635554,0.030727681514958582,0.028984578895811519,0.027296648424949794,0.025665917035177687,0.02409402600931233,0.022582243832247169,0.021131481153120451,0.019742307589502274,0.018414970102173887,0.017149412669298945,0.015945296992348947,0.01480202397277814,0.013718755707851275,0.012694437765890288,0.011727821515191012],[0.011044846359213179,0.011955171261707937,0.012919837570560803,0.013940021202826272,0.015016715184861822,0.016150708623746127,0.017342565729241678,0.01859260509890439,0.019900879492112829,0.021267156329962029,0.022690899166826779,0.024171250385646135,0.025707015372336058,0.02729664842494979,0.028938240650060305,0.030629510092160125,0.032367794331533688,0.03415004577197954,0.035972829821924332,0.03783232615092031,0.039724333178355359,0.041644275922601955,0.043587217307021441,0.045547872984525603,0.047520629705141315,0.049499567211648866,0.051478483607350072,0.053450924097894988,0.055410212966425447,0.057349488598682573,0.059261741332801064,0.061139853867915095,0.062976643927074416,0.064764908833948087,0.066497471629993796,0.068167228329775453,0.06976719588746097,0.071290560427712049,0.072730725279610262,0.07408135834329517,0.075336438315890236,0.076490299306233647,0.077537673377003749,0.07847373056801453,0.079294115975647755,0.079994983490372401,0.080573025826773378,0.081025500518072377,0.081350251589285771,0.081545726669368129,0.081610989352296118,0.081545726669368129,0.081350251589285771,0.081025500518072377,0.080573025826773378,0.079994983490372387,0.079294115975647755,0.078473730568014516,0.077537673377003749,0.076490299306233647,0.075336438315890236,0.07408135834329517,0.072730725279610262,0.071290560427712049,0.06976719588746097,0.068167228329775453,0.066497471629993782,0.064764908833948073,0.062976643927074416,0.061139853867915088,0.05926174133280105,0.057349488598682587,0.055410212966425447,0.053450924097894988,0.051478483607350072,0.049499567211648866,0.047520629705141315,0.045547872984525603,0.043587217307021441,0.041644275922601955,0.039724333178355352,0.037832326150920297,0.035972829821924318,0.034150045771979519,0.032367794331533688,0.030629510092160125,0.028938240650060305,0.02729664842494979,0.025707015372336058,0.024171250385646135,0.022690899166826779,0.021267156329962029,0.019900879492112823,0.018592605098904379,0.017342565729241671,0.016150708623746124,0.015016715184861827,0.013940021202826272,0.012919837570560803,0.011955171261707937,0.011044846359213179],[0.010401644579994087,0.01125895628720219,0.012167444803623449,0.013128217566234222,0.014142209772038899,0.015210164574097377,0.016332613325153466,0.017509856069085818,0.018741942492805981,0.020028653561749991,0.021369484070453838,0.022763626345586124,0.024209955341971179,0.025707015372336058,0.027253008708552792,0.028845786285857222,0.030482840731787714,0.032161301928329056,0.03387793529895012,0.035629142991928639,0.037410968107659134,0.039219102090702992,0.041048895377382336,0.042895371357026355,0.044753243669892209,0.046616936827700663,0.04848061010410043,0.050338184602701154,0.05218337337012955,0.054009714381433482,0.055810606185675786,0.057579345961326189,0.059309169694682549,0.060993294160629506,0.062624960354152909,0.064197477993721969,0.065704270694435588,0.067138921390163947,0.068495217570196276,0.06976719588746097,0.070949185692462891,0.072035851049854716,0.073022230803101745,0.073903776267002202,0.074676386147781243,0.075336438315890236,0.075880818087222857,0.076306942703832731,0.076612781744944999,0.076796873242566108,0.076858335322714244,0.076796873242566108,0.076612781744944999,0.076306942703832731,0.075880818087222857,0.075336438315890222,0.074676386147781229,0.073903776267002202,0.073022230803101759,0.072035851049854716,0.070949185692462891,0.06976719588746097,0.068495217570196276,0.067138921390163947,0.065704270694435588,0.064197477993721969,0.062624960354152909,0.060993294160629492,0.059309169694682543,0.057579345961326175,0.055810606185675779,0.054009714381433496,0.05218337337012955,0.050338184602701154,0.04848061010410043,0.046616936827700663,0.044753243669892209,0.042895371357026355,0.041048895377382336,0.039219102090702992,0.037410968107659127,0.035629142991928632,0.033877935298950113,0.032161301928329035,0.030482840731787714,0.028845786285857222,0.027253008708552792,0.025707015372336058,0.024209955341971179,0.022763626345586124,0.021369484070453838,0.020028653561749991,0.018741942492805971,0.017509856069085807,0.016332613325153459,0.01521016457409737,0.014142209772038904,0.013128217566234222,0.012167444803623449,0.01125895628720219,0.010401644579994087],[0.0097958999563872596,0.010603285716462414,0.011458867980396527,0.012363689693057112,0.013318631589814818,0.014324393545864478,0.015381475970375038,0.01649016143402993,0.017650496730200235,0.018862275579901982,0.020125022198546991,0.021437975948037032,0.022800077300726976,0.024209955341971175,0.025665917035177687,0.027165938467371243,0.028707658284094995,0.030288373509995012,0.031905037935613112,0.033554263231800177,0.035232322930844807,0.036935159388043932,0.0386583938092291,0.040397339398973067,0.042147017651158261,0.043902177768665902,0.045657319162567954,0.04740671694384066,0.049144450282772756,0.05086443347344919,0.052560449503507141,0.054226185893354449,0.055855272534781772,0.05744132122695212,0.058977966578660883,0.060458907920042632,0.061877951845038352,0.063229054988357278,0.06450636662774753,0.065704270694435588,0.066817426771844574,0.067840809665310836,0.068769747133564471,0.069599955386208001,0.070327571970222449,0.070949185692462891,0.071461863253904648,0.07186317230471502,0.072151200666619966,0.072324571510013938,0.072382454317257761,0.072324571510013938,0.072151200666619966,0.07186317230471502,0.071461863253904648,0.070949185692462877,0.070327571970222436,0.069599955386207987,0.068769747133564485,0.067840809665310836,0.066817426771844574,0.065704270694435588,0.06450636662774753,0.063229054988357278,0.061877951845038352,0.060458907920042632,0.058977966578660869,0.057441321226952113,0.055855272534781758,0.054226185893354435,0.052560449503507134,0.050864433473449204,0.049144450282772756,0.04740671694384066,0.045657319162567954,0.043902177768665902,0.042147017651158261,0.040397339398973067,0.0386583938092291,0.036935159388043932,0.0352323229308448,0.03355426323180017,0.031905037935613105,0.030288373509994991,0.028707658284094995,0.027165938467371243,0.025665917035177687,0.024209955341971175,0.022800077300726976,0.021437975948037032,0.020125022198546991,0.018862275579901982,0.017650496730200225,0.016490161434029923,0.015381475970375032,0.014324393545864473,0.013318631589814823,0.012363689693057112,0.011458867980396527,0.010603285716462414,0.0097958999563872596],[0.009225431153465009,0.0099857984272247527,0.010791555458961617,0.011643684457162313,0.012543014867162392,0.013490205806598283,0.014485728543077576,0.015529849191648161,0.01662261182064733,0.017763822163843954,0.018953032144187257,0.020189525419693436,0.021472304164803956,0.022800077300726976,0.024171250385646135,0.025583917370102276,0.027035854414216715,0.028524515951665965,0.030047033170420446,0.0316002150622594,0.03318055217205669,0.034784223153941078,0.036407104214864851,0.038044781497118464,0.039692566420210157,0.041345513969640417,0.042998443885842993,0.044645964671376596,0.046282500298809787,0.047902319466149923,0.049499567211648859,0.051068298665907716,0.052602514686939848,0.054096199093763571,0.05554335718669997,0.056938055218331986,0.058274460458491148,0.059546881480083108,0.060749808280395202,0.061877951845038345,0.062926282759085891,0.063890068472429257,0.064764908833948073,0.065546769521776696,0.066232013014649219,0.06681742677184456,0.067300248316374878,0.067678186947434438,0.067949441843342881,0.068112716354808922,0.068167228329775439,0.068112716354808922,0.067949441843342881,0.067678186947434438,0.067300248316374878,0.066817426771844546,0.066232013014649219,0.065546769521776682,0.064764908833948073,0.063890068472429257,0.062926282759085891,0.061877951845038345,0.060749808280395202,0.059546881480083108,0.058274460458491148,0.056938055218331986,0.055543357186699963,0.054096199093763557,0.052602514686939841,0.051068298665907709,0.049499567211648846,0.04790231946614993,0.046282500298809787,0.044645964671376596,0.042998443885842993,0.041345513969640417,0.039692566420210157,0.038044781497118464,0.036407104214864851,0.034784223153941078,0.033180552172056683,0.031600215062259386,0.030047033170420435,0.028524515951665944,0.027035854414216715,0.025583917370102276,0.024171250385646135,0.022800077300726976,0.021472304164803956,0.020189525419693436,0.018953032144187257,0.017763822163843954,0.016622611820647323,0.015529849191648154,0.014485728543077571,0.013490205806598278,0.012543014867162396,0.011643684457162313,0.010791555458961617,0.0099857984272247527,0.009225431153465009],[0.0086881838673565723,0.0094042707982816432,0.010163104193457539,0.010965609062001632,0.011812566546113488,0.012704597379406555,0.013642145384999492,0.014625461180606253,0.015654586268223952,0.016729337694806039,0.017849293477277785,0.019013778990164921,0.02022185451674572,0.021472304164803956,0.022763626345586124,0.02409402600931233,0.025461408822456455,0.026863377460937157,0.028297230179331459,0.029759961799270672,0.031248267240384795,0.032758547694661744,0.03428691952006533,0.035829225901948425,0.037381051301491032,0.038937738679419444,0.040494409450999413,0.042045986095157827,0.043587217307021447,0.045112705549642362,0.046616936827700656,0.04809431247403969,0.049539182709504498,0.050945881708218906,0.05230876387463583,0.053622241015886626,0.054880820073564658,0.056079141063487006,0.057212014860518919,0.058274460458491141,0.059261741332801071,0.060169400535603046,0.060993294160629492,0.061729622826630276,0.062374960845087014,0.062926282759085891,0.063380986965774905,0.063736916164378182,0.06399237440490585,0.064146140549042843,0.064197477993721955,0.064146140549042843,0.06399237440490585,0.063736916164378182,0.063380986965774905,0.062926282759085878,0.062374960845087007,0.061729622826630269,0.060993294160629499,0.060169400535603046,0.059261741332801071,0.058274460458491141,0.057212014860518919,0.056079141063487006,0.054880820073564658,0.053622241015886626,0.052308763874635816,0.050945881708218899,0.049539182709504491,0.048094312474039683,0.046616936827700649,0.045112705549642369,0.043587217307021447,0.042045986095157827,0.040494409450999413,0.038937738679419444,0.037381051301491032,0.035829225901948425,0.03428691952006533,0.032758547694661744,0.031248267240384792,0.029759961799270665,0.028297230179331452,0.02686337746093714,0.025461408822456455,0.02409402600931233,0.022763626345586124,0.021472304164803956,0.02022185451674572,0.019013778990164921,0.017849293477277785,0.016729337694806039,0.015654586268223945,0.014625461180606246,0.013642145384999487,0.012704597379406551,0.011812566546113491,0.010965609062001632,0.010163104193457539,0.0094042707982816432,0.0086881838673565723],[0.0081822234275352561,0.0088566087020436803,0.0095712510805196615,0.010327021703743177,0.011124656223733468,0.011964739225392481,0.012847688685592556,0.013773740627208183,0.014742934135348313,0.015755096911322399,0.016809831546436886,0.017906502702346654,0.019044225387171564,0.020221854516745717,0.021437975948037032,0.022690899166826782,0.023978651804078578,0.025298976144997102,0.026649327781564217,0.028026876543375202,0.029428509822956944,0.030850838390560482,0.032290204769854995,0.033742694220233141,0.035204148343837574,0.036670181306248807,0.038136198629390057,0.039597418483996116,0.041048895377382343,0.042485546100682482,0.043902177768665895,0.045293517755169099,0.046654245298561381,0.047979024524979083,0.049262538612765007,0.050499524800068633,0.051684809919301689,0.052813346127460123,0.053880246490531698,0.054880820073564651,0.055810606185675793,0.056665407431456045,0.057441321226952113,0.058134769449653047,0.058742525907609144,0.059261741332801064,0.059689965627932343,0.060025167123643974,0.060265748634384761,0.060410560135399,0.060458907920042625,0.060410560135399,0.060265748634384761,0.060025167123643974,0.059689965627932343,0.059261741332801057,0.058742525907609137,0.05813476944965304,0.05744132122695212,0.056665407431456045,0.055810606185675793,0.054880820073564651,0.053880246490531698,0.052813346127460123,0.051684809919301689,0.050499524800068633,0.049262538612765,0.047979024524979076,0.046654245298561374,0.045293517755169092,0.043902177768665882,0.042485546100682489,0.041048895377382343,0.039597418483996116,0.038136198629390057,0.036670181306248807,0.035204148343837574,0.033742694220233141,0.032290204769854995,0.030850838390560482,0.029428509822956941,0.028026876543375195,0.02664932778156421,0.025298976144997085,0.023978651804078578,0.022690899166826782,0.021437975948037032,0.020221854516745717,0.019044225387171564,0.017906502702346654,0.016809831546436886,0.015755096911322399,0.014742934135348306,0.013773740627208176,0.012847688685592553,0.011964739225392478,0.011124656223733471,0.010327021703743177,0.0095712510805196615,0.0088566087020436803,0.0081822234275352561],[0.0077057278299148555,0.0083408399634183686,0.009013864809663338,0.0097256227781401094,0.010476806679829462,0.011267967056058918,0.012099497542622706,0.012971620417493135,0.013884372489639607,0.014837591494266182,0.01583090316595993,0.01686370916560059,0.017935176039222941,0.019044225387171571,0.020189525419693443,0.021369484070453849,0.022582243832247172,0.023825678469352237,0.025097391748538592,0.026394718315695075,0.027714726827496535,0.029054225427569233,0.030409769634422382,0.031777672684193799,0.0331540183452649,0.034534676194329254,0.035915319314883801,0.037291444349720919,0.03865839380922912,0.040011380507581344,0.041345513969640417,0.042655828623086728,0.043937313563324795,0.04518494365359417,0.046393711699826694,0.047558661419562852,0.048674920907041723,0.049737736282750987,0.050742505205559951,0.051684809919301702,0.052560449503507162,0.053365471000046641,0.054096199093763578,0.05474926403578035,0.055321627512940189,0.055810606185675807,0.056213892639249557,0.056529573519515167,0.056756144653766959,0.056892522989477265,0.056938055218332,0.056892522989477265,0.056756144653766959,0.056529573519515167,0.056213892639249557,0.0558106061856758,0.055321627512940182,0.054749264035780343,0.054096199093763585,0.053365471000046641,0.052560449503507162,0.051684809919301702,0.050742505205559951,0.049737736282750987,0.048674920907041723,0.047558661419562852,0.046393711699826687,0.045184943653594163,0.043937313563324788,0.042655828623086721,0.04134551396964041,0.040011380507581358,0.03865839380922912,0.037291444349720919,0.035915319314883801,0.034534676194329254,0.0331540183452649,0.031777672684193799,0.030409769634422382,0.029054225427569233,0.027714726827496532,0.026394718315695068,0.025097391748538585,0.02382567846935222,0.022582243832247172,0.021369484070453849,0.020189525419693443,0.019044225387171571,0.017935176039222941,0.01686370916560059,0.01583090316595993,0.014837591494266182,0.013884372489639602,0.012971620417493128,0.012099497542622703,0.011267967056058915,0.010476806679829465,0.0097256227781401094,0.009013864809663338,0.0083408399634183686,0.0077057278299148555],[0.0072569811756669289,0.0078551072578495612,0.0084889381882640655,0.0091592465994714666,0.0098666849562819344,0.010611771738992007,0.011394877659831836,0.012216212052312339,0.013075809581815419,0.013973517433111206,0.014908983136307659,0.015881643196842259,0.016890712697330185,0.017935176039222941,0.019013778990164928,0.020125022198547001,0.021267156329962036,0.022438178971017787,0.023635833434243622,0.0248576095836682,0.026100746784112141,0.027362239058446359,0.028638842516166243,0.029927085093822692,0.031223278623372028,0.032523533218635547,0.033823773943110903,0.03511975969469789,0.036407104214864865,0.037681299101784249,0.038937738679419451,0.040171746547870917,0.041378603614909464,0.042553577384957672,0.043691952260229386,0.044789060589685813,0.045840314185270341,0.046841236011861347,0.047787491747810482,0.048674920907041716,0.04949956721164888,0.050257707905862675,0.050945881708218912,0.051560915108737566,0.052099946731845655,0.052560449503507162,0.05294025038235789,0.053237547439322692,0.053450924097894988,0.053579360377616202,0.053622241015886633,0.053579360377616202,0.053450924097894988,0.053237547439322692,0.05294025038235789,0.052560449503507155,0.052099946731845648,0.051560915108737559,0.050945881708218919,0.050257707905862675,0.04949956721164888,0.048674920907041716,0.047787491747810482,0.046841236011861347,0.045840314185270341,0.044789060589685813,0.043691952260229379,0.042553577384957665,0.041378603614909457,0.04017174654787091,0.038937738679419444,0.037681299101784256,0.036407104214864865,0.03511975969469789,0.033823773943110903,0.032523533218635547,0.031223278623372028,0.029927085093822692,0.028638842516166243,0.027362239058446359,0.026100746784112137,0.024857609583668193,0.023635833434243612,0.022438178971017769,0.021267156329962036,0.020125022198547001,0.019013778990164928,0.017935176039222941,0.016890712697330185,0.015881643196842259,0.014908983136307659,0.013973517433111206,0.013075809581815414,0.012216212052312334,0.011394877659831833,0.010611771738992004,0.0098666849562819379,0.0091592465994714666,0.0084889381882640655,0.0078551072578495612,0.0072569811756669289],[0.0068343674921316367,0.0073976614229429383,0.0079945809134960247,0.0086258536017343596,0.0092920939558755779,0.0099937902622743192,0.010731291644561105,0.011504795245612206,0.012314333712054846,0.013159763127925342,0.01404075154958021,0.014956768297825607,0.01590707416530671,0.016890712697330185,0.017906502702346658,0.018953032144187264,0.020028653561749998,0.021131481153120458,0.022259389650075432,0.023410015095582631,0.024580757621339946,0.025768786304698445,0.026971046164630051,0.028184267334920046,0.029404976429710995,0.030629510092160125,0.031854030691592899,0.033074544108468051,0.034286919520065344,0.035486911073440409,0.036670181306248814,0.037832326150920303,0.038968901333762712,0.040075449958285887,0.041147531041740182,0.042180748755922107,0.043170782108046542,0.044113414785220309,0.04500456487703787,0.045840314185270334,0.04661693682770067,0.047330926844978166,0.047979024524979083,0.048558241168557267,0.04906588203368082,0.049499567211648873,0.049857250209174614,0.050137234033363044,0.050338184602701147,0.050459141335768093,0.05049952480006864,0.050459141335768093,0.050338184602701147,0.050137234033363044,0.049857250209174614,0.049499567211648866,0.049065882033680813,0.04855824116855726,0.04797902452497909,0.047330926844978166,0.04661693682770067,0.045840314185270334,0.04500456487703787,0.044113414785220309,0.043170782108046542,0.042180748755922107,0.041147531041740175,0.04007544995828588,0.038968901333762705,0.037832326150920297,0.036670181306248807,0.035486911073440416,0.034286919520065344,0.033074544108468051,0.031854030691592899,0.030629510092160125,0.029404976429710995,0.028184267334920046,0.026971046164630051,0.025768786304698445,0.024580757621339943,0.023410015095582624,0.022259389650075425,0.021131481153120444,0.020028653561749998,0.018953032144187264,0.017906502702346658,0.016890712697330185,0.01590707416530671,0.014956768297825607,0.01404075154958021,0.013159763127925342,0.012314333712054841,0.011504795245612201,0.010731291644561101,0.0099937902622743158,0.0092920939558755813,0.0086258536017343596,0.0079945809134960247,0.0073976614229429383,0.0068343674921316367],[0.0064363649135707034,0.0069668551595920463,0.007529012765200121,0.008123522994003372,0.0087509645303761804,0.0094117972250895802,0.010106349870396634,0.010834808128466263,0.011597202744734124,0.012393398184249805,0.013223081834262724,0.01408575391992941,0.014980718281980126,0.01590707416530671,0.01686370916560059,0.017849293477277796,0.018862275579901989,0.019900879492112833,0.020963103711673342,0.022046721947691597,0.023149285736408683,0.024268129015276509,0.025400374711512061,0.026542943381084753,0.027692563912382603,0.028845786285857218,0.02999899635704633,0.031148432605823076,0.032290204769855009,0.03342031425542432,0.034534676194329254,0.035629142991928639,0.036699529188881648,0.037741637438144016,0.038751285379667842,0.039724333178355366,0.040656711476451682,0.041544449500011509,0.042383703050585628,0.043170782108046542,0.043902177768665916,0.04457458824427106,0.045184943653594163,0.045730429345777805,0.046208507508349192,0.04661693682770067,0.046953789989036522,0.04721746882463447,0.04740671694384066,0.047520629705141322,0.047558661419562845,0.047520629705141322,0.04740671694384066,0.04721746882463447,0.046953789989036522,0.046616936827700663,0.046208507508349185,0.045730429345777798,0.045184943653594163,0.04457458824427106,0.043902177768665916,0.043170782108046542,0.042383703050585628,0.041544449500011509,0.040656711476451682,0.039724333178355366,0.038751285379667835,0.037741637438144009,0.036699529188881648,0.035629142991928632,0.034534676194329247,0.033420314255424327,0.032290204769855009,0.031148432605823076,0.02999899635704633,0.028845786285857218,0.027692563912382603,0.026542943381084753,0.025400374711512061,0.024268129015276509,0.023149285736408679,0.02204672194769159,0.020963103711673339,0.019900879492112819,0.018862275579901989,0.017849293477277796,0.01686370916560059,0.01590707416530671,0.014980718281980126,0.01408575391992941,0.013223081834262724,0.012393398184249805,0.011597202744734119,0.010834808128466258,0.01010634987039663,0.0094117972250895784,0.0087509645303761839,0.008123522994003372,0.007529012765200121,0.0069668551595920463,0.0064363649135707034],[0.006061540200806936,0.0065611370999222188,0.0070905571951685453,0.007650445843508504,0.0082413480293620257,0.0088636968238760151,0.0095178018719333166,0.010203838023579855,0.010921834233776498,0.01167166286051389,0.012453029496190784,0.013265463470584823,0.014108309165586039,0.014980718281980124,0.015881643196842259,0.016809831546436893,0.017763822163843958,0.018741942492805981,0.019742307589502277,0.020762820812129393,0.021801176284357422,0.022854863203034249,0.023921172043052299,0.024997202693240402,0.026079874536696999,0.02716593846737124,0.02825199081218931,0.029334489104903369,0.030409769634422382,0.031474066666998694,0.032523533218635541,0.03355426323180017,0.034562314989328644,0.035543735578639511,0.036494586201372997,0.037410968107659134,0.038289048920689885,0.039125089106392709,0.039915468335008072,0.040656711476451675,0.041345513969640424,0.041978766307575861,0.042553577384957658,0.043067296463433866,0.04351753352122472,0.043902177768665902,0.044219414129037737,0.044467737504660682,0.04464596467137659,0.044753243669892209,0.044789060589685799,0.044753243669892209,0.04464596467137659,0.044467737504660682,0.044219414129037737,0.043902177768665895,0.043517533521224713,0.043067296463433859,0.042553577384957665,0.041978766307575861,0.041345513969640424,0.040656711476451675,0.039915468335008072,0.039125089106392709,0.038289048920689885,0.037410968107659134,0.03649458620137299,0.035543735578639504,0.034562314989328637,0.033554263231800163,0.032523533218635534,0.031474066666998701,0.030409769634422382,0.029334489104903369,0.02825199081218931,0.02716593846737124,0.026079874536696999,0.024997202693240402,0.023921172043052299,0.022854863203034249,0.021801176284357418,0.020762820812129389,0.019742307589502271,0.018741942492805967,0.017763822163843958,0.016809831546436893,0.015881643196842259,0.014980718281980124,0.014108309165586039,0.013265463470584823,0.012453029496190784,0.01167166286051389,0.010921834233776495,0.01020383802357985,0.0095178018719333131,0.0088636968238760116,0.0082413480293620292,0.007650445843508504,0.0070905571951685453,0.0065611370999222188,0.006061540200806936],[0.0057085435800151166,0.0061790462206905592,0.0066776352897603445,0.0072049185615233402,0.0077614092829775957,0.0083475153051697816,0.0089635282406685703,0.0096096127570459051,0.010285796123057005,0.010991958129984462,0.011727821515191006,0.012492943018154205,0.013286705200990517,0.014108309165586039,0.014956768297825607,0.01583090316595993,0.016729337694806046,0.017650496730200235,0.018592605098904386,0.019553688258028373,0.02053157461502585,0.021523899584537359,0.022528111431913717,0.023541478935310473,0.024561100878988173,0.025583917370102276,0.026606722950067944,0.027626181449811549,0.028638842516166246,0.029641159714645576,0.030629510092160118,0.031600215062259393,0.032549562455516982,0.033473829559059302,0.034369306952286197,0.035232322930844807,0.036059268298177988,0.036846621293724097,0.037590972419315721,0.038289048920689878,0.038937738679419451,0.039534113272096355,0.04007544995828588,0.040559252366620356,0.04098326965935311,0.041345513969640417,0.041644275922601962,0.041878138070623572,0.04204598609515782,0.042147017651158268,0.0421807487559221,0.042147017651158268,0.04204598609515782,0.041878138070623572,0.041644275922601962,0.04134551396964041,0.040983269659353103,0.040559252366620356,0.040075449958285887,0.039534113272096355,0.038937738679419451,0.038289048920689878,0.037590972419315721,0.036846621293724097,0.036059268298177988,0.035232322930844807,0.034369306952286197,0.033473829559059302,0.032549562455516975,0.031600215062259393,0.030629510092160112,0.029641159714645583,0.028638842516166246,0.027626181449811549,0.026606722950067944,0.025583917370102276,0.024561100878988173,0.023541478935310473,0.022528111431913717,0.021523899584537359,0.020531574615025847,0.019553688258028366,0.018592605098904379,0.017650496730200225,0.016729337694806046,0.01583090316595993,0.014956768297825607,0.014108309165586039,0.013286705200990517,0.012492943018154205,0.011727821515191006,0.010991958129984462,0.010285796123057,0.0096096127570458999,0.0089635282406685668,0.0083475153051697781,0.0077614092829775992,0.0072049185615233402,0.0066776352897603445,0.0061790462206905592,0.0057085435800151166],[0.0053761038820782934,0.0058192065820241584,0.0062887600841068699,0.0067853367686055242,0.0073094199933398532,0.0078613938579605962,0.0084415329928424765,0.0090499924760645816,0.009686797988373453,0.010351836321462407,0.011044846359213174,0.01176541065458659,0.012512947726482244,0.013286705200990515,0.014085753919929408,0.014908983136307659,0.015755096911322403,0.01662261182064733,0.017509856069085811,0.01841497010217389,0.019335908791070021,0.02027044525314603,0.021216176355210205,0.022170529929396082,0.023130773713615976,0.024094026009312326,0.025057268029276065,0.026017357887795595,0.026971046164630055,0.027914992953559412,0.028845786285857211,0.029759961799270668,0.03065402350429132,0.031524465481966121,0.032367794331533688,0.03318055217205669,0.033959339990222881,0.03470084111683952,0.035401844607455227,0.036059268298177988,0.036670181306248814,0.037231825746362683,0.037741637438144002,0.038197265387576056,0.038596589835498171,0.038937738679419444,0.039219102090702992,0.039439345167457576,0.039597418483996109,0.039692566420210157,0.039724333178355359,0.039692566420210157,0.039597418483996109,0.039439345167457576,0.039219102090702992,0.038937738679419437,0.038596589835498164,0.038197265387576049,0.037741637438144009,0.037231825746362683,0.036670181306248814,0.036059268298177988,0.035401844607455227,0.03470084111683952,0.033959339990222881,0.03318055217205669,0.032367794331533681,0.031524465481966114,0.030654023504291313,0.029759961799270665,0.028845786285857204,0.027914992953559419,0.026971046164630055,0.026017357887795595,0.025057268029276065,0.024094026009312326,0.023130773713615976,0.022170529929396082,0.021216176355210205,0.02027044525314603,0.019335908791070017,0.018414970102173883,0.017509856069085807,0.01662261182064732,0.015755096911322403,0.014908983136307659,0.014085753919929408,0.013286705200990515,0.012512947726482244,0.01176541065458659,0.011044846359213174,0.010351836321462407,0.0096867979883734495,0.0090499924760645781,0.008441532992842473,0.0078613938579605927,0.0073094199933398567,0.0067853367686055242,0.0062887600841068699,0.0058192065820241584,0.0053761038820782934],[0.0050630239650059326,0.0054803223725503709,0.0059225312074321461,0.0063901895170978343,0.0068837525107990887,0.0074035819199643376,0.0079499363817403419,0.0085229619431619209,0.0091226827894453633,0.0097489923050225278,0.010401644579994082,0.011080246477543888,0.011784250379394635,0.012512947726482244,0.013265463470584821,0.01404075154958021,0.014837591494266181,0.015654586268223952,0.016490161434029923,0.017342565729241675,0.01820987312404963,0.019089986419374119,0.019980642429605702,0.020879418778273325,0.021783742317846348,0.022690899166826779,0.023598046338486677,0.02450222491629429,0.025400374711512061,0.026289350318916466,0.027165938467371233,0.028026876543375198,0.028868872147999509,0.029688623531116572,0.030482840731787711,0.031248267240384795,0.031981701986721171,0.032680021449381487,0.033340201674762121,0.033959339990222874,0.034534676194329247,0.035063613008513267,0.035543735578639504,0.035972829821924325,0.036348899424370487,0.036670181306248814,0.036935159388043939,0.037142576506498874,0.037291444349720905,0.037381051301491032,0.037410968107659127,0.037381051301491032,0.037291444349720905,0.037142576506498874,0.036935159388043939,0.036670181306248807,0.03634889942437048,0.035972829821924325,0.035543735578639504,0.035063613008513267,0.034534676194329247,0.033959339990222874,0.033340201674762121,0.032680021449381487,0.031981701986721171,0.031248267240384795,0.030482840731787704,0.029688623531116565,0.028868872147999505,0.028026876543375191,0.027165938467371226,0.026289350318916473,0.025400374711512061,0.02450222491629429,0.023598046338486677,0.022690899166826779,0.021783742317846348,0.020879418778273325,0.019980642429605702,0.019089986419374119,0.018209873124049626,0.017342565729241671,0.016490161434029919,0.015654586268223941,0.014837591494266181,0.01404075154958021,0.013265463470584821,0.012512947726482244,0.011784250379394635,0.011080246477543888,0.010401644579994082,0.0097489923050225278,0.0091226827894453598,0.0085229619431619157,0.0079499363817403385,0.007403581919964335,0.0068837525107990913,0.0063901895170978343,0.0059225312074321461,0.0054803223725503709,0.0050630239650059326],[0.0047681764029296851,0.005161173243076223,0.0055776298402054917,0.0060180538500845971,0.0064828739726421041,0.0069724308737079905,0.0074869681285741419,0.008026623279158188,0.0085914191022390656,0.0091812551910559689,0.0097958999563872544,0.010434983155922634,0.011097989062190594,0.011784250379394635,0.012492943018154203,0.013223081834262724,0.013973517433111204,0.014742934135348313,0.015529849191648156,0.016332613325153462,0.017149412669298945,0.017978272156371506,0.01881706039843126,0.019663496087230781,0.020515155923686027,0.021369484070453838,0.02222380310346439,0.023075326420070246,0.023921172043052299,0.024758377741327286,0.025583917370102266,0.026394718315695061,0.027187679913564064,0.027959692692540346,0.028707658284094988,0.029428509822956941,0.030119232654754902,0.030776885157799999,0.031398619479837131,0.031981701986721164,0.032523533218635541,0.033021667150741091,0.033473829559059295,0.033877935298950113,0.034232104312693037,0.034534676194329247,0.034784223153941078,0.034979561239760183,0.035119759694697869,0.035204148343837567,0.035232322930844794,0.035204148343837567,0.035119759694697869,0.034979561239760183,0.034784223153941078,0.03453467619432924,0.034232104312693031,0.033877935298950113,0.033473829559059295,0.033021667150741091,0.032523533218635541,0.031981701986721164,0.031398619479837131,0.030776885157799999,0.030119232654754902,0.029428509822956941,0.028707658284094984,0.027959692692540342,0.027187679913564057,0.026394718315695058,0.025583917370102262,0.024758377741327289,0.023921172043052299,0.023075326420070246,0.02222380310346439,0.021369484070453838,0.020515155923686027,0.019663496087230781,0.01881706039843126,0.017978272156371506,0.017149412669298942,0.016332613325153456,0.015529849191648151,0.014742934135348303,0.013973517433111204,0.013223081834262724,0.012492943018154203,0.011784250379394635,0.011097989062190594,0.010434983155922634,0.0097958999563872544,0.0091812551910559689,0.0085914191022390604,0.0080266232791581828,0.0074869681285741393,0.0069724308737079879,0.0064828739726421067,0.0060180538500845971,0.0055776298402054917,0.005161173243076223,0.0047681764029296851],[0.0044904994261524981,0.0048606099120131856,0.0052528139649667153,0.0056675896772098158,0.0061053407831307598,0.0065663881097260245,0.0070509610475667653,0.0075591891287528868,0.0080910938036469812,0.0086465805127227922,0.009225431153465009,0.0098272970447969756,0.010451692492877022,0.011097989062190599,0.011765410654586594,0.012453029496190791,0.013159763127925347,0.013884372489639609,0.014625461180606255,0.015381475970375041,0.016150708623746134,0.016931299091995904,0.017721240109555263,0.018518383221226602,0.019320446249878314,0.020125022198546998,0.020929589564202329,0.021731524023301758,0.02252811143191373,0.023316562065863744,0.02409402600931233,0.024857609583668196,0.025604392693035518,0.026331446947749197,0.027035854414216721,0.027714726827496539,0.028365225093020734,0.028984578895811516,0.029570106229618136,0.030119232654754913,0.030629510092160132,0.031098634962392006,0.031524465481966128,0.031905037935613126,0.032238581751650716,0.032523533218635554,0.032758547694661758,0.032942510175944427,0.033074544108468051,0.033154018345264907,0.033180552172056697,0.033154018345264907,0.033074544108468051,0.032942510175944427,0.032758547694661758,0.032523533218635547,0.032238581751650716,0.031905037935613119,0.031524465481966128,0.031098634962392006,0.030629510092160132,0.030119232654754913,0.029570106229618136,0.028984578895811516,0.028365225093020734,0.027714726827496539,0.027035854414216718,0.026331446947749193,0.025604392693035515,0.024857609583668193,0.024094026009312326,0.023316562065863751,0.02252811143191373,0.021731524023301758,0.020929589564202329,0.020125022198546998,0.019320446249878314,0.018518383221226602,0.017721240109555263,0.016931299091995904,0.016150708623746131,0.015381475970375038,0.01462546118060625,0.0138843724896396,0.013159763127925347,0.012453029496190791,0.011765410654586594,0.011097989062190599,0.010451692492877022,0.0098272970447969756,0.009225431153465009,0.0086465805127227922,0.0080910938036469777,0.0075591891287528834,0.0070509610475667627,0.0065663881097260219,0.0061053407831307624,0.0056675896772098158,0.0052528139649667153,0.0048606099120131856,0.0044904994261524981],[0.004228993097630843,0.0045775500267220739,0.0049469138937217058,0.0053375349489044035,0.0057497934149980312,0.0061839914354892851,0.0066403450422824195,0.0071189762241150849,0.0076199051821780033,0.0081430428636630331,0.0086881838673565706,0.0092549998177870879,0.0098430333057203216,0.010451692492877021,0.011080246477543892,0.011727821515191011,0.012393398184249806,0.013075809581815418,0.013773740627208183,0.014485728543077579,0.015210164574097379,0.015945296992348933,0.01668923542630979,0.017439956537072848,0.018195311051156196,0.018953032144187264,0.019710745154040765,0.020465978585879674,0.021216176355210212,0.021958711198746355,0.022690899166826782,0.023410015095582628,0.024113308942264537,0.024798022853345408,0.025461408822456458,0.026100746784112137,0.026713362979740897,0.027296648424949783,0.027848077301373009,0.028365225093020731,0.028845786285857222,0.029287591450463911,0.029688623531116575,0.030047033170420449,0.030361152906761005,0.030629510092160125,0.030850838390560496,0.031024087730942666,0.031148432605823069,0.031223278623372024,0.031248267240384799,0.031223278623372024,0.031148432605823069,0.031024087730942666,0.030850838390560496,0.030629510092160122,0.030361152906761002,0.030047033170420446,0.029688623531116579,0.029287591450463911,0.028845786285857222,0.028365225093020731,0.027848077301373009,0.027296648424949783,0.026713362979740897,0.026100746784112137,0.025461408822456455,0.024798022853345404,0.024113308942264534,0.023410015095582624,0.022690899166826775,0.021958711198746358,0.021216176355210212,0.020465978585879674,0.019710745154040765,0.018953032144187264,0.018195311051156196,0.017439956537072848,0.01668923542630979,0.015945296992348933,0.015210164574097377,0.014485728543077574,0.013773740627208177,0.013075809581815409,0.012393398184249806,0.011727821515191011,0.011080246477543892,0.010451692492877021,0.0098430333057203216,0.0092549998177870879,0.0086881838673565706,0.0081430428636630331,0.0076199051821779999,0.0071189762241150815,0.0066403450422824169,0.0061839914354892824,0.0057497934149980329,0.0053375349489044035,0.0049469138937217058,0.0045775500267220739,0.004228993097630843],[0.003982715712121318,0.0043109742658744791,0.0046588280558022624,0.0050267011116445831,0.0054149515136814059,0.0058238638099325554,0.0062536414515835812,0.0067043993233010992,0.0071761564498500673,0.0076688289644541614,0.0081822234275352561,0.0087160305867205641,0.0092698196702159265,0.0098430333057203234,0.010434983155922639,0.011044846359213181,0.011671662860513896,0.012314333712054849,0.012971620417493132,0.013642145384999495,0.014324393545864482,0.015016715184861818,0.01571733001713636,0.016424332533865982,0.017135698625512442,0.017849293477277792,0.018562880716593191,0.019274132777276194,0.019980642429605712,0.02067993541019858,0.021369484070453842,0.022046721947691597,0.022709059149184658,0.023353898426292381,0.023978651804078585,0.02458075762133995,0.025157697827082423,0.025707015372336054,0.026226331530945658,0.026713362979740897,0.027165938467371246,0.027582014902152181,0.027959692692540353,0.028297230179331469,0.028593057006315838,0.028845786285857222,0.02905422542756924,0.029217385511808035,0.029334489104903372,0.029404976429710999,0.029428509822956951,0.029404976429710999,0.029334489104903372,0.029217385511808035,0.02905422542756924,0.028845786285857218,0.028593057006315835,0.028297230179331466,0.027959692692540356,0.027582014902152181,0.027165938467371246,0.026713362979740897,0.026226331530945658,0.025707015372336054,0.025157697827082423,0.02458075762133995,0.023978651804078582,0.023353898426292378,0.022709059149184654,0.022046721947691594,0.021369484070453838,0.020679935410198583,0.019980642429605712,0.019274132777276194,0.018562880716593191,0.017849293477277792,0.017135698625512442,0.016424332533865982,0.01571733001713636,0.015016715184861818,0.01432439354586448,0.013642145384999492,0.012971620417493128,0.012314333712054841,0.011671662860513896,0.011044846359213181,0.010434983155922639,0.0098430333057203234,0.0092698196702159265,0.0087160305867205641,0.0081822234275352561,0.0076688289644541614,0.0071761564498500647,0.0067043993233010966,0.0062536414515835794,0.0058238638099325536,0.0054149515136814076,0.0050267011116445831,0.0046588280558022624,0.0043109742658744791,0.003982715712121318],[0.003750780405024592,0.0040599226687949774,0.0043875190310218295,0.0047339688278753844,0.0050996092866634896,0.0054847083846193178,0.005889457724853735,0.006313965501671211,0.006758249631920646,0.0072222311328465497,0.0077057278299148511,0.008208448480208937,0.0087299873981309933,0.009269819670215923,0.0098272970447969739,0.010401644579994086,0.010991958129984465,0.011597202744734122,0.012216212052312336,0.01284768868559256,0.013490205806598285,0.014142209772038894,0.014802023972778133,0.015467853868188894,0.016137793223695976,0.01680983154643689,0.017481862700042431,0.018151694665232393,0.018817060398431271,0.019475629726138054,0.020125022198546994,0.020762820812129393,0.021386586497769002,0.021993873258811161,0.022582243832247169,0.023149285736408679,0.023692627560175743,0.024209955341971172,0.024699028881866907,0.02515769782708242,0.02558391737010228,0.02597576339963914,0.02633144694774919,0.026649327781564223,0.026927926995300867,0.02716593846737124,0.027362239058446359,0.027515897439079076,0.027626181449811545,0.027692563912382603,0.027714726827496532,0.027692563912382603,0.027626181449811545,0.027515897439079076,0.027362239058446359,0.027165938467371236,0.026927926995300864,0.02664932778156422,0.026331446947749193,0.02597576339963914,0.02558391737010228,0.02515769782708242,0.024699028881866907,0.024209955341971172,0.023692627560175743,0.023149285736408679,0.022582243832247165,0.021993873258811157,0.021386586497768999,0.020762820812129389,0.020125022198546987,0.019475629726138057,0.018817060398431271,0.018151694665232393,0.017481862700042431,0.01680983154643689,0.016137793223695976,0.015467853868188894,0.014802023972778133,0.014142209772038894,0.013490205806598283,0.012847688685592554,0.012216212052312332,0.011597202744734116,0.010991958129984465,0.010401644579994086,0.0098272970447969739,0.009269819670215923,0.0087299873981309933,0.008208448480208937,0.0077057278299148511,0.0072222311328465497,0.0067582496319206426,0.0063139655016712084,0.0058894577248537324,0.005484708384619316,0.0050996092866634913,0.0047339688278753844,0.0043875190310218295,0.0040599226687949774,0.003750780405024592],[0.0035323519587149243,0.0038234911785658202,0.0041320098138422886,0.0044582839451864347,0.0048026311613165451,0.0051653038336866306,0.0055464824073110288,0.0059462687757484258,0.0063646798124516683,0.0068016411342628714,0.0072569811756669255,0.0077304256544143057,0.0082215925101972055,0.008729987398130995,0.0092549998177870896,0.0097958999563872596,0.01035183632146241,0.010921834233776502,0.011504795245612206,0.012099497542622706,0.012704597379406558,0.013318631589814814,0.013940021202826268,0.014567076183724232,0.01519800130839309,0.01583090316595993,0.016463798271889336,0.017094622260166281,0.017721240109555263,0.018341457345295933,0.018953032144187261,0.019553688258028373,0.020141128658030617,0.020713049791295374,0.021267156329962032,0.021801176284357425,0.022312876343594228,0.022800077300726973,0.023260669414915277,0.023692627560175743,0.024094026009312333,0.024463052702555957,0.024798022853345408,0.025097391748538592,0.025359766607120221,0.02558391737010228,0.025768786304698452,0.025913496317866332,0.026017357887795595,0.026079874536697002,0.026100746784112137,0.026079874536697002,0.026017357887795595,0.025913496317866332,0.025768786304698452,0.025583917370102276,0.025359766607120218,0.025097391748538589,0.024798022853345411,0.024463052702555957,0.024094026009312333,0.023692627560175743,0.023260669414915277,0.022800077300726973,0.022312876343594228,0.021801176284357425,0.021267156329962029,0.02071304979129537,0.020141128658030614,0.019553688258028369,0.018953032144187257,0.018341457345295936,0.017721240109555263,0.017094622260166281,0.016463798271889336,0.01583090316595993,0.01519800130839309,0.014567076183724232,0.013940021202826268,0.013318631589814814,0.012704597379406556,0.012099497542622703,0.011504795245612202,0.010921834233776493,0.01035183632146241,0.0097958999563872596,0.0092549998177870896,0.008729987398130995,0.0082215925101972055,0.0077304256544143057,0.0072569811756669255,0.0068016411342628714,0.0063646798124516657,0.0059462687757484232,0.0055464824073110262,0.0051653038336866288,0.0048026311613165468,0.0044582839451864347,0.0041320098138422886,0.0038234911785658202,0.0035323519587149243],[0.0033266437948545678,0.0036008283864455287,0.0038913802950987205,0.0041986537002246457,0.0045229476956144543,0.0048644999557528211,0.0052234804173545112,0.0055999850401592969,0.0059940297149866277,0.0064055443904165125,0.0068343674921316341,0.0072802407108371976,0.0077428042356856219,0.0082215925101972037,0.0087160305867205641,0.009225431153465009,0.0097489923050225313,0.010285796123057005,0.010834808128466258,0.011394877659831834,0.011964739225392483,0.012543014867162387,0.013128217566234217,0.013718755707851268,0.014312938613611619,0.014908983136307657,0.015505021300551017,0.01609910895964441,0.016689235426309793,0.017273334022048014,0.017849293477277785,0.018414970102173887,0.018968200636490545,0.019506815675806605,0.020028653561749994,0.02053157461502585,0.021013475582648031,0.021472304164803949,0.021906073482395084,0.022312876343594221,0.022690899166826782,0.023038435418469502,0.023353898426292374,0.023635833434243615,0.023882928770559978,0.024094026009312326,0.024268129015276509,0.024404411773332527,0.02450222491629429,0.024561100878988173,0.024580757621339943,0.024561100878988173,0.02450222491629429,0.024404411773332527,0.024268129015276509,0.024094026009312323,0.023882928770559975,0.023635833434243615,0.023353898426292378,0.023038435418469502,0.022690899166826782,0.022312876343594221,0.021906073482395084,0.021472304164803949,0.021013475582648031,0.02053157461502585,0.020028653561749991,0.019506815675806602,0.018968200636490542,0.018414970102173883,0.017849293477277782,0.017273334022048017,0.016689235426309793,0.01609910895964441,0.015505021300551017,0.014908983136307657,0.014312938613611619,0.013718755707851268,0.013128217566234217,0.012543014867162387,0.011964739225392481,0.011394877659831831,0.010834808128466255,0.010285796123056998,0.0097489923050225313,0.009225431153465009,0.0087160305867205641,0.0082215925101972037,0.0077428042356856219,0.0072802407108371976,0.0068343674921316341,0.0064055443904165125,0.0059940297149866251,0.0055999850401592943,0.0052234804173545094,0.0048644999557528193,0.004522947695614456,0.0041986537002246457,0.0038913802950987205,0.0036008283864455287,0.0033266437948545678],[0.003132915141862147,0.0033911324658777958,0.0036647639486125823,0.003954143143673843,0.0042595517269862987,0.0045812135319501538,0.0049192885989363276,0.0052738672994243905,0.0056449645988245079,0.006032514525193807,0.0064363649135706991,0.0068562724974226526,0.0072918984196546147,0.0077428042356856219,0.008208448480208937,0.0086881838673565706,0.0091812551910559724,0.009686797988373453,0.010203838023579853,0.010731291644561103,0.011267967056058916,0.011812566546113483,0.012363689693057107,0.012919837570560798,0.013479417957667928,0.01404075154958021,0.014602079153327268,0.015161569840501517,0.01571733001713636,0.016267413358718983,0.016809831546436886,0.017342565729241675,0.017863578625356969,0.018370827166639916,0.018862275579901985,0.019335908791070021,0.01978974603107652,0.020221854516745713,0.020630363075810083,0.021013475582648027,0.021369484070453842,0.021696781386385765,0.021993873258811154,0.022259389650075428,0.022492095274232252,0.022690899166826779,0.022854863203034252,0.022983209471110454,0.023075326420070246,0.023130773713615976,0.023149285736408676,0.023130773713615976,0.023075326420070246,0.022983209471110454,0.022854863203034252,0.022690899166826779,0.022492095274232248,0.022259389650075428,0.021993873258811157,0.021696781386385765,0.021369484070453842,0.021013475582648027,0.020630363075810083,0.020221854516745713,0.01978974603107652,0.019335908791070021,0.018862275579901982,0.018370827166639916,0.017863578625356966,0.017342565729241671,0.016809831546436883,0.016267413358718986,0.01571733001713636,0.015161569840501517,0.014602079153327268,0.01404075154958021,0.013479417957667928,0.012919837570560798,0.012363689693057107,0.011812566546113483,0.011267967056058915,0.010731291644561099,0.01020383802357985,0.0096867979883734478,0.0091812551910559724,0.0086881838673565706,0.008208448480208937,0.0077428042356856219,0.0072918984196546147,0.0068562724974226526,0.0064363649135706991,0.006032514525193807,0.0056449645988245062,0.0052738672994243879,0.0049192885989363258,0.0045812135319501521,0.0042595517269863005,0.003954143143673843,0.0036647639486125823,0.0033911324658777958,0.003132915141862147],[0.0029504683673348361,0.003193648285049807,0.0034513447107614994,0.0037238717734273535,0.004011494745443234,0.0043144244251668868,0.0046328115329435839,0.0049667411774276336,0.005316227452511561,0.0056812082281593535,0.0060615402008069351,0.0064569942706617584,0.0068672513141297513,0.0072918984196546173,0.0077304256544143074,0.0081822234275352578,0.008646580512722794,0.0091226827894453667,0.0096096127570459051,0.010106349870396636,0.010611771738992009,0.011124656223733468,0.011643684457162313,0.012167444803623447,0.012694437765890286,0.013223081834262728,0.013751720263193542,0.014278628749244928,0.014802023972778142,0.015320072954396165,0.01583090316595993,0.016332613325153466,0.016823284792254867,0.017300993478147494,0.017763822163843961,0.018209873124049637,0.018637280940707521,0.019044225387171567,0.019428944259763995,0.019789746031076527,0.020125022198547001,0.020433259202629006,0.020713049791295374,0.020963103711673349,0.021182257615269828,0.021369484070453849,0.021523899584537369,0.021644771547829431,0.021731524023301755,0.021783742317846359,0.021801176284357425,0.021783742317846359,0.021731524023301755,0.021644771547829431,0.021523899584537369,0.021369484070453845,0.021182257615269824,0.020963103711673346,0.020713049791295377,0.020433259202629006,0.020125022198547001,0.019789746031076527,0.019428944259763995,0.019044225387171567,0.018637280940707521,0.018209873124049637,0.017763822163843958,0.017300993478147491,0.016823284792254863,0.016332613325153462,0.015830903165959927,0.015320072954396169,0.014802023972778142,0.014278628749244928,0.013751720263193542,0.013223081834262728,0.012694437765890286,0.012167444803623447,0.011643684457162313,0.011124656223733468,0.010611771738992009,0.010106349870396632,0.0096096127570459017,0.0091226827894453615,0.008646580512722794,0.0081822234275352578,0.0077304256544143074,0.0072918984196546173,0.0068672513141297513,0.0064569942706617584,0.0060615402008069351,0.0056812082281593535,0.0053162274525115584,0.0049667411774276318,0.0046328115329435831,0.0043144244251668851,0.0040114947454432358,0.0037238717734273535,0.0034513447107614994,0.003193648285049807,0.0029504683673348361],[0.0027786464658181719,0.003007664687602067,0.0032503540417687673,0.0035070103638293608,0.0037778834779180117,0.0040631719064517834,0.0043630175925063429,0.0046775006883938179,0.0050066344672423284,0.0053503604171874896,0.0057085435800151166,0.0060809681976659374,0.0064673337308572242,0.0068672513141297513,0.0072802407108372011,0.0077057278299148555,0.0081430428636630366,0.0085914191022390691,0.0090499924760645833,0.00951780187193332,0.0099937902622743227,0.010476806679829458,0.010965609062001632,0.011458867980396527,0.011955171261707939,0.012453029496190791,0.012950882419647527,0.013447106144255294,0.013940021202826275,0.014427901360373568,0.01490898313630766,0.015381475970375041,0.015843572955732889,0.016293462053491702,0.01672933769480605,0.017149412669298952,0.017551930192404027,0.017935176039222938,0.018297490628831008,0.018637280940707521,0.018953032144187271,0.019243318822569962,0.019506815675806609,0.019742307589502284,0.019948698963305991,0.020125022198547001,0.02027044525314604,0.020384278181279202,0.020465978585879674,0.020515155923686038,0.020531574615025857,0.020515155923686038,0.020465978585879674,0.020384278181279202,0.02027044525314604,0.020125022198546998,0.019948698963305988,0.019742307589502281,0.019506815675806612,0.019243318822569962,0.018953032144187271,0.018637280940707521,0.018297490628831008,0.017935176039222938,0.017551930192404027,0.017149412669298952,0.016729337694806046,0.016293462053491702,0.015843572955732885,0.015381475970375038,0.014908983136307659,0.014427901360373571,0.013940021202826275,0.013447106144255294,0.012950882419647527,0.012453029496190791,0.011955171261707939,0.011458867980396527,0.010965609062001632,0.010476806679829458,0.009993790262274321,0.0095178018719333183,0.0090499924760645799,0.0085914191022390639,0.0081430428636630366,0.0077057278299148555,0.0072802407108372011,0.0068672513141297513,0.0064673337308572242,0.0060809681976659374,0.0057085435800151166,0.0053503604171874896,0.0050066344672423267,0.0046775006883938161,0.004363017592506342,0.0040631719064517817,0.0037778834779180134,0.0035070103638293608,0.0032503540417687673,0.003007664687602067,0.0027786464658181719],[0.0026168306928767713,0.0028325119316973757,0.0030610681581300404,0.003302777979566884,0.0035578766715170956,0.0038265511953521859,0.0041089352280266073,0.0044051042541452057,0.0047150707738692951,0.005038779682800202,0.0053761038820782934,0.0057268401784155102,0.0060907055345744325,0.0064673337308572233,0.0068562724974226552,0.0072569811756669281,0.0076688289644541632,0.0080910938036469812,0.0085229619431619209,0.008963528240668572,0.0094117972250895819,0.0098666849562819309,0.010327021703743177,0.010791555458961617,0.01125895628720219,0.011727821515191011,0.0121966817414438,0.012664007646002472,0.013128217566234222,0.013587685795251759,0.014040751549580212,0.014485728543077577,0.014920915094963799,0.015344604691279268,0.01575509691132241,0.016150708623746134,0.016529785351152671,0.016890712697330182,0.017231927727823192,0.017551930192404027,0.017849293477277796,0.018122675175550593,0.01837082716663992,0.01859260509890439,0.018786977174790449,0.018953032144187268,0.019089986419374129,0.019197190233843985,0.019274132777276191,0.019320446249878314,0.019335908791070024,0.019320446249878314,0.019274132777276191,0.019197190233843985,0.019089986419374129,0.018953032144187264,0.018786977174790446,0.018592605098904386,0.018370827166639923,0.018122675175550593,0.017849293477277796,0.017551930192404027,0.017231927727823192,0.016890712697330182,0.016529785351152671,0.016150708623746134,0.015755096911322406,0.015344604691279266,0.014920915094963795,0.014485728543077576,0.01404075154958021,0.013587685795251762,0.013128217566234222,0.012664007646002472,0.0121966817414438,0.011727821515191011,0.01125895628720219,0.010791555458961617,0.010327021703743177,0.0098666849562819309,0.0094117972250895819,0.0089635282406685685,0.0085229619431619191,0.0080910938036469759,0.0076688289644541632,0.0072569811756669281,0.0068562724974226552,0.0064673337308572233,0.0060907055345744325,0.0057268401784155102,0.0053761038820782934,0.005038779682800202,0.0047150707738692925,0.004405104254145204,0.0041089352280266065,0.0038265511953521846,0.0035578766715170969,0.003302777979566884,0.0030610681581300404,0.0028325119316973757,0.0026168306928767713],[0.002464438336946039,0.0026675592782267983,0.0028828054262109329,0.0031104391634591338,0.0033506820641015767,0.0036037102017271007,0.0038696494685503667,0.0041485709532950495,0.0044404864281697388,0.0047453439978061207,0.0050630239650059326,0.0053933349695370189,0.0057360104569674922,0.0060907055345744317,0.0064569942706617584,0.0068343674921316367,0.0072222311328465523,0.0076199051821780042,0.0080266232791581897,0.0084415329928424782,0.0088636968238760168,0.0092920939558755761,0.0097256227781401059,0.010163104193457539,0.010603285716462414,0.011044846359213179,0.011486402291506341,0.011926513254044877,0.012363689693057114,0.012796400575454593,0.013223081834262726,0.013642145384999494,0.014051988645058758,0.014451004480117295,0.014837591494266184,0.015210164574097381,0.015567165591476041,0.015907074165306706,0.016228418379350892,0.016529785351152668,0.016809831546436897,0.017067292734001246,0.017300993478147491,0.017509856069085818,0.017692908796474453,0.017849293477277792,0.017978272156371516,0.018079232906704174,0.018151694665232393,0.018195311051156196,0.018209873124049637,0.018195311051156196,0.018151694665232393,0.018079232906704174,0.017978272156371516,0.017849293477277792,0.017692908796474453,0.017509856069085814,0.017300993478147491,0.017067292734001246,0.016809831546436897,0.016529785351152668,0.016228418379350892,0.015907074165306706,0.015567165591476041,0.015210164574097381,0.014837591494266182,0.014451004480117291,0.014051988645058754,0.01364214538499949,0.013223081834262723,0.012796400575454597,0.012363689693057114,0.011926513254044877,0.011486402291506341,0.011044846359213179,0.010603285716462414,0.010163104193457539,0.0097256227781401059,0.0092920939558755761,0.0088636968238760151,0.0084415329928424765,0.0080266232791581862,0.007619905182177999,0.0072222311328465523,0.0068343674921316367,0.0064569942706617584,0.0060907055345744317,0.0057360104569674922,0.0053933349695370189,0.0050630239650059326,0.0047453439978061207,0.0044404864281697371,0.0041485709532950478,0.0038696494685503654,0.0036037102017270994,0.003350682064101578,0.0031104391634591338,0.0028828054262109329,0.0026675592782267983,0.002464438336946039],[0.0023209206209411277,0.0025122127194675955,0.0027149239076296803,0.0029293012880172715,0.0031555535312877288,0.0033938464573023217,0.0036442986268838719,0.0039069769888710739,0.0041818926299124603,0.0044689966767906949,0.0047681764029296851,0.0050792515920496488,0.0054019712126403639,0.0057360104569674922,0.0060809681976659374,0.0064363649135707026,0.0068016411342628732,0.0071761564498500673,0.0075591891287528842,0.0079499363817403437,0.0083475153051697833,0.008750964530376177,0.0091592465994714631,0.0095712510805196615,0.0099857984272247527,0.010401644579994086,0.010817486296621515,0.011231967191981933,0.011643684457162315,0.012051196219500206,0.012453029496190787,0.01284768868559256,0.013233664532244919,0.013609443494041551,0.01397351743311121,0.014324393545864482,0.014660604442485198,0.014980718281980122,0.01528334886583944,0.015567165591476039,0.015830903165959934,0.016073370981182521,0.016293462053491699,0.01649016143402993,0.016662554000460416,0.016809831546436893,0.016931299091995908,0.017026380345943257,0.017094622260166278,0.017135698625512442,0.017149412669298949,0.017135698625512442,0.017094622260166278,0.017026380345943257,0.016931299091995908,0.01680983154643689,0.016662554000460413,0.016490161434029926,0.016293462053491702,0.016073370981182521,0.015830903165959934,0.015567165591476039,0.01528334886583944,0.014980718281980122,0.014660604442485198,0.014324393545864482,0.013973517433111206,0.01360944349404155,0.013233664532244917,0.012847688685592556,0.012453029496190786,0.01205119621950021,0.011643684457162315,0.011231967191981933,0.010817486296621515,0.010401644579994086,0.0099857984272247527,0.0095712510805196615,0.0091592465994714631,0.008750964530376177,0.0083475153051697816,0.0079499363817403419,0.0075591891287528825,0.007176156449850063,0.0068016411342628732,0.0064363649135707026,0.0060809681976659374,0.0057360104569674922,0.0054019712126403639,0.0050792515920496488,0.0047681764029296851,0.0044689966767906949,0.0041818926299124586,0.0039069769888710722,0.0036442986268838706,0.0033938464573023204,0.0031555535312877301,0.0029293012880172715,0.0027149239076296803,0.0025122127194675955,0.0023209206209411277],[0.0021857607260666861,0.0023659128400138171,0.0025568190475855918,0.0027587120612373246,0.0029717883995933167,0.0031962042259178758,0.0034320711965890073,0.0036794523616485593,0.0039383581621089151,0.0042087425709073463,0.0044904994261524955,0.0047834590065436895,0.0050873848995077898,0.005401971212640363,0.0057268401784155102,0.006061540200806936,0.0064055443904165142,0.0067582496319206469,0.0071189762241150832,0.0074869681285741445,0.0078613938579605979,0.008241348029362024,0.0086258536017343578,0.0090138648096633345,0.0094042707982816432,0.0097958999563872579,0.010187524936691762,0.010577868343790448,0.010965609062001634,0.011349389186789873,0.011727821515191007,0.012099497542622704,0.01246299590582005,0.012816891204507229,0.013159763127925345,0.013490205806598286,0.013806837304840237,0.014108309165586036,0.014393315916242638,0.014660604442485197,0.014908983136307662,0.015137330725219954,0.015344604691279264,0.015529849191648163,0.015692202396565959,0.01583090316595993,0.015945296992348937,0.016034841145125271,0.01609910895964441,0.016137793223695976,0.016150708623746131,0.016137793223695976,0.01609910895964441,0.016034841145125271,0.015945296992348937,0.01583090316595993,0.015692202396565956,0.015529849191648161,0.015344604691279268,0.015137330725219954,0.014908983136307662,0.014660604442485197,0.014393315916242638,0.014108309165586036,0.013806837304840237,0.013490205806598286,0.013159763127925344,0.012816891204507228,0.012462995905820048,0.012099497542622703,0.011727821515191006,0.011349389186789875,0.010965609062001634,0.010577868343790448,0.010187524936691762,0.0097958999563872579,0.0094042707982816432,0.0090138648096633345,0.0086258536017343578,0.008241348029362024,0.0078613938579605979,0.0074869681285741419,0.0071189762241150815,0.0067582496319206417,0.0064055443904165142,0.006061540200806936,0.0057268401784155102,0.005401971212640363,0.0050873848995077898,0.0047834590065436895,0.0044904994261524955,0.0042087425709073463,0.0039383581621089134,0.003679452361648558,0.003432071196589006,0.0031962042259178745,0.002971788399593318,0.0027587120612373246,0.0025568190475855918,0.0023659128400138171,0.0021857607260666861],[0.0020584719307109615,0.0022281328022765974,0.0024079214978087677,0.0025980571776444104,0.0027987249160540809,0.0030100717820615527,0.0032322029296835805,0.0034651777372134178,0.0037090060376262215,0.0039636444842667288,0.0042289930976308412,0.0045048920402169911,0.0047911186670485037,0.0050873848995077898,0.0053933349695370189,0.0057085435800151166,0.0060325145251938096,0.0063646798124516683,0.0067043993233010975,0.0070509610475667645,0.0074035819199643402,0.007761409282977594,0.0081235229940033685,0.008488938188264062,0.0088566087020436803,0.009225431153465009,0.0095942496703814197,0.0099618612471054011,0.010327021703743179,0.01068845221396328,0.011044846359213175,0.011394877659831834,0.01173720752630702,0.01207049356721281,0.012393398184249806,0.012704597379406558,0.013002789694666471,0.013286705200990514,0.01355511445059099,0.013806837304840235,0.014040751549580214,0.014255801210147287,0.014451004480117291,0.014625461180606253,0.014778359670911569,0.014908983136307659,0.01501671518486182,0.015101044692136419,0.015161569840501517,0.01519800130839309,0.015210164574097377,0.01519800130839309,0.015161569840501517,0.015101044692136419,0.01501671518486182,0.014908983136307657,0.014778359670911567,0.01462546118060625,0.014451004480117293,0.014255801210147287,0.014040751549580214,0.013806837304840235,0.01355511445059099,0.013286705200990514,0.013002789694666471,0.012704597379406558,0.012393398184249805,0.012070493567212808,0.011737207526307018,0.011394877659831833,0.011044846359213174,0.010688452213963282,0.010327021703743179,0.0099618612471054011,0.0095942496703814197,0.009225431153465009,0.0088566087020436803,0.008488938188264062,0.0081235229940033685,0.007761409282977594,0.0074035819199643384,0.0070509610475667618,0.0067043993233010949,0.0063646798124516639,0.0060325145251938096,0.0057085435800151166,0.0053933349695370189,0.0050873848995077898,0.0047911186670485037,0.0045048920402169911,0.0042289930976308412,0.0039636444842667288,0.0037090060376262198,0.0034651777372134165,0.0032322029296835797,0.0030100717820615518,0.0027987249160540818,0.0025980571776444104,0.0024079214978087677,0.0022281328022765974,0.0020584719307109615],[0.0019385958577222773,0.0020983764492997861,0.0022676950662913605,0.0024467581061294987,0.0026357398651982882,0.0028347788478883078,0.0030439740845231008,0.0032633814954733183,0.0034930103410862222,0.0037328197990192371,0.003982715712121318,0.0042425475511023514,0.0045121056368197235,0.0047911186670485054,0.0050792515920496505,0.005376103882078296,0.0056812082281593561,0.0059940297149866312,0.0063139655016712128,0.0066403450422824221,0.0069724308737079957,0.007309419993339855,0.0076504458435085049,0.0079945809134960247,0.0083408399634183686,0.0086881838673565741,0.0090355240659175939,0.0093817276110112237,0.0097256227781401128,0.010066005214020663,0.010401644579994089,0.010731291644561108,0.011053685771594069,0.011367562744457851,0.011671662860513897,0.01196473922539249,0.012245566172091649,0.012512947726482248,0.012765726038241939,0.013002789694666476,0.013223081834262733,0.013425607977544133,0.013609443494041555,0.013773740627208189,0.013917735002616312,0.014040751549580219,0.014142209772038903,0.014221628311124754,0.014278628749244928,0.014312938613611626,0.014324393545864485,0.014312938613611626,0.014278628749244928,0.014221628311124754,0.014142209772038903,0.014040751549580217,0.013917735002616309,0.013773740627208186,0.013609443494041557,0.013425607977544133,0.013223081834262733,0.013002789694666476,0.012765726038241939,0.012512947726482248,0.012245566172091649,0.01196473922539249,0.011671662860513896,0.011367562744457849,0.011053685771594067,0.010731291644561105,0.010401644579994086,0.010066005214020665,0.0097256227781401128,0.0093817276110112237,0.0090355240659175939,0.0086881838673565741,0.0083408399634183686,0.0079945809134960247,0.0076504458435085049,0.007309419993339855,0.0069724308737079948,0.0066403450422824204,0.006313965501671211,0.0059940297149866269,0.0056812082281593561,0.005376103882078296,0.0050792515920496505,0.0047911186670485054,0.0045121056368197235,0.0042425475511023514,0.003982715712121318,0.0037328197990192371,0.0034930103410862209,0.0032633814954733165,0.0030439740845231,0.0028347788478883065,0.0026357398651982891,0.0024467581061294987,0.0022676950662913605,0.0020983764492997861,0.0019385958577222773],[0.0018257008237561761,0.0019761765180589838,0.0021356347864171839,0.0023042700066125258,0.0024822463247978752,0.0026696941794960246,0.0028667068339534372,0.0030733369519918962,0.0032895932546780221,0.0035154372969773994,0.0037507804050245903,0.0039954808156729008,0.0042493410605423838,0.0045121056368197208,0.0047834590065436895,0.0050630239650059326,0.0053503604171874887,0.0056449645988245088,0.005946268775748424,0.0062536414515835803,0.0065663881097260237,0.0068837525107990878,0.0072049185615233376,0.0075290127652001175,0.0078551072578495577,0.0081822234275352543,0.0085093361076281331,0.0088353783277984495,0.0091592465994714631,0.0094798067054387807,0.0097958999563872561,0.010106349870396632,0.010409969225072131,0.010705567426024026,0.010991958129984464,0.011267967056058918,0.011532439914534941,0.011784250379394633,0.012022308028269212,0.012245566172091642,0.012453029496190789,0.012643761435056813,0.012816891204507226,0.012971620417493132,0.013107229213288116,0.013223081834262726,0.013318631589814816,0.013393425153234946,0.013447106144255289,0.01347941795766793,0.013490205806598283,0.01347941795766793,0.013447106144255289,0.013393425153234946,0.013318631589814816,0.013223081834262724,0.013107229213288114,0.01297162041749313,0.012816891204507228,0.012643761435056813,0.012453029496190789,0.012245566172091642,0.012022308028269212,0.011784250379394633,0.011532439914534941,0.011267967056058918,0.010991958129984462,0.010705567426024023,0.010409969225072127,0.01010634987039663,0.0097958999563872544,0.0094798067054387824,0.0091592465994714631,0.0088353783277984495,0.0085093361076281331,0.0081822234275352543,0.0078551072578495577,0.0075290127652001175,0.0072049185615233376,0.0068837525107990878,0.0065663881097260228,0.0062536414515835786,0.0059462687757484223,0.0056449645988245053,0.0053503604171874887,0.0050630239650059326,0.0047834590065436895,0.0045121056368197208,0.0042493410605423838,0.0039954808156729008,0.0037507804050245903,0.0035154372969773994,0.0032895932546780208,0.0030733369519918945,0.0028667068339534364,0.0026696941794960237,0.0024822463247978761,0.0023042700066125258,0.0021356347864171839,0.0019761765180589838,0.0018257008237561761],[0.0017193802847491144,0.0018610929568099643,0.0020112650985364766,0.00217007976802962,0.0023376915523144874,0.0025142232937656584,0.0026997628244009382,0.0028943597411398856,0.0030980222571737395,0.0033107141663325937,0.0035323519587149243,0.0037628021268170044,0.0040018787019220963,0.0042493410605423856,0.0045048920402169937,0.0047681764029296877,0.0050387796828002037,0.0053162274525115618,0.0055999850401592987,0.0058894577248537368,0.0061839914354892877,0.0064828739726421059,0.006785336768605525,0.0070905571951685462,0.0073976614229429392,0.0077057278299148555,0.0080137909505120179,0.0083208459499194889,0.0086258536017343613,0.0089277457404163905,0.0092254311534650107,0.00951780187193332,0.0098037398118764416,0.010082123713724246,0.010351836321462414,0.010611771738992011,0.010860842897200376,0.011097989062190597,0.011322183312849128,0.011532439914534945,0.011727821515191014,0.011907446090636795,0.012070493567212813,0.012216212052312341,0.012343923606634126,0.012453029496190792,0.012543014867162396,0.012613452792531859,0.012664007646002472,0.012694437765890288,0.012704597379406561,0.012694437765890288,0.012664007646002472,0.012613452792531859,0.012543014867162396,0.012453029496190791,0.012343923606634125,0.012216212052312339,0.012070493567212815,0.011907446090636795,0.011727821515191014,0.011532439914534945,0.011322183312849128,0.011097989062190597,0.010860842897200376,0.010611771738992011,0.010351836321462412,0.010082123713724245,0.0098037398118764399,0.0095178018719333183,0.009225431153465009,0.0089277457404163922,0.0086258536017343613,0.0083208459499194889,0.0080137909505120179,0.0077057278299148555,0.0073976614229429392,0.0070905571951685462,0.006785336768605525,0.0064828739726421059,0.0061839914354892868,0.005889457724853735,0.0055999850401592969,0.0053162274525115584,0.0050387796828002037,0.0047681764029296877,0.0045048920402169937,0.0042493410605423856,0.0040018787019220963,0.0037628021268170044,0.0035323519587149243,0.0033107141663325937,0.0030980222571737382,0.0028943597411398843,0.0026997628244009374,0.0025142232937656575,0.0023376915523144882,0.00217007976802962,0.0020112650985364766,0.0018610929568099643,0.0017193802847491144],[0.0016192513719207016,0.0017527113404270653,0.001894138137437482,0.0020437041605790283,0.0022015549944292903,0.0023678063275798674,0.002542540877110042,0.0027258053516396297,0.0029176074860608461,0.0031179131826869779,0.0033266437948545656,0.0035436735899316328,0.0037688274291763999,0.0040018787019220946,0.0042425475511023488,0.0044904994261524955,0.0047453439978061198,0.0050066344672423267,0.0052738672994243887,0.0055464824073110271,0.0058238638099325536,0.0061053407831307546,0.0063901895170978317,0.0066776352897603411,0.0069668551595920428,0.0072569811756669237,0.0075471040967506195,0.0078362776050523077,0.0081235229940033685,0.0084078343031819998,0.0086881838673565671,0.0089635282406685668,0.009232814451313142,0.0094949865367942015,0.0097489923050225295,0.0099937902622743175,0.010228356645413706,0.010451692492877016,0.010662830686780717,0.010860842897200369,0.011044846359213175,0.01121401041372814,0.011367562744457842,0.011504795245612202,0.011625069458001378,0.011727821515191006,0.011812566546113484,0.011878902486045697,0.01192651325404487,0.011955171261707934,0.011964739225392481,0.011955171261707934,0.01192651325404487,0.011878902486045697,0.011812566546113484,0.011727821515191004,0.011625069458001376,0.011504795245612201,0.011367562744457844,0.01121401041372814,0.011044846359213175,0.010860842897200369,0.010662830686780717,0.010451692492877016,0.010228356645413706,0.0099937902622743175,0.0097489923050225278,0.0094949865367941998,0.0092328144513131403,0.0089635282406685651,0.0086881838673565671,0.0084078343031820015,0.0081235229940033685,0.0078362776050523077,0.0075471040967506195,0.0072569811756669237,0.0069668551595920428,0.0066776352897603411,0.0063901895170978317,0.0061053407831307546,0.0058238638099325528,0.0055464824073110253,0.005273867299424387,0.0050066344672423232,0.0047453439978061198,0.0044904994261524955,0.0042425475511023488,0.0040018787019220946,0.0037688274291763999,0.0035436735899316328,0.0033266437948545656,0.0031179131826869779,0.0029176074860608452,0.0027258053516396284,0.0025425408771100411,0.0023678063275798665,0.0022015549944292912,0.0020437041605790283,0.001894138137437482,0.0017527113404270653,0.0016192513719207016],[0.0015249535130325551,0.0016506413780251192,0.0017838321195479485,0.0019246880955718982,0.0020733464124887747,0.0022299160217110875,0.0023944748232504263,0.0025670668056283459,0.0027476992532920064,0.0029363400542493836,0.0031329151418621466,0.003337306105596786,0.0035493480059978367,0.0037688274291764012,0.0039954808156729017,0.004228993097630843,0.0044689966767906967,0.0047150707738692951,0.0049667411774276327,0.0052234804173545129,0.0054847083846193195,0.0057497934149980294,0.006018053850084598,0.0062887600841068699,0.0065611370999222197,0.0068343674921316367,0.0071075949695881225,0.0073799283237587828,0.0076504458435085057,0.0079182001509898459,0.0081822234275352561,0.0084415329928424782,0.0086951371954108354,0.0089420415672127173,0.0091812551910559759,0.0094117972250895836,0.0096327035255013935,0.0098430333057203199,0.01004187576842386,0.01022835664541371,0.010401644579994089,0.010560957286893595,0.010705567426024026,0.010834808128466263,0.010948078115999169,0.011044846359213179,0.011124656223733469,0.011187129059263603,0.011231967191981933,0.011258956287202191,0.01126796705605892,0.011258956287202191,0.011231967191981933,0.011187129059263603,0.011124656223733469,0.011044846359213179,0.010948078115999167,0.010834808128466262,0.010705567426024028,0.010560957286893595,0.010401644579994089,0.01022835664541371,0.01004187576842386,0.0098430333057203199,0.0096327035255013935,0.0094117972250895836,0.0091812551910559741,0.0089420415672127156,0.0086951371954108337,0.0084415329928424765,0.0081822234275352543,0.0079182001509898476,0.0076504458435085057,0.0073799283237587828,0.0071075949695881225,0.0068343674921316367,0.0065611370999222197,0.0062887600841068699,0.006018053850084598,0.0057497934149980294,0.0054847083846193186,0.0052234804173545112,0.004966741177427631,0.0047150707738692925,0.0044689966767906967,0.004228993097630843,0.0039954808156729017,0.0037688274291764012,0.0035493480059978367,0.003337306105596786,0.0031329151418621466,0.0029363400542493836,0.0027476992532920056,0.0025670668056283446,0.0023944748232504255,0.0022299160217110867,0.0020733464124887756,0.0019246880955718982,0.0017838321195479485,0.0016506413780251192,0.0015249535130325551],[0.0014361471339387648,0.0015545155074906871,0.0016799498240586746,0.0018126029866214236,0.001952604117116065,0.0021000558221187845,0.0022550314650976629,0.002417572472882185,0.0025876857057063334,0.0027653409216349166,0.0029504683673348335,0.0031429565279652207,0.003342650069396734,0.003549348005997835,0.0037628021268170018,0.0039827157121213163,0.0042087425709073454,0.0044404864281697371,0.0046775006883938144,0.0049192885989363267,0.0051653038336866288,0.0054149515136814007,0.0056675896772098106,0.0059225312074321435,0.0061790462206905558,0.0064363649135706991,0.0066936808614399068,0.0069501547557098723,0.0072049185615233376,0.0074570800720236766,0.0077057278299148485,0.0079499363817403385,0.008188771825287133,0.0084212976058370432,0.0086465805127227888,0.0088636968238760116,0.0090717385428491643,0.0092698196702159178,0.0094570824493606601,0.0096327035255013883,0.0097958999563872561,0.009945935013494514,0.010082123713724238,0.010203838023579851,0.010310511680557872,0.010401644579994082,0.010476806679829455,0.010535641380644178,0.010577868343790443,0.010603285716462409,0.010611771738992004,0.010603285716462409,0.010577868343790443,0.010535641380644178,0.010476806679829455,0.01040164457999408,0.01031051168055787,0.01020383802357985,0.01008212371372424,0.009945935013494514,0.0097958999563872561,0.0096327035255013883,0.0094570824493606601,0.0092698196702159178,0.0090717385428491643,0.0088636968238760116,0.008646580512722787,0.0084212976058370432,0.0081887718252871312,0.0079499363817403385,0.0077057278299148477,0.0074570800720236774,0.0072049185615233376,0.0069501547557098723,0.0066936808614399068,0.0064363649135706991,0.0061790462206905558,0.0059225312074321435,0.0056675896772098106,0.0054149515136814007,0.005165303833686628,0.004919288598936325,0.0046775006883938127,0.0044404864281697336,0.0042087425709073454,0.0039827157121213163,0.0037628021268170018,0.003549348005997835,0.003342650069396734,0.0031429565279652207,0.0029504683673348335,0.0027653409216349166,0.0025876857057063325,0.0024175724728821841,0.002255031465097662,0.0021000558221187836,0.0019526041171160659,0.0018126029866214236,0.0016799498240586746,0.0015545155074906871,0.0014361471339387648],[0.0013525124357521971,0.0014639875718614492,0.001582117162499559,0.0017070452062689419,0.0018388933056304956,0.001977758091818584,0.0021237086559455064,0.0022767840123300107,0.0024369906216971538,0.0026043000032649451,0.0027786464658181701,0.0029599249886347371,0.0031479892835407732,0.0033426500693967353,0.0035436735899316341,0.0037507804050245916,0.0039636444842667297,0.0041818926299124603,0.0044051042541452048,0.0046328115329435839,0.0048644999557528219,0.0050996092866634878,0.0053375349489044018,0.0055776298402054926,0.0058192065820241584,0.0060615402008069351,0.0063038712344357685,0.0065454092518494591,0.006785336768605525,0.0070228135359297764,0.0072569811756669255,0.0074869681285741436,0.0077118948786693772,0.0079308794119352776,0.0081430428636630348,0.0083475153051697833,0.0085434416176045982,0.0087299873981309915,0.008906344841989931,0.009071738542849166,0.009225431153465009,0.0093667288490429119,0.0094949865367942032,0.0096096127570459034,0.0097100742238555356,0.0097958999563872596,0.0098666849562819309,0.0099220933908532767,0.0099618612471053993,0.009985798427224751,0.0099937902622743192,0.009985798427224751,0.0099618612471053993,0.0099220933908532767,0.0098666849562819309,0.0097958999563872579,0.0097100742238555339,0.0096096127570459034,0.009494986536794205,0.0093667288490429119,0.009225431153465009,0.009071738542849166,0.008906344841989931,0.0087299873981309915,0.0085434416176045982,0.0083475153051697833,0.0081430428636630331,0.0079308794119352759,0.0077118948786693755,0.0074869681285741419,0.0072569811756669237,0.0070228135359297773,0.006785336768605525,0.0065454092518494591,0.0063038712344357685,0.0060615402008069351,0.0058192065820241584,0.0055776298402054926,0.0053375349489044018,0.0050996092866634878,0.0048644999557528211,0.0046328115329435822,0.0044051042541452031,0.0041818926299124577,0.0039636444842667297,0.0037507804050245916,0.0035436735899316341,0.0033426500693967353,0.0031479892835407732,0.0029599249886347371,0.0027786464658181701,0.0026043000032649451,0.0024369906216971525,0.0022767840123300099,0.0021237086559455056,0.0019777580918185832,0.0018388933056304963,0.0017070452062689419,0.001582117162499559,0.0014639875718614492,0.0013525124357521971],[0.0012737482432230646,0.0013787315727872352,0.0014899818316170329,0.0016076346324890984,0.0017318044962883017,0.0018625824268840032,0.0020000334918353524,0.0021441944334440479,0.0022950713361918093,0.0024526373778882694,0.0026168306928767713,0.0027875523763659571,0.0029646646593419908,0.0031479892835407745,0.0033373061055967873,0.0035323519587149256,0.0037328197990192384,0.0039383581621089177,0.0041485709532950504,0.0043630175925063446,0.0045812135319501564,0.0048026311613165451,0.0050267011116445831,0.0052528139649667153,0.0054803223725503744,0.0057085435800151192,0.0059367623528735671,0.0061642342911860347,0.0063901895170978386,0.0066138367141140575,0.0068343674921316384,0.0070509610475667671,0.0072627890834608255,0.0074690209502941505,0.0076688289644541658,0.0078613938579606014,0.008045910310207658,0.0082215925101972072,0.0083876796960571307,0.0085434416176046017,0.0086881838673565758,0.0088212530257290294,0.008942041567212719,0.0090499924760645868,0.0091446035224977493,0.0092254311534650142,0.0092920939558755813,0.009344275654416298,0.0093817276110112237,0.0094042707982816467,0.0094117972250895854,0.0094042707982816467,0.0093817276110112237,0.009344275654416298,0.0092920939558755813,0.0092254311534650125,0.0091446035224977476,0.0090499924760645851,0.008942041567212719,0.0088212530257290294,0.0086881838673565758,0.0085434416176046017,0.0083876796960571307,0.0082215925101972072,0.008045910310207658,0.0078613938579606014,0.0076688289644541649,0.0074690209502941488,0.0072627890834608246,0.0070509610475667653,0.0068343674921316367,0.0066138367141140584,0.0063901895170978386,0.0061642342911860347,0.0059367623528735671,0.0057085435800151192,0.0054803223725503744,0.0052528139649667153,0.0050267011116445831,0.0048026311613165451,0.0045812135319501564,0.0043630175925063429,0.0041485709532950487,0.0039383581621089151,0.0037328197990192384,0.0035323519587149256,0.0033373061055967873,0.0031479892835407745,0.0029646646593419908,0.0027875523763659571,0.0026168306928767713,0.0024526373778882694,0.0022950713361918084,0.002144194433444047,0.0020000334918353515,0.0018625824268840025,0.0017318044962883023,0.0016076346324890984,0.0014899818316170329,0.0013787315727872352,0.0012737482432230646],[0.001199570920182725,0.0012984404965838473,0.0014032120447018187,0.00151401327983998,0.0016309520537060563,0.0017541140705166303,0.0018835606085911957,0.0020193262705263748,0.0021614167864712564,0.0023098068962382396,0.0024644383369460377,0.0026252179635699482,0.002792016030138914,0.0029646646593419891,0.003142956527965222,0.0033266437948545674,0.0035154372969773999,0.0037090060376262215,0.0039069769888710731,0.0041089352280266065,0.0043144244251668859,0.0045229476956144526,0.0047339688278753827,0.0049469138937217041,0.005161173243076223,0.0053761038820782925,0.0055910322282544979,0.0058052572321428443,0.006018053850084598,0.0062286768482700018,0.0064363649135707,0.0066403450422824178,0.0068398371737062539,0.0070340590315847483,0.0072222311328465506,0.0074035819199643393,0.0075773529705534075,0.0077428042356856202,0.0078992192568113108,0.0080459103102076528,0.0081822234275352561,0.0083075432414043381,0.0084212976058370449,0.0085229619431619209,0.0086120632711779652,0.0086881838673565706,0.0087509645303761787,0.0088001074033640103,0.0088353783277984477,0.0088566087020436803,0.0088636968238760151,0.0088566087020436803,0.0088353783277984477,0.0088001074033640103,0.0087509645303761787,0.0086881838673565689,0.0086120632711779634,0.0085229619431619191,0.0084212976058370467,0.0083075432414043381,0.0081822234275352561,0.0080459103102076528,0.0078992192568113108,0.0077428042356856202,0.0075773529705534075,0.0074035819199643393,0.0072222311328465488,0.0070340590315847475,0.0068398371737062522,0.0066403450422824169,0.0064363649135706991,0.0062286768482700027,0.006018053850084598,0.0058052572321428443,0.0055910322282544979,0.0053761038820782925,0.005161173243076223,0.0049469138937217041,0.0047339688278753827,0.0045229476956144526,0.0043144244251668851,0.0041089352280266056,0.0039069769888710713,0.0037090060376262189,0.0035154372969773999,0.0033266437948545674,0.003142956527965222,0.0029646646593419891,0.002792016030138914,0.0026252179635699482,0.0024644383369460377,0.0023098068962382396,0.0021614167864712555,0.002019326270526374,0.0018835606085911953,0.0017541140705166296,0.0016309520537060569,0.00151401327983998,0.0014032120447018187,0.0012984404965838473,0.001199570920182725],[0.0011297133481471126,0.0012228252086521878,0.0013214953367984088,0.0014258440103288579,0.0015359728001567573,0.0016519624194736631,0.0017738705780275519,0.0019017298633166929,0.0020355456717922695,0.0021752942143054878,0.0023209206209411277,0.0024723371710184444,0.0026294216743835211,0.0027920160301389153,0.0029599249886347384,0.0031329151418621483,0.0033107141663325946,0.0034930103410862222,0.0036794523616485602,0.0038696494685503675,0.0040631719064517843,0.0042595517269862996,0.0044582839451864338,0.0046588280558022624,0.0048606099120131856,0.0050630239650059344,0.0052654358586966023,0.0054671853695655954,0.0056675896772098158,0.005865946946858009,0.006061540200806936,0.006253641451583582,0.0064415160656876788,0.0066244273230844858,0.0068016411342628749,0.0069724308737079957,0.0071360822861164545,0.0072918984196546164,0.0074392045390706237,0.0075773529705534109,0.0077057278299148563,0.0078237495859721368,0.0079308794119352793,0.0080266232791581914,0.0081105357497789597,0.0081822234275352596,0.0082413480293620292,0.0082876290442204046,0.0083208459499194871,0.0083408399634183686,0.0083475153051697851,0.0083408399634183686,0.0083208459499194871,0.0082876290442204046,0.0082413480293620292,0.0081822234275352578,0.008110535749778958,0.0080266232791581897,0.0079308794119352793,0.0078237495859721368,0.0077057278299148563,0.0075773529705534109,0.0074392045390706237,0.0072918984196546164,0.0071360822861164545,0.0069724308737079957,0.0068016411342628732,0.006624427323084485,0.0064415160656876779,0.0062536414515835812,0.0060615402008069351,0.0058659469468580099,0.0056675896772098158,0.0054671853695655954,0.0052654358586966023,0.0050630239650059344,0.0048606099120131856,0.0046588280558022624,0.0044582839451864338,0.0042595517269862996,0.0040631719064517834,0.0038696494685503667,0.0036794523616485589,0.00349301034108622,0.0033107141663325946,0.0031329151418621483,0.0029599249886347384,0.0027920160301389153,0.0026294216743835211,0.0024723371710184444,0.0023209206209411277,0.0021752942143054878,0.0020355456717922687,0.001901729863316692,0.0017738705780275513,0.0016519624194736625,0.0015359728001567579,0.0014258440103288579,0.0013214953367984088,0.0012228252086521878,0.0011297133481471126],[0.0010639239644016649,0.0011516134122813888,0.0012445374394937127,0.0013428093193512511,0.0014465247077377205,0.0015557596174743207,0.0016705683975549383,0.0017909817377296815,0.0019170047201848819,0.0020486149411439213,0.0021857607260666848,0.0023283594627271855,0.0024762960767721102,0.0026294216743835202,0.0027875523763659558,0.0029504683673348352,0.0031179131826869792,0.0032895932546780221,0.0034651777372134169,0.0036442986268838714,0.0038265511953521855,0.0040114947454432314,0.0041986537002246449,0.0043875190310218278,0.0045775500267220721,0.0047681764029296851,0.0049588007455831822,0.005148801279587569,0.0053375349489044027,0.005524340790437678,0.0057085435800151149,0.0058894577248537342,0.0060663913731777994,0.0062386507081874116,0.0064055443904165133,0.0065663881097260237,0.0067205092058032793,0.006867251314129747,0.0070059789929756691,0.007136082286116451,0.0072569811756669263,0.0073681298797130049,0.0074690209502941453,0.0075591891287528842,0.0076382149175089533,0.007705727829914852,0.0077614092829775948,0.0078049951013494986,0.0078362776050523077,0.0078551072578495577,0.0078613938579605962,0.0078551072578495577,0.0078362776050523077,0.0078049951013494986,0.0077614092829775948,0.0077057278299148511,0.0076382149175089516,0.0075591891287528825,0.0074690209502941462,0.0073681298797130049,0.0072569811756669263,0.007136082286116451,0.0070059789929756691,0.006867251314129747,0.0067205092058032793,0.0065663881097260237,0.0064055443904165125,0.0062386507081874099,0.0060663913731777977,0.0058894577248537324,0.005708543580015114,0.0055243407904376788,0.0053375349489044027,0.005148801279587569,0.0049588007455831822,0.0047681764029296851,0.0045775500267220721,0.0043875190310218278,0.0041986537002246449,0.0040114947454432314,0.003826551195352185,0.0036442986268838701,0.003465177737213416,0.0032895932546780199,0.0031179131826869792,0.0029504683673348352,0.0027875523763659558,0.0026294216743835202,0.0024762960767721102,0.0023283594627271855,0.0021857607260666848,0.0020486149411439213,0.0019170047201848811,0.0017909817377296806,0.0016705683975549379,0.00155575961747432,0.0014465247077377209,0.0013428093193512511,0.0012445374394937127,0.0011516134122813888,0.0010639239644016649],[0.0010019658561038391,0.0010845486680865477,0.001172061221232932,0.0012646101923314138,0.0013622856667007065,0.0014651592305199132,0.001573282067743913,0.0016866830808909014,0.0018053670561837193,0.0019293128945401291,0.0020584719307109611,0.0021927663634317405,0.0023320878197577921,0.002476296076772111,0.0026252179635699495,0.0027786464658181719,0.0029363400542493849,0.0030980222571737395,0.0032633814954733174,0.0034320711965890086,0.0036037102017271016,0.0037778834779180108,0.0039541431436738439,0.0041320098138422886,0.0043109742658744791,0.0044904994261524972,0.0046700226713013724,0.0048489584355887712,0.0050267011116445839,0.0052026282278669822,0.0053761038820782942,0.0055464824073110297,0.0057131122421003018,0.0058753399743911626,0.0060325145251938113,0.0061839914354892877,0.0063291372176519775,0.0064673337308572233,0.0065979825386207778,0.006720509205803281,0.0068343674921316384,0.0069390433995560876,0.0070340590315847509,0.0071189762241150858,0.0071933999092040728,0.0072569811756669289,0.0073094199933398558,0.0073504675712497596,0.0073799283237587828,0.0073976614229429392,0.0074035819199643419,0.0073976614229429392,0.0073799283237587828,0.0073504675712497596,0.0073094199933398558,0.0072569811756669281,0.0071933999092040719,0.0071189762241150849,0.0070340590315847518,0.0069390433995560876,0.0068343674921316384,0.006720509205803281,0.0065979825386207778,0.0064673337308572233,0.0063291372176519775,0.0061839914354892877,0.0060325145251938104,0.0058753399743911618,0.005713112242100301,0.0055464824073110288,0.0053761038820782934,0.005202628227866983,0.0050267011116445839,0.0048489584355887712,0.0046700226713013724,0.0044904994261524972,0.0043109742658744791,0.0041320098138422886,0.0039541431436738439,0.0037778834779180108,0.0036037102017271012,0.0034320711965890073,0.0032633814954733161,0.0030980222571737374,0.0029363400542493849,0.0027786464658181719,0.0026252179635699495,0.002476296076772111,0.0023320878197577921,0.0021927663634317405,0.0020584719307109611,0.0019293128945401291,0.0018053670561837185,0.0016866830808909008,0.0015732820677439123,0.0014651592305199128,0.001362285666700707,0.0012646101923314138,0.001172061221232932,0.0010845486680865477,0.0010019658561038391],[0.00094361590714097407,0.0010213894705499451,0.0011038056893466165,0.0011909650279468805,0.0012829523255088976,0.0013798349993572423,0.0014816612527253077,0.0015884583049796627,0.0017002306636152277,0.0018169584582646606,0.0019385958577222754,0.0020650695915165212,0.0021962775978517034,0.0023320878197577908,0.0024723371710184436,0.0026168306928767704,0.0027653409216349179,0.0029176074860608465,0.0030733369519918953,0.0032322029296835801,0.0033938464573023209,0.003557876671517093,0.0037238717734273505,0.0038913802950987187,0.0040599226687949757,0.0042289930976308412,0.0043980617228660014,0.0045665770794616652,0.0047339688278753836,0.0048996507464293916,0.0050630239650059309,0.0052234804173545103,0.0053804064859960497,0.0055331868106313822,0.0056812082281593517,0.0058238638099325545,0.005960556959772721,0.0060907055345744282,0.0062137459480812104,0.006329137217651974,0.0064363649135707008,0.0065349449707037951,0.0066244273230844815,0.0067043993233010966,0.0067744889103765471,0.0068343674921316341,0.0068837525107990878,0.006922409663864172,0.0069501547557098732,0.0069668551595920428,0.0069724308737079913,0.0069668551595920428,0.0069501547557098732,0.006922409663864172,0.0068837525107990878,0.0068343674921316332,0.0067744889103765462,0.0067043993233010957,0.0066244273230844824,0.0065349449707037951,0.0064363649135707008,0.006329137217651974,0.0062137459480812104,0.0060907055345744282,0.005960556959772721,0.0058238638099325545,0.0056812082281593509,0.0055331868106313813,0.0053804064859960489,0.0052234804173545086,0.00506302396500593,0.0048996507464293933,0.0047339688278753836,0.0045665770794616652,0.0043980617228660014,0.0042289930976308412,0.0040599226687949757,0.0038913802950987187,0.0037238717734273505,0.003557876671517093,0.0033938464573023204,0.0032322029296835792,0.003073336951991894,0.0029176074860608448,0.0027653409216349179,0.0026168306928767704,0.0024723371710184436,0.0023320878197577908,0.0021962775978517034,0.0020650695915165212,0.0019385958577222754,0.0018169584582646606,0.0017002306636152268,0.0015884583049796618,0.0014816612527253073,0.0013798349993572416,0.001282952325508898,0.0011909650279468805,0.0011038056893466165,0.0010213894705499451,0.00094361590714097407],[0.00088866399467129741,0.00096190837834033219,0.0010395250501951568,0.0011216086240595459,0.0012082389984437144,0.0012994796645928958,0.0013953760186027036,0.0014959536947071986,0.001601216937905233,0.0017111470349895743,0.0018257008237561757,0.0019448093006735722,0.0020683763475623442,0.0021962775978517039,0.0023283594627271859,0.0024644383369460386,0.002604300003264946,0.0027476992532920064,0.0028943597411398847,0.0030439740845231,0.0031962042259178762,0.0033506820641015754,0.0035070103638293591,0.0036647639486125823,0.0038234911785658197,0.0039827157121213172,0.0041419385471096384,0.0043006403333157375,0.0044582839451864347,0.0046143172999367939,0.004768176402929686,0.0049192885989363284,0.0050670760047777383,0.0052109590959487822,0.0053503604171874896,0.0054847083846193195,0.0056134411451227058,0.0057360104569674905,0.0058518855546057184,0.0059605569597727228,0.006061540200806936,0.0061543794023335933,0.0062386507081874116,0.0063139655016712119,0.006379973388952436,0.0064363649135707026,0.0064828739726421059,0.0065192799083681396,0.0065454092518494583,0.0065611370999222197,0.0065663881097260245,0.0065611370999222197,0.0065454092518494583,0.0065192799083681396,0.0064828739726421059,0.0064363649135707017,0.0063799733889524351,0.006313965501671211,0.0062386507081874125,0.0061543794023335933,0.006061540200806936,0.0059605569597727228,0.0058518855546057184,0.0057360104569674905,0.0056134411451227058,0.0054847083846193195,0.0053503604171874887,0.0052109590959487813,0.0050670760047777375,0.0049192885989363276,0.0047681764029296851,0.0046143172999367947,0.0044582839451864347,0.0043006403333157375,0.0041419385471096384,0.0039827157121213172,0.0038234911785658197,0.0036647639486125823,0.0035070103638293591,0.0033506820641015754,0.0031962042259178758,0.0030439740845230991,0.0028943597411398838,0.0027476992532920047,0.002604300003264946,0.0024644383369460386,0.0023283594627271859,0.0021962775978517039,0.0020683763475623442,0.0019448093006735722,0.0018257008237561757,0.0017111470349895743,0.0016012169379052324,0.001495953694707198,0.0013953760186027032,0.0012994796645928953,0.0012082389984437148,0.0011216086240595459,0.0010395250501951568,0.00096190837834033219,0.00088866399467129741],[0.00083691223245473004,0.00090589119527846433,0.00097898782404618498,0.0010562912227015096,0.001137876636827645,0.0012238038602275449,0.0013141156453340217,0.0014088361335595591,0.0015079693226935213,0.0016114975893010272,0.0017193802847491142,0.0018315524239591564,0.0019479234862387438,0.002068376347562345,0.0021927663634317414,0.0023209206209411286,0.0024526373778882699,0.002587685705706336,0.0027258053516396315,0.002866706833953439,0.0030100717820615544,0.0031555535312877293,0.003302777979566884,0.0034513447107614994,0.0036008283864455305,0.0037507804050245929,0.0039007308239533312,0.0040501905376187051,0.0041986537002246483,0.0043456003797847061,0.0044904994261524981,0.0046328115329435857,0.0047719924702754463,0.0049074964625228047,0.0050387796828002046,0.005165303833686634,0.0052865397818391184,0.0054019712126403647,0.0055110982699216595,0.0056134411451227075,0.0057085435800151201,0.005795976247339206,0.0058753399743911635,0.0059462687757484284,0.006008432662926712,0.0060615402008069386,0.0061053407831307615,0.0061396266022094876,0.0061642342911860338,0.0061790462206905618,0.0061839914354892885,0.0061790462206905618,0.0061642342911860338,0.0061396266022094876,0.0061053407831307615,0.0060615402008069377,0.0060084326629267111,0.0059462687757484275,0.0058753399743911644,0.005795976247339206,0.0057085435800151201,0.0056134411451227075,0.0055110982699216595,0.0054019712126403647,0.0052865397818391184,0.005165303833686634,0.0050387796828002037,0.0049074964625228038,0.0047719924702754454,0.0046328115329435848,0.0044904994261524972,0.004345600379784707,0.0041986537002246483,0.0040501905376187051,0.0039007308239533312,0.0037507804050245929,0.0036008283864455305,0.0034513447107614994,0.003302777979566884,0.0031555535312877293,0.003010071782061554,0.0028667068339534381,0.0027258053516396306,0.0025876857057063342,0.0024526373778882699,0.0023209206209411286,0.0021927663634317414,0.002068376347562345,0.0019479234862387438,0.0018315524239591564,0.0017193802847491142,0.0016114975893010272,0.0015079693226935206,0.0014088361335595585,0.0013141156453340213,0.0012238038602275444,0.0011378766368276454,0.0010562912227015096,0.00097898782404618498,0.00090589119527846433,0.00083691223245473004],[0.00078817425824868079,0.00085313619899950015,0.00092197601149751347,0.00099477761067662263,0.0010716118601584001,0.0011525350716257963,0.0012375875078037583,0.001326791904218354,0.0014201520258458188,0.0015176512755602223,0.0016192513719207014,0.0017248911142849943,0.0018344852534754334,0.0019479234862387429,0.0020650695915165221,0.0021857607260666861,0.0023098068962382401,0.0024369906216971538,0.0025670668056283451,0.0026997628244009374,0.0028347788478883069,0.0029717883995933158,0.0031104391634591325,0.003250354041768766,0.0033911324658777958,0.0035323519587149238,0.0036735699450581093,0.0038143258025878151,0.0039541431436738439,0.0040925323148114758,0.0042289930976308421,0.004363017592506342,0.0044940932630365008,0.0046217061170941379,0.0047453439978061215,0.0048644999557528219,0.0049786756719182911,0.0050873848995077889,0.0051901568917097291,0.005286539781839115,0.0053761038820782942,0.0054584448672407894,0.005533186810631383,0.0055999850401592969,0.0056585287843735378,0.0057085435800151166,0.0057497934149980303,0.0057820825834112603,0.0058052572321428443,0.0058192065820241584,0.0058238638099325554,0.0058192065820241584,0.0058052572321428443,0.0057820825834112603,0.0057497934149980303,0.0057085435800151157,0.005658528784373537,0.0055999850401592961,0.0055331868106313839,0.0054584448672407894,0.0053761038820782942,0.005286539781839115,0.0051901568917097291,0.0050873848995077889,0.0049786756719182911,0.0048644999557528219,0.0047453439978061207,0.0046217061170941371,0.0044940932630364999,0.0043630175925063411,0.0042289930976308412,0.0040925323148114767,0.0039541431436738439,0.0038143258025878151,0.0036735699450581093,0.0035323519587149238,0.0033911324658777958,0.003250354041768766,0.0031104391634591325,0.0029717883995933158,0.0028347788478883065,0.0026997628244009365,0.0025670668056283442,0.0024369906216971521,0.0023098068962382401,0.0021857607260666861,0.0020650695915165221,0.0019479234862387429,0.0018344852534754334,0.0017248911142849943,0.0016192513719207014,0.0015176512755602223,0.0014201520258458184,0.0013267919042183533,0.0012375875078037579,0.0011525350716257959,0.0010716118601584005,0.00099477761067662263,0.00092197601149751347,0.00085313619899950015,0.00078817425824868079],[0.00074227456270268037,0.00080345341453460335,0.00086828430844382201,0.00093684627253892325,0.0010092060436654253,0.0010854166541691573,0.0011655160220564998,0.0012495255588395558,0.0013374488102394142,0.0014292701456715135,0.0015249535130325549,0.0016244412757282234,0.0017276531491064746,0.0018344852534754343,0.0019448093006735731,0.0020584719307109624,0.0021752942143054886,0.0022950713361918093,0.0024175724728821867,0.0025425408771100441,0.0026696941794960263,0.0027987249160540814,0.002929301288017272,0.0030610681581300409,0.003193648285049807,0.0033266437948545691,0.0034596378858967659,0.0035921967604124806,0.0037238717734273544,0.0038542017866368969,0.0039827157121213189,0.0041089352280266091,0.0042323776457476861,0.0043525589057286313,0.0044689966767906984,0.0045812135319501573,0.0046887401720313773,0.0047911186670485046,0.0048879056843500893,0.0049786756719182928,0.0050630239650059361,0.0051405697844923602,0.005210959095948783,0.0052738672994243931,0.0053290017213885928,0.005376103882078296,0.0054149515136814068,0.0054453603073119161,0.0054671853695655954,0.0054803223725503744,0.0054847083846193212,0.0054803223725503744,0.0054671853695655954,0.0054453603073119161,0.0054149515136814068,0.0053761038820782951,0.005329001721388592,0.0052738672994243922,0.0052109590959487839,0.0051405697844923602,0.0050630239650059361,0.0049786756719182928,0.0048879056843500893,0.0047911186670485046,0.0046887401720313773,0.0045812135319501573,0.0044689966767906975,0.0043525589057286304,0.0042323776457476852,0.0041089352280266082,0.003982715712121318,0.0038542017866368978,0.0037238717734273544,0.0035921967604124806,0.0034596378858967659,0.0033266437948545691,0.003193648285049807,0.0030610681581300409,0.002929301288017272,0.0027987249160540814,0.0026696941794960259,0.0025425408771100433,0.0024175724728821859,0.002295071336191808,0.0021752942143054886,0.0020584719307109624,0.0019448093006735731,0.0018344852534754343,0.0017276531491064746,0.0016244412757282234,0.0015249535130325549,0.0014292701456715135,0.0013374488102394135,0.0012495255588395552,0.0011655160220564993,0.0010854166541691568,0.0010092060436654258,0.00093684627253892325,0.00086828430844382201,0.00080345341453460335,0.00074227456270268037],[0.00069904785733514163,0.00075666393019585239,0.00081771936676011756,0.00088228859289776046,0.00095043445900297365,0.0010222069090581917,0.0010976416528970078,0.0011767588551221313,0.0012595618549679295,0.0013460359321042232,0.0014361471339387648,0.0015298411803711914,0.0016270424621636166,0.0017276531491064735,0.0018315524239591555,0.0019385958577222762,0.0020486149411439222,0.0021614167864712568,0.0022767840123300103,0.0023944748232504259,0.0025142232937656575,0.0026357398651982861,0.0027587120612373233,0.0028828054262109316,0.0030076646876020657,0.0031329151418621466,0.0032581642599819622,0.003383003506612707,0.0035070103638293595,0.0036297505479316733,0.0037507804050245903,0.0038696494685503654,0.0039859031594999678,0.0040990856077514903,0.0042087425709073471,0.0043144244251668859,0.0044156892012108574,0.00451210563681972,0.0046032562170257568,0.0046887401720313747,0.004768176402929686,0.004841206305449727,0.0049074964625228012,0.0049667411774276318,0.0050186648206131841,0.0050630239650059326,0.0050996092866634887,0.0051282472100137848,0.0051488012795875681,0.0051611732430762239,0.0051653038336866306,0.0051611732430762239,0.0051488012795875681,0.0051282472100137848,0.0050996092866634887,0.0050630239650059318,0.0050186648206131832,0.0049667411774276318,0.0049074964625228021,0.004841206305449727,0.004768176402929686,0.0046887401720313747,0.0046032562170257568,0.00451210563681972,0.0044156892012108574,0.0043144244251668859,0.0042087425709073463,0.0040990856077514895,0.0039859031594999678,0.0038696494685503649,0.0037507804050245898,0.0036297505479316742,0.0035070103638293595,0.003383003506612707,0.0032581642599819622,0.0031329151418621466,0.0030076646876020657,0.0028828054262109316,0.0027587120612373233,0.0026357398651982861,0.0025142232937656571,0.002394474823250425,0.0022767840123300094,0.0021614167864712551,0.0020486149411439222,0.0019385958577222762,0.0018315524239591555,0.0017276531491064735,0.0016270424621636166,0.0015298411803711914,0.0014361471339387648,0.0013460359321042232,0.0012595618549679289,0.0011767588551221308,0.0010976416528970074,0.0010222069090581912,0.00095043445900297398,0.00088228859289776046,0.00081771936676011756,0.00075666393019585239,0.00069904785733514163],[0.00065833847931629831,0.00071259925330092165,0.00077009909803964953,0.0008309081051770628,0.00089508546498533355,0.00096267821293578469,0.0010337199792831947,0.0011082297543352289,0.0011862106828643836,0.0012676489017857738,0.0013525124357521969,0.0014407501656902521,0.0015322908855012866,0.001627042462163617,0.0017248911142849948,0.0018257008237561765,0.0019293128945401293,0.0020355456717922695,0.002144194433444047,0.0022550314650976642,0.0023678063275798687,0.0024822463247978752,0.00259805717764441,0.0027149239076296799,0.0028325119316973753,0.0029504683673348357,0.0030684235446427825,0.0031859927195189951,0.003302777979566884,0.0034183703318000449,0.0035323519587149243,0.0036442986268838723,0.0037537822299184721,0.0038603734455059904,0.0039636444842667306,0.0040631719064517843,0.0041585394810313486,0.0042493410605423847,0.0043351834441960569,0.0044156892012108592,0.0044904994261524981,0.0045592763982369878,0.0046217061170941379,0.0046775006883938179,0.0047264005340004536,0.0047681764029296868,0.0048026311613165451,0.0048296013418433585,0.0048489584355887703,0.0048606099120131856,0.0048644999557528228,0.0048606099120131856,0.0048489584355887703,0.0048296013418433585,0.0048026311613165451,0.0047681764029296868,0.0047264005340004536,0.004677500688393817,0.0046217061170941388,0.0045592763982369878,0.0044904994261524981,0.0044156892012108592,0.0043351834441960569,0.0042493410605423847,0.0041585394810313486,0.0040631719064517843,0.0039636444842667297,0.0038603734455059896,0.0037537822299184712,0.0036442986268838714,0.0035323519587149234,0.0034183703318000453,0.003302777979566884,0.0031859927195189951,0.0030684235446427825,0.0029504683673348357,0.0028325119316973753,0.0027149239076296799,0.00259805717764441,0.0024822463247978752,0.0023678063275798683,0.0022550314650976637,0.0021441944334440466,0.0020355456717922682,0.0019293128945401293,0.0018257008237561765,0.0017248911142849948,0.001627042462163617,0.0015322908855012866,0.0014407501656902521,0.0013525124357521969,0.0012676489017857738,0.0011862106828643831,0.0011082297543352285,0.0010337199792831942,0.00096267821293578436,0.00089508546498533387,0.0008309081051770628,0.00077009909803964953,0.00071259925330092165,0.00065833847931629831],[0.00061999983091387686,0.00067110070341742608,0.0007252520178789608,0.000782519784123448,0.00084295974544995264,0.00090661619819718692,0.00097352081414635652,0.0010436914776957029,0.0011171311504804288,0.0011938267767388638,0.0012737482432230633,0.0013568474078027087,0.0014430572110995139,0.0015322908855012857,0.0016244412757282223,0.0017193802847491133,0.0018169584582646608,0.0019170047201848819,0.0020193262705263744,0.002123708655945506,0.0022299160217110867,0.0023376915523144852,0.0024467581061294965,0.0025568190475855905,0.002667559278226797,0.0027786464658181701,0.0028897324683594358,0.0030004549475006171,0.0031104391634591325,0.0032192999411459009,0.0033266437948545661,0.003432071196589006,0.003535178970936009,0.0036355627973679661,0.0037328197990192358,0.003826551195352185,0.0039163649947451694,0.0040018787019220937,0.0040827220143254545,0.004158539481031346,0.0042289930976308412,0.0042937648106673278,0.0043525589057286278,0.004405104254145204,0.0044511563944352791,0.0044904994261524955,0.0045229476956144526,0.0045483472550989701,0.0045665770794616643,0.0045775500267220713,0.004581213531950153,0.0045775500267220713,0.0045665770794616643,0.0045483472550989701,0.0045229476956144526,0.0044904994261524946,0.0044511563944352791,0.0044051042541452031,0.0043525589057286287,0.0042937648106673278,0.0042289930976308412,0.004158539481031346,0.0040827220143254545,0.0040018787019220937,0.0039163649947451694,0.003826551195352185,0.003732819799019235,0.0036355627973679657,0.0035351789709360086,0.0034320711965890056,0.0033266437948545656,0.0032192999411459018,0.0031104391634591325,0.0030004549475006171,0.0028897324683594358,0.0027786464658181701,0.002667559278226797,0.0025568190475855905,0.0024467581061294965,0.0023376915523144852,0.0022299160217110867,0.0021237086559455051,0.002019326270526374,0.0019170047201848806,0.0018169584582646608,0.0017193802847491133,0.0016244412757282223,0.0015322908855012857,0.0014430572110995139,0.0013568474078027087,0.0012737482432230633,0.0011938267767388638,0.0011171311504804284,0.0010436914776957025,0.0009735208141463562,0.00090661619819718659,0.00084295974544995296,0.000782519784123448,0.0007252520178789608,0.00067110070341742608,0.00061999983091387686],[0.00058389385158292065,0.00063201884094197375,0.00068301662834881509,0.00073694937951546634,0.00079386959150397199,0.00085381898103509897,0.00091682737546910204,0.00098291161769794937,0.0010520744968846368,0.0011243037175758636,0.001199570920182725,0.0012778307661543155,0.0013590201013465211,0.0014430572110995146,0.001529841180371192,0.0016192513719207023,0.0017111470349895749,0.0018053670561837193,0.0019017298633166924,0.002000033491835352,0.0021000558221187862,0.0022015549944292907,0.0023042700066125258,0.0024079214978087677,0.002512212719467596,0.0026168306928767713,0.0027214475502477854,0.0028257220541734714,0.002929301288017272,0.0030318225075410704,0.0031329151418621475,0.0032322029296835814,0.0033293061747003967,0.0034238441021794911,0.0035154372969774012,0.0036037102017271016,0.003688293652621865,0.0037688274291764012,0.0038449627935753577,0.0039163649947451711,0.0039827157121213189,0.0040437154142385781,0.0040990856077514912,0.0041485709532950495,0.0041919412257158889,0.0042289930976308438,0.0042595517269862996,0.0042834721312774819,0.0043006403333157375,0.0043109742658744791,0.0043144244251668868,0.0043109742658744791,0.0043006403333157375,0.0042834721312774819,0.0042595517269862996,0.004228993097630843,0.0041919412257158889,0.0041485709532950495,0.0040990856077514921,0.0040437154142385781,0.0039827157121213189,0.0039163649947451711,0.0038449627935753577,0.0037688274291764012,0.003688293652621865,0.0036037102017271016,0.0035154372969774007,0.0034238441021794907,0.0033293061747003963,0.003232202929683581,0.0031329151418621466,0.0030318225075410708,0.002929301288017272,0.0028257220541734714,0.0027214475502477854,0.0026168306928767713,0.002512212719467596,0.0024079214978087677,0.0023042700066125258,0.0022015549944292907,0.0021000558221187858,0.0020000334918353515,0.0019017298633166918,0.0018053670561837183,0.0017111470349895749,0.0016192513719207023,0.001529841180371192,0.0014430572110995146,0.0013590201013465211,0.0012778307661543155,0.001199570920182725,0.0011243037175758636,0.0010520744968846364,0.00098291161769794894,0.00091682737546910171,0.00085381898103509865,0.00079386959150397232,0.00073694937951546634,0.00068301662834881509,0.00063201884094197375,0.00058389385158292065],[0.00054989052079869999,0.00059521292895617567,0.00064324083642720831,0.00069403278867458497,0.00074763822556945657,0.00080409643443989879,0.00086343550563593011,0.00092567130119584906,0.00099080644785444353,0.0010588293661898704,0.0011297133481471123,0.0012034156954869226,0.0012798769318762254,0.0013590201013465215,0.0014407501656902527,0.0015249535130325558,0.0016114975893010278,0.0017002306636152292,0.0017909817377296825,0.0018835606085911975,0.0019777580918185853,0.0020733464124887751,0.00217007976802962,0.0022676950662913605,0.0023659128400138184,0.0024644383369460399,0.0025629627828331028,0.0026611648123874058,0.0027587120612373264,0.0028552629097246445,0.0029504683673348365,0.0030439740845231013,0.0031354224767758797,0.0032244549439542506,0.0033107141663325959,0.0033938464573023239,0.0034735041514831772,0.003549348005997838,0.0036210495919402883,0.0036882936526218663,0.0037507804050245942,0.003808227761037833,0.0038603734455059913,0.0039069769888710765,0.0039478215732489099,0.0039827157121213198,0.0040114947454432358,0.0040340221338336672,0.0040501905376187051,0.0040599226687949791,0.0040631719064517851,0.0040599226687949791,0.0040501905376187051,0.0040340221338336672,0.0040114947454432358,0.0039827157121213198,0.0039478215732489091,0.0039069769888710757,0.0038603734455059922,0.003808227761037833,0.0037507804050245942,0.0036882936526218663,0.0036210495919402883,0.003549348005997838,0.0034735041514831772,0.0033938464573023239,0.003310714166332595,0.0032244549439542497,0.0031354224767758789,0.0030439740845231008,0.0029504683673348361,0.0028552629097246453,0.0027587120612373264,0.0026611648123874058,0.0025629627828331028,0.0024644383369460399,0.0023659128400138184,0.0022676950662913605,0.00217007976802962,0.0020733464124887751,0.0019777580918185853,0.0018835606085911968,0.0017909817377296821,0.0017002306636152281,0.0016114975893010278,0.0015249535130325558,0.0014407501656902527,0.0013590201013465215,0.0012798769318762254,0.0012034156954869226,0.0011297133481471123,0.0010588293661898704,0.00099080644785444309,0.00092567130119584862,0.00086343550563592979,0.00080409643443989846,0.0007476382255694569,0.00069403278867458497,0.00064324083642720831,0.00059521292895617567,0.00054989052079869999],[0.00051786738984238708,0.00056055042642172708,0.00060578140630021147,0.00065361546551829565,0.00070409916479317425,0.0007572695035370483,0.00081315293624530127,0.0008717644012230329,0.00093310637223590568,0.00099716794419510858,0.0010639239644016647,0.0011333342211682052,0.0012053427017936519,0.0012798769318762247,0.0013568474078027091,0.0014361471339387657,0.0015176512755602227,0.0016012169379052332,0.001686683080890901,0.0017738705780275517,0.0018625824268840028,0.0019526041171160655,0.0020437041605790287,0.0021356347864171839,0.0022281328022765974,0.0023209206209411277,0.0024137074497686036,0.0025061906383288383,0.0025980571776444104,0.0026889853424372332,0.002778646465818171,0.0028667068339534377,0.0029528296864304044,0.0030366773063564977,0.0031179131826869801,0.0031962042259178767,0.0032712230171245043,0.0033426500693967353,0.0034101760800390778,0.0034735041514831751,0.0035323519587149247,0.0035864538411563805,0.0036355627973679674,0.0036794523616485598,0.0037179183426045924,0.003750780405024592,0.0037778834779180113,0.0037990989733383967,0.0038143258025878151,0.0038234911785658202,0.0038265511953521863,0.0038234911785658202,0.0038143258025878151,0.0037990989733383967,0.0037778834779180113,0.0037507804050245916,0.003717918342604592,0.0036794523616485589,0.0036355627973679678,0.0035864538411563805,0.0035323519587149247,0.0034735041514831751,0.0034101760800390778,0.0033426500693967353,0.0032712230171245043,0.0031962042259178767,0.0031179131826869796,0.0030366773063564972,0.002952829686430404,0.0028667068339534372,0.0027786464658181701,0.002688985342437234,0.0025980571776444104,0.0025061906383288383,0.0024137074497686036,0.0023209206209411277,0.0022281328022765974,0.0021356347864171839,0.0020437041605790287,0.0019526041171160655,0.0018625824268840025,0.0017738705780275513,0.0016866830808909003,0.0016012169379052321,0.0015176512755602227,0.0014361471339387657,0.0013568474078027091,0.0012798769318762247,0.0012053427017936519,0.0011333342211682052,0.0010639239644016647,0.00099716794419510858,0.00093310637223590536,0.00087176440122303258,0.00081315293624530094,0.00075726950353704797,0.00070409916479317446,0.00065361546551829565,0.00060578140630021147,0.00056055042642172708,0.00051786738984238708],[0.00048770914085340811,0.0005279065108895097,0.00057050344355832915,0.00061555186402728948,0.00066309562152850297,0.00071316956079614405,0.00076579859573571872,0.00082099679471316176,0.00087876648743323842,0.00093909740387007081,0.0010019658561038389,0.0010673339741935428,0.0011351490073638773,0.0012053427017936524,0.0012778307661543158,0.0013525124357521975,0.0014292701456715138,0.0015079693226935215,0.0015884583049796635,0.0016705683975549394,0.0017541140705166316,0.0018388933056304958,0.0019246880955718982,0.0020112650985364766,0.0020983764492997856,0.0021857607260666865,0.0022731440706401564,0.0023602414575789698,0.0024467581061294987,0.0025323910268352833,0.0026168306928767717,0.0026997628244009382,0.002780870272394854,0.0028598349870667008,0.0029363400542493853,0.0030100717820615544,0.0030807218189723186,0.0031479892835407737,0.0032115828854581648,0.0032712230171245051,0.0033266437948545695,0.0033775950289380769,0.0034238441021794911,0.0034651777372134195,0.003501403633827338,0.0035323519587149256,0.0035578766715170965,0.0035778566726664346,0.0035921967604124801,0.00360082838644553,0.0036037102017271025,0.00360082838644553,0.0035921967604124801,0.0035778566726664346,0.0035578766715170965,0.0035323519587149251,0.0035014036338273376,0.0034651777372134186,0.003423844102179492,0.0033775950289380769,0.0033266437948545695,0.0032712230171245051,0.0032115828854581648,0.0031479892835407737,0.0030807218189723186,0.0030100717820615544,0.0029363400542493849,0.0028598349870667004,0.0027808702723948536,0.0026997628244009378,0.0026168306928767708,0.0025323910268352837,0.0024467581061294987,0.0023602414575789698,0.0022731440706401564,0.0021857607260666865,0.0020983764492997856,0.0020112650985364766,0.0019246880955718982,0.0018388933056304958,0.0017541140705166314,0.0016705683975549389,0.0015884583049796629,0.0015079693226935204,0.0014292701456715138,0.0013525124357521975,0.0012778307661543158,0.0012053427017936524,0.0011351490073638773,0.0010673339741935428,0.0010019658561038389,0.00093909740387007081,0.00087876648743323799,0.00082099679471316132,0.00076579859573571839,0.00071316956079614383,0.0006630956215285033,0.00061555186402728948,0.00057050344355832915,0.0005279065108895097,0.00048770914085340811],[0.00045930717156058431,0.00049716362900394692,0.00053727990943091728,0.00057970491412257484,0.00062447993873054777,0.00067163779878966375,0.00072120195733252129,0.00077318566344720355,0.00082759111116703188,0.00088440862854587555,0.00094361590714097385,0.0010051772823850039,0.0010690430754686641,0.0011351490073638764,0.0012034156954869217,0.0012737482432230638,0.0013460359321042236,0.0014201520258458188,0.0014959536947071982,0.0015732820677439123,0.0016519624194736625,0.0017318044962883002,0.0018126029866214234,0.0018941381374374818,0.0019761765180589834,0.0020584719307109606,0.0021407664654562262,0.0022227916954430647,0.0023042700066125258,0.0023849160542404658,0.0024644383369460377,0.0025425408771100424,0.0026189249950402411,0.0026932911627227858,0.0027653409216349184,0.0028347788478883065,0.0029013145469472821,0.0029646646593419887,0.0030245548581906627,0.0030807218189723169,0.003132915141862147,0.0031808992070643436,0.0032244549439542475,0.0032633814954733161,0.0032974977601015949,0.0033266437948545674,0.0033506820641015754,0.003369498520564995,0.0033830035066127065,0.0033911324658777958,0.0033938464573023213,0.0033911324658777958,0.0033830035066127065,0.003369498520564995,0.0033506820641015754,0.0033266437948545669,0.0032974977601015944,0.0032633814954733157,0.003224454943954248,0.0031808992070643436,0.003132915141862147,0.0030807218189723169,0.0030245548581906627,0.0029646646593419887,0.0029013145469472821,0.0028347788478883065,0.0027653409216349179,0.0026932911627227853,0.0026189249950402406,0.0025425408771100415,0.0024644383369460373,0.0023849160542404662,0.0023042700066125258,0.0022227916954430647,0.0021407664654562262,0.0020584719307109606,0.0019761765180589834,0.0018941381374374818,0.0018126029866214234,0.0017318044962883002,0.0016519624194736623,0.0015732820677439119,0.0014959536947071978,0.0014201520258458179,0.0013460359321042236,0.0012737482432230638,0.0012034156954869217,0.0011351490073638764,0.0010690430754686641,0.0010051772823850039,0.00094361590714097385,0.00088440862854587555,0.00082759111116703144,0.00077318566344720312,0.00072120195733252107,0.00067163779878966353,0.00062447993873054799,0.00057970491412257484,0.00053727990943091728,0.00049716362900394692,0.00045930717156058431],[0.00043255920419665438,0.00046821107318395478,0.00050599116330939543,0.00054594552806514385,0.00058811305823129481,0.0006325246583146995,0.00067920242496730956,0.00072815883571038394,0.0007793959568066903,0.0008329046795603921,0.00088866399467129741,0.00094664031451479637,0.0010067868533502177,0.0010690430754686647,0.0011333342211682057,0.0011995709201827254,0.0012676489017857742,0.0013374488102394142,0.0014088361335595589,0.0014816612527253088,0.0015557596174743215,0.0016309520537060567,0.0017070452062689419,0.0017838321195479485,0.0018610929568099643,0.0019385958577222769,0.0020160979318531846,0.00209334638431388,0.00217007976802962,0.0022460293554593604,0.0023209206209411281,0.0023944748232504268,0.0024664106764462046,0.0025364460956682046,0.0026043000032649468,0.0026696941794960263,0.0027323551410870046,0.0027920160301389148,0.0028484184953239044,0.0029013145469472838,0.0029504683673348365,0.0029956580581194593,0.0030366773063564985,0.0030733369519918975,0.0031054664400371849,0.0031329151418621483,0.0031555535312877297,0.0031732742026327103,0.0031859927195189951,0.003193648285049807,0.0031962042259178771,0.003193648285049807,0.0031859927195189951,0.0031732742026327103,0.0031555535312877297,0.0031329151418621479,0.0031054664400371845,0.0030733369519918971,0.003036677306356499,0.0029956580581194593,0.0029504683673348365,0.0029013145469472838,0.0028484184953239044,0.0027920160301389148,0.0027323551410870046,0.0026696941794960263,0.0026043000032649464,0.0025364460956682042,0.0024664106764462042,0.0023944748232504263,0.0023209206209411277,0.0022460293554593608,0.00217007976802962,0.00209334638431388,0.0020160979318531846,0.0019385958577222769,0.0018610929568099643,0.0017838321195479485,0.0017070452062689419,0.0016309520537060567,0.0015557596174743213,0.0014816612527253083,0.0014088361335595585,0.0013374488102394133,0.0012676489017857742,0.0011995709201827254,0.0011333342211682057,0.0010690430754686647,0.0010067868533502177,0.00094664031451479637,0.00088866399467129741,0.0008329046795603921,0.00077939595680668998,0.00072815883571038362,0.00067920242496730934,0.00063252465831469928,0.00058811305823129514,0.00054594552806514385,0.00050599116330939543,0.00046821107318395478,0.00043255920419665438],[0.00040736891718783579,0.00044094458295606745,0.00047652453191182397,0.00051415213560067634,0.00055386401998000121,0.00059568928981827891,0.00063964875495862864,0.0006857541662880389,0.00073400746973950148,0.00078440008706633037,0.00083691223245472928,0.00089151227427107331,0.0009481561513641208,0.0010067868533502173,0.0010673339741935424,0.0011297133481471119,0.0011938267767388642,0.0012595618549679295,0.0013267919042183535,0.0013953760186027034,0.001465159230519913,0.0015359728001567562,0.0016076346324890971,0.0016799498240586746,0.0017527113404270653,0.0018257008237561757,0.0018986895284518817,0.0019714393812536339,0.0020437041605790287,0.002115230788360714,0.0021857607260666852,0.0022550314650976633,0.0023227781003305704,0.0023887349742485542,0.0024526373778882686,0.0025142232937656575,0.0025732351650323256,0.0026294216743835194,0.0026825395157014627,0.0027323551410870029,0.002778646465818171,0.0028212045138827674,0.0028598349870666991,0.0028943597411398843,0.0029246181534631553,0.0029504683673348348,0.0029717883995933163,0.0029884770993773217,0.0030004549475006171,0.0030076646876020657,0.0030100717820615527,0.0030076646876020657,0.0030004549475006171,0.0029884770993773217,0.0029717883995933163,0.0029504683673348344,0.0029246181534631549,0.0028943597411398838,0.0028598349870666995,0.0028212045138827674,0.002778646465818171,0.0027323551410870029,0.0026825395157014627,0.0026294216743835194,0.0025732351650323256,0.0025142232937656575,0.0024526373778882681,0.0023887349742485538,0.00232277810033057,0.0022550314650976629,0.0021857607260666848,0.0021152307883607144,0.0020437041605790287,0.0019714393812536339,0.0018986895284518817,0.0018257008237561757,0.0017527113404270653,0.0016799498240586746,0.0016076346324890971,0.0015359728001567562,0.0014651592305199128,0.001395376018602703,0.0013267919042183531,0.0012595618549679287,0.0011938267767388642,0.0011297133481471119,0.0010673339741935424,0.0010067868533502173,0.0009481561513641208,0.00089151227427107331,0.00083691223245472928,0.00078440008706633037,0.00073400746973950126,0.00068575416628803858,0.00063964875495862842,0.00059568928981827869,0.00055386401998000143,0.00051415213560067634,0.00047652453191182397,0.00044094458295606745,0.00040736891718783579],[0.00038364559829212277,0.00041526596950412211,0.00044877390353739157,0.00048421024617531657,0.00052160949044556309,0.00056099904618684402,0.00060239851137135854,0.00064581895256771063,0.00069126220238657646,0.00073872018213946692,0.00078817425824868079,0.00083959464116353051,0.00089293983565446786,0.00094815615136412113,0.0010051772823850044,0.0010639239644016653,0.0011243037175758639,0.0011862106828643838,0.0012495255588395554,0.0013141156453340215,0.0013798349993572431,0.0014465247077377207,0.0015140132798399802,0.0015821171624995592,0.0016506413780251192,0.0017193802847491142,0.0017881184581837843,0.0018566316893759492,0.0019246880955718984,0.0019920493368235713,0.0020584719307109615,0.0021237086559455069,0.0021875100342775276,0.0022496258788795732,0.0023098068962382409,0.0023678063275798691,0.0024233816149992564,0.0024762960767721106,0.0025263205758259055,0.0025732351650323265,0.0026168306928767717,0.0026569103531625827,0.0026932911627227866,0.002725805351639631,0.0027543016512082564,0.0027786464658181719,0.0027987249160540814,0.0028144417416222926,0.0028257220541734714,0.0028325119316973757,0.0028347788478883078,0.0028325119316973757,0.0028257220541734714,0.0028144417416222926,0.0027987249160540814,0.0027786464658181714,0.002754301651208256,0.0027258053516396306,0.0026932911627227871,0.0026569103531625827,0.0026168306928767717,0.0025732351650323265,0.0025263205758259055,0.0024762960767721106,0.0024233816149992564,0.0023678063275798691,0.0023098068962382405,0.0022496258788795727,0.0021875100342775271,0.0021237086559455064,0.0020584719307109611,0.0019920493368235717,0.0019246880955718984,0.0018566316893759492,0.0017881184581837843,0.0017193802847491142,0.0016506413780251192,0.0015821171624995592,0.0015140132798399802,0.0014465247077377207,0.0013798349993572429,0.0013141156453340211,0.001249525558839555,0.0011862106828643831,0.0011243037175758639,0.0010639239644016653,0.0010051772823850044,0.00094815615136412113,0.00089293983565446786,0.00083959464116353051,0.00078817425824868079,0.00073872018213946692,0.00069126220238657624,0.0006458189525677103,0.00060239851137135832,0.00056099904618684381,0.00052160949044556331,0.00048421024617531657,0.00044877390353739157,0.00041526596950412211,0.00038364559829212277],[0.00036130381793723085,0.0003910827620834602,0.00042263934594967395,0.00045601203664601098,0.00049123331848258307,0.00052832900507336124,0.0005673175530934929,0.00060820938464479764,0.00065100622561501439,0.00069570046778184597,0.00074227456270267961,0.00079070045563520651,0.00084093906784392511,0.00089293983565446732,0.00094664031451479583,0.0010019658561038385,0.0010588293661898697,0.0011171311504804288,0.0011767588551221311,0.0012375875078037581,0.0012994796645928953,0.0013622856667007052,0.0014258440103288566,0.0014899818316170313,0.0015545155074906871,0.0016192513719207014,0.0016839865457648365,0.0017485098769828755,0.0018126029866214238,0.0018760414145704615,0.0019385958577222754,0.0020000334918353507,0.0020601193671422385,0.0021186178665620753,0.0021752942143054869,0.0022299160217110867,0.0022822548563464166,0.0023320878197577903,0.0023791991187769733,0.0024233816149992547,0.0024644383369460381,0.00250218393952132,0.0025364460956682029,0.0025670668056283446,0.0025939036099004681,0.00261683069287677,0.0026357398651982861,0.0026505414140989576,0.0026611648123874027,0.002667559278226797,0.0026696941794960246,0.002667559278226797,0.0026611648123874027,0.0026505414140989576,0.0026357398651982861,0.0026168306928767695,0.0025939036099004676,0.0025670668056283442,0.0025364460956682029,0.00250218393952132,0.0024644383369460381,0.0024233816149992547,0.0023791991187769733,0.0023320878197577903,0.0022822548563464166,0.0022299160217110867,0.0021752942143054865,0.0021186178665620749,0.0020601193671422381,0.0020000334918353502,0.0019385958577222749,0.0018760414145704619,0.0018126029866214238,0.0017485098769828755,0.0016839865457648365,0.0016192513719207014,0.0015545155074906871,0.0014899818316170313,0.0014258440103288566,0.0013622856667007052,0.0012994796645928951,0.0012375875078037577,0.0011767588551221306,0.0011171311504804282,0.0010588293661898697,0.0010019658561038385,0.00094664031451479583,0.00089293983565446732,0.00084093906784392511,0.00079070045563520651,0.00074227456270267961,0.00069570046778184597,0.00065100622561501406,0.00060820938464479731,0.00056731755309349268,0.00052832900507336113,0.00049123331848258329,0.00045601203664601098,0.00042263934594967395,0.0003910827620834602,0.00036130381793723085],[0.00034026312158186468,0.00036830787502636979,0.00039802674651264678,0.00042945596300073409,0.00046262611706179277,0.0004975615190419445,0.00053427955078325085,0.00057279002745157107,0.00061309457442676647,0.00065518602655491418,0.00069904785733514152,0.00074465364580614355,0.0007919665890008074,0.00084093906784392554,0.00089151227427107364,0.0009436159071409744,0.00099716794419510879,0.0010520744968846368,0.0011082297543352287,0.0011655160220564995,0.0012238038602275447,0.0012829523255088976,0.0013428093193512511,0.0014032120447018189,0.0014639875718614494,0.0015249535130325549,0.0015859188038343721,0.0016466845887642305,0.0017070452062689422,0.0017667892677776858,0.0018257008237561761,0.0018835606085911964,0.0019401473549245888,0.00199523916694609,0.0020486149411439226,0.0021000558221187862,0.0021493466803074708,0.0021962775978517039,0.002240645348399053,0.0022822548563464179,0.0023209206209411281,0.002356468090745295,0.0023887349742485547,0.0024175724728821867,0.0024428464233404146,0.002464438336946039,0.0024822463247978757,0.0024961858985946411,0.0025061906383288383,0.002512212719467596,0.0025142232937656584,0.002512212719467596,0.0025061906383288383,0.0024961858985946411,0.0024822463247978757,0.0024644383369460386,0.0024428464233404142,0.0024175724728821863,0.0023887349742485551,0.002356468090745295,0.0023209206209411281,0.0022822548563464179,0.002240645348399053,0.0021962775978517039,0.0021493466803074708,0.0021000558221187862,0.0020486149411439222,0.0019952391669460895,0.0019401473549245886,0.0018835606085911959,0.0018257008237561759,0.001766789267777686,0.0017070452062689422,0.0016466845887642305,0.0015859188038343721,0.0015249535130325549,0.0014639875718614494,0.0014032120447018189,0.0013428093193512511,0.0012829523255088976,0.0012238038602275444,0.0011655160220564991,0.0011082297543352283,0.0010520744968846361,0.00099716794419510879,0.0009436159071409744,0.00089151227427107364,0.00084093906784392554,0.0007919665890008074,0.00074465364580614355,0.00069904785733514152,0.00065518602655491418,0.00061309457442676625,0.00057279002745157074,0.00053427955078325063,0.00049756151904194429,0.00046262611706179293,0.00042945596300073409,0.00039802674651264678,0.00036830787502636979,0.00034026312158186468],[0.00032044773999246543,0.00034685929413961499,0.00037484747328353892,0.00040444639469036084,0.00043568486935859145,0.00046858579191000728,0.00050316553194699033,0.00053943333304463795,0.00057739072592805736,0.00061703096270940608,0.0006583384793162982,0.00070128839342443333,0.000745846045304654,0.00079196658900080772,0.00083959464116353073,0.00088866399467129784,0.00093909740387007113,0.00099080644785444353,0.0010436914776957035,0.0010976416528970085,0.0011525350716257972,0.0012082389984437146,0.0012646101923314138,0.0013214953367984088,0.001378731572787235,0.0014361471339387659,0.0014935620825955675,0.0015507891436979165,0.0016076346324890984,0.001663899470710309,0.0017193802847491144,0.0017738705780275521,0.0018271619687952698,0.0018790454834480099,0.00192931289454013,0.0019777580918185853,0.0020241784738906192,0.0020683763475623446,0.0021101603214627512,0.0021493466803074713,0.0021857607260666869,0.0022192380723869082,0.0022496258788795732,0.002276784012330012,0.0023005861224951363,0.0023209206209411286,0.0023376915523144878,0.0023508193485295616,0.0023602414575789698,0.002365912840013818,0.0023678063275798696,0.002365912840013818,0.0023602414575789698,0.0023508193485295616,0.0023376915523144878,0.0023209206209411281,0.0023005861224951359,0.0022767840123300116,0.0022496258788795736,0.0022192380723869082,0.0021857607260666869,0.0021493466803074713,0.0021101603214627512,0.0020683763475623446,0.0020241784738906192,0.0019777580918185853,0.0019293128945401298,0.0018790454834480097,0.0018271619687952694,0.0017738705780275519,0.001719380284749114,0.0016638994707103094,0.0016076346324890984,0.0015507891436979165,0.0014935620825955675,0.0014361471339387659,0.001378731572787235,0.0013214953367984088,0.0012646101923314138,0.0012082389984437146,0.001152535071625797,0.0010976416528970083,0.0010436914776957031,0.00099080644785444288,0.00093909740387007113,0.00088866399467129784,0.00083959464116353073,0.00079196658900080772,0.000745846045304654,0.00070128839342443333,0.0006583384793162982,0.00061703096270940608,0.00057739072592805714,0.00053943333304463774,0.00050316553194699012,0.00046858579191000712,0.00043568486935859161,0.00040444639469036084,0.00037484747328353892,0.00034685929413961499,0.00032044773999246543],[0.00030178631639213066,0.00032665978136475608,0.00035301805584210598,0.0003808932702553984,0.00041031255778120797,0.00044129747976233359,0.00047386345250972748,0.0005080191812945799,0.00054376610769950751,0.00058109787680306346,0.00061999983091387686,0.00066044853674140827,0.00070241135298199358,0.00074584604530465368,0.00079070045563520684,0.0008369122324547296,0.00088440862854587588,0.00093310637223590568,0.00098291161769794894,0.0010337199792831945,0.0010854166541691568,0.0011378766368276441,0.0011909650279468805,0.0012445374394937125,0.0012984404965838475,0.0013525124357521969,0.0014065837980947332,0.001460478214602184,0.0015140132798399802,0.0015670015089645716,0.0016192513719207016,0.0016705683975549385,0.001720756339325354,0.0017696183933030034,0.0018169584582646615,0.0018625824268840028,0.0019062994963548743,0.0019479234862387425,0.0019872741509303553,0.0020241784738906179,0.0020584719307109615,0.0020899997081538627,0.0021186178665620757,0.002144194433444047,0.0021666104166220262,0.0021857607260666856,0.0022015549944292907,0.0022139182873087688,0.0022227916954430647,0.0022281328022765974,0.0022299160217110875,0.0022281328022765974,0.0022227916954430647,0.0022139182873087688,0.0022015549944292907,0.0021857607260666856,0.0021666104166220257,0.0021441944334440466,0.0021186178665620762,0.0020899997081538627,0.0020584719307109615,0.0020241784738906179,0.0019872741509303553,0.0019479234862387425,0.0019062994963548743,0.0018625824268840028,0.0018169584582646611,0.0017696183933030029,0.0017207563393253538,0.0016705683975549383,0.0016192513719207014,0.001567001508964572,0.0015140132798399802,0.001460478214602184,0.0014065837980947332,0.0013525124357521969,0.0012984404965838475,0.0012445374394937125,0.0011909650279468805,0.0011378766368276441,0.0010854166541691568,0.0010337199792831942,0.00098291161769794872,0.00093310637223590503,0.00088440862854587588,0.0008369122324547296,0.00079070045563520684,0.00074584604530465368,0.00070241135298199358,0.00066044853674140827,0.00061999983091387686,0.00058109787680306346,0.00054376610769950719,0.00050801918129457968,0.00047386345250972732,0.00044129747976233343,0.00041031255778120813,0.0003808932702553984,0.00035301805584210598,0.00032665978136475608,0.00030178631639213066],[0.00028421164949914352,0.00030763659663771229,0.00033245988470695934,0.00035871177300745465,0.00038641781460257963,0.00041559831520027873,0.00044626779333544549,0.00047843444732374214,0.00051209963479654922,0.00054725737091423454,0.00058389385158292054,0.00062198700816067218,0.00066150610022536855,0.0007024113529819939,0.00074465364580614376,0.00078817425824868111,0.00083290467956039231,0.00087876648743323842,0.00092567130119584873,0.00097352081414635739,0.0010222069090581923,0.0010716118601584003,0.0011216086240595461,0.0011720612212329318,0.0012228252086521878,0.0012737482432230644,0.0013246707345598481,0.0013754265845847828,0.0014258440103288581,0.0014757464452158345,0.0015249535130325551,0.0015732820677439132,0.0016205472913168818,0.0016665638407911112,0.0017111470349895754,0.0017541140705166316,0.0017952852560565373,0.0018344852534754339,0.0018715443138549606,0.0019062994963548751,0.0019385958577222773,0.0019682876003407393,0.0019952391669460904,0.0020193262705263761,0.0020404368484688183,0.0020584719307109619,0.0020733464124887751,0.0020849897232409825,0.00209334638431388,0.0020983764492997856,0.0021000558221187867,0.0020983764492997856,0.00209334638431388,0.0020849897232409825,0.0020733464124887751,0.0020584719307109619,0.0020404368484688178,0.0020193262705263757,0.0019952391669460904,0.0019682876003407393,0.0019385958577222773,0.0019062994963548751,0.0018715443138549606,0.0018344852534754339,0.0017952852560565373,0.0017541140705166316,0.0017111470349895749,0.001666563840791111,0.0016205472913168816,0.001573282067743913,0.0015249535130325547,0.0014757464452158347,0.0014258440103288581,0.0013754265845847828,0.0013246707345598481,0.0012737482432230644,0.0012228252086521878,0.0011720612212329318,0.0011216086240595461,0.0010716118601584003,0.0010222069090581921,0.00097352081414635706,0.00092567130119584852,0.00087876648743323788,0.00083290467956039231,0.00078817425824868111,0.00074465364580614376,0.0007024113529819939,0.00066150610022536855,0.00062198700816067218,0.00058389385158292054,0.00054725737091423454,0.000512099634796549,0.00047843444732374192,0.00044626779333544533,0.00041559831520027857,0.00038641781460257974,0.00035871177300745465,0.00033245988470695934,0.00030763659663771229,0.00028421164949914352],[0.00026766045152977079,0.00028972123594596063,0.00031309892825652253,0.00033782202559754426,0.00036391459293784288,0.00039139575347298989,0.00042027918024422749,0.00045057259413448163,0.00048227727371283606,0.00051538758266958605,0.00054989052079869945,0.00058576530463589737,0.00062298298394187926,0.00066150610022536823,0.000701288393424433,0.00074227456270268004,0.00078440008706633058,0.00082759111116703199,0.00087176440122303269,0.00091682737546910182,0.00096267821293578458,0.0010092060436654245,0.0010562912227015089,0.0011038056893466165,0.0011516134122813888,0.0011995709201827248,0.0012475279164854587,0.0012953279759108634,0.0013428093193512511,0.0013898056626673028,0.0014361471339387651,0.0014816612527253081,0.0015261739639582602,0.0015695107182110142,0.0016114975893010267,0.0016519624194736627,0.0016907359818207626,0.0017276531491064733,0.0017625540578198688,0.0017952852560565362,0.0018257008237561761,0.0018536634538945558,0.0018790454834480088,0.0019017298633166922,0.00192161105690635,0.0019385958577222762,0.0019526041171160657,0.0019635693742359947,0.0019714393812536339,0.0019761765180589838,0.001977758091818584,0.0019761765180589838,0.0019714393812536339,0.0019635693742359947,0.0019526041171160657,0.001938595857722276,0.0019216110569063498,0.0019017298633166918,0.001879045483448009,0.0018536634538945558,0.0018257008237561761,0.0017952852560565362,0.0017625540578198688,0.0017276531491064733,0.0016907359818207626,0.0016519624194736627,0.0016114975893010263,0.001569510718211014,0.0015261739639582598,0.0014816612527253077,0.0014361471339387648,0.001389805662667303,0.0013428093193512511,0.0012953279759108634,0.0012475279164854587,0.0011995709201827248,0.0011516134122813888,0.0011038056893466165,0.0010562912227015089,0.0010092060436654245,0.00096267821293578436,0.00091682737546910161,0.00087176440122303247,0.00082759111116703144,0.00078440008706633058,0.00074227456270268004,0.000701288393424433,0.00066150610022536823,0.00062298298394187926,0.00058576530463589737,0.00054989052079869945,0.00051538758266958605,0.00048227727371283585,0.00045057259413448141,0.00042027918024422739,0.00039139575347298973,0.00036391459293784304,0.00033782202559754426,0.00031309892825652253,0.00028972123594596063,0.00026766045152977079]],"type":"surface","frame":null}],"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- # Examples of joint pdfs `\(f(x,y) = \frac{2 \exp(-2x)}{\sqrt{2\pi}}\exp\left(-\frac{(y)^2}{2}\right)\)` if `\(x \in [0,\infty), y \in \Re\)`, `\(f(x,y) = 0\)` otherwise <img src="12-multivariate-pdf_files/figure-html/joint-pdf-exp-2d-1.png" width="864" style="display: block; margin: auto;" /> --- # Examples of joint pdfs: plane `\(f(x,y) = x + y\)`, if `\(x \in [0,1], y \in [0,1]\)` <div class="plotly html-widget html-fill-item" id="htmlwidget-88fdd2a34d502a66744b" style="width:864px;height:504px;"></div> <script type="application/json" data-for="htmlwidget-88fdd2a34d502a66744b">{"x":{"visdat":{"d43112e17a4f":["function () ","plotlyVisDat"]},"cur_data":"d43112e17a4f","attrs":{"d43112e17a4f":{"x":{},"y":{},"z":{},"alpha_stroke":1,"sizes":[10,100],"spans":[1,20],"type":"surface","inherit":true}},"layout":{"margin":{"b":40,"l":60,"t":25,"r":10},"scene":{"xaxis":{"title":"x"},"yaxis":{"title":"y"},"zaxis":{"title":"z_mat"}},"hovermode":"closest","showlegend":false,"legend":{"yanchor":"top","y":0.5}},"source":"A","config":{"modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"data":[{"colorbar":{"title":"z_mat","ticklen":2,"len":0.5,"lenmode":"fraction","y":1,"yanchor":"top"},"colorscale":[["0","rgba(68,1,84,1)"],["0.0416666666666667","rgba(70,19,97,1)"],["0.0833333333333333","rgba(72,32,111,1)"],["0.125","rgba(71,45,122,1)"],["0.166666666666667","rgba(68,58,128,1)"],["0.208333333333333","rgba(64,70,135,1)"],["0.25","rgba(60,82,138,1)"],["0.291666666666667","rgba(56,93,140,1)"],["0.333333333333333","rgba(49,104,142,1)"],["0.375","rgba(46,114,142,1)"],["0.416666666666667","rgba(42,123,142,1)"],["0.458333333333333","rgba(38,133,141,1)"],["0.5","rgba(37,144,140,1)"],["0.541666666666667","rgba(33,154,138,1)"],["0.583333333333333","rgba(39,164,133,1)"],["0.625","rgba(47,174,127,1)"],["0.666666666666667","rgba(53,183,121,1)"],["0.708333333333333","rgba(79,191,110,1)"],["0.75","rgba(98,199,98,1)"],["0.791666666666667","rgba(119,207,85,1)"],["0.833333333333333","rgba(147,214,70,1)"],["0.875","rgba(172,220,52,1)"],["0.916666666666667","rgba(199,225,42,1)"],["0.958333333333333","rgba(226,228,40,1)"],["1","rgba(253,231,37,1)"]],"showscale":true,"x":[0,0.029999999999999999,0.059999999999999998,0.089999999999999997,0.12,0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3],"y":[0,0.029999999999999999,0.059999999999999998,0.089999999999999997,0.12,0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3],"z":[[0,0.029999999999999999,0.059999999999999998,0.089999999999999997,0.12,0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3],[0.029999999999999999,0.059999999999999998,0.089999999999999997,0.12,0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.30000000000000004,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.42000000000000004,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.57000000000000006,0.59999999999999998,0.63,0.66000000000000003,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.83999999999999997,0.87,0.90000000000000002,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1100000000000001,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.0399999999999996,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.2499999999999996,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.4599999999999995,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999995,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,2.9999999999999996,3.0299999999999998],[0.059999999999999998,0.089999999999999997,0.12,0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.33000000000000002,0.35999999999999999,0.38999999999999996,0.41999999999999998,0.45000000000000001,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.57000000000000006,0.60000000000000009,0.62999999999999989,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.84000000000000008,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1100000000000001,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2200000000000002,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001],[0.089999999999999997,0.12,0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999993,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.53999999999999992,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.74999999999999989,0.77999999999999992,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999988,1.02,1.05,1.0800000000000001,1.1100000000000001,1.1400000000000001,1.1700000000000002,1.2,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3800000000000001,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6500000000000001,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8600000000000001,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999],[0.12,0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.66000000000000003,0.68999999999999995,0.71999999999999997,0.75,0.77999999999999992,0.80999999999999994,0.83999999999999997,0.87,0.90000000000000002,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2000000000000002,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6800000000000002,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2200000000000002,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001],[0.14999999999999999,0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.42000000000000004,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.66000000000000003,0.69000000000000006,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.90000000000000002,0.93000000000000005,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0799999999999998,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.2899999999999998,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.4999999999999998,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.9799999999999998,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999],[0.17999999999999999,0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.45000000000000001,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.57000000000000006,0.59999999999999998,0.62999999999999989,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.83999999999999986,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0799999999999998,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.2899999999999998,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.4999999999999998,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.9799999999999998,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2200000000000002,2.25,2.2800000000000002,2.3100000000000001,2.3400000000000003,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5500000000000003,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7600000000000002,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002],[0.20999999999999999,0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.53999999999999992,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.77999999999999992,0.80999999999999994,0.83999999999999997,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21],[0.23999999999999999,0.27000000000000002,0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.4000000000000004,2.4299999999999997,2.46,2.4900000000000002,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6100000000000003,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2400000000000002],[0.27000000000000002,0.30000000000000004,0.33000000000000002,0.35999999999999999,0.39000000000000001,0.42000000000000004,0.45000000000000001,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.57000000000000006,0.59999999999999998,0.63,0.66000000000000003,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.83999999999999997,0.87,0.90000000000000002,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27],[0.29999999999999999,0.32999999999999996,0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.57000000000000006,0.59999999999999998,0.62999999999999989,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.84000000000000008,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3800000000000001,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8600000000000001,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.2099999999999995,3.2399999999999998,3.2699999999999996,3.2999999999999998],[0.32999999999999996,0.35999999999999999,0.38999999999999996,0.41999999999999993,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.53999999999999992,0.56999999999999995,0.59999999999999998,0.62999999999999989,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.77999999999999992,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999988,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999997,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001],[0.35999999999999999,0.39000000000000001,0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.90000000000000002,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999997,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999999],[0.39000000000000001,0.42000000000000004,0.45000000000000001,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.57000000000000006,0.59999999999999998,0.63,0.66000000000000003,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.83999999999999997,0.87,0.90000000000000002,0.93000000000000005,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.4700000000000002,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6800000000000002,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9500000000000002,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5500000000000003,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7600000000000002,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001],[0.41999999999999998,0.44999999999999996,0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.83999999999999997,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0799999999999998,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999],[0.44999999999999996,0.47999999999999998,0.51000000000000001,0.53999999999999992,0.56999999999999995,0.59999999999999998,0.62999999999999989,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.77999999999999992,0.80999999999999994,0.83999999999999997,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6100000000000003,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4500000000000002],[0.47999999999999998,0.51000000000000001,0.54000000000000004,0.56999999999999995,0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48],[0.51000000000000001,0.54000000000000004,0.57000000000000006,0.59999999999999998,0.63,0.66000000000000003,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.83999999999999997,0.87,0.90000000000000002,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0700000000000003,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6100000000000003,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998],[0.54000000000000004,0.57000000000000006,0.60000000000000009,0.63,0.66000000000000003,0.69000000000000006,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.84000000000000008,0.87,0.90000000000000002,0.93000000000000005,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0700000000000003,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54],[0.56999999999999995,0.59999999999999998,0.62999999999999989,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.77999999999999992,0.80999999999999994,0.83999999999999997,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999997,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8899999999999997,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.2099999999999995,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.5399999999999996,3.5699999999999998],[0.59999999999999998,0.63,0.65999999999999992,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6800000000000002,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7600000000000002,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001],[0.63,0.66000000000000003,0.68999999999999995,0.71999999999999997,0.75,0.78000000000000003,0.81000000000000005,0.83999999999999997,0.87,0.90000000000000002,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6800000000000002,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.5399999999999996,3.5699999999999998,3.5999999999999996,3.6299999999999999],[0.65999999999999992,0.68999999999999995,0.71999999999999997,0.74999999999999989,0.77999999999999992,0.80999999999999994,0.83999999999999986,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999988,1.02,1.0499999999999998,1.0799999999999998,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.9799999999999998,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999994,3.5999999999999996,3.6299999999999999,3.6600000000000001],[0.68999999999999995,0.71999999999999997,0.75,0.77999999999999992,0.80999999999999994,0.83999999999999997,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999],[0.71999999999999997,0.75,0.78000000000000003,0.80999999999999994,0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998],[0.75,0.78000000000000003,0.81000000000000005,0.83999999999999997,0.87,0.90000000000000002,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75],[0.78000000000000003,0.81000000000000005,0.84000000000000008,0.87,0.90000000000000002,0.93000000000000005,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8600000000000001,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0700000000000003,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9400000000000004,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1500000000000004,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002],[0.80999999999999994,0.83999999999999997,0.86999999999999988,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001],[0.83999999999999997,0.87,0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.5399999999999996,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.7499999999999996,3.7799999999999998,3.8099999999999996,3.8399999999999999],[0.87,0.90000000000000002,0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.9500000000000002,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7200000000000002,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001],[0.89999999999999991,0.92999999999999994,0.95999999999999996,0.98999999999999988,1.02,1.0499999999999998,1.0799999999999998,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.5399999999999996,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999999],[0.92999999999999994,0.95999999999999996,0.98999999999999999,1.02,1.0499999999999998,1.0799999999999998,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999994,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997],[0.95999999999999996,0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96],[0.98999999999999999,1.02,1.05,1.0800000000000001,1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0700000000000003,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1500000000000004,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002],[1.02,1.05,1.0800000000000001,1.1100000000000001,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0700000000000003,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996],[1.05,1.0800000000000001,1.1100000000000001,1.1400000000000001,1.1699999999999999,1.2,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3799999999999999,1.4100000000000001,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6499999999999999,1.6800000000000002,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0700000000000003,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6100000000000003,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1500000000000004,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.9000000000000004,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998],[1.0800000000000001,1.1100000000000001,1.1400000000000001,1.1700000000000002,1.2000000000000002,1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3800000000000001,1.4100000000000001,1.4399999999999999,1.4700000000000002,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6499999999999999,1.6800000000000002,1.71,1.74,1.77,1.8,1.8300000000000001,1.8600000000000001,1.8900000000000001,1.9199999999999999,1.9500000000000002,1.98,2.0099999999999998,2.04,2.0700000000000003,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6100000000000003,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9300000000000002,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001],[1.1099999999999999,1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.2899999999999998,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999997,1.71,1.7399999999999998,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.5399999999999996,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.7499999999999996,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994],[1.1399999999999999,1.1699999999999999,1.2,1.23,1.2599999999999998,1.2899999999999998,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.5,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999994,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999994,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997],[1.1699999999999999,1.2,1.23,1.26,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999],[1.2,1.23,1.26,1.29,1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002],[1.23,1.26,1.29,1.3200000000000001,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004],[1.26,1.29,1.3200000000000001,1.3500000000000001,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1100000000000003,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998],[1.29,1.3200000000000001,1.3500000000000001,1.3800000000000001,1.4100000000000001,1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6499999999999999,1.6800000000000002,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0700000000000003,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1400000000000006,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29],[1.3199999999999998,1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.4999999999999998,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999997,1.71,1.7399999999999998,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999997,1.9199999999999999,1.9499999999999997,1.9799999999999998,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.5399999999999996,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.7499999999999996,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.9599999999999995,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3200000000000003],[1.3499999999999999,1.3799999999999999,1.4099999999999999,1.4399999999999999,1.4699999999999998,1.4999999999999998,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999997,1.71,1.7399999999999998,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999994,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999994,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999993,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3199999999999994,4.3499999999999996],[1.3799999999999999,1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999],[1.4099999999999999,1.4399999999999999,1.47,1.5,1.5299999999999998,1.5599999999999998,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001],[1.4399999999999999,1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995],[1.47,1.5,1.53,1.5600000000000001,1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998],[1.5,1.53,1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5],[1.53,1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8900000000000001,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0700000000000003,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6100000000000003,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6900000000000004,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.9000000000000004,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1100000000000003,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5300000000000002],[1.5600000000000001,1.5900000000000001,1.6200000000000001,1.6500000000000001,1.6800000000000002,1.71,1.74,1.77,1.8,1.8300000000000001,1.8600000000000001,1.8900000000000001,1.9199999999999999,1.9500000000000002,1.98,2.0099999999999998,2.04,2.0700000000000003,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6100000000000003,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7200000000000002,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9300000000000002,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1400000000000006,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005],[1.5899999999999999,1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999],[1.6199999999999999,1.6499999999999999,1.6799999999999999,1.71,1.7399999999999998,1.7699999999999998,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6200000000000001],[1.6499999999999999,1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004],[1.6799999999999999,1.71,1.74,1.77,1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5300000000000002,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6499999999999995,4.6799999999999997],[1.71,1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71],[1.74,1.77,1.8,1.8300000000000001,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.9000000000000004,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1100000000000003,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5300000000000002,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6499999999999995,4.6799999999999997,4.71,4.7400000000000002],[1.77,1.8,1.8300000000000001,1.8600000000000001,1.8900000000000001,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9300000000000002,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1400000000000006,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996],[1.7999999999999998,1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.9799999999999998,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998],[1.8299999999999998,1.8599999999999999,1.8899999999999999,1.9199999999999999,1.9499999999999997,1.9799999999999998,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6499999999999995,4.6799999999999997,4.71,4.7399999999999993,4.7699999999999996,4.7999999999999998,4.8300000000000001],[1.8599999999999999,1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994],[1.8899999999999999,1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999995,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6499999999999995,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997],[1.9199999999999999,1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999],[1.95,1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1100000000000003,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5300000000000002,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6499999999999995,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9500000000000002],[1.98,2.0099999999999998,2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1400000000000006,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004],[2.0099999999999998,2.0399999999999996,2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998],[2.04,2.0699999999999998,2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2200000000000002,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1400000000000006,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04],[2.0699999999999998,2.0999999999999996,2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003],[2.1000000000000001,2.1299999999999999,2.1600000000000001,2.1899999999999999,2.2200000000000002,2.25,2.2800000000000002,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6100000000000003,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1500000000000004,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1400000000000006,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4700000000000006,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9500000000000002,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996],[2.1299999999999999,2.1599999999999997,2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999],[2.1600000000000001,2.1899999999999999,2.2200000000000002,2.25,2.2800000000000002,2.3100000000000001,2.3400000000000003,2.3700000000000001,2.4000000000000004,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5500000000000003,2.5800000000000001,2.6100000000000003,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7600000000000002,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9400000000000004,2.9700000000000002,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1500000000000004,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6900000000000004,3.7200000000000002,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.9000000000000004,3.9300000000000002,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1100000000000003,4.1400000000000006,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4700000000000006,4.5,4.5300000000000002,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9500000000000002,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001],[2.1899999999999999,2.2199999999999998,2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995],[2.2199999999999998,2.2499999999999996,2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.5399999999999996,3.5699999999999994,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.129999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998],[2.25,2.2799999999999998,2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25],[2.2799999999999998,2.3099999999999996,2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994],[2.3100000000000001,2.3399999999999999,2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4700000000000006,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3100000000000005],[2.3399999999999999,2.3699999999999997,2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999],[2.3700000000000001,2.3999999999999999,2.4300000000000002,2.46,2.4900000000000002,2.52,2.5500000000000003,2.5800000000000001,2.6100000000000003,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7600000000000002,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1500000000000004,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.9000000000000004,3.9300000000000002,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1100000000000003,4.1400000000000006,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4700000000000006,4.5,4.5300000000000002,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9500000000000002,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2200000000000006,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3700000000000001],[2.3999999999999999,2.4299999999999997,2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.4000000000000004],[2.4299999999999997,2.4599999999999995,2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.5399999999999996,3.5699999999999994,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.7499999999999996,3.7799999999999994,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0699999999999994,5.0999999999999996,5.129999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.3999999999999995,5.4299999999999997],[2.46,2.4899999999999998,2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3699999999999992,5.4000000000000004,5.4299999999999997,5.46],[2.4899999999999998,2.5199999999999996,2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.129999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.3999999999999995,5.4299999999999997,5.4599999999999991,5.4900000000000002],[2.52,2.5499999999999998,2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3700000000000001,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996],[2.5499999999999998,2.5799999999999996,2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.4000000000000004,5.4299999999999997,5.4599999999999991,5.4900000000000002,5.5199999999999996,5.5499999999999998],[2.5800000000000001,2.6099999999999999,2.6400000000000001,2.6699999999999999,2.7000000000000002,2.73,2.7600000000000002,2.79,2.8200000000000003,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1100000000000003,4.1400000000000006,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5300000000000002,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9500000000000002,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3700000000000001,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001],[2.6099999999999999,2.6399999999999997,2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994],[2.6399999999999997,2.6699999999999995,2.6999999999999997,2.7299999999999995,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.2099999999999995,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.5399999999999996,3.5699999999999994,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.7499999999999996,3.7799999999999994,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.9599999999999995,3.9899999999999993,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0699999999999994,5.0999999999999996,5.129999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.3999999999999995,5.4299999999999997,5.4599999999999991,5.4900000000000002,5.5199999999999996,5.5499999999999989,5.5800000000000001,5.6099999999999994,5.6399999999999997],[2.6699999999999999,2.6999999999999997,2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999],[2.6999999999999997,2.7299999999999995,2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999995,2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.5399999999999996,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.7099999999999991,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.129999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.3999999999999995,5.4299999999999997,5.4599999999999991,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993],[2.73,2.7599999999999998,2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3699999999999992,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993,5.7300000000000004],[2.7599999999999998,2.7899999999999996,2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.3999999999999995,5.4299999999999997,5.4599999999999991,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993,5.7299999999999995,5.7599999999999998],[2.79,2.8199999999999998,2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5300000000000002,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9500000000000002,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3700000000000001,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6400000000000006,5.6699999999999999,5.6999999999999993,5.7300000000000004,5.7599999999999998,5.79],[2.8199999999999998,2.8499999999999996,2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.4000000000000004,5.4299999999999997,5.4599999999999991,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993,5.7299999999999995,5.7599999999999998,5.7899999999999991,5.8200000000000003],[2.8500000000000001,2.8799999999999999,2.9100000000000001,2.9399999999999999,2.9700000000000002,3,3.0300000000000002,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3600000000000003,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5700000000000003,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7200000000000002,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.9000000000000004,3.9300000000000002,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1100000000000003,4.1400000000000006,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5300000000000002,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8900000000000006,4.9199999999999999,4.9500000000000002,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2200000000000006,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3700000000000001,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6400000000000006,5.6699999999999999,5.7000000000000002,5.7300000000000004,5.7599999999999998,5.79,5.8200000000000003,5.8499999999999996],[2.8799999999999999,2.9099999999999997,2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993,5.7300000000000004,5.7599999999999998,5.7899999999999991,5.8200000000000003,5.8499999999999996,5.8799999999999999],[2.9099999999999997,2.9399999999999995,2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999995,3.1799999999999997,3.2099999999999995,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999994,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.5399999999999996,3.5699999999999994,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.7499999999999996,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.7099999999999991,4.7399999999999993,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.129999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.3999999999999995,5.4299999999999997,5.4599999999999991,5.4900000000000002,5.5199999999999996,5.5499999999999989,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993,5.7299999999999995,5.7599999999999998,5.7899999999999991,5.8199999999999994,5.8499999999999996,5.879999999999999,5.9100000000000001],[2.9399999999999999,2.9699999999999998,3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7799999999999998,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3699999999999992,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993,5.7300000000000004,5.7599999999999998,5.79,5.8200000000000003,5.8499999999999996,5.8799999999999999,5.9100000000000001,5.9399999999999995],[2.9699999999999998,2.9999999999999996,3.0299999999999998,3.0599999999999996,3.0899999999999999,3.1199999999999997,3.1499999999999999,3.1799999999999997,3.21,3.2399999999999998,3.2699999999999996,3.2999999999999998,3.3299999999999996,3.3599999999999999,3.3899999999999997,3.4199999999999999,3.4499999999999997,3.4799999999999995,3.5099999999999998,3.5399999999999996,3.5699999999999998,3.5999999999999996,3.6299999999999999,3.6599999999999997,3.6899999999999995,3.7199999999999998,3.75,3.7799999999999998,3.8099999999999996,3.8399999999999999,3.8699999999999997,3.8999999999999995,3.9299999999999997,3.96,3.9899999999999998,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.1999999999999993,4.2299999999999995,4.2599999999999998,4.2899999999999991,4.3199999999999994,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5299999999999994,4.5599999999999996,4.5899999999999999,4.6199999999999992,4.6499999999999995,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9499999999999993,4.9799999999999995,5.0099999999999998,5.0399999999999991,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3099999999999996,5.3399999999999999,5.3699999999999992,5.3999999999999995,5.4299999999999997,5.4599999999999991,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993,5.7299999999999995,5.7599999999999998,5.7899999999999991,5.8200000000000003,5.8499999999999996,5.879999999999999,5.9100000000000001,5.9399999999999995,5.9699999999999998],[3,3.0299999999999998,3.0600000000000001,3.0899999999999999,3.1200000000000001,3.1499999999999999,3.1800000000000002,3.21,3.2400000000000002,3.27,3.2999999999999998,3.3300000000000001,3.3599999999999999,3.3900000000000001,3.4199999999999999,3.4500000000000002,3.48,3.5099999999999998,3.54,3.5699999999999998,3.6000000000000001,3.6299999999999999,3.6600000000000001,3.6899999999999999,3.7199999999999998,3.75,3.7800000000000002,3.8100000000000001,3.8399999999999999,3.8700000000000001,3.8999999999999999,3.9299999999999997,3.96,3.9900000000000002,4.0199999999999996,4.0499999999999998,4.0800000000000001,4.1099999999999994,4.1399999999999997,4.1699999999999999,4.2000000000000002,4.2300000000000004,4.2599999999999998,4.29,4.3200000000000003,4.3499999999999996,4.3799999999999999,4.4100000000000001,4.4399999999999995,4.4699999999999998,4.5,4.5300000000000002,4.5600000000000005,4.5899999999999999,4.6200000000000001,4.6500000000000004,4.6799999999999997,4.71,4.7400000000000002,4.7699999999999996,4.7999999999999998,4.8300000000000001,4.8599999999999994,4.8899999999999997,4.9199999999999999,4.9500000000000002,4.9800000000000004,5.0099999999999998,5.04,5.0700000000000003,5.0999999999999996,5.1299999999999999,5.1600000000000001,5.1899999999999995,5.2199999999999998,5.25,5.2799999999999994,5.3100000000000005,5.3399999999999999,5.3700000000000001,5.4000000000000004,5.4299999999999997,5.46,5.4900000000000002,5.5199999999999996,5.5499999999999998,5.5800000000000001,5.6099999999999994,5.6399999999999997,5.6699999999999999,5.6999999999999993,5.7300000000000004,5.7599999999999998,5.79,5.8200000000000003,5.8499999999999996,5.8799999999999999,5.9100000000000001,5.9399999999999995,5.9699999999999998,6]],"type":"surface","frame":null}],"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- # Examples of joint pdfs: plane `\(f(x,y) = x + y\)`, if `\(x \in [0,1], y \in [0,1]\)` <img src="12-multivariate-pdf_files/figure-html/joint-pdf-plus-2d-1.png" width="864" style="display: block; margin: auto;" /> --- class: middle # Evaluating probability -- ### IT WORKS THE SAME-*ish* --- # Multivariate CDF For jointly continuous random variables `\(X\)` and `\(Y\)` define, `\(F(b,a)\)` as `$$F(b,a) = \Pr\{ X \leq b , Y \leq a\} = \int_{-\infty}^{a} \int_{-\infty}^{b} f(x,y) \, dx\, dy$$` --- # Multivariate CDF <img src="12-multivariate-pdf_files/figure-html/multi-cdf-1.png" width="864" style="display: block; margin: auto;" /> --- # Multivariate CDF <img src="12-multivariate-pdf_files/figure-html/multi-cdf-1-1.png" width="864" style="display: block; margin: auto;" /> --- # Multivariate CDF <img src="12-multivariate-pdf_files/figure-html/multi-cdf-2-1.png" width="864" style="display: block; margin: auto;" /> --- # Multivariate CDF <img src="12-multivariate-pdf_files/figure-html/multi-cdf-3-1.png" width="864" style="display: block; margin: auto;" /> --- # Multivariate CDF <img src="12-multivariate-pdf_files/figure-html/multi-cdf-4-1.png" width="864" style="display: block; margin: auto;" /> --- class: middle # MARGINAL PROBABILITIES! -- Remember how we talked about `\(f_X\)`? .... -- Now we can see why/how that would be worthwhile. (how one variable changes relative to another vs on its own) --- # Marginalization Define `\(f_{X}(x)\)` as the pdf for `\(X\)`, `$$f_{X}(x) = \int_{-\infty}^{\infty} f(x,y) \, dy$$` -- Similarly, define `\(f_{Y}(y)\)` as the pdf for `\(Y\)`, `$$f_{Y}(y) = \int_{-\infty}^{\infty} f(x,y)\, dx$$` -- `\(X\)` and `\(Y\)` are continuous random variables with joint pdf `\(f(x,y)\)`. Define the conditional probability function `\(f(x|y)\)` as `$$f(x|y) = \frac{f(x, y) }{f_{Y}(y) }$$` --- # Marginalization in action `\(f(x,y) = -x^2 - y^2\)`, if `\(x \in [-2,2], y \in [-2,2]\)` <div class="plotly html-widget html-fill-item" id="htmlwidget-8e1fe96c0688a849169a" style="width:864px;height:504px;"></div> <script type="application/json" data-for="htmlwidget-8e1fe96c0688a849169a">{"x":{"visdat":{"d4312880686d":["function () ","plotlyVisDat"]},"cur_data":"d4312880686d","attrs":{"d4312880686d":{"x":{},"y":{},"z":{},"alpha_stroke":1,"sizes":[10,100],"spans":[1,20],"type":"surface","inherit":true}},"layout":{"margin":{"b":40,"l":60,"t":25,"r":10},"scene":{"xaxis":{"title":"x"},"yaxis":{"title":"y"},"zaxis":{"title":"z_mat"}},"hovermode":"closest","showlegend":false,"legend":{"yanchor":"top","y":0.5}},"source":"A","config":{"modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"data":[{"colorbar":{"title":"z_mat","ticklen":2,"len":0.5,"lenmode":"fraction","y":1,"yanchor":"top"},"colorscale":[["0","rgba(68,1,84,1)"],["0.0416666666666666","rgba(70,19,97,1)"],["0.0833333333333334","rgba(72,32,111,1)"],["0.125","rgba(71,45,122,1)"],["0.166666666666667","rgba(68,58,128,1)"],["0.208333333333333","rgba(64,70,135,1)"],["0.25","rgba(60,82,138,1)"],["0.291666666666667","rgba(56,93,140,1)"],["0.333333333333333","rgba(49,104,142,1)"],["0.375","rgba(46,114,142,1)"],["0.416666666666667","rgba(42,123,142,1)"],["0.458333333333333","rgba(38,133,141,1)"],["0.5","rgba(37,144,140,1)"],["0.541666666666667","rgba(33,154,138,1)"],["0.583333333333333","rgba(39,164,133,1)"],["0.625","rgba(47,174,127,1)"],["0.666666666666667","rgba(53,183,121,1)"],["0.708333333333333","rgba(79,191,110,1)"],["0.75","rgba(98,199,98,1)"],["0.791666666666667","rgba(119,207,85,1)"],["0.833333333333333","rgba(147,214,70,1)"],["0.875","rgba(172,220,52,1)"],["0.916666666666667","rgba(199,225,42,1)"],["0.958333333333333","rgba(226,228,40,1)"],["1","rgba(253,231,37,1)"]],"showscale":true,"x":[-2,-1.96,-1.9199999999999999,-1.8799999999999999,-1.8400000000000001,-1.8,-1.76,-1.72,-1.6799999999999999,-1.6400000000000001,-1.6000000000000001,-1.5600000000000001,-1.52,-1.48,-1.4399999999999999,-1.3999999999999999,-1.3599999999999999,-1.3199999999999998,-1.28,-1.24,-1.2,-1.1600000000000001,-1.1200000000000001,-1.0800000000000001,-1.04,-1,-0.95999999999999996,-0.91999999999999993,-0.87999999999999989,-0.84000000000000008,-0.80000000000000004,-0.76000000000000001,-0.71999999999999997,-0.67999999999999994,-0.6399999999999999,-0.59999999999999987,-0.56000000000000005,-0.52000000000000002,-0.47999999999999998,-0.43999999999999995,-0.39999999999999991,-0.35999999999999988,-0.32000000000000006,-0.28000000000000003,-0.23999999999999999,-0.19999999999999996,-0.15999999999999992,-0.11999999999999988,-0.080000000000000071,-0.040000000000000036,0,0.040000000000000036,0.080000000000000071,0.12000000000000011,0.16000000000000014,0.20000000000000018,0.24000000000000021,0.28000000000000025,0.31999999999999984,0.35999999999999988,0.39999999999999991,0.43999999999999995,0.47999999999999998,0.52000000000000002,0.56000000000000005,0.60000000000000009,0.64000000000000012,0.68000000000000016,0.7200000000000002,0.76000000000000023,0.80000000000000027,0.83999999999999986,0.87999999999999989,0.91999999999999993,0.95999999999999996,1,1.04,1.0800000000000001,1.1200000000000001,1.1600000000000001,1.2000000000000002,1.2400000000000002,1.2800000000000002,1.3200000000000003,1.3599999999999999,1.3999999999999999,1.4399999999999999,1.48,1.52,1.5600000000000001,1.6000000000000001,1.6400000000000001,1.6800000000000002,1.7200000000000002,1.7600000000000002,1.8000000000000003,1.8399999999999999,1.8799999999999999,1.9199999999999999,1.96,2],"y":[-2,-1.96,-1.9199999999999999,-1.8799999999999999,-1.8400000000000001,-1.8,-1.76,-1.72,-1.6799999999999999,-1.6400000000000001,-1.6000000000000001,-1.5600000000000001,-1.52,-1.48,-1.4399999999999999,-1.3999999999999999,-1.3599999999999999,-1.3199999999999998,-1.28,-1.24,-1.2,-1.1600000000000001,-1.1200000000000001,-1.0800000000000001,-1.04,-1,-0.95999999999999996,-0.91999999999999993,-0.87999999999999989,-0.84000000000000008,-0.80000000000000004,-0.76000000000000001,-0.71999999999999997,-0.67999999999999994,-0.6399999999999999,-0.59999999999999987,-0.56000000000000005,-0.52000000000000002,-0.47999999999999998,-0.43999999999999995,-0.39999999999999991,-0.35999999999999988,-0.32000000000000006,-0.28000000000000003,-0.23999999999999999,-0.19999999999999996,-0.15999999999999992,-0.11999999999999988,-0.080000000000000071,-0.040000000000000036,0,0.040000000000000036,0.080000000000000071,0.12000000000000011,0.16000000000000014,0.20000000000000018,0.24000000000000021,0.28000000000000025,0.31999999999999984,0.35999999999999988,0.39999999999999991,0.43999999999999995,0.47999999999999998,0.52000000000000002,0.56000000000000005,0.60000000000000009,0.64000000000000012,0.68000000000000016,0.7200000000000002,0.76000000000000023,0.80000000000000027,0.83999999999999986,0.87999999999999989,0.91999999999999993,0.95999999999999996,1,1.04,1.0800000000000001,1.1200000000000001,1.1600000000000001,1.2000000000000002,1.2400000000000002,1.2800000000000002,1.3200000000000003,1.3599999999999999,1.3999999999999999,1.4399999999999999,1.48,1.52,1.5600000000000001,1.6000000000000001,1.6400000000000001,1.6800000000000002,1.7200000000000002,1.7600000000000002,1.8000000000000003,1.8399999999999999,1.8799999999999999,1.9199999999999999,1.96,2],"z":[[-8,-7.8415999999999997,-7.6863999999999999,-7.5343999999999998,-7.3856000000000002,-7.2400000000000002,-7.0975999999999999,-6.9583999999999993,-6.8224,-6.6896000000000004,-6.5600000000000005,-6.4336000000000002,-6.3103999999999996,-6.1904000000000003,-6.0735999999999999,-5.96,-5.8495999999999997,-5.7423999999999999,-5.6383999999999999,-5.5376000000000003,-5.4399999999999995,-5.3456000000000001,-5.2544000000000004,-5.1664000000000003,-5.0815999999999999,-5,-4.9215999999999998,-4.8464,-4.7744,-4.7056000000000004,-4.6400000000000006,-4.5776000000000003,-4.5183999999999997,-4.4623999999999997,-4.4096000000000002,-4.3599999999999994,-4.3136000000000001,-4.2704000000000004,-4.2304000000000004,-4.1936,-4.1600000000000001,-4.1295999999999999,-4.1024000000000003,-4.0784000000000002,-4.0575999999999999,-4.04,-4.0255999999999998,-4.0144000000000002,-4.0064000000000002,-4.0015999999999998,-4,-4.0015999999999998,-4.0064000000000002,-4.0144000000000002,-4.0255999999999998,-4.04,-4.0575999999999999,-4.0784000000000002,-4.1024000000000003,-4.1295999999999999,-4.1600000000000001,-4.1936,-4.2304000000000004,-4.2704000000000004,-4.3136000000000001,-4.3600000000000003,-4.4096000000000002,-4.4624000000000006,-4.5184000000000006,-4.5776000000000003,-4.6400000000000006,-4.7055999999999996,-4.7744,-4.8464,-4.9215999999999998,-5,-5.0815999999999999,-5.1664000000000003,-5.2544000000000004,-5.3456000000000001,-5.4400000000000004,-5.5376000000000003,-5.6384000000000007,-5.7424000000000008,-5.8495999999999997,-5.96,-6.0735999999999999,-6.1904000000000003,-6.3103999999999996,-6.4336000000000002,-6.5600000000000005,-6.6896000000000004,-6.8224,-6.958400000000001,-7.0976000000000008,-7.2400000000000011,-7.3855999999999993,-7.5343999999999998,-7.6863999999999999,-7.8415999999999997,-8],[-7.8415999999999997,-7.6831999999999994,-7.5279999999999996,-7.3759999999999994,-7.2271999999999998,-7.0815999999999999,-6.9391999999999996,-6.7999999999999989,-6.6639999999999997,-6.5312000000000001,-6.4016000000000002,-6.2751999999999999,-6.1519999999999992,-6.032,-5.9151999999999996,-5.8015999999999996,-5.6911999999999994,-5.5839999999999996,-5.4799999999999995,-5.3792,-5.2815999999999992,-5.1871999999999998,-5.0960000000000001,-5.008,-4.9231999999999996,-4.8415999999999997,-4.7631999999999994,-4.6879999999999997,-4.6159999999999997,-4.5472000000000001,-4.4816000000000003,-4.4192,-4.3599999999999994,-4.3039999999999994,-4.2511999999999999,-4.2015999999999991,-4.1551999999999998,-4.1120000000000001,-4.0720000000000001,-4.0351999999999997,-4.0015999999999998,-3.9711999999999996,-3.944,-3.9199999999999995,-3.8991999999999996,-3.8815999999999997,-3.8671999999999995,-3.8559999999999999,-3.8479999999999999,-3.8431999999999995,-3.8415999999999997,-3.8431999999999995,-3.8479999999999999,-3.8559999999999999,-3.8671999999999995,-3.8815999999999997,-3.8992,-3.9199999999999999,-3.9439999999999995,-3.9711999999999996,-4.0015999999999998,-4.0351999999999997,-4.0720000000000001,-4.1120000000000001,-4.1551999999999998,-4.2016,-4.2511999999999999,-4.3040000000000003,-4.3600000000000003,-4.4192,-4.4816000000000003,-4.5471999999999992,-4.6159999999999997,-4.6879999999999997,-4.7631999999999994,-4.8415999999999997,-4.9231999999999996,-5.008,-5.0960000000000001,-5.1871999999999998,-5.2816000000000001,-5.3792,-5.4800000000000004,-5.5840000000000005,-5.6911999999999994,-5.8015999999999996,-5.9151999999999996,-6.032,-6.1519999999999992,-6.2751999999999999,-6.4016000000000002,-6.5312000000000001,-6.6639999999999997,-6.8000000000000007,-6.9392000000000005,-7.0816000000000008,-7.227199999999999,-7.3759999999999994,-7.5279999999999996,-7.6831999999999994,-7.8415999999999997],[-7.6863999999999999,-7.5279999999999996,-7.3727999999999998,-7.2207999999999997,-7.0720000000000001,-6.9264000000000001,-6.7839999999999998,-6.6448,-6.508799999999999,-6.3760000000000003,-6.2464000000000004,-6.1200000000000001,-5.9968000000000004,-5.8767999999999994,-5.7599999999999998,-5.6463999999999999,-5.5359999999999996,-5.428799999999999,-5.3247999999999998,-5.2240000000000002,-5.1264000000000003,-5.032,-4.9408000000000003,-4.8528000000000002,-4.7679999999999998,-4.6863999999999999,-4.6079999999999997,-4.5327999999999999,-4.4607999999999999,-4.3920000000000003,-4.3263999999999996,-4.2640000000000002,-4.2047999999999996,-4.1487999999999996,-4.0960000000000001,-4.0463999999999993,-4,-3.9567999999999999,-3.9167999999999998,-3.8799999999999999,-3.8464,-3.8159999999999998,-3.7888000000000002,-3.7647999999999997,-3.7439999999999998,-3.7263999999999999,-3.7119999999999997,-3.7008000000000001,-3.6928000000000001,-3.6879999999999997,-3.6863999999999999,-3.6879999999999997,-3.6928000000000001,-3.7008000000000001,-3.7119999999999997,-3.7263999999999999,-3.7440000000000002,-3.7648000000000001,-3.7887999999999997,-3.8159999999999998,-3.8464,-3.8799999999999999,-3.9167999999999998,-3.9567999999999999,-4,-4.0464000000000002,-4.0960000000000001,-4.1488000000000005,-4.2048000000000005,-4.2640000000000002,-4.3264000000000005,-4.3919999999999995,-4.4607999999999999,-4.5327999999999999,-4.6079999999999997,-4.6863999999999999,-4.7679999999999998,-4.8528000000000002,-4.9408000000000003,-5.032,-5.1264000000000003,-5.2240000000000002,-5.3248000000000006,-5.4288000000000007,-5.5359999999999996,-5.6463999999999999,-5.7599999999999998,-5.8767999999999994,-5.9968000000000004,-6.1200000000000001,-6.2464000000000004,-6.3760000000000003,-6.5088000000000008,-6.6448,-6.7840000000000007,-6.926400000000001,-7.0719999999999992,-7.2207999999999997,-7.3727999999999998,-7.5279999999999996,-7.6863999999999999],[-7.5343999999999998,-7.3759999999999994,-7.2207999999999997,-7.0687999999999995,-6.9199999999999999,-6.7744,-6.6319999999999997,-6.492799999999999,-6.3567999999999998,-6.2240000000000002,-6.0944000000000003,-5.968,-5.8447999999999993,-5.7248000000000001,-5.6079999999999997,-5.4943999999999997,-5.3839999999999995,-5.2767999999999997,-5.1727999999999996,-5.0720000000000001,-4.9743999999999993,-4.8799999999999999,-4.7888000000000002,-4.7008000000000001,-4.6159999999999997,-4.5343999999999998,-4.4559999999999995,-4.3807999999999998,-4.3087999999999997,-4.2400000000000002,-4.1744000000000003,-4.1120000000000001,-4.0527999999999995,-3.9967999999999995,-3.9439999999999995,-3.8943999999999996,-3.8479999999999999,-3.8047999999999997,-3.7647999999999997,-3.7279999999999998,-3.6943999999999999,-3.6639999999999997,-3.6368,-3.6127999999999996,-3.5919999999999996,-3.5743999999999998,-3.5599999999999996,-3.5488,-3.5407999999999999,-3.5359999999999996,-3.5343999999999998,-3.5359999999999996,-3.5407999999999999,-3.5488,-3.5599999999999996,-3.5743999999999998,-3.5920000000000001,-3.6128,-3.6367999999999996,-3.6639999999999997,-3.6943999999999999,-3.7279999999999998,-3.7647999999999997,-3.8047999999999997,-3.8479999999999999,-3.8944000000000001,-3.944,-3.9967999999999999,-4.0528000000000004,-4.1120000000000001,-4.1744000000000003,-4.2399999999999993,-4.3087999999999997,-4.3807999999999998,-4.4559999999999995,-4.5343999999999998,-4.6159999999999997,-4.7008000000000001,-4.7888000000000002,-4.8799999999999999,-4.9744000000000002,-5.0720000000000001,-5.1728000000000005,-5.2768000000000006,-5.3839999999999995,-5.4943999999999997,-5.6079999999999997,-5.7248000000000001,-5.8447999999999993,-5.968,-6.0944000000000003,-6.2240000000000002,-6.3567999999999998,-6.4928000000000008,-6.6320000000000006,-6.7744000000000009,-6.919999999999999,-7.0687999999999995,-7.2207999999999997,-7.3759999999999994,-7.5343999999999998],[-7.3856000000000002,-7.2271999999999998,-7.0720000000000001,-6.9199999999999999,-6.7712000000000003,-6.6256000000000004,-6.4832000000000001,-6.3439999999999994,-6.2080000000000002,-6.0752000000000006,-5.9456000000000007,-5.8192000000000004,-5.6959999999999997,-5.5760000000000005,-5.4592000000000001,-5.3456000000000001,-5.2351999999999999,-5.1280000000000001,-5.024,-4.9232000000000005,-4.8255999999999997,-4.7312000000000003,-4.6400000000000006,-4.5520000000000005,-4.4672000000000001,-4.3856000000000002,-4.3071999999999999,-4.2320000000000002,-4.1600000000000001,-4.0912000000000006,-4.0256000000000007,-3.9632000000000001,-3.9039999999999999,-3.8479999999999999,-3.7951999999999999,-3.7456,-3.6992000000000003,-3.6560000000000001,-3.6160000000000001,-3.5792000000000002,-3.5456000000000003,-3.5152000000000001,-3.4880000000000004,-3.464,-3.4432,-3.4256000000000002,-3.4112,-3.4000000000000004,-3.3920000000000003,-3.3872,-3.3856000000000002,-3.3872,-3.3920000000000003,-3.4000000000000004,-3.4112,-3.4256000000000002,-3.4432000000000005,-3.4640000000000004,-3.488,-3.5152000000000001,-3.5456000000000003,-3.5792000000000002,-3.6160000000000001,-3.6560000000000001,-3.6992000000000003,-3.7456000000000005,-3.7952000000000004,-3.8480000000000003,-3.9040000000000004,-3.9632000000000005,-4.0256000000000007,-4.0911999999999997,-4.1600000000000001,-4.2320000000000002,-4.3071999999999999,-4.3856000000000002,-4.4672000000000001,-4.5520000000000005,-4.6400000000000006,-4.7312000000000003,-4.8256000000000006,-4.9232000000000005,-5.0240000000000009,-5.128000000000001,-5.2351999999999999,-5.3456000000000001,-5.4592000000000001,-5.5760000000000005,-5.6959999999999997,-5.8192000000000004,-5.9456000000000007,-6.0752000000000006,-6.2080000000000002,-6.3440000000000012,-6.483200000000001,-6.6256000000000013,-6.7711999999999994,-6.9199999999999999,-7.0720000000000001,-7.2271999999999998,-7.3856000000000002],[-7.2400000000000002,-7.0815999999999999,-6.9264000000000001,-6.7744,-6.6256000000000004,-6.4800000000000004,-6.3376000000000001,-6.1983999999999995,-6.0624000000000002,-5.9296000000000006,-5.8000000000000007,-5.6736000000000004,-5.5503999999999998,-5.4304000000000006,-5.3136000000000001,-5.2000000000000002,-5.0895999999999999,-4.9824000000000002,-4.8784000000000001,-4.7776000000000005,-4.6799999999999997,-4.5856000000000003,-4.4944000000000006,-4.4064000000000005,-4.3216000000000001,-4.2400000000000002,-4.1616,-4.0864000000000003,-4.0144000000000002,-3.9456000000000002,-3.8800000000000003,-3.8176000000000001,-3.7584,-3.7023999999999999,-3.6496,-3.6000000000000001,-3.5536000000000003,-3.5104000000000002,-3.4704000000000002,-3.4336000000000002,-3.4000000000000004,-3.3696000000000002,-3.3424000000000005,-3.3184,-3.2976000000000001,-3.2800000000000002,-3.2656000000000001,-3.2544000000000004,-3.2464000000000004,-3.2416,-3.2400000000000002,-3.2416,-3.2464000000000004,-3.2544000000000004,-3.2656000000000001,-3.2800000000000002,-3.2976000000000005,-3.3184000000000005,-3.3424,-3.3696000000000002,-3.4000000000000004,-3.4336000000000002,-3.4704000000000002,-3.5104000000000002,-3.5536000000000003,-3.6000000000000005,-3.6496000000000004,-3.7024000000000004,-3.7584000000000004,-3.8176000000000005,-3.8800000000000008,-3.9455999999999998,-4.0144000000000002,-4.0864000000000003,-4.1616,-4.2400000000000002,-4.3216000000000001,-4.4064000000000005,-4.4944000000000006,-4.5856000000000003,-4.6800000000000006,-4.7776000000000005,-4.878400000000001,-4.9824000000000011,-5.0895999999999999,-5.2000000000000002,-5.3136000000000001,-5.4304000000000006,-5.5503999999999998,-5.6736000000000004,-5.8000000000000007,-5.9296000000000006,-6.0624000000000002,-6.1984000000000012,-6.337600000000001,-6.4800000000000013,-6.6255999999999995,-6.7744,-6.9264000000000001,-7.0815999999999999,-7.2400000000000002],[-7.0975999999999999,-6.9391999999999996,-6.7839999999999998,-6.6319999999999997,-6.4832000000000001,-6.3376000000000001,-6.1951999999999998,-6.0559999999999992,-5.9199999999999999,-5.7872000000000003,-5.6576000000000004,-5.5312000000000001,-5.4079999999999995,-5.2880000000000003,-5.1711999999999998,-5.0575999999999999,-4.9471999999999996,-4.8399999999999999,-4.7359999999999998,-4.6352000000000002,-4.5375999999999994,-4.4432,-4.3520000000000003,-4.2640000000000002,-4.1791999999999998,-4.0975999999999999,-4.0191999999999997,-3.944,-3.8719999999999999,-3.8031999999999999,-3.7376,-3.6751999999999998,-3.6159999999999997,-3.5599999999999996,-3.5071999999999997,-3.4575999999999998,-3.4112,-3.3679999999999999,-3.3279999999999998,-3.2911999999999999,-3.2576000000000001,-3.2271999999999998,-3.2000000000000002,-3.1759999999999997,-3.1551999999999998,-3.1375999999999999,-3.1231999999999998,-3.1120000000000001,-3.1040000000000001,-3.0991999999999997,-3.0975999999999999,-3.0991999999999997,-3.1040000000000001,-3.1120000000000001,-3.1231999999999998,-3.1375999999999999,-3.1552000000000002,-3.1760000000000002,-3.1999999999999997,-3.2271999999999998,-3.2576000000000001,-3.2911999999999999,-3.3279999999999998,-3.3679999999999999,-3.4112,-3.4576000000000002,-3.5072000000000001,-3.5600000000000001,-3.6160000000000001,-3.6752000000000002,-3.7376000000000005,-3.8031999999999995,-3.8719999999999999,-3.944,-4.0191999999999997,-4.0975999999999999,-4.1791999999999998,-4.2640000000000002,-4.3520000000000003,-4.4432,-4.5376000000000003,-4.6352000000000002,-4.7360000000000007,-4.8400000000000007,-4.9471999999999996,-5.0575999999999999,-5.1711999999999998,-5.2880000000000003,-5.4079999999999995,-5.5312000000000001,-5.6576000000000004,-5.7872000000000003,-5.9199999999999999,-6.0560000000000009,-6.1952000000000007,-6.337600000000001,-6.4831999999999992,-6.6319999999999997,-6.7839999999999998,-6.9391999999999996,-7.0975999999999999],[-6.9583999999999993,-6.7999999999999989,-6.6448,-6.492799999999999,-6.3439999999999994,-6.1983999999999995,-6.0559999999999992,-5.9167999999999994,-5.7807999999999993,-5.6479999999999997,-5.5183999999999997,-5.3919999999999995,-5.2687999999999997,-5.1487999999999996,-5.032,-4.9183999999999992,-4.8079999999999998,-4.7007999999999992,-4.5968,-4.4959999999999996,-4.3983999999999996,-4.3040000000000003,-4.2127999999999997,-4.1247999999999996,-4.04,-3.9583999999999997,-3.8799999999999999,-3.8047999999999993,-3.7327999999999997,-3.6639999999999997,-3.5983999999999998,-3.5359999999999996,-3.4767999999999999,-3.4207999999999998,-3.3679999999999994,-3.3183999999999996,-3.2719999999999998,-3.2287999999999997,-3.1887999999999996,-3.1519999999999997,-3.1183999999999994,-3.0879999999999996,-3.0607999999999995,-3.0367999999999995,-3.0159999999999996,-2.9983999999999997,-2.9839999999999995,-2.9727999999999999,-2.9647999999999999,-2.9599999999999995,-2.9583999999999997,-2.9599999999999995,-2.9647999999999999,-2.9727999999999999,-2.9839999999999995,-2.9983999999999997,-3.016,-3.0367999999999999,-3.0607999999999995,-3.0879999999999996,-3.1183999999999994,-3.1519999999999997,-3.1887999999999996,-3.2287999999999997,-3.2719999999999998,-3.3183999999999996,-3.3679999999999999,-3.4207999999999998,-3.4767999999999999,-3.536,-3.5984000000000003,-3.6639999999999997,-3.7327999999999997,-3.8047999999999993,-3.8799999999999999,-3.9583999999999997,-4.04,-4.1247999999999996,-4.2127999999999997,-4.3040000000000003,-4.3984000000000005,-4.4960000000000004,-4.5968,-4.700800000000001,-4.8079999999999998,-4.9183999999999992,-5.032,-5.1487999999999996,-5.2687999999999997,-5.3919999999999995,-5.5183999999999997,-5.6479999999999997,-5.7808000000000002,-5.9168000000000003,-6.0560000000000009,-6.1984000000000012,-6.3439999999999994,-6.492799999999999,-6.6448,-6.7999999999999989,-6.9583999999999993],[-6.8224,-6.6639999999999997,-6.508799999999999,-6.3567999999999998,-6.2080000000000002,-6.0624000000000002,-5.9199999999999999,-5.7807999999999993,-5.6447999999999992,-5.5120000000000005,-5.3824000000000005,-5.2560000000000002,-5.1327999999999996,-5.0127999999999995,-4.895999999999999,-4.7823999999999991,-4.6719999999999988,-4.5647999999999991,-4.4607999999999999,-4.3599999999999994,-4.2623999999999995,-4.1680000000000001,-4.0767999999999995,-3.9887999999999995,-3.9039999999999999,-3.8223999999999996,-3.7439999999999998,-3.6687999999999992,-3.5967999999999996,-3.5279999999999996,-3.4623999999999997,-3.3999999999999995,-3.3407999999999998,-3.2847999999999997,-3.2319999999999993,-3.1823999999999995,-3.1359999999999997,-3.0927999999999995,-3.0527999999999995,-3.0159999999999996,-2.9823999999999993,-2.9519999999999995,-2.9247999999999994,-2.9007999999999994,-2.8799999999999994,-2.8623999999999996,-2.8479999999999994,-2.8367999999999998,-2.8287999999999998,-2.8239999999999994,-2.8223999999999996,-2.8239999999999994,-2.8287999999999998,-2.8367999999999998,-2.8479999999999994,-2.8623999999999996,-2.8799999999999999,-2.9007999999999998,-2.9247999999999994,-2.9519999999999995,-2.9823999999999993,-3.0159999999999996,-3.0527999999999995,-3.0927999999999995,-3.1359999999999997,-3.1823999999999995,-3.2319999999999998,-3.2847999999999997,-3.3407999999999998,-3.3999999999999999,-3.4624000000000001,-3.5279999999999996,-3.5967999999999996,-3.6687999999999992,-3.7439999999999998,-3.8223999999999996,-3.9039999999999999,-3.9887999999999995,-4.0767999999999995,-4.1680000000000001,-4.2623999999999995,-4.3600000000000003,-4.4608000000000008,-4.5648,-4.6719999999999988,-4.7823999999999991,-4.895999999999999,-5.0127999999999995,-5.1327999999999996,-5.2560000000000002,-5.3824000000000005,-5.5120000000000005,-5.6448,-5.7808000000000002,-5.9199999999999999,-6.0624000000000002,-6.2079999999999984,-6.3567999999999998,-6.508799999999999,-6.6639999999999997,-6.8224],[-6.6896000000000004,-6.5312000000000001,-6.3760000000000003,-6.2240000000000002,-6.0752000000000006,-5.9296000000000006,-5.7872000000000003,-5.6479999999999997,-5.5120000000000005,-5.3792000000000009,-5.2496000000000009,-5.1232000000000006,-5,-4.8800000000000008,-4.7632000000000003,-4.6496000000000004,-4.5392000000000001,-4.4320000000000004,-4.3280000000000003,-4.2272000000000007,-4.1295999999999999,-4.0352000000000006,-3.9440000000000008,-3.8560000000000008,-3.7712000000000003,-3.6896000000000004,-3.6112000000000002,-3.5360000000000005,-3.4640000000000004,-3.3952000000000004,-3.3296000000000006,-3.2672000000000003,-3.2080000000000002,-3.1520000000000001,-3.0992000000000002,-3.0496000000000003,-3.0032000000000005,-2.9600000000000004,-2.9200000000000004,-2.8832000000000004,-2.8496000000000006,-2.8192000000000004,-2.7920000000000007,-2.7680000000000002,-2.7472000000000003,-2.7296000000000005,-2.7152000000000003,-2.7040000000000006,-2.6960000000000006,-2.6912000000000003,-2.6896000000000004,-2.6912000000000003,-2.6960000000000006,-2.7040000000000006,-2.7152000000000003,-2.7296000000000005,-2.7472000000000008,-2.7680000000000007,-2.7920000000000003,-2.8192000000000004,-2.8496000000000006,-2.8832000000000004,-2.9200000000000004,-2.9600000000000004,-3.0032000000000005,-3.0496000000000008,-3.0992000000000006,-3.1520000000000006,-3.2080000000000006,-3.2672000000000008,-3.329600000000001,-3.3952,-3.4640000000000004,-3.5360000000000005,-3.6112000000000002,-3.6896000000000004,-3.7712000000000003,-3.8560000000000008,-3.9440000000000008,-4.0352000000000006,-4.1296000000000008,-4.2272000000000007,-4.3280000000000012,-4.4320000000000013,-4.5392000000000001,-4.6496000000000004,-4.7632000000000003,-4.8800000000000008,-5,-5.1232000000000006,-5.2496000000000009,-5.3792000000000009,-5.5120000000000005,-5.6480000000000015,-5.7872000000000012,-5.9296000000000015,-6.0751999999999997,-6.2240000000000002,-6.3760000000000003,-6.5312000000000001,-6.6896000000000004],[-6.5600000000000005,-6.4016000000000002,-6.2464000000000004,-6.0944000000000003,-5.9456000000000007,-5.8000000000000007,-5.6576000000000004,-5.5183999999999997,-5.3824000000000005,-5.2496000000000009,-5.120000000000001,-4.9936000000000007,-4.8704000000000001,-4.7504000000000008,-4.6336000000000004,-4.5200000000000005,-4.4096000000000002,-4.3024000000000004,-4.1984000000000004,-4.0976000000000008,-4,-3.9056000000000006,-3.8144000000000009,-3.7264000000000008,-3.6416000000000004,-3.5600000000000005,-3.4816000000000003,-3.4064000000000005,-3.3344000000000005,-3.2656000000000005,-3.2000000000000006,-3.1376000000000004,-3.0784000000000002,-3.0224000000000002,-2.9696000000000002,-2.9200000000000004,-2.8736000000000006,-2.8304000000000005,-2.7904000000000004,-2.7536000000000005,-2.7200000000000006,-2.6896000000000004,-2.6624000000000008,-2.6384000000000003,-2.6176000000000004,-2.6000000000000005,-2.5856000000000003,-2.5744000000000007,-2.5664000000000007,-2.5616000000000003,-2.5600000000000005,-2.5616000000000003,-2.5664000000000007,-2.5744000000000007,-2.5856000000000003,-2.6000000000000005,-2.6176000000000008,-2.6384000000000007,-2.6624000000000003,-2.6896000000000004,-2.7200000000000006,-2.7536000000000005,-2.7904000000000004,-2.8304000000000005,-2.8736000000000006,-2.9200000000000008,-2.9696000000000007,-3.0224000000000006,-3.0784000000000007,-3.1376000000000008,-3.2000000000000011,-3.2656000000000001,-3.3344000000000005,-3.4064000000000005,-3.4816000000000003,-3.5600000000000005,-3.6416000000000004,-3.7264000000000008,-3.8144000000000009,-3.9056000000000006,-4.0000000000000009,-4.0976000000000008,-4.1984000000000012,-4.3024000000000013,-4.4096000000000002,-4.5200000000000005,-4.6336000000000004,-4.7504000000000008,-4.8704000000000001,-4.9936000000000007,-5.120000000000001,-5.2496000000000009,-5.3824000000000005,-5.5184000000000015,-5.6576000000000013,-5.8000000000000016,-5.9455999999999998,-6.0944000000000003,-6.2464000000000004,-6.4016000000000002,-6.5600000000000005],[-6.4336000000000002,-6.2751999999999999,-6.1200000000000001,-5.968,-5.8192000000000004,-5.6736000000000004,-5.5312000000000001,-5.3919999999999995,-5.2560000000000002,-5.1232000000000006,-4.9936000000000007,-4.8672000000000004,-4.7439999999999998,-4.6240000000000006,-4.5072000000000001,-4.3936000000000002,-4.2831999999999999,-4.1760000000000002,-4.0720000000000001,-3.9712000000000005,-3.8736000000000002,-3.7792000000000003,-3.6880000000000006,-3.6000000000000005,-3.5152000000000001,-3.4336000000000002,-3.3552,-3.2800000000000002,-3.2080000000000002,-3.1392000000000002,-3.0736000000000003,-3.0112000000000001,-2.952,-2.8959999999999999,-2.8431999999999999,-2.7936000000000001,-2.7472000000000003,-2.7040000000000002,-2.6640000000000001,-2.6272000000000002,-2.5936000000000003,-2.5632000000000001,-2.5360000000000005,-2.512,-2.4912000000000001,-2.4736000000000002,-2.4592000000000001,-2.4480000000000004,-2.4400000000000004,-2.4352,-2.4336000000000002,-2.4352,-2.4400000000000004,-2.4480000000000004,-2.4592000000000001,-2.4736000000000002,-2.4912000000000005,-2.5120000000000005,-2.536,-2.5632000000000001,-2.5936000000000003,-2.6272000000000002,-2.6640000000000001,-2.7040000000000002,-2.7472000000000003,-2.7936000000000005,-2.8432000000000004,-2.8960000000000004,-2.9520000000000004,-3.0112000000000005,-3.0736000000000008,-3.1391999999999998,-3.2080000000000002,-3.2800000000000002,-3.3552,-3.4336000000000002,-3.5152000000000001,-3.6000000000000005,-3.6880000000000006,-3.7792000000000003,-3.8736000000000006,-3.9712000000000005,-4.072000000000001,-4.176000000000001,-4.2831999999999999,-4.3936000000000002,-4.5072000000000001,-4.6240000000000006,-4.7439999999999998,-4.8672000000000004,-4.9936000000000007,-5.1232000000000006,-5.2560000000000002,-5.3920000000000012,-5.531200000000001,-5.6736000000000013,-5.8191999999999995,-5.968,-6.1200000000000001,-6.2751999999999999,-6.4336000000000002],[-6.3103999999999996,-6.1519999999999992,-5.9968000000000004,-5.8447999999999993,-5.6959999999999997,-5.5503999999999998,-5.4079999999999995,-5.2687999999999997,-5.1327999999999996,-5,-4.8704000000000001,-4.7439999999999998,-4.6208,-4.5007999999999999,-4.3840000000000003,-4.2703999999999995,-4.1600000000000001,-4.0527999999999995,-3.9488000000000003,-3.8479999999999999,-3.7504,-3.6560000000000006,-3.5648,-3.4767999999999999,-3.3920000000000003,-3.3104,-3.2320000000000002,-3.1567999999999996,-3.0848,-3.016,-2.9504000000000001,-2.8879999999999999,-2.8288000000000002,-2.7728000000000002,-2.7199999999999998,-2.6703999999999999,-2.6240000000000001,-2.5808,-2.5407999999999999,-2.504,-2.4703999999999997,-2.4399999999999999,-2.4127999999999998,-2.3887999999999998,-2.3679999999999999,-2.3504,-2.3359999999999999,-2.3248000000000002,-2.3168000000000002,-2.3119999999999998,-2.3104,-2.3119999999999998,-2.3168000000000002,-2.3248000000000002,-2.3359999999999999,-2.3504,-2.3680000000000003,-2.3888000000000003,-2.4127999999999998,-2.4399999999999999,-2.4703999999999997,-2.504,-2.5407999999999999,-2.5808,-2.6240000000000001,-2.6703999999999999,-2.7200000000000002,-2.7728000000000002,-2.8288000000000002,-2.8880000000000003,-2.9504000000000006,-3.016,-3.0848,-3.1567999999999996,-3.2320000000000002,-3.3104,-3.3920000000000003,-3.4767999999999999,-3.5648,-3.6560000000000006,-3.7504000000000004,-3.8480000000000008,-3.9488000000000008,-4.0528000000000013,-4.1600000000000001,-4.2703999999999995,-4.3840000000000003,-4.5007999999999999,-4.6208,-4.7439999999999998,-4.8704000000000001,-5,-5.1328000000000005,-5.2688000000000006,-5.4080000000000013,-5.5504000000000016,-5.6959999999999997,-5.8447999999999993,-5.9968000000000004,-6.1519999999999992,-6.3103999999999996],[-6.1904000000000003,-6.032,-5.8767999999999994,-5.7248000000000001,-5.5760000000000005,-5.4304000000000006,-5.2880000000000003,-5.1487999999999996,-5.0127999999999995,-4.8800000000000008,-4.7504000000000008,-4.6240000000000006,-4.5007999999999999,-4.3807999999999998,-4.2639999999999993,-4.1503999999999994,-4.0399999999999991,-3.9327999999999994,-3.8288000000000002,-3.7279999999999998,-3.6303999999999998,-3.5360000000000005,-3.4447999999999999,-3.3567999999999998,-3.2720000000000002,-3.1903999999999999,-3.1120000000000001,-3.0367999999999995,-2.9647999999999999,-2.8959999999999999,-2.8304,-2.7679999999999998,-2.7088000000000001,-2.6528,-2.5999999999999996,-2.5503999999999998,-2.504,-2.4607999999999999,-2.4207999999999998,-2.3839999999999999,-2.3503999999999996,-2.3199999999999998,-2.2927999999999997,-2.2687999999999997,-2.2479999999999998,-2.2303999999999999,-2.2159999999999997,-2.2048000000000001,-2.1968000000000001,-2.1919999999999997,-2.1903999999999999,-2.1919999999999997,-2.1968000000000001,-2.2048000000000001,-2.2159999999999997,-2.2303999999999999,-2.2480000000000002,-2.2688000000000001,-2.2927999999999997,-2.3199999999999998,-2.3503999999999996,-2.3839999999999999,-2.4207999999999998,-2.4607999999999999,-2.504,-2.5503999999999998,-2.6000000000000001,-2.6528,-2.7088000000000001,-2.7680000000000002,-2.8304000000000005,-2.8959999999999999,-2.9647999999999999,-3.0367999999999995,-3.1120000000000001,-3.1903999999999999,-3.2720000000000002,-3.3567999999999998,-3.4447999999999999,-3.5360000000000005,-3.6304000000000003,-3.7280000000000006,-3.8288000000000006,-3.9328000000000007,-4.0399999999999991,-4.1503999999999994,-4.2639999999999993,-4.3807999999999998,-4.5007999999999999,-4.6240000000000006,-4.7504000000000008,-4.8800000000000008,-5.0128000000000004,-5.1488000000000005,-5.2880000000000003,-5.4304000000000006,-5.5759999999999987,-5.7248000000000001,-5.8767999999999994,-6.032,-6.1904000000000003],[-6.0735999999999999,-5.9151999999999996,-5.7599999999999998,-5.6079999999999997,-5.4592000000000001,-5.3136000000000001,-5.1711999999999998,-5.032,-4.895999999999999,-4.7632000000000003,-4.6336000000000004,-4.5072000000000001,-4.3840000000000003,-4.2639999999999993,-4.1471999999999998,-4.0335999999999999,-3.9231999999999996,-3.8159999999999994,-3.7119999999999997,-3.6112000000000002,-3.5135999999999998,-3.4192,-3.3280000000000003,-3.2400000000000002,-3.1551999999999998,-3.0735999999999999,-2.9951999999999996,-2.9199999999999999,-2.8479999999999999,-2.7791999999999999,-2.7136,-2.6511999999999998,-2.5919999999999996,-2.5359999999999996,-2.4831999999999996,-2.4335999999999998,-2.3872,-2.3439999999999999,-2.3039999999999998,-2.2671999999999999,-2.2336,-2.2031999999999998,-2.1760000000000002,-2.1519999999999997,-2.1311999999999998,-2.1135999999999999,-2.0991999999999997,-2.0880000000000001,-2.0800000000000001,-2.0751999999999997,-2.0735999999999999,-2.0751999999999997,-2.0800000000000001,-2.0880000000000001,-2.0991999999999997,-2.1135999999999999,-2.1312000000000002,-2.1520000000000001,-2.1759999999999997,-2.2031999999999998,-2.2336,-2.2671999999999999,-2.3039999999999998,-2.3439999999999999,-2.3872,-2.4336000000000002,-2.4832000000000001,-2.536,-2.5920000000000001,-2.6512000000000002,-2.7136000000000005,-2.7791999999999994,-2.8479999999999999,-2.9199999999999999,-2.9951999999999996,-3.0735999999999999,-3.1551999999999998,-3.2400000000000002,-3.3280000000000003,-3.4192,-3.5136000000000003,-3.6112000000000002,-3.7120000000000006,-3.8160000000000007,-3.9231999999999996,-4.0335999999999999,-4.1471999999999998,-4.2639999999999993,-4.3840000000000003,-4.5072000000000001,-4.6336000000000004,-4.7632000000000003,-4.8960000000000008,-5.032,-5.1712000000000007,-5.313600000000001,-5.4591999999999992,-5.6079999999999997,-5.7599999999999998,-5.9151999999999996,-6.0735999999999999],[-5.96,-5.8015999999999996,-5.6463999999999999,-5.4943999999999997,-5.3456000000000001,-5.2000000000000002,-5.0575999999999999,-4.9183999999999992,-4.7823999999999991,-4.6496000000000004,-4.5200000000000005,-4.3936000000000002,-4.2703999999999995,-4.1503999999999994,-4.0335999999999999,-3.9199999999999995,-3.8095999999999997,-3.702399999999999,-3.5983999999999998,-3.4975999999999998,-3.3999999999999995,-3.3056000000000001,-3.2143999999999999,-3.1263999999999998,-3.0415999999999999,-2.96,-2.8815999999999997,-2.8063999999999996,-2.7343999999999995,-2.6656,-2.5999999999999996,-2.5375999999999999,-2.4783999999999997,-2.4223999999999997,-2.3695999999999997,-2.3199999999999994,-2.2735999999999996,-2.2303999999999999,-2.1903999999999999,-2.1535999999999995,-2.1199999999999997,-2.0895999999999995,-2.0623999999999998,-2.0383999999999998,-2.0175999999999998,-1.9999999999999998,-1.9855999999999998,-1.9743999999999997,-1.9663999999999997,-1.9615999999999998,-1.9599999999999997,-1.9615999999999998,-1.9663999999999997,-1.9743999999999997,-1.9855999999999998,-1.9999999999999998,-2.0175999999999998,-2.0383999999999998,-2.0623999999999998,-2.0895999999999995,-2.1199999999999997,-2.1535999999999995,-2.1903999999999999,-2.2303999999999999,-2.2735999999999996,-2.3199999999999998,-2.3696000000000002,-2.4224000000000001,-2.4784000000000002,-2.5376000000000003,-2.6000000000000001,-2.6655999999999995,-2.7343999999999995,-2.8063999999999996,-2.8815999999999997,-2.96,-3.0415999999999999,-3.1263999999999998,-3.2143999999999999,-3.3056000000000001,-3.4000000000000004,-3.4976000000000003,-3.5984000000000007,-3.7024000000000008,-3.8095999999999997,-3.9199999999999995,-4.0335999999999999,-4.1503999999999994,-4.2703999999999995,-4.3936000000000002,-4.5200000000000005,-4.6496000000000004,-4.7824,-4.9184000000000001,-5.0576000000000008,-5.2000000000000011,-5.3455999999999992,-5.4943999999999997,-5.6463999999999999,-5.8015999999999996,-5.96],[-5.8495999999999997,-5.6911999999999994,-5.5359999999999996,-5.3839999999999995,-5.2351999999999999,-5.0895999999999999,-4.9471999999999996,-4.8079999999999998,-4.6719999999999988,-4.5392000000000001,-4.4096000000000002,-4.2831999999999999,-4.1600000000000001,-4.0399999999999991,-3.9231999999999996,-3.8095999999999997,-3.6991999999999994,-3.5919999999999992,-3.4879999999999995,-3.3872,-3.2895999999999996,-3.1951999999999998,-3.1040000000000001,-3.016,-2.9311999999999996,-2.8495999999999997,-2.7711999999999994,-2.6959999999999997,-2.6239999999999997,-2.5551999999999997,-2.4895999999999998,-2.4271999999999996,-2.3679999999999994,-2.3119999999999994,-2.2591999999999994,-2.2095999999999996,-2.1631999999999998,-2.1199999999999997,-2.0799999999999996,-2.0431999999999997,-2.0095999999999998,-1.9791999999999996,-1.9519999999999997,-1.9279999999999997,-1.9071999999999998,-1.8895999999999997,-1.8751999999999998,-1.8639999999999997,-1.8559999999999997,-1.8511999999999997,-1.8495999999999997,-1.8511999999999997,-1.8559999999999997,-1.8639999999999997,-1.8751999999999998,-1.8895999999999997,-1.9071999999999998,-1.9279999999999999,-1.9519999999999995,-1.9791999999999996,-2.0095999999999998,-2.0431999999999997,-2.0799999999999996,-2.1199999999999997,-2.1631999999999998,-2.2096,-2.2591999999999999,-2.3119999999999998,-2.3679999999999999,-2.4272,-2.4896000000000003,-2.5551999999999992,-2.6239999999999997,-2.6959999999999997,-2.7711999999999994,-2.8495999999999997,-2.9311999999999996,-3.016,-3.1040000000000001,-3.1951999999999998,-3.2896000000000001,-3.3872,-3.4880000000000004,-3.5920000000000005,-3.6991999999999994,-3.8095999999999997,-3.9231999999999996,-4.0399999999999991,-4.1600000000000001,-4.2831999999999999,-4.4096000000000002,-4.5392000000000001,-4.6720000000000006,-4.8079999999999998,-4.9472000000000005,-5.0896000000000008,-5.235199999999999,-5.3839999999999995,-5.5359999999999996,-5.6911999999999994,-5.8495999999999997],[-5.7423999999999999,-5.5839999999999996,-5.428799999999999,-5.2767999999999997,-5.1280000000000001,-4.9824000000000002,-4.8399999999999999,-4.7007999999999992,-4.5647999999999991,-4.4320000000000004,-4.3024000000000004,-4.1760000000000002,-4.0527999999999995,-3.9327999999999994,-3.8159999999999994,-3.702399999999999,-3.5919999999999992,-3.484799999999999,-3.3807999999999998,-3.2799999999999994,-3.1823999999999995,-3.0880000000000001,-2.9967999999999995,-2.9087999999999994,-2.8239999999999998,-2.7423999999999995,-2.6639999999999997,-2.5887999999999991,-2.5167999999999995,-2.4479999999999995,-2.3823999999999996,-2.3199999999999994,-2.2607999999999997,-2.2047999999999996,-2.1519999999999992,-2.1023999999999994,-2.0559999999999996,-2.0127999999999995,-1.9727999999999994,-1.9359999999999995,-1.9023999999999994,-1.8719999999999994,-1.8447999999999996,-1.8207999999999995,-1.7999999999999996,-1.7823999999999995,-1.7679999999999996,-1.7567999999999995,-1.7487999999999995,-1.7439999999999996,-1.7423999999999995,-1.7439999999999996,-1.7487999999999995,-1.7567999999999995,-1.7679999999999996,-1.7823999999999995,-1.7999999999999996,-1.8207999999999998,-1.8447999999999993,-1.8719999999999994,-1.9023999999999994,-1.9359999999999995,-1.9727999999999994,-2.0127999999999995,-2.0559999999999996,-2.1023999999999994,-2.1519999999999997,-2.2047999999999996,-2.2607999999999997,-2.3199999999999998,-2.3824000000000001,-2.4479999999999995,-2.5167999999999995,-2.5887999999999991,-2.6639999999999997,-2.7423999999999995,-2.8239999999999998,-2.9087999999999994,-2.9967999999999995,-3.0880000000000001,-3.1823999999999999,-3.2800000000000002,-3.3808000000000002,-3.4848000000000003,-3.5919999999999992,-3.702399999999999,-3.8159999999999994,-3.9327999999999994,-4.0527999999999995,-4.1760000000000002,-4.3024000000000004,-4.4320000000000004,-4.5648,-4.7008000000000001,-4.8399999999999999,-4.9824000000000002,-5.1279999999999983,-5.2767999999999997,-5.428799999999999,-5.5839999999999996,-5.7423999999999999],[-5.6383999999999999,-5.4799999999999995,-5.3247999999999998,-5.1727999999999996,-5.024,-4.8784000000000001,-4.7359999999999998,-4.5968,-4.4607999999999999,-4.3280000000000003,-4.1984000000000004,-4.0720000000000001,-3.9488000000000003,-3.8288000000000002,-3.7119999999999997,-3.5983999999999998,-3.4879999999999995,-3.3807999999999998,-3.2768000000000002,-3.1760000000000002,-3.0784000000000002,-2.9840000000000004,-2.8928000000000003,-2.8048000000000002,-2.7200000000000002,-2.6383999999999999,-2.5600000000000001,-2.4847999999999999,-2.4127999999999998,-2.3440000000000003,-2.2784000000000004,-2.2160000000000002,-2.1568000000000001,-2.1008,-2.048,-1.9984,-1.9520000000000002,-1.9088000000000001,-1.8688,-1.8320000000000001,-1.7984,-1.768,-1.7408000000000001,-1.7168000000000001,-1.6960000000000002,-1.6784000000000001,-1.6640000000000001,-1.6528,-1.6448,-1.6400000000000001,-1.6384000000000001,-1.6400000000000001,-1.6448,-1.6528,-1.6640000000000001,-1.6784000000000001,-1.6960000000000002,-1.7168000000000001,-1.7407999999999999,-1.768,-1.7984,-1.8320000000000001,-1.8688,-1.9088000000000001,-1.9520000000000002,-1.9984000000000002,-2.048,-2.1008000000000004,-2.1568000000000005,-2.2160000000000002,-2.2784000000000004,-2.3439999999999999,-2.4127999999999998,-2.4847999999999999,-2.5600000000000001,-2.6383999999999999,-2.7200000000000002,-2.8048000000000002,-2.8928000000000003,-2.9840000000000004,-3.0784000000000002,-3.1760000000000006,-3.2768000000000006,-3.3808000000000007,-3.4879999999999995,-3.5983999999999998,-3.7119999999999997,-3.8288000000000002,-3.9488000000000003,-4.0720000000000001,-4.1984000000000004,-4.3280000000000003,-4.4608000000000008,-4.5968000000000009,-4.7360000000000007,-4.878400000000001,-5.0239999999999991,-5.1727999999999996,-5.3247999999999998,-5.4799999999999995,-5.6383999999999999],[-5.5376000000000003,-5.3792,-5.2240000000000002,-5.0720000000000001,-4.9232000000000005,-4.7776000000000005,-4.6352000000000002,-4.4959999999999996,-4.3599999999999994,-4.2272000000000007,-4.0976000000000008,-3.9712000000000005,-3.8479999999999999,-3.7279999999999998,-3.6112000000000002,-3.4975999999999998,-3.3872,-3.2799999999999994,-3.1760000000000002,-3.0752000000000002,-2.9775999999999998,-2.8832000000000004,-2.7920000000000003,-2.7040000000000002,-2.6192000000000002,-2.5376000000000003,-2.4592000000000001,-2.3839999999999999,-2.3119999999999998,-2.2432000000000003,-2.1776,-2.1152000000000002,-2.056,-2,-1.9472,-1.8976,-1.8512000000000002,-1.8080000000000001,-1.768,-1.7312000000000001,-1.6976,-1.6672,-1.6400000000000001,-1.6160000000000001,-1.5952000000000002,-1.5776000000000001,-1.5632000000000001,-1.552,-1.544,-1.5392000000000001,-1.5376000000000001,-1.5392000000000001,-1.544,-1.552,-1.5632000000000001,-1.5776000000000001,-1.5952000000000002,-1.6160000000000001,-1.6399999999999999,-1.6672,-1.6976,-1.7312000000000001,-1.768,-1.8080000000000001,-1.8512000000000002,-1.8976000000000002,-1.9472000000000003,-2.0000000000000004,-2.0560000000000005,-2.1152000000000006,-2.1776000000000004,-2.2431999999999999,-2.3119999999999998,-2.3839999999999999,-2.4592000000000001,-2.5376000000000003,-2.6192000000000002,-2.7040000000000002,-2.7920000000000003,-2.8832000000000004,-2.9776000000000007,-3.0752000000000006,-3.176000000000001,-3.2800000000000011,-3.3872,-3.4975999999999998,-3.6112000000000002,-3.7279999999999998,-3.8479999999999999,-3.9712000000000005,-4.0976000000000008,-4.2272000000000007,-4.3600000000000003,-4.4960000000000004,-4.6352000000000011,-4.7776000000000014,-4.9231999999999996,-5.0720000000000001,-5.2240000000000002,-5.3792,-5.5376000000000003],[-5.4399999999999995,-5.2815999999999992,-5.1264000000000003,-4.9743999999999993,-4.8255999999999997,-4.6799999999999997,-4.5375999999999994,-4.3983999999999996,-4.2623999999999995,-4.1295999999999999,-4,-3.8736000000000002,-3.7504,-3.6303999999999998,-3.5135999999999998,-3.3999999999999995,-3.2895999999999996,-3.1823999999999995,-3.0784000000000002,-2.9775999999999998,-2.8799999999999999,-2.7856000000000005,-2.6943999999999999,-2.6063999999999998,-2.5216000000000003,-2.4399999999999999,-2.3616000000000001,-2.2863999999999995,-2.2143999999999999,-2.1456,-2.0800000000000001,-2.0175999999999998,-1.9583999999999999,-1.9023999999999999,-1.8495999999999997,-1.7999999999999998,-1.7536,-1.7103999999999999,-1.6703999999999999,-1.6335999999999999,-1.5999999999999999,-1.5695999999999999,-1.5424,-1.5184,-1.4976,-1.48,-1.4656,-1.4543999999999999,-1.4463999999999999,-1.4416,-1.4399999999999999,-1.4416,-1.4463999999999999,-1.4543999999999999,-1.4656,-1.48,-1.4976,-1.5184000000000002,-1.5423999999999998,-1.5695999999999999,-1.5999999999999999,-1.6335999999999999,-1.6703999999999999,-1.7103999999999999,-1.7536,-1.8,-1.8496000000000001,-1.9024000000000001,-1.9584000000000001,-2.0176000000000003,-2.0800000000000005,-2.1456,-2.2143999999999999,-2.2863999999999995,-2.3616000000000001,-2.4399999999999999,-2.5216000000000003,-2.6063999999999998,-2.6943999999999999,-2.7856000000000005,-2.8800000000000003,-2.9776000000000007,-3.0784000000000007,-3.1824000000000008,-3.2895999999999996,-3.3999999999999995,-3.5135999999999998,-3.6303999999999998,-3.7504,-3.8736000000000002,-4,-4.1295999999999999,-4.2624000000000004,-4.3984000000000005,-4.5376000000000012,-4.6800000000000015,-4.8255999999999997,-4.9743999999999993,-5.1264000000000003,-5.2815999999999992,-5.4399999999999995],[-5.3456000000000001,-5.1871999999999998,-5.032,-4.8799999999999999,-4.7312000000000003,-4.5856000000000003,-4.4432,-4.3040000000000003,-4.1680000000000001,-4.0352000000000006,-3.9056000000000006,-3.7792000000000003,-3.6560000000000006,-3.5360000000000005,-3.4192,-3.3056000000000001,-3.1951999999999998,-3.0880000000000001,-2.9840000000000004,-2.8832000000000004,-2.7856000000000005,-2.6912000000000007,-2.6000000000000005,-2.5120000000000005,-2.4272000000000005,-2.3456000000000001,-2.2672000000000003,-2.1920000000000002,-2.1200000000000001,-2.0512000000000006,-1.9856000000000005,-1.9232000000000005,-1.8640000000000003,-1.8080000000000003,-1.7552000000000003,-1.7056000000000002,-1.6592000000000005,-1.6160000000000003,-1.5760000000000003,-1.5392000000000003,-1.5056000000000003,-1.4752000000000003,-1.4480000000000004,-1.4240000000000004,-1.4032000000000004,-1.3856000000000004,-1.3712000000000004,-1.3600000000000003,-1.3520000000000003,-1.3472000000000004,-1.3456000000000004,-1.3472000000000004,-1.3520000000000003,-1.3600000000000003,-1.3712000000000004,-1.3856000000000004,-1.4032000000000004,-1.4240000000000004,-1.4480000000000002,-1.4752000000000003,-1.5056000000000003,-1.5392000000000003,-1.5760000000000003,-1.6160000000000003,-1.6592000000000005,-1.7056000000000004,-1.7552000000000005,-1.8080000000000005,-1.8640000000000008,-1.9232000000000007,-1.9856000000000007,-2.0512000000000001,-2.1200000000000001,-2.1920000000000002,-2.2672000000000003,-2.3456000000000001,-2.4272000000000005,-2.5120000000000005,-2.6000000000000005,-2.6912000000000007,-2.7856000000000005,-2.8832000000000009,-2.9840000000000009,-3.088000000000001,-3.1951999999999998,-3.3056000000000001,-3.4192,-3.5360000000000005,-3.6560000000000006,-3.7792000000000003,-3.9056000000000006,-4.0352000000000006,-4.168000000000001,-4.3040000000000012,-4.4432000000000009,-4.5856000000000012,-4.7311999999999994,-4.8799999999999999,-5.032,-5.1871999999999998,-5.3456000000000001],[-5.2544000000000004,-5.0960000000000001,-4.9408000000000003,-4.7888000000000002,-4.6400000000000006,-4.4944000000000006,-4.3520000000000003,-4.2127999999999997,-4.0767999999999995,-3.9440000000000008,-3.8144000000000009,-3.6880000000000006,-3.5648,-3.4447999999999999,-3.3280000000000003,-3.2143999999999999,-3.1040000000000001,-2.9967999999999995,-2.8928000000000003,-2.7920000000000003,-2.6943999999999999,-2.6000000000000005,-2.5088000000000004,-2.4208000000000003,-2.3360000000000003,-2.2544000000000004,-2.1760000000000002,-2.1008,-2.0287999999999999,-1.9600000000000004,-1.8944000000000003,-1.8320000000000003,-1.7728000000000002,-1.7168000000000001,-1.6640000000000001,-1.6144000000000001,-1.5680000000000003,-1.5248000000000002,-1.4848000000000001,-1.4480000000000002,-1.4144000000000001,-1.3840000000000001,-1.3568000000000002,-1.3328000000000002,-1.3120000000000003,-1.2944000000000002,-1.2800000000000002,-1.2688000000000001,-1.2608000000000001,-1.2560000000000002,-1.2544000000000002,-1.2560000000000002,-1.2608000000000001,-1.2688000000000001,-1.2800000000000002,-1.2944000000000002,-1.3120000000000003,-1.3328000000000002,-1.3568,-1.3840000000000001,-1.4144000000000001,-1.4480000000000002,-1.4848000000000001,-1.5248000000000002,-1.5680000000000003,-1.6144000000000003,-1.6640000000000004,-1.7168000000000003,-1.7728000000000006,-1.8320000000000005,-1.8944000000000005,-1.96,-2.0287999999999999,-2.1008,-2.1760000000000002,-2.2544000000000004,-2.3360000000000003,-2.4208000000000003,-2.5088000000000004,-2.6000000000000005,-2.6944000000000008,-2.7920000000000007,-2.8928000000000011,-2.9968000000000012,-3.1040000000000001,-3.2143999999999999,-3.3280000000000003,-3.4447999999999999,-3.5648,-3.6880000000000006,-3.8144000000000009,-3.9440000000000008,-4.0768000000000004,-4.2128000000000005,-4.3520000000000012,-4.4944000000000015,-4.6399999999999997,-4.7888000000000002,-4.9408000000000003,-5.0960000000000001,-5.2544000000000004],[-5.1664000000000003,-5.008,-4.8528000000000002,-4.7008000000000001,-4.5520000000000005,-4.4064000000000005,-4.2640000000000002,-4.1247999999999996,-3.9887999999999995,-3.8560000000000008,-3.7264000000000008,-3.6000000000000005,-3.4767999999999999,-3.3567999999999998,-3.2400000000000002,-3.1263999999999998,-3.016,-2.9087999999999994,-2.8048000000000002,-2.7040000000000002,-2.6063999999999998,-2.5120000000000005,-2.4208000000000003,-2.3328000000000002,-2.2480000000000002,-2.1664000000000003,-2.0880000000000001,-2.0127999999999999,-1.9407999999999999,-1.8720000000000003,-1.8064000000000002,-1.7440000000000002,-1.6848000000000001,-1.6288,-1.5760000000000001,-1.5264,-1.4800000000000002,-1.4368000000000001,-1.3968,-1.3600000000000001,-1.3264,-1.296,-1.2688000000000001,-1.2448000000000001,-1.2240000000000002,-1.2064000000000001,-1.1920000000000002,-1.1808000000000001,-1.1728000000000001,-1.1680000000000001,-1.1664000000000001,-1.1680000000000001,-1.1728000000000001,-1.1808000000000001,-1.1920000000000002,-1.2064000000000001,-1.2240000000000002,-1.2448000000000001,-1.2687999999999999,-1.296,-1.3264,-1.3600000000000001,-1.3968,-1.4368000000000001,-1.4800000000000002,-1.5264000000000002,-1.5760000000000003,-1.6288000000000002,-1.6848000000000005,-1.7440000000000004,-1.8064000000000004,-1.8719999999999999,-1.9407999999999999,-2.0127999999999999,-2.0880000000000001,-2.1664000000000003,-2.2480000000000002,-2.3328000000000002,-2.4208000000000003,-2.5120000000000005,-2.6064000000000007,-2.7040000000000006,-2.8048000000000011,-2.9088000000000012,-3.016,-3.1263999999999998,-3.2400000000000002,-3.3567999999999998,-3.4767999999999999,-3.6000000000000005,-3.7264000000000008,-3.8560000000000008,-3.9888000000000003,-4.1248000000000005,-4.2640000000000011,-4.4064000000000014,-4.5519999999999996,-4.7008000000000001,-4.8528000000000002,-5.008,-5.1664000000000003],[-5.0815999999999999,-4.9231999999999996,-4.7679999999999998,-4.6159999999999997,-4.4672000000000001,-4.3216000000000001,-4.1791999999999998,-4.04,-3.9039999999999999,-3.7712000000000003,-3.6416000000000004,-3.5152000000000001,-3.3920000000000003,-3.2720000000000002,-3.1551999999999998,-3.0415999999999999,-2.9311999999999996,-2.8239999999999998,-2.7200000000000002,-2.6192000000000002,-2.5216000000000003,-2.4272000000000005,-2.3360000000000003,-2.2480000000000002,-2.1632000000000002,-2.0815999999999999,-2.0032000000000001,-1.9279999999999999,-1.8559999999999999,-1.7872000000000003,-1.7216000000000002,-1.6592000000000002,-1.6000000000000001,-1.544,-1.4912000000000001,-1.4416,-1.3952000000000002,-1.3520000000000001,-1.3120000000000001,-1.2752000000000001,-1.2416,-1.2112000000000001,-1.1840000000000002,-1.1600000000000001,-1.1392000000000002,-1.1216000000000002,-1.1072000000000002,-1.0960000000000001,-1.0880000000000001,-1.0832000000000002,-1.0816000000000001,-1.0832000000000002,-1.0880000000000001,-1.0960000000000001,-1.1072000000000002,-1.1216000000000002,-1.1392000000000002,-1.1600000000000001,-1.1839999999999999,-1.2112000000000001,-1.2416,-1.2752000000000001,-1.3120000000000001,-1.3520000000000001,-1.3952000000000002,-1.4416000000000002,-1.4912000000000003,-1.5440000000000003,-1.6000000000000005,-1.6592000000000005,-1.7216000000000005,-1.7871999999999999,-1.8559999999999999,-1.9279999999999999,-2.0032000000000001,-2.0815999999999999,-2.1632000000000002,-2.2480000000000002,-2.3360000000000003,-2.4272000000000005,-2.5216000000000003,-2.6192000000000006,-2.7200000000000006,-2.8240000000000007,-2.9311999999999996,-3.0415999999999999,-3.1551999999999998,-3.2720000000000002,-3.3920000000000003,-3.5152000000000001,-3.6416000000000004,-3.7712000000000003,-3.9040000000000008,-4.0400000000000009,-4.1792000000000007,-4.321600000000001,-4.4671999999999992,-4.6159999999999997,-4.7679999999999998,-4.9231999999999996,-5.0815999999999999],[-5,-4.8415999999999997,-4.6863999999999999,-4.5343999999999998,-4.3856000000000002,-4.2400000000000002,-4.0975999999999999,-3.9583999999999997,-3.8223999999999996,-3.6896000000000004,-3.5600000000000005,-3.4336000000000002,-3.3104,-3.1903999999999999,-3.0735999999999999,-2.96,-2.8495999999999997,-2.7423999999999995,-2.6383999999999999,-2.5376000000000003,-2.4399999999999999,-2.3456000000000001,-2.2544000000000004,-2.1664000000000003,-2.0815999999999999,-2,-1.9216,-1.8463999999999998,-1.7744,-1.7056,-1.6400000000000001,-1.5775999999999999,-1.5184,-1.4623999999999999,-1.4095999999999997,-1.3599999999999999,-1.3136000000000001,-1.2704,-1.2303999999999999,-1.1936,-1.1599999999999999,-1.1295999999999999,-1.1024,-1.0784,-1.0576000000000001,-1.04,-1.0256000000000001,-1.0144,-1.0064,-1.0016,-1,-1.0016,-1.0064,-1.0144,-1.0256000000000001,-1.04,-1.0576000000000001,-1.0784000000000002,-1.1023999999999998,-1.1295999999999999,-1.1599999999999999,-1.1936,-1.2303999999999999,-1.2704,-1.3136000000000001,-1.3600000000000001,-1.4096000000000002,-1.4624000000000001,-1.5184000000000002,-1.5776000000000003,-1.6400000000000006,-1.7055999999999998,-1.7744,-1.8463999999999998,-1.9216,-2,-2.0815999999999999,-2.1664000000000003,-2.2544000000000004,-2.3456000000000001,-2.4400000000000004,-2.5376000000000003,-2.6384000000000007,-2.7424000000000008,-2.8495999999999997,-2.96,-3.0735999999999999,-3.1903999999999999,-3.3104,-3.4336000000000002,-3.5600000000000005,-3.6896000000000004,-3.8224000000000005,-3.9584000000000006,-4.0976000000000008,-4.2400000000000011,-4.3855999999999993,-4.5343999999999998,-4.6863999999999999,-4.8415999999999997,-5],[-4.9215999999999998,-4.7631999999999994,-4.6079999999999997,-4.4559999999999995,-4.3071999999999999,-4.1616,-4.0191999999999997,-3.8799999999999999,-3.7439999999999998,-3.6112000000000002,-3.4816000000000003,-3.3552,-3.2320000000000002,-3.1120000000000001,-2.9951999999999996,-2.8815999999999997,-2.7711999999999994,-2.6639999999999997,-2.5600000000000001,-2.4592000000000001,-2.3616000000000001,-2.2672000000000003,-2.1760000000000002,-2.0880000000000001,-2.0032000000000001,-1.9216,-1.8431999999999999,-1.7679999999999998,-1.6959999999999997,-1.6272000000000002,-1.5616000000000001,-1.4992000000000001,-1.4399999999999999,-1.3839999999999999,-1.3311999999999999,-1.2815999999999999,-1.2352000000000001,-1.1919999999999999,-1.1519999999999999,-1.1152,-1.0815999999999999,-1.0511999999999999,-1.024,-1,-0.97919999999999996,-0.96160000000000001,-0.94719999999999993,-0.93599999999999994,-0.92799999999999994,-0.92320000000000002,-0.92159999999999997,-0.92320000000000002,-0.92799999999999994,-0.93600000000000005,-0.94720000000000004,-0.96160000000000001,-0.97920000000000007,-1,-1.0239999999999998,-1.0511999999999999,-1.0815999999999999,-1.1152,-1.1519999999999999,-1.1919999999999999,-1.2352000000000001,-1.2816000000000001,-1.3312000000000002,-1.3840000000000001,-1.4400000000000004,-1.4992000000000003,-1.5616000000000003,-1.6271999999999998,-1.6959999999999997,-1.7679999999999998,-1.8431999999999999,-1.9216,-2.0032000000000001,-2.0880000000000001,-2.1760000000000002,-2.2672000000000003,-2.3616000000000001,-2.4592000000000005,-2.5600000000000005,-2.6640000000000006,-2.7711999999999994,-2.8815999999999997,-2.9951999999999996,-3.1120000000000001,-3.2320000000000002,-3.3552,-3.4816000000000003,-3.6112000000000002,-3.7440000000000007,-3.8800000000000008,-4.0192000000000005,-4.1616000000000009,-4.307199999999999,-4.4559999999999995,-4.6079999999999997,-4.7631999999999994,-4.9215999999999998],[-4.8464,-4.6879999999999997,-4.5327999999999999,-4.3807999999999998,-4.2320000000000002,-4.0864000000000003,-3.944,-3.8047999999999993,-3.6687999999999992,-3.5360000000000005,-3.4064000000000005,-3.2800000000000002,-3.1567999999999996,-3.0367999999999995,-2.9199999999999999,-2.8063999999999996,-2.6959999999999997,-2.5887999999999991,-2.4847999999999999,-2.3839999999999999,-2.2863999999999995,-2.1920000000000002,-2.1008,-2.0127999999999999,-1.9279999999999999,-1.8463999999999998,-1.7679999999999998,-1.6927999999999996,-1.6207999999999996,-1.552,-1.4863999999999999,-1.4239999999999999,-1.3647999999999998,-1.3087999999999997,-1.2559999999999998,-1.2063999999999997,-1.1599999999999999,-1.1167999999999998,-1.0767999999999998,-1.0399999999999998,-1.0063999999999997,-0.97599999999999976,-0.94879999999999987,-0.92479999999999984,-0.9039999999999998,-0.88639999999999985,-0.87199999999999978,-0.86079999999999979,-0.85279999999999978,-0.84799999999999986,-0.84639999999999982,-0.84799999999999986,-0.85279999999999978,-0.8607999999999999,-0.87199999999999989,-0.88639999999999985,-0.90399999999999991,-0.92479999999999996,-0.94879999999999975,-0.97599999999999976,-1.0063999999999997,-1.0399999999999998,-1.0767999999999998,-1.1167999999999998,-1.1599999999999999,-1.2063999999999999,-1.256,-1.3088,-1.3648000000000002,-1.4240000000000002,-1.4864000000000002,-1.5519999999999996,-1.6207999999999996,-1.6927999999999996,-1.7679999999999998,-1.8463999999999998,-1.9279999999999999,-2.0127999999999999,-2.1008,-2.1920000000000002,-2.2864000000000004,-2.3840000000000003,-2.4848000000000008,-2.5888000000000009,-2.6959999999999997,-2.8063999999999996,-2.9199999999999999,-3.0367999999999995,-3.1567999999999996,-3.2800000000000002,-3.4064000000000005,-3.5360000000000005,-3.6688000000000001,-3.8048000000000002,-3.9440000000000008,-4.0864000000000011,-4.2319999999999993,-4.3807999999999998,-4.5327999999999999,-4.6879999999999997,-4.8464],[-4.7744,-4.6159999999999997,-4.4607999999999999,-4.3087999999999997,-4.1600000000000001,-4.0144000000000002,-3.8719999999999999,-3.7327999999999997,-3.5967999999999996,-3.4640000000000004,-3.3344000000000005,-3.2080000000000002,-3.0848,-2.9647999999999999,-2.8479999999999999,-2.7343999999999995,-2.6239999999999997,-2.5167999999999995,-2.4127999999999998,-2.3119999999999998,-2.2143999999999999,-2.1200000000000001,-2.0287999999999999,-1.9407999999999999,-1.8559999999999999,-1.7744,-1.6959999999999997,-1.6207999999999996,-1.5487999999999997,-1.48,-1.4144000000000001,-1.3519999999999999,-1.2927999999999997,-1.2367999999999997,-1.1839999999999997,-1.1343999999999996,-1.0879999999999999,-1.0448,-1.0047999999999999,-0.96799999999999986,-0.93439999999999979,-0.9039999999999998,-0.87679999999999991,-0.85279999999999989,-0.83199999999999985,-0.81439999999999979,-0.79999999999999982,-0.78879999999999983,-0.78079999999999983,-0.77599999999999991,-0.77439999999999987,-0.77599999999999991,-0.78079999999999983,-0.78879999999999995,-0.79999999999999993,-0.8143999999999999,-0.83199999999999996,-0.8528,-0.8767999999999998,-0.9039999999999998,-0.93439999999999979,-0.96799999999999986,-1.0047999999999999,-1.0448,-1.0879999999999999,-1.1343999999999999,-1.1840000000000002,-1.2368000000000001,-1.2928000000000002,-1.3520000000000003,-1.4144000000000003,-1.4799999999999995,-1.5487999999999997,-1.6207999999999996,-1.6959999999999997,-1.7744,-1.8559999999999999,-1.9407999999999999,-2.0287999999999999,-2.1200000000000001,-2.2144000000000004,-2.3120000000000003,-2.4128000000000007,-2.5168000000000008,-2.6239999999999997,-2.7343999999999995,-2.8479999999999999,-2.9647999999999999,-3.0848,-3.2080000000000002,-3.3344000000000005,-3.4640000000000004,-3.5968000000000004,-3.7328000000000006,-3.8720000000000008,-4.0144000000000011,-4.1599999999999993,-4.3087999999999997,-4.4607999999999999,-4.6159999999999997,-4.7744],[-4.7056000000000004,-4.5472000000000001,-4.3920000000000003,-4.2400000000000002,-4.0912000000000006,-3.9456000000000002,-3.8031999999999999,-3.6639999999999997,-3.5279999999999996,-3.3952000000000004,-3.2656000000000005,-3.1392000000000002,-3.016,-2.8959999999999999,-2.7791999999999999,-2.6656,-2.5551999999999997,-2.4479999999999995,-2.3440000000000003,-2.2432000000000003,-2.1456,-2.0512000000000006,-1.9600000000000004,-1.8720000000000003,-1.7872000000000003,-1.7056,-1.6272000000000002,-1.552,-1.48,-1.4112000000000002,-1.3456000000000001,-1.2832000000000001,-1.2240000000000002,-1.1680000000000001,-1.1152,-1.0655999999999999,-1.0192000000000001,-0.9760000000000002,-0.93600000000000017,-0.89920000000000011,-0.86560000000000004,-0.83520000000000005,-0.80800000000000016,-0.78400000000000014,-0.7632000000000001,-0.74560000000000004,-0.73120000000000007,-0.72000000000000008,-0.71200000000000008,-0.70720000000000016,-0.70560000000000012,-0.70720000000000016,-0.71200000000000008,-0.7200000000000002,-0.73120000000000018,-0.74560000000000015,-0.76320000000000021,-0.78400000000000025,-0.80800000000000005,-0.83520000000000005,-0.86560000000000004,-0.89920000000000011,-0.93600000000000017,-0.9760000000000002,-1.0192000000000001,-1.0656000000000003,-1.1152000000000002,-1.1680000000000004,-1.2240000000000004,-1.2832000000000003,-1.3456000000000006,-1.4112,-1.48,-1.552,-1.6272000000000002,-1.7056,-1.7872000000000003,-1.8720000000000003,-1.9600000000000004,-2.0512000000000006,-2.1456000000000004,-2.2432000000000007,-2.3440000000000007,-2.4480000000000008,-2.5551999999999997,-2.6656,-2.7791999999999999,-2.8959999999999999,-3.016,-3.1392000000000002,-3.2656000000000005,-3.3952000000000004,-3.5280000000000005,-3.6640000000000006,-3.8032000000000008,-3.9456000000000011,-4.0911999999999997,-4.2400000000000002,-4.3920000000000003,-4.5472000000000001,-4.7056000000000004],[-4.6400000000000006,-4.4816000000000003,-4.3263999999999996,-4.1744000000000003,-4.0256000000000007,-3.8800000000000003,-3.7376,-3.5983999999999998,-3.4623999999999997,-3.3296000000000006,-3.2000000000000006,-3.0736000000000003,-2.9504000000000001,-2.8304,-2.7136,-2.5999999999999996,-2.4895999999999998,-2.3823999999999996,-2.2784000000000004,-2.1776,-2.0800000000000001,-1.9856000000000005,-1.8944000000000003,-1.8064000000000002,-1.7216000000000002,-1.6400000000000001,-1.5616000000000001,-1.4863999999999999,-1.4144000000000001,-1.3456000000000001,-1.2800000000000002,-1.2176,-1.1584000000000001,-1.1024,-1.0495999999999999,-1,-0.95360000000000023,-0.9104000000000001,-0.87040000000000006,-0.83360000000000012,-0.80000000000000004,-0.76960000000000006,-0.74240000000000017,-0.71840000000000015,-0.69760000000000011,-0.68000000000000016,-0.66560000000000008,-0.65440000000000009,-0.64640000000000009,-0.64160000000000017,-0.64000000000000012,-0.64160000000000017,-0.64640000000000009,-0.6544000000000002,-0.66560000000000019,-0.68000000000000016,-0.69760000000000022,-0.71840000000000026,-0.74240000000000006,-0.76960000000000006,-0.80000000000000004,-0.83360000000000012,-0.87040000000000006,-0.9104000000000001,-0.95360000000000023,-1.0000000000000002,-1.0496000000000003,-1.1024000000000003,-1.1584000000000003,-1.2176000000000005,-1.2800000000000007,-1.3455999999999999,-1.4144000000000001,-1.4863999999999999,-1.5616000000000001,-1.6400000000000001,-1.7216000000000002,-1.8064000000000002,-1.8944000000000003,-1.9856000000000005,-2.0800000000000005,-2.1776000000000009,-2.2784000000000009,-2.382400000000001,-2.4895999999999998,-2.5999999999999996,-2.7136,-2.8304,-2.9504000000000001,-3.0736000000000003,-3.2000000000000006,-3.3296000000000006,-3.4624000000000006,-3.5984000000000007,-3.7376000000000009,-3.8800000000000012,-4.025599999999999,-4.1744000000000003,-4.3263999999999996,-4.4816000000000003,-4.6400000000000006],[-4.5776000000000003,-4.4192,-4.2640000000000002,-4.1120000000000001,-3.9632000000000001,-3.8176000000000001,-3.6751999999999998,-3.5359999999999996,-3.3999999999999995,-3.2672000000000003,-3.1376000000000004,-3.0112000000000001,-2.8879999999999999,-2.7679999999999998,-2.6511999999999998,-2.5375999999999999,-2.4271999999999996,-2.3199999999999994,-2.2160000000000002,-2.1152000000000002,-2.0175999999999998,-1.9232000000000005,-1.8320000000000003,-1.7440000000000002,-1.6592000000000002,-1.5775999999999999,-1.4992000000000001,-1.4239999999999999,-1.3519999999999999,-1.2832000000000001,-1.2176,-1.1552,-1.0960000000000001,-1.04,-0.98719999999999986,-0.93759999999999977,-0.89119999999999999,-0.84800000000000009,-0.80800000000000005,-0.7712,-0.73759999999999992,-0.70719999999999994,-0.68000000000000005,-0.65600000000000003,-0.63519999999999999,-0.61759999999999993,-0.60319999999999996,-0.59199999999999997,-0.58399999999999996,-0.57920000000000005,-0.5776,-0.57920000000000005,-0.58399999999999996,-0.59200000000000008,-0.60320000000000007,-0.61760000000000004,-0.6352000000000001,-0.65600000000000014,-0.67999999999999994,-0.70719999999999994,-0.73759999999999992,-0.7712,-0.80800000000000005,-0.84800000000000009,-0.89119999999999999,-0.9376000000000001,-0.98720000000000019,-1.0400000000000003,-1.0960000000000003,-1.1552000000000002,-1.2176000000000005,-1.2831999999999999,-1.3519999999999999,-1.4239999999999999,-1.4992000000000001,-1.5775999999999999,-1.6592000000000002,-1.7440000000000002,-1.8320000000000003,-1.9232000000000005,-2.0176000000000003,-2.1152000000000006,-2.2160000000000006,-2.3200000000000007,-2.4271999999999996,-2.5375999999999999,-2.6511999999999998,-2.7679999999999998,-2.8879999999999999,-3.0112000000000001,-3.1376000000000004,-3.2672000000000003,-3.4000000000000004,-3.5360000000000005,-3.6752000000000007,-3.817600000000001,-3.9631999999999992,-4.1120000000000001,-4.2640000000000002,-4.4192,-4.5776000000000003],[-4.5183999999999997,-4.3599999999999994,-4.2047999999999996,-4.0527999999999995,-3.9039999999999999,-3.7584,-3.6159999999999997,-3.4767999999999999,-3.3407999999999998,-3.2080000000000002,-3.0784000000000002,-2.952,-2.8288000000000002,-2.7088000000000001,-2.5919999999999996,-2.4783999999999997,-2.3679999999999994,-2.2607999999999997,-2.1568000000000001,-2.056,-1.9583999999999999,-1.8640000000000003,-1.7728000000000002,-1.6848000000000001,-1.6000000000000001,-1.5184,-1.4399999999999999,-1.3647999999999998,-1.2927999999999997,-1.2240000000000002,-1.1584000000000001,-1.0960000000000001,-1.0367999999999999,-0.98079999999999989,-0.92799999999999983,-0.87839999999999985,-0.83200000000000007,-0.78879999999999995,-0.74879999999999991,-0.71199999999999997,-0.67839999999999989,-0.64799999999999991,-0.62080000000000002,-0.5968,-0.57599999999999996,-0.55840000000000001,-0.54399999999999993,-0.53279999999999994,-0.52479999999999993,-0.52000000000000002,-0.51839999999999997,-0.52000000000000002,-0.52479999999999993,-0.53280000000000005,-0.54400000000000004,-0.55840000000000001,-0.57600000000000007,-0.59680000000000011,-0.62079999999999991,-0.64799999999999991,-0.67839999999999989,-0.71199999999999997,-0.74879999999999991,-0.78879999999999995,-0.83200000000000007,-0.87840000000000007,-0.92800000000000016,-0.98080000000000012,-1.0368000000000004,-1.0960000000000003,-1.1584000000000003,-1.2239999999999998,-1.2927999999999997,-1.3647999999999998,-1.4399999999999999,-1.5184,-1.6000000000000001,-1.6848000000000001,-1.7728000000000002,-1.8640000000000003,-1.9584000000000004,-2.0560000000000005,-2.1568000000000005,-2.2608000000000006,-2.3679999999999994,-2.4783999999999997,-2.5919999999999996,-2.7088000000000001,-2.8288000000000002,-2.952,-3.0784000000000002,-3.2080000000000002,-3.3408000000000007,-3.4768000000000008,-3.6160000000000005,-3.7584000000000009,-3.903999999999999,-4.0527999999999995,-4.2047999999999996,-4.3599999999999994,-4.5183999999999997],[-4.4623999999999997,-4.3039999999999994,-4.1487999999999996,-3.9967999999999995,-3.8479999999999999,-3.7023999999999999,-3.5599999999999996,-3.4207999999999998,-3.2847999999999997,-3.1520000000000001,-3.0224000000000002,-2.8959999999999999,-2.7728000000000002,-2.6528,-2.5359999999999996,-2.4223999999999997,-2.3119999999999994,-2.2047999999999996,-2.1008,-2,-1.9023999999999999,-1.8080000000000003,-1.7168000000000001,-1.6288,-1.544,-1.4623999999999999,-1.3839999999999999,-1.3087999999999997,-1.2367999999999997,-1.1680000000000001,-1.1024,-1.04,-0.98079999999999989,-0.92479999999999984,-0.87199999999999978,-0.8223999999999998,-0.77600000000000002,-0.7327999999999999,-0.69279999999999986,-0.65599999999999992,-0.62239999999999984,-0.59199999999999986,-0.56479999999999997,-0.54079999999999995,-0.51999999999999991,-0.50239999999999996,-0.48799999999999988,-0.47679999999999989,-0.46879999999999994,-0.46399999999999991,-0.46239999999999992,-0.46399999999999991,-0.46879999999999994,-0.47679999999999995,-0.48799999999999999,-0.50239999999999996,-0.52000000000000002,-0.54080000000000006,-0.56479999999999986,-0.59199999999999986,-0.62239999999999984,-0.65599999999999992,-0.69279999999999986,-0.7327999999999999,-0.77600000000000002,-0.82240000000000002,-0.87200000000000011,-0.92480000000000007,-0.98080000000000023,-1.0400000000000003,-1.1024000000000003,-1.1679999999999997,-1.2367999999999997,-1.3087999999999997,-1.3839999999999999,-1.4623999999999999,-1.544,-1.6288,-1.7168000000000001,-1.8080000000000003,-1.9024000000000003,-2.0000000000000004,-2.1008000000000004,-2.2048000000000005,-2.3119999999999994,-2.4223999999999997,-2.5359999999999996,-2.6528,-2.7728000000000002,-2.8959999999999999,-3.0224000000000002,-3.1520000000000001,-3.2848000000000006,-3.4208000000000007,-3.5600000000000005,-3.7024000000000008,-3.847999999999999,-3.9967999999999995,-4.1487999999999996,-4.3039999999999994,-4.4623999999999997],[-4.4096000000000002,-4.2511999999999999,-4.0960000000000001,-3.9439999999999995,-3.7951999999999999,-3.6496,-3.5071999999999997,-3.3679999999999994,-3.2319999999999993,-3.0992000000000002,-2.9696000000000002,-2.8431999999999999,-2.7199999999999998,-2.5999999999999996,-2.4831999999999996,-2.3695999999999997,-2.2591999999999994,-2.1519999999999992,-2.048,-1.9472,-1.8495999999999997,-1.7552000000000003,-1.6640000000000001,-1.5760000000000001,-1.4912000000000001,-1.4095999999999997,-1.3311999999999999,-1.2559999999999998,-1.1839999999999997,-1.1152,-1.0495999999999999,-0.98719999999999986,-0.92799999999999983,-0.87199999999999978,-0.81919999999999971,-0.76959999999999962,-0.72319999999999984,-0.67999999999999994,-0.6399999999999999,-0.60319999999999985,-0.56959999999999977,-0.53919999999999979,-0.5119999999999999,-0.48799999999999988,-0.46719999999999984,-0.44959999999999983,-0.43519999999999981,-0.42399999999999982,-0.41599999999999987,-0.41119999999999984,-0.40959999999999985,-0.41119999999999984,-0.41599999999999987,-0.42399999999999988,-0.43519999999999992,-0.44959999999999994,-0.46719999999999995,-0.48799999999999999,-0.51199999999999979,-0.53919999999999979,-0.56959999999999977,-0.60319999999999985,-0.6399999999999999,-0.67999999999999994,-0.72319999999999984,-0.76959999999999995,-0.81920000000000004,-0.87200000000000011,-0.92800000000000016,-0.98720000000000019,-1.0496000000000003,-1.1151999999999997,-1.1839999999999997,-1.2559999999999998,-1.3311999999999999,-1.4095999999999997,-1.4912000000000001,-1.5760000000000001,-1.6640000000000001,-1.7552000000000003,-1.8496000000000001,-1.9472000000000005,-2.0480000000000005,-2.1520000000000006,-2.2591999999999994,-2.3695999999999997,-2.4831999999999996,-2.5999999999999996,-2.7199999999999998,-2.8431999999999999,-2.9696000000000002,-3.0992000000000002,-3.2320000000000002,-3.3680000000000003,-3.5072000000000005,-3.6496000000000008,-3.795199999999999,-3.9439999999999995,-4.0960000000000001,-4.2511999999999999,-4.4096000000000002],[-4.3599999999999994,-4.2015999999999991,-4.0463999999999993,-3.8943999999999996,-3.7456,-3.6000000000000001,-3.4575999999999998,-3.3183999999999996,-3.1823999999999995,-3.0496000000000003,-2.9200000000000004,-2.7936000000000001,-2.6703999999999999,-2.5503999999999998,-2.4335999999999998,-2.3199999999999994,-2.2095999999999996,-2.1023999999999994,-1.9984,-1.8976,-1.7999999999999998,-1.7056000000000002,-1.6144000000000001,-1.5264,-1.4416,-1.3599999999999999,-1.2815999999999999,-1.2063999999999997,-1.1343999999999996,-1.0655999999999999,-1,-0.93759999999999977,-0.87839999999999985,-0.8223999999999998,-0.76959999999999962,-0.71999999999999964,-0.67359999999999987,-0.63039999999999985,-0.59039999999999981,-0.55359999999999976,-0.5199999999999998,-0.4895999999999997,-0.46239999999999987,-0.43839999999999985,-0.4175999999999998,-0.3999999999999998,-0.38559999999999978,-0.37439999999999979,-0.36639999999999984,-0.36159999999999981,-0.35999999999999982,-0.36159999999999981,-0.36639999999999984,-0.37439999999999984,-0.38559999999999989,-0.39999999999999991,-0.41759999999999992,-0.43839999999999996,-0.4623999999999997,-0.4895999999999997,-0.5199999999999998,-0.55359999999999976,-0.59039999999999981,-0.63039999999999985,-0.67359999999999987,-0.71999999999999997,-0.76960000000000006,-0.82240000000000002,-0.87840000000000007,-0.93760000000000021,-1.0000000000000002,-1.0655999999999997,-1.1343999999999996,-1.2063999999999997,-1.2815999999999999,-1.3599999999999999,-1.4416,-1.5264,-1.6144000000000001,-1.7056000000000002,-1.8000000000000003,-1.8976000000000004,-1.9984000000000006,-2.1024000000000007,-2.2095999999999996,-2.3199999999999994,-2.4335999999999998,-2.5503999999999998,-2.6703999999999999,-2.7936000000000001,-2.9200000000000004,-3.0496000000000003,-3.1824000000000003,-3.3184000000000005,-3.4576000000000007,-3.600000000000001,-3.7455999999999992,-3.8943999999999996,-4.0463999999999993,-4.2015999999999991,-4.3599999999999994],[-4.3136000000000001,-4.1551999999999998,-4,-3.8479999999999999,-3.6992000000000003,-3.5536000000000003,-3.4112,-3.2719999999999998,-3.1359999999999997,-3.0032000000000005,-2.8736000000000006,-2.7472000000000003,-2.6240000000000001,-2.504,-2.3872,-2.2735999999999996,-2.1631999999999998,-2.0559999999999996,-1.9520000000000002,-1.8512000000000002,-1.7536,-1.6592000000000005,-1.5680000000000003,-1.4800000000000002,-1.3952000000000002,-1.3136000000000001,-1.2352000000000001,-1.1599999999999999,-1.0879999999999999,-1.0192000000000001,-0.95360000000000023,-0.89119999999999999,-0.83200000000000007,-0.77600000000000002,-0.72319999999999984,-0.67359999999999987,-0.62720000000000009,-0.58400000000000007,-0.54400000000000004,-0.50719999999999998,-0.47359999999999997,-0.44319999999999993,-0.41600000000000009,-0.39200000000000007,-0.37120000000000003,-0.35360000000000003,-0.3392,-0.32800000000000001,-0.32000000000000006,-0.31520000000000004,-0.31360000000000005,-0.31520000000000004,-0.32000000000000006,-0.32800000000000007,-0.33920000000000011,-0.35360000000000014,-0.37120000000000014,-0.39200000000000018,-0.41599999999999993,-0.44319999999999993,-0.47359999999999997,-0.50719999999999998,-0.54400000000000004,-0.58400000000000007,-0.62720000000000009,-0.6736000000000002,-0.72320000000000029,-0.77600000000000025,-0.83200000000000029,-0.89120000000000044,-0.95360000000000045,-1.0191999999999999,-1.0879999999999999,-1.1599999999999999,-1.2352000000000001,-1.3136000000000001,-1.3952000000000002,-1.4800000000000002,-1.5680000000000003,-1.6592000000000005,-1.7536000000000005,-1.8512000000000006,-1.9520000000000008,-2.0560000000000009,-2.1631999999999998,-2.2735999999999996,-2.3872,-2.504,-2.6240000000000001,-2.7472000000000003,-2.8736000000000006,-3.0032000000000005,-3.1360000000000006,-3.2720000000000007,-3.4112000000000009,-3.5536000000000012,-3.6991999999999994,-3.8479999999999999,-4,-4.1551999999999998,-4.3136000000000001],[-4.2704000000000004,-4.1120000000000001,-3.9567999999999999,-3.8047999999999997,-3.6560000000000001,-3.5104000000000002,-3.3679999999999999,-3.2287999999999997,-3.0927999999999995,-2.9600000000000004,-2.8304000000000005,-2.7040000000000002,-2.5808,-2.4607999999999999,-2.3439999999999999,-2.2303999999999999,-2.1199999999999997,-2.0127999999999995,-1.9088000000000001,-1.8080000000000001,-1.7103999999999999,-1.6160000000000003,-1.5248000000000002,-1.4368000000000001,-1.3520000000000001,-1.2704,-1.1919999999999999,-1.1167999999999998,-1.0448,-0.9760000000000002,-0.9104000000000001,-0.84800000000000009,-0.78879999999999995,-0.7327999999999999,-0.67999999999999994,-0.63039999999999985,-0.58400000000000007,-0.54080000000000006,-0.50080000000000002,-0.46399999999999997,-0.43039999999999995,-0.39999999999999991,-0.37280000000000008,-0.34880000000000005,-0.32800000000000001,-0.31040000000000001,-0.29599999999999999,-0.2848,-0.27680000000000005,-0.27200000000000002,-0.27040000000000003,-0.27200000000000002,-0.27680000000000005,-0.28480000000000005,-0.2960000000000001,-0.31040000000000012,-0.32800000000000012,-0.34880000000000017,-0.37279999999999991,-0.39999999999999991,-0.43039999999999995,-0.46399999999999997,-0.50080000000000002,-0.54080000000000006,-0.58400000000000007,-0.63040000000000007,-0.68000000000000016,-0.73280000000000023,-0.78880000000000039,-0.84800000000000031,-0.91040000000000054,-0.97599999999999976,-1.0448,-1.1167999999999998,-1.1919999999999999,-1.2704,-1.3520000000000001,-1.4368000000000001,-1.5248000000000002,-1.6160000000000003,-1.7104000000000004,-1.8080000000000005,-1.9088000000000007,-2.0128000000000008,-2.1199999999999997,-2.2303999999999999,-2.3439999999999999,-2.4607999999999999,-2.5808,-2.7040000000000002,-2.8304000000000005,-2.9600000000000004,-3.0928000000000004,-3.2288000000000006,-3.3680000000000008,-3.5104000000000011,-3.6559999999999993,-3.8047999999999997,-3.9567999999999999,-4.1120000000000001,-4.2704000000000004],[-4.2304000000000004,-4.0720000000000001,-3.9167999999999998,-3.7647999999999997,-3.6160000000000001,-3.4704000000000002,-3.3279999999999998,-3.1887999999999996,-3.0527999999999995,-2.9200000000000004,-2.7904000000000004,-2.6640000000000001,-2.5407999999999999,-2.4207999999999998,-2.3039999999999998,-2.1903999999999999,-2.0799999999999996,-1.9727999999999994,-1.8688,-1.768,-1.6703999999999999,-1.5760000000000003,-1.4848000000000001,-1.3968,-1.3120000000000001,-1.2303999999999999,-1.1519999999999999,-1.0767999999999998,-1.0047999999999999,-0.93600000000000017,-0.87040000000000006,-0.80800000000000005,-0.74879999999999991,-0.69279999999999986,-0.6399999999999999,-0.59039999999999981,-0.54400000000000004,-0.50080000000000002,-0.46079999999999999,-0.42399999999999993,-0.39039999999999991,-0.35999999999999988,-0.33280000000000004,-0.30880000000000002,-0.28799999999999998,-0.27039999999999997,-0.25599999999999995,-0.24479999999999996,-0.23680000000000001,-0.23199999999999998,-0.23039999999999999,-0.23199999999999998,-0.23680000000000001,-0.24480000000000002,-0.25600000000000006,-0.27040000000000008,-0.28800000000000009,-0.30880000000000013,-0.33279999999999987,-0.35999999999999988,-0.39039999999999991,-0.42399999999999993,-0.46079999999999999,-0.50080000000000002,-0.54400000000000004,-0.59040000000000004,-0.64000000000000012,-0.69280000000000019,-0.74880000000000035,-0.80800000000000027,-0.87040000000000051,-0.93599999999999972,-1.0047999999999999,-1.0767999999999998,-1.1519999999999999,-1.2303999999999999,-1.3120000000000001,-1.3968,-1.4848000000000001,-1.5760000000000003,-1.6704000000000003,-1.7680000000000005,-1.8688000000000007,-1.9728000000000008,-2.0799999999999996,-2.1903999999999999,-2.3039999999999998,-2.4207999999999998,-2.5407999999999999,-2.6640000000000001,-2.7904000000000004,-2.9200000000000004,-3.0528000000000004,-3.1888000000000005,-3.3280000000000007,-3.470400000000001,-3.6159999999999992,-3.7647999999999997,-3.9167999999999998,-4.0720000000000001,-4.2304000000000004],[-4.1936,-4.0351999999999997,-3.8799999999999999,-3.7279999999999998,-3.5792000000000002,-3.4336000000000002,-3.2911999999999999,-3.1519999999999997,-3.0159999999999996,-2.8832000000000004,-2.7536000000000005,-2.6272000000000002,-2.504,-2.3839999999999999,-2.2671999999999999,-2.1535999999999995,-2.0431999999999997,-1.9359999999999995,-1.8320000000000001,-1.7312000000000001,-1.6335999999999999,-1.5392000000000003,-1.4480000000000002,-1.3600000000000001,-1.2752000000000001,-1.1936,-1.1152,-1.0399999999999998,-0.96799999999999986,-0.89920000000000011,-0.83360000000000012,-0.7712,-0.71199999999999997,-0.65599999999999992,-0.60319999999999985,-0.55359999999999976,-0.50719999999999998,-0.46399999999999997,-0.42399999999999993,-0.38719999999999993,-0.35359999999999991,-0.32319999999999988,-0.29600000000000004,-0.27199999999999996,-0.25119999999999998,-0.23359999999999995,-0.21919999999999995,-0.20799999999999993,-0.19999999999999998,-0.19519999999999996,-0.19359999999999997,-0.19519999999999996,-0.19999999999999998,-0.20799999999999999,-0.21920000000000001,-0.23360000000000003,-0.25120000000000009,-0.27200000000000013,-0.29599999999999987,-0.32319999999999988,-0.35359999999999991,-0.38719999999999993,-0.42399999999999993,-0.46399999999999997,-0.50719999999999998,-0.55360000000000009,-0.60320000000000018,-0.65600000000000014,-0.7120000000000003,-0.77120000000000033,-0.83360000000000045,-0.89919999999999978,-0.96799999999999986,-1.0399999999999998,-1.1152,-1.1936,-1.2752000000000001,-1.3600000000000001,-1.4480000000000002,-1.5392000000000003,-1.6336000000000004,-1.7312000000000005,-1.8320000000000007,-1.9360000000000008,-2.0431999999999997,-2.1535999999999995,-2.2671999999999999,-2.3839999999999999,-2.504,-2.6272000000000002,-2.7536000000000005,-2.8832000000000004,-3.0160000000000005,-3.1520000000000006,-3.2912000000000008,-3.4336000000000011,-3.5791999999999993,-3.7279999999999998,-3.8799999999999999,-4.0351999999999997,-4.1936],[-4.1600000000000001,-4.0015999999999998,-3.8464,-3.6943999999999999,-3.5456000000000003,-3.4000000000000004,-3.2576000000000001,-3.1183999999999994,-2.9823999999999993,-2.8496000000000006,-2.7200000000000006,-2.5936000000000003,-2.4703999999999997,-2.3503999999999996,-2.2336,-2.1199999999999997,-2.0095999999999998,-1.9023999999999994,-1.7984,-1.6976,-1.5999999999999999,-1.5056000000000003,-1.4144000000000001,-1.3264,-1.2416,-1.1599999999999999,-1.0815999999999999,-1.0063999999999997,-0.93439999999999979,-0.86560000000000004,-0.80000000000000004,-0.73759999999999992,-0.67839999999999989,-0.62239999999999984,-0.56959999999999977,-0.5199999999999998,-0.47359999999999997,-0.43039999999999995,-0.39039999999999991,-0.35359999999999991,-0.31999999999999984,-0.28959999999999986,-0.26239999999999997,-0.23839999999999995,-0.2175999999999999,-0.1999999999999999,-0.1855999999999999,-0.17439999999999989,-0.16639999999999994,-0.16159999999999991,-0.15999999999999992,-0.16159999999999991,-0.16639999999999994,-0.17439999999999994,-0.18559999999999996,-0.19999999999999998,-0.21760000000000002,-0.23840000000000006,-0.2623999999999998,-0.28959999999999986,-0.31999999999999984,-0.35359999999999991,-0.39039999999999991,-0.43039999999999995,-0.47359999999999997,-0.52000000000000002,-0.56960000000000011,-0.62240000000000006,-0.67840000000000023,-0.73760000000000026,-0.80000000000000038,-0.8655999999999997,-0.93439999999999979,-1.0063999999999997,-1.0815999999999999,-1.1599999999999999,-1.2416,-1.3264,-1.4144000000000001,-1.5056000000000003,-1.6000000000000003,-1.6976000000000004,-1.7984000000000007,-1.9024000000000008,-2.0095999999999998,-2.1199999999999997,-2.2336,-2.3503999999999996,-2.4703999999999997,-2.5936000000000003,-2.7200000000000006,-2.8496000000000006,-2.9824000000000002,-3.1184000000000003,-3.2576000000000009,-3.4000000000000012,-3.5455999999999994,-3.6943999999999999,-3.8464,-4.0015999999999998,-4.1600000000000001],[-4.1295999999999999,-3.9711999999999996,-3.8159999999999998,-3.6639999999999997,-3.5152000000000001,-3.3696000000000002,-3.2271999999999998,-3.0879999999999996,-2.9519999999999995,-2.8192000000000004,-2.6896000000000004,-2.5632000000000001,-2.4399999999999999,-2.3199999999999998,-2.2031999999999998,-2.0895999999999995,-1.9791999999999996,-1.8719999999999994,-1.768,-1.6672,-1.5695999999999999,-1.4752000000000003,-1.3840000000000001,-1.296,-1.2112000000000001,-1.1295999999999999,-1.0511999999999999,-0.97599999999999976,-0.9039999999999998,-0.83520000000000005,-0.76960000000000006,-0.70719999999999994,-0.64799999999999991,-0.59199999999999986,-0.53919999999999979,-0.4895999999999997,-0.44319999999999993,-0.39999999999999991,-0.35999999999999988,-0.32319999999999988,-0.28959999999999986,-0.25919999999999982,-0.23199999999999996,-0.20799999999999991,-0.18719999999999992,-0.16959999999999989,-0.15519999999999989,-0.14399999999999988,-0.13599999999999993,-0.1311999999999999,-0.12959999999999991,-0.1311999999999999,-0.13599999999999993,-0.14399999999999993,-0.15519999999999995,-0.16959999999999997,-0.18720000000000001,-0.20800000000000005,-0.23199999999999982,-0.25919999999999982,-0.28959999999999986,-0.32319999999999988,-0.35999999999999988,-0.39999999999999991,-0.44319999999999993,-0.48960000000000004,-0.53920000000000012,-0.59200000000000008,-0.64800000000000024,-0.70720000000000027,-0.76960000000000039,-0.83519999999999972,-0.9039999999999998,-0.97599999999999976,-1.0511999999999999,-1.1295999999999999,-1.2112000000000001,-1.296,-1.3840000000000001,-1.4752000000000003,-1.5696000000000003,-1.6672000000000005,-1.7680000000000007,-1.8720000000000008,-1.9791999999999996,-2.0895999999999995,-2.2031999999999998,-2.3199999999999998,-2.4399999999999999,-2.5632000000000001,-2.6896000000000004,-2.8192000000000004,-2.9520000000000004,-3.0880000000000005,-3.2272000000000007,-3.369600000000001,-3.5151999999999992,-3.6639999999999997,-3.8159999999999998,-3.9711999999999996,-4.1295999999999999],[-4.1024000000000003,-3.944,-3.7888000000000002,-3.6368,-3.4880000000000004,-3.3424000000000005,-3.2000000000000002,-3.0607999999999995,-2.9247999999999994,-2.7920000000000007,-2.6624000000000008,-2.5360000000000005,-2.4127999999999998,-2.2927999999999997,-2.1760000000000002,-2.0623999999999998,-1.9519999999999997,-1.8447999999999996,-1.7408000000000001,-1.6400000000000001,-1.5424,-1.4480000000000004,-1.3568000000000002,-1.2688000000000001,-1.1840000000000002,-1.1024,-1.024,-0.94879999999999987,-0.87679999999999991,-0.80800000000000016,-0.74240000000000017,-0.68000000000000005,-0.62080000000000002,-0.56479999999999997,-0.5119999999999999,-0.46239999999999987,-0.41600000000000009,-0.37280000000000008,-0.33280000000000004,-0.29600000000000004,-0.26239999999999997,-0.23199999999999996,-0.20480000000000009,-0.18080000000000007,-0.16000000000000003,-0.14240000000000003,-0.12800000000000003,-0.11680000000000001,-0.10880000000000006,-0.10400000000000005,-0.10240000000000005,-0.10400000000000005,-0.10880000000000006,-0.11680000000000007,-0.12800000000000009,-0.14240000000000011,-0.16000000000000014,-0.18080000000000018,-0.20479999999999993,-0.23199999999999996,-0.26239999999999997,-0.29600000000000004,-0.33280000000000004,-0.37280000000000008,-0.41600000000000009,-0.46240000000000014,-0.51200000000000023,-0.56480000000000019,-0.62080000000000035,-0.68000000000000038,-0.7424000000000005,-0.80799999999999983,-0.87679999999999991,-0.94879999999999987,-1.024,-1.1024,-1.1840000000000002,-1.2688000000000001,-1.3568000000000002,-1.4480000000000004,-1.5424000000000004,-1.6400000000000006,-1.7408000000000008,-1.8448000000000009,-1.9519999999999997,-2.0623999999999998,-2.1760000000000002,-2.2927999999999997,-2.4127999999999998,-2.5360000000000005,-2.6624000000000008,-2.7920000000000007,-2.9248000000000003,-3.0608000000000004,-3.2000000000000011,-3.3424000000000014,-3.4879999999999995,-3.6368,-3.7888000000000002,-3.944,-4.1024000000000003],[-4.0784000000000002,-3.9199999999999995,-3.7647999999999997,-3.6127999999999996,-3.464,-3.3184,-3.1759999999999997,-3.0367999999999995,-2.9007999999999994,-2.7680000000000002,-2.6384000000000003,-2.512,-2.3887999999999998,-2.2687999999999997,-2.1519999999999997,-2.0383999999999998,-1.9279999999999997,-1.8207999999999995,-1.7168000000000001,-1.6160000000000001,-1.5184,-1.4240000000000004,-1.3328000000000002,-1.2448000000000001,-1.1600000000000001,-1.0784,-1,-0.92479999999999984,-0.85279999999999989,-0.78400000000000014,-0.71840000000000015,-0.65600000000000003,-0.5968,-0.54079999999999995,-0.48799999999999988,-0.43839999999999985,-0.39200000000000007,-0.34880000000000005,-0.30880000000000002,-0.27199999999999996,-0.23839999999999995,-0.20799999999999991,-0.18080000000000007,-0.15680000000000002,-0.13600000000000001,-0.11839999999999999,-0.10399999999999998,-0.09279999999999998,-0.084800000000000028,-0.080000000000000016,-0.078400000000000011,-0.080000000000000016,-0.084800000000000028,-0.092800000000000035,-0.10400000000000006,-0.11840000000000009,-0.13600000000000012,-0.15680000000000016,-0.18079999999999991,-0.20799999999999991,-0.23839999999999995,-0.27199999999999996,-0.30880000000000002,-0.34880000000000005,-0.39200000000000007,-0.43840000000000012,-0.48800000000000021,-0.54080000000000017,-0.59680000000000033,-0.65600000000000036,-0.71840000000000048,-0.78399999999999981,-0.85279999999999989,-0.92479999999999984,-1,-1.0784,-1.1600000000000001,-1.2448000000000001,-1.3328000000000002,-1.4240000000000004,-1.5184000000000004,-1.6160000000000005,-1.7168000000000008,-1.8208000000000009,-1.9279999999999997,-2.0383999999999998,-2.1519999999999997,-2.2687999999999997,-2.3887999999999998,-2.512,-2.6384000000000003,-2.7680000000000002,-2.9008000000000003,-3.0368000000000004,-3.1760000000000006,-3.3184000000000009,-3.4639999999999991,-3.6127999999999996,-3.7647999999999997,-3.9199999999999995,-4.0784000000000002],[-4.0575999999999999,-3.8991999999999996,-3.7439999999999998,-3.5919999999999996,-3.4432,-3.2976000000000001,-3.1551999999999998,-3.0159999999999996,-2.8799999999999994,-2.7472000000000003,-2.6176000000000004,-2.4912000000000001,-2.3679999999999999,-2.2479999999999998,-2.1311999999999998,-2.0175999999999998,-1.9071999999999998,-1.7999999999999996,-1.6960000000000002,-1.5952000000000002,-1.4976,-1.4032000000000004,-1.3120000000000003,-1.2240000000000002,-1.1392000000000002,-1.0576000000000001,-0.97919999999999996,-0.9039999999999998,-0.83199999999999985,-0.7632000000000001,-0.69760000000000011,-0.63519999999999999,-0.57599999999999996,-0.51999999999999991,-0.46719999999999984,-0.4175999999999998,-0.37120000000000003,-0.32800000000000001,-0.28799999999999998,-0.25119999999999998,-0.2175999999999999,-0.18719999999999992,-0.16000000000000003,-0.13600000000000001,-0.1152,-0.097599999999999978,-0.083199999999999968,-0.071999999999999967,-0.064000000000000015,-0.059200000000000003,-0.057599999999999998,-0.059200000000000003,-0.064000000000000015,-0.072000000000000022,-0.083200000000000052,-0.097600000000000076,-0.11520000000000011,-0.13600000000000012,-0.15999999999999989,-0.18719999999999992,-0.2175999999999999,-0.25119999999999998,-0.28799999999999998,-0.32800000000000001,-0.37120000000000003,-0.41760000000000008,-0.46720000000000017,-0.52000000000000024,-0.57600000000000029,-0.63520000000000032,-0.69760000000000044,-0.76319999999999977,-0.83199999999999985,-0.9039999999999998,-0.97919999999999996,-1.0576000000000001,-1.1392000000000002,-1.2240000000000002,-1.3120000000000003,-1.4032000000000004,-1.4976000000000005,-1.5952000000000006,-1.6960000000000008,-1.8000000000000009,-1.9071999999999998,-2.0175999999999998,-2.1311999999999998,-2.2479999999999998,-2.3679999999999999,-2.4912000000000001,-2.6176000000000004,-2.7472000000000003,-2.8800000000000003,-3.0160000000000005,-3.1552000000000007,-3.297600000000001,-3.4431999999999992,-3.5919999999999996,-3.7439999999999998,-3.8991999999999996,-4.0575999999999999],[-4.04,-3.8815999999999997,-3.7263999999999999,-3.5743999999999998,-3.4256000000000002,-3.2800000000000002,-3.1375999999999999,-2.9983999999999997,-2.8623999999999996,-2.7296000000000005,-2.6000000000000005,-2.4736000000000002,-2.3504,-2.2303999999999999,-2.1135999999999999,-1.9999999999999998,-1.8895999999999997,-1.7823999999999995,-1.6784000000000001,-1.5776000000000001,-1.48,-1.3856000000000004,-1.2944000000000002,-1.2064000000000001,-1.1216000000000002,-1.04,-0.96160000000000001,-0.88639999999999985,-0.81439999999999979,-0.74560000000000004,-0.68000000000000016,-0.61759999999999993,-0.55840000000000001,-0.50239999999999996,-0.44959999999999983,-0.3999999999999998,-0.35360000000000003,-0.31040000000000001,-0.27039999999999997,-0.23359999999999995,-0.1999999999999999,-0.16959999999999989,-0.14240000000000003,-0.11839999999999999,-0.097599999999999978,-0.07999999999999996,-0.06559999999999995,-0.054399999999999948,-0.04639999999999999,-0.041599999999999984,-0.03999999999999998,-0.041599999999999984,-0.04639999999999999,-0.054400000000000004,-0.065600000000000019,-0.080000000000000043,-0.097600000000000076,-0.11840000000000012,-0.14239999999999986,-0.16959999999999989,-0.1999999999999999,-0.23359999999999995,-0.27039999999999997,-0.31040000000000001,-0.35360000000000003,-0.40000000000000008,-0.44960000000000017,-0.50240000000000018,-0.55840000000000023,-0.61760000000000037,-0.68000000000000038,-0.74559999999999982,-0.81439999999999979,-0.88639999999999985,-0.96160000000000001,-1.04,-1.1216000000000002,-1.2064000000000001,-1.2944000000000002,-1.3856000000000004,-1.4800000000000004,-1.5776000000000006,-1.6784000000000008,-1.7824000000000009,-1.8895999999999997,-1.9999999999999998,-2.1135999999999999,-2.2303999999999999,-2.3504,-2.4736000000000002,-2.6000000000000005,-2.7296000000000005,-2.8624000000000005,-2.9984000000000006,-3.1376000000000008,-3.2800000000000011,-3.4255999999999993,-3.5743999999999998,-3.7263999999999999,-3.8815999999999997,-4.04],[-4.0255999999999998,-3.8671999999999995,-3.7119999999999997,-3.5599999999999996,-3.4112,-3.2656000000000001,-3.1231999999999998,-2.9839999999999995,-2.8479999999999994,-2.7152000000000003,-2.5856000000000003,-2.4592000000000001,-2.3359999999999999,-2.2159999999999997,-2.0991999999999997,-1.9855999999999998,-1.8751999999999998,-1.7679999999999996,-1.6640000000000001,-1.5632000000000001,-1.4656,-1.3712000000000004,-1.2800000000000002,-1.1920000000000002,-1.1072000000000002,-1.0256000000000001,-0.94719999999999993,-0.87199999999999978,-0.79999999999999982,-0.73120000000000007,-0.66560000000000008,-0.60319999999999996,-0.54399999999999993,-0.48799999999999988,-0.43519999999999981,-0.38559999999999978,-0.3392,-0.29599999999999999,-0.25599999999999995,-0.21919999999999995,-0.1855999999999999,-0.15519999999999989,-0.12800000000000003,-0.10399999999999998,-0.083199999999999968,-0.06559999999999995,-0.051199999999999947,-0.039999999999999945,-0.031999999999999987,-0.027199999999999978,-0.025599999999999973,-0.027199999999999978,-0.031999999999999987,-0.040000000000000001,-0.051200000000000023,-0.065600000000000047,-0.083200000000000079,-0.10400000000000011,-0.12799999999999986,-0.15519999999999989,-0.1855999999999999,-0.21919999999999995,-0.25599999999999995,-0.29599999999999999,-0.3392,-0.38560000000000005,-0.43520000000000014,-0.48800000000000016,-0.54400000000000026,-0.60320000000000029,-0.66560000000000041,-0.73119999999999974,-0.79999999999999982,-0.87199999999999978,-0.94719999999999993,-1.0256000000000001,-1.1072000000000002,-1.1920000000000002,-1.2800000000000002,-1.3712000000000004,-1.4656000000000005,-1.5632000000000006,-1.6640000000000008,-1.7680000000000009,-1.8751999999999998,-1.9855999999999998,-2.0991999999999997,-2.2159999999999997,-2.3359999999999999,-2.4592000000000001,-2.5856000000000003,-2.7152000000000003,-2.8480000000000003,-2.9840000000000004,-3.1232000000000006,-3.2656000000000009,-3.4111999999999991,-3.5599999999999996,-3.7119999999999997,-3.8671999999999995,-4.0255999999999998],[-4.0144000000000002,-3.8559999999999999,-3.7008000000000001,-3.5488,-3.4000000000000004,-3.2544000000000004,-3.1120000000000001,-2.9727999999999999,-2.8367999999999998,-2.7040000000000006,-2.5744000000000007,-2.4480000000000004,-2.3248000000000002,-2.2048000000000001,-2.0880000000000001,-1.9743999999999997,-1.8639999999999997,-1.7567999999999995,-1.6528,-1.552,-1.4543999999999999,-1.3600000000000003,-1.2688000000000001,-1.1808000000000001,-1.0960000000000001,-1.0144,-0.93599999999999994,-0.86079999999999979,-0.78879999999999983,-0.72000000000000008,-0.65440000000000009,-0.59199999999999997,-0.53279999999999994,-0.47679999999999989,-0.42399999999999982,-0.37439999999999979,-0.32800000000000001,-0.2848,-0.24479999999999996,-0.20799999999999993,-0.17439999999999989,-0.14399999999999988,-0.11680000000000001,-0.09279999999999998,-0.071999999999999967,-0.054399999999999948,-0.039999999999999945,-0.028799999999999944,-0.020799999999999985,-0.015999999999999976,-0.014399999999999972,-0.015999999999999976,-0.020799999999999985,-0.028799999999999999,-0.040000000000000022,-0.054400000000000046,-0.072000000000000078,-0.092800000000000105,-0.11679999999999986,-0.14399999999999988,-0.17439999999999989,-0.20799999999999993,-0.24479999999999996,-0.2848,-0.32800000000000001,-0.37440000000000007,-0.42400000000000015,-0.47680000000000017,-0.53280000000000027,-0.5920000000000003,-0.65440000000000043,-0.71999999999999975,-0.78879999999999983,-0.86079999999999979,-0.93599999999999994,-1.0144,-1.0960000000000001,-1.1808000000000001,-1.2688000000000001,-1.3600000000000003,-1.4544000000000004,-1.5520000000000005,-1.6528000000000007,-1.7568000000000008,-1.8639999999999997,-1.9743999999999997,-2.0880000000000001,-2.2048000000000001,-2.3248000000000002,-2.4480000000000004,-2.5744000000000007,-2.7040000000000006,-2.8368000000000007,-2.9728000000000008,-3.112000000000001,-3.2544000000000013,-3.3999999999999995,-3.5488,-3.7008000000000001,-3.8559999999999999,-4.0144000000000002],[-4.0064000000000002,-3.8479999999999999,-3.6928000000000001,-3.5407999999999999,-3.3920000000000003,-3.2464000000000004,-3.1040000000000001,-2.9647999999999999,-2.8287999999999998,-2.6960000000000006,-2.5664000000000007,-2.4400000000000004,-2.3168000000000002,-2.1968000000000001,-2.0800000000000001,-1.9663999999999997,-1.8559999999999997,-1.7487999999999995,-1.6448,-1.544,-1.4463999999999999,-1.3520000000000003,-1.2608000000000001,-1.1728000000000001,-1.0880000000000001,-1.0064,-0.92799999999999994,-0.85279999999999978,-0.78079999999999983,-0.71200000000000008,-0.64640000000000009,-0.58399999999999996,-0.52479999999999993,-0.46879999999999994,-0.41599999999999987,-0.36639999999999984,-0.32000000000000006,-0.27680000000000005,-0.23680000000000001,-0.19999999999999998,-0.16639999999999994,-0.13599999999999993,-0.10880000000000006,-0.084800000000000028,-0.064000000000000015,-0.04639999999999999,-0.031999999999999987,-0.020799999999999985,-0.012800000000000023,-0.008000000000000014,-0.0064000000000000116,-0.008000000000000014,-0.012800000000000023,-0.020800000000000037,-0.032000000000000056,-0.04640000000000008,-0.064000000000000112,-0.084800000000000153,-0.10879999999999991,-0.13599999999999993,-0.16639999999999994,-0.19999999999999998,-0.23680000000000001,-0.27680000000000005,-0.32000000000000006,-0.36640000000000011,-0.4160000000000002,-0.46880000000000022,-0.52480000000000027,-0.5840000000000003,-0.64640000000000042,-0.71199999999999974,-0.78079999999999983,-0.85279999999999978,-0.92799999999999994,-1.0064,-1.0880000000000001,-1.1728000000000001,-1.2608000000000001,-1.3520000000000003,-1.4464000000000004,-1.5440000000000005,-1.6448000000000007,-1.7488000000000008,-1.8559999999999997,-1.9663999999999997,-2.0800000000000001,-2.1968000000000001,-2.3168000000000002,-2.4400000000000004,-2.5664000000000007,-2.6960000000000006,-2.8288000000000006,-2.9648000000000008,-3.104000000000001,-3.2464000000000013,-3.3919999999999995,-3.5407999999999999,-3.6928000000000001,-3.8479999999999999,-4.0064000000000002],[-4.0015999999999998,-3.8431999999999995,-3.6879999999999997,-3.5359999999999996,-3.3872,-3.2416,-3.0991999999999997,-2.9599999999999995,-2.8239999999999994,-2.6912000000000003,-2.5616000000000003,-2.4352,-2.3119999999999998,-2.1919999999999997,-2.0751999999999997,-1.9615999999999998,-1.8511999999999997,-1.7439999999999996,-1.6400000000000001,-1.5392000000000001,-1.4416,-1.3472000000000004,-1.2560000000000002,-1.1680000000000001,-1.0832000000000002,-1.0016,-0.92320000000000002,-0.84799999999999986,-0.77599999999999991,-0.70720000000000016,-0.64160000000000017,-0.57920000000000005,-0.52000000000000002,-0.46399999999999991,-0.41119999999999984,-0.36159999999999981,-0.31520000000000004,-0.27200000000000002,-0.23199999999999998,-0.19519999999999996,-0.16159999999999991,-0.1311999999999999,-0.10400000000000005,-0.080000000000000016,-0.059200000000000003,-0.041599999999999984,-0.027199999999999978,-0.015999999999999976,-0.008000000000000014,-0.0032000000000000058,-0.0016000000000000029,-0.0032000000000000058,-0.008000000000000014,-0.016000000000000028,-0.027200000000000051,-0.041600000000000074,-0.059200000000000107,-0.08000000000000014,-0.1039999999999999,-0.1311999999999999,-0.16159999999999991,-0.19519999999999996,-0.23199999999999998,-0.27200000000000002,-0.31520000000000004,-0.36160000000000009,-0.41120000000000018,-0.46400000000000019,-0.52000000000000035,-0.57920000000000038,-0.6416000000000005,-0.70719999999999983,-0.77599999999999991,-0.84799999999999986,-0.92320000000000002,-1.0016,-1.0832000000000002,-1.1680000000000001,-1.2560000000000002,-1.3472000000000004,-1.4416000000000004,-1.5392000000000006,-1.6400000000000008,-1.7440000000000009,-1.8511999999999997,-1.9615999999999998,-2.0751999999999997,-2.1919999999999997,-2.3119999999999998,-2.4352,-2.5616000000000003,-2.6912000000000003,-2.8240000000000003,-2.9600000000000004,-3.0992000000000006,-3.2416000000000009,-3.3871999999999991,-3.5359999999999996,-3.6879999999999997,-3.8431999999999995,-4.0015999999999998],[-4,-3.8415999999999997,-3.6863999999999999,-3.5343999999999998,-3.3856000000000002,-3.2400000000000002,-3.0975999999999999,-2.9583999999999997,-2.8223999999999996,-2.6896000000000004,-2.5600000000000005,-2.4336000000000002,-2.3104,-2.1903999999999999,-2.0735999999999999,-1.9599999999999997,-1.8495999999999997,-1.7423999999999995,-1.6384000000000001,-1.5376000000000001,-1.4399999999999999,-1.3456000000000004,-1.2544000000000002,-1.1664000000000001,-1.0816000000000001,-1,-0.92159999999999997,-0.84639999999999982,-0.77439999999999987,-0.70560000000000012,-0.64000000000000012,-0.5776,-0.51839999999999997,-0.46239999999999992,-0.40959999999999985,-0.35999999999999982,-0.31360000000000005,-0.27040000000000003,-0.23039999999999999,-0.19359999999999997,-0.15999999999999992,-0.12959999999999991,-0.10240000000000005,-0.078400000000000011,-0.057599999999999998,-0.03999999999999998,-0.025599999999999973,-0.014399999999999972,-0.0064000000000000116,-0.0016000000000000029,-0,-0.0016000000000000029,-0.0064000000000000116,-0.014400000000000026,-0.025600000000000046,-0.04000000000000007,-0.057600000000000103,-0.078400000000000136,-0.10239999999999989,-0.12959999999999991,-0.15999999999999992,-0.19359999999999997,-0.23039999999999999,-0.27040000000000003,-0.31360000000000005,-0.3600000000000001,-0.40960000000000019,-0.4624000000000002,-0.51840000000000031,-0.57760000000000034,-0.64000000000000046,-0.70559999999999978,-0.77439999999999987,-0.84639999999999982,-0.92159999999999997,-1,-1.0816000000000001,-1.1664000000000001,-1.2544000000000002,-1.3456000000000004,-1.4400000000000004,-1.5376000000000005,-1.6384000000000007,-1.7424000000000008,-1.8495999999999997,-1.9599999999999997,-2.0735999999999999,-2.1903999999999999,-2.3104,-2.4336000000000002,-2.5600000000000005,-2.6896000000000004,-2.8224000000000005,-2.9584000000000006,-3.0976000000000008,-3.2400000000000011,-3.3855999999999993,-3.5343999999999998,-3.6863999999999999,-3.8415999999999997,-4],[-4.0015999999999998,-3.8431999999999995,-3.6879999999999997,-3.5359999999999996,-3.3872,-3.2416,-3.0991999999999997,-2.9599999999999995,-2.8239999999999994,-2.6912000000000003,-2.5616000000000003,-2.4352,-2.3119999999999998,-2.1919999999999997,-2.0751999999999997,-1.9615999999999998,-1.8511999999999997,-1.7439999999999996,-1.6400000000000001,-1.5392000000000001,-1.4416,-1.3472000000000004,-1.2560000000000002,-1.1680000000000001,-1.0832000000000002,-1.0016,-0.92320000000000002,-0.84799999999999986,-0.77599999999999991,-0.70720000000000016,-0.64160000000000017,-0.57920000000000005,-0.52000000000000002,-0.46399999999999991,-0.41119999999999984,-0.36159999999999981,-0.31520000000000004,-0.27200000000000002,-0.23199999999999998,-0.19519999999999996,-0.16159999999999991,-0.1311999999999999,-0.10400000000000005,-0.080000000000000016,-0.059200000000000003,-0.041599999999999984,-0.027199999999999978,-0.015999999999999976,-0.008000000000000014,-0.0032000000000000058,-0.0016000000000000029,-0.0032000000000000058,-0.008000000000000014,-0.016000000000000028,-0.027200000000000051,-0.041600000000000074,-0.059200000000000107,-0.08000000000000014,-0.1039999999999999,-0.1311999999999999,-0.16159999999999991,-0.19519999999999996,-0.23199999999999998,-0.27200000000000002,-0.31520000000000004,-0.36160000000000009,-0.41120000000000018,-0.46400000000000019,-0.52000000000000035,-0.57920000000000038,-0.6416000000000005,-0.70719999999999983,-0.77599999999999991,-0.84799999999999986,-0.92320000000000002,-1.0016,-1.0832000000000002,-1.1680000000000001,-1.2560000000000002,-1.3472000000000004,-1.4416000000000004,-1.5392000000000006,-1.6400000000000008,-1.7440000000000009,-1.8511999999999997,-1.9615999999999998,-2.0751999999999997,-2.1919999999999997,-2.3119999999999998,-2.4352,-2.5616000000000003,-2.6912000000000003,-2.8240000000000003,-2.9600000000000004,-3.0992000000000006,-3.2416000000000009,-3.3871999999999991,-3.5359999999999996,-3.6879999999999997,-3.8431999999999995,-4.0015999999999998],[-4.0064000000000002,-3.8479999999999999,-3.6928000000000001,-3.5407999999999999,-3.3920000000000003,-3.2464000000000004,-3.1040000000000001,-2.9647999999999999,-2.8287999999999998,-2.6960000000000006,-2.5664000000000007,-2.4400000000000004,-2.3168000000000002,-2.1968000000000001,-2.0800000000000001,-1.9663999999999997,-1.8559999999999997,-1.7487999999999995,-1.6448,-1.544,-1.4463999999999999,-1.3520000000000003,-1.2608000000000001,-1.1728000000000001,-1.0880000000000001,-1.0064,-0.92799999999999994,-0.85279999999999978,-0.78079999999999983,-0.71200000000000008,-0.64640000000000009,-0.58399999999999996,-0.52479999999999993,-0.46879999999999994,-0.41599999999999987,-0.36639999999999984,-0.32000000000000006,-0.27680000000000005,-0.23680000000000001,-0.19999999999999998,-0.16639999999999994,-0.13599999999999993,-0.10880000000000006,-0.084800000000000028,-0.064000000000000015,-0.04639999999999999,-0.031999999999999987,-0.020799999999999985,-0.012800000000000023,-0.008000000000000014,-0.0064000000000000116,-0.008000000000000014,-0.012800000000000023,-0.020800000000000037,-0.032000000000000056,-0.04640000000000008,-0.064000000000000112,-0.084800000000000153,-0.10879999999999991,-0.13599999999999993,-0.16639999999999994,-0.19999999999999998,-0.23680000000000001,-0.27680000000000005,-0.32000000000000006,-0.36640000000000011,-0.4160000000000002,-0.46880000000000022,-0.52480000000000027,-0.5840000000000003,-0.64640000000000042,-0.71199999999999974,-0.78079999999999983,-0.85279999999999978,-0.92799999999999994,-1.0064,-1.0880000000000001,-1.1728000000000001,-1.2608000000000001,-1.3520000000000003,-1.4464000000000004,-1.5440000000000005,-1.6448000000000007,-1.7488000000000008,-1.8559999999999997,-1.9663999999999997,-2.0800000000000001,-2.1968000000000001,-2.3168000000000002,-2.4400000000000004,-2.5664000000000007,-2.6960000000000006,-2.8288000000000006,-2.9648000000000008,-3.104000000000001,-3.2464000000000013,-3.3919999999999995,-3.5407999999999999,-3.6928000000000001,-3.8479999999999999,-4.0064000000000002],[-4.0144000000000002,-3.8559999999999999,-3.7008000000000001,-3.5488,-3.4000000000000004,-3.2544000000000004,-3.1120000000000001,-2.9727999999999999,-2.8367999999999998,-2.7040000000000006,-2.5744000000000007,-2.4480000000000004,-2.3248000000000002,-2.2048000000000001,-2.0880000000000001,-1.9743999999999997,-1.8639999999999997,-1.7567999999999995,-1.6528,-1.552,-1.4543999999999999,-1.3600000000000003,-1.2688000000000001,-1.1808000000000001,-1.0960000000000001,-1.0144,-0.93600000000000005,-0.8607999999999999,-0.78879999999999995,-0.7200000000000002,-0.6544000000000002,-0.59200000000000008,-0.53280000000000005,-0.47679999999999995,-0.42399999999999988,-0.37439999999999984,-0.32800000000000007,-0.28480000000000005,-0.24480000000000002,-0.20799999999999999,-0.17439999999999994,-0.14399999999999993,-0.11680000000000007,-0.092800000000000035,-0.072000000000000022,-0.054400000000000004,-0.040000000000000001,-0.028799999999999999,-0.020800000000000037,-0.016000000000000028,-0.014400000000000026,-0.016000000000000028,-0.020800000000000037,-0.028800000000000051,-0.04000000000000007,-0.054400000000000094,-0.072000000000000133,-0.09280000000000016,-0.11679999999999992,-0.14399999999999993,-0.17439999999999994,-0.20799999999999999,-0.24480000000000002,-0.28480000000000005,-0.32800000000000007,-0.37440000000000012,-0.42400000000000021,-0.47680000000000022,-0.53280000000000038,-0.59200000000000041,-0.65440000000000054,-0.71999999999999986,-0.78879999999999995,-0.8607999999999999,-0.93600000000000005,-1.0144,-1.0960000000000001,-1.1808000000000001,-1.2688000000000001,-1.3600000000000003,-1.4544000000000004,-1.5520000000000005,-1.6528000000000007,-1.7568000000000008,-1.8639999999999997,-1.9743999999999997,-2.0880000000000001,-2.2048000000000001,-2.3248000000000002,-2.4480000000000004,-2.5744000000000007,-2.7040000000000006,-2.8368000000000007,-2.9728000000000008,-3.112000000000001,-3.2544000000000013,-3.3999999999999995,-3.5488,-3.7008000000000001,-3.8559999999999999,-4.0144000000000002],[-4.0255999999999998,-3.8671999999999995,-3.7119999999999997,-3.5599999999999996,-3.4112,-3.2656000000000001,-3.1231999999999998,-2.9839999999999995,-2.8479999999999994,-2.7152000000000003,-2.5856000000000003,-2.4592000000000001,-2.3359999999999999,-2.2159999999999997,-2.0991999999999997,-1.9855999999999998,-1.8751999999999998,-1.7679999999999996,-1.6640000000000001,-1.5632000000000001,-1.4656,-1.3712000000000004,-1.2800000000000002,-1.1920000000000002,-1.1072000000000002,-1.0256000000000001,-0.94720000000000004,-0.87199999999999989,-0.79999999999999993,-0.73120000000000018,-0.66560000000000019,-0.60320000000000007,-0.54400000000000004,-0.48799999999999999,-0.43519999999999992,-0.38559999999999989,-0.33920000000000011,-0.2960000000000001,-0.25600000000000006,-0.21920000000000001,-0.18559999999999996,-0.15519999999999995,-0.12800000000000009,-0.10400000000000006,-0.083200000000000052,-0.065600000000000019,-0.051200000000000023,-0.040000000000000022,-0.032000000000000056,-0.027200000000000051,-0.025600000000000046,-0.027200000000000051,-0.032000000000000056,-0.04000000000000007,-0.051200000000000093,-0.065600000000000117,-0.083200000000000149,-0.10400000000000018,-0.12799999999999995,-0.15519999999999995,-0.18559999999999996,-0.21920000000000001,-0.25600000000000006,-0.2960000000000001,-0.33920000000000011,-0.38560000000000016,-0.43520000000000025,-0.48800000000000027,-0.54400000000000037,-0.6032000000000004,-0.66560000000000052,-0.73119999999999985,-0.79999999999999993,-0.87199999999999989,-0.94720000000000004,-1.0256000000000001,-1.1072000000000002,-1.1920000000000002,-1.2800000000000002,-1.3712000000000004,-1.4656000000000005,-1.5632000000000006,-1.6640000000000008,-1.7680000000000009,-1.8751999999999998,-1.9855999999999998,-2.0991999999999997,-2.2159999999999997,-2.3359999999999999,-2.4592000000000001,-2.5856000000000003,-2.7152000000000003,-2.8480000000000003,-2.9840000000000004,-3.1232000000000006,-3.2656000000000009,-3.4111999999999991,-3.5599999999999996,-3.7119999999999997,-3.8671999999999995,-4.0255999999999998],[-4.04,-3.8815999999999997,-3.7263999999999999,-3.5743999999999998,-3.4256000000000002,-3.2800000000000002,-3.1375999999999999,-2.9983999999999997,-2.8623999999999996,-2.7296000000000005,-2.6000000000000005,-2.4736000000000002,-2.3504,-2.2303999999999999,-2.1135999999999999,-1.9999999999999998,-1.8895999999999997,-1.7823999999999995,-1.6784000000000001,-1.5776000000000001,-1.48,-1.3856000000000004,-1.2944000000000002,-1.2064000000000001,-1.1216000000000002,-1.04,-0.96160000000000001,-0.88639999999999985,-0.8143999999999999,-0.74560000000000015,-0.68000000000000016,-0.61760000000000004,-0.55840000000000001,-0.50239999999999996,-0.44959999999999994,-0.39999999999999991,-0.35360000000000014,-0.31040000000000012,-0.27040000000000008,-0.23360000000000003,-0.19999999999999998,-0.16959999999999997,-0.14240000000000011,-0.11840000000000009,-0.097600000000000076,-0.080000000000000043,-0.065600000000000047,-0.054400000000000046,-0.04640000000000008,-0.041600000000000074,-0.04000000000000007,-0.041600000000000074,-0.04640000000000008,-0.054400000000000094,-0.065600000000000117,-0.08000000000000014,-0.097600000000000173,-0.1184000000000002,-0.14239999999999997,-0.16959999999999997,-0.19999999999999998,-0.23360000000000003,-0.27040000000000008,-0.31040000000000012,-0.35360000000000014,-0.40000000000000019,-0.44960000000000028,-0.50240000000000029,-0.55840000000000034,-0.61760000000000037,-0.68000000000000049,-0.74559999999999982,-0.8143999999999999,-0.88639999999999985,-0.96160000000000001,-1.04,-1.1216000000000002,-1.2064000000000001,-1.2944000000000002,-1.3856000000000004,-1.4800000000000004,-1.5776000000000006,-1.6784000000000008,-1.7824000000000009,-1.8895999999999997,-1.9999999999999998,-2.1135999999999999,-2.2303999999999999,-2.3504,-2.4736000000000002,-2.6000000000000005,-2.7296000000000005,-2.8624000000000005,-2.9984000000000006,-3.1376000000000008,-3.2800000000000011,-3.4255999999999993,-3.5743999999999998,-3.7263999999999999,-3.8815999999999997,-4.04],[-4.0575999999999999,-3.8992,-3.7440000000000002,-3.5920000000000001,-3.4432000000000005,-3.2976000000000005,-3.1552000000000002,-3.016,-2.8799999999999999,-2.7472000000000008,-2.6176000000000008,-2.4912000000000005,-2.3680000000000003,-2.2480000000000002,-2.1312000000000002,-2.0175999999999998,-1.9071999999999998,-1.7999999999999996,-1.6960000000000002,-1.5952000000000002,-1.4976,-1.4032000000000004,-1.3120000000000003,-1.2240000000000002,-1.1392000000000002,-1.0576000000000001,-0.97920000000000007,-0.90399999999999991,-0.83199999999999996,-0.76320000000000021,-0.69760000000000022,-0.6352000000000001,-0.57600000000000007,-0.52000000000000002,-0.46719999999999995,-0.41759999999999992,-0.37120000000000014,-0.32800000000000012,-0.28800000000000009,-0.25120000000000009,-0.21760000000000002,-0.18720000000000001,-0.16000000000000014,-0.13600000000000012,-0.11520000000000011,-0.097600000000000076,-0.083200000000000079,-0.072000000000000078,-0.064000000000000112,-0.059200000000000107,-0.057600000000000103,-0.059200000000000107,-0.064000000000000112,-0.072000000000000133,-0.083200000000000149,-0.097600000000000173,-0.11520000000000021,-0.13600000000000023,-0.16,-0.18720000000000001,-0.21760000000000002,-0.25120000000000009,-0.28800000000000009,-0.32800000000000012,-0.37120000000000014,-0.41760000000000019,-0.46720000000000028,-0.52000000000000035,-0.5760000000000004,-0.63520000000000043,-0.69760000000000055,-0.76319999999999988,-0.83199999999999996,-0.90399999999999991,-0.97920000000000007,-1.0576000000000001,-1.1392000000000002,-1.2240000000000002,-1.3120000000000003,-1.4032000000000004,-1.4976000000000005,-1.5952000000000006,-1.6960000000000008,-1.8000000000000009,-1.9071999999999998,-2.0175999999999998,-2.1312000000000002,-2.2480000000000002,-2.3680000000000003,-2.4912000000000005,-2.6176000000000008,-2.7472000000000008,-2.8800000000000008,-3.0160000000000009,-3.1552000000000011,-3.2976000000000014,-3.4431999999999996,-3.5920000000000001,-3.7440000000000002,-3.8992,-4.0575999999999999],[-4.0784000000000002,-3.9199999999999999,-3.7648000000000001,-3.6128,-3.4640000000000004,-3.3184000000000005,-3.1760000000000002,-3.0367999999999999,-2.9007999999999998,-2.7680000000000007,-2.6384000000000007,-2.5120000000000005,-2.3888000000000003,-2.2688000000000001,-2.1520000000000001,-2.0383999999999998,-1.9279999999999999,-1.8207999999999998,-1.7168000000000001,-1.6160000000000001,-1.5184000000000002,-1.4240000000000004,-1.3328000000000002,-1.2448000000000001,-1.1600000000000001,-1.0784000000000002,-1,-0.92479999999999996,-0.8528,-0.78400000000000025,-0.71840000000000026,-0.65600000000000014,-0.59680000000000011,-0.54080000000000006,-0.48799999999999999,-0.43839999999999996,-0.39200000000000018,-0.34880000000000017,-0.30880000000000013,-0.27200000000000013,-0.23840000000000006,-0.20800000000000005,-0.18080000000000018,-0.15680000000000016,-0.13600000000000012,-0.11840000000000012,-0.10400000000000011,-0.092800000000000105,-0.084800000000000153,-0.08000000000000014,-0.078400000000000136,-0.08000000000000014,-0.084800000000000153,-0.09280000000000016,-0.10400000000000018,-0.1184000000000002,-0.13600000000000023,-0.15680000000000027,-0.18080000000000002,-0.20800000000000005,-0.23840000000000006,-0.27200000000000013,-0.30880000000000013,-0.34880000000000017,-0.39200000000000018,-0.43840000000000023,-0.48800000000000032,-0.54080000000000039,-0.59680000000000044,-0.65600000000000047,-0.71840000000000059,-0.78399999999999992,-0.8528,-0.92479999999999996,-1,-1.0784000000000002,-1.1600000000000001,-1.2448000000000001,-1.3328000000000002,-1.4240000000000004,-1.5184000000000006,-1.6160000000000005,-1.716800000000001,-1.8208000000000011,-1.9279999999999999,-2.0383999999999998,-2.1520000000000001,-2.2688000000000001,-2.3888000000000003,-2.5120000000000005,-2.6384000000000007,-2.7680000000000007,-2.9008000000000007,-3.0368000000000008,-3.176000000000001,-3.3184000000000013,-3.4639999999999995,-3.6128,-3.7648000000000001,-3.9199999999999999,-4.0784000000000002],[-4.1024000000000003,-3.9439999999999995,-3.7887999999999997,-3.6367999999999996,-3.488,-3.3424,-3.1999999999999997,-3.0607999999999995,-2.9247999999999994,-2.7920000000000003,-2.6624000000000003,-2.536,-2.4127999999999998,-2.2927999999999997,-2.1759999999999997,-2.0623999999999998,-1.9519999999999995,-1.8447999999999993,-1.7407999999999999,-1.6399999999999999,-1.5423999999999998,-1.4480000000000002,-1.3568,-1.2687999999999999,-1.1839999999999999,-1.1023999999999998,-1.0239999999999998,-0.94879999999999975,-0.8767999999999998,-0.80800000000000005,-0.74240000000000006,-0.67999999999999994,-0.62079999999999991,-0.56479999999999986,-0.51199999999999979,-0.4623999999999997,-0.41599999999999993,-0.37279999999999991,-0.33279999999999987,-0.29599999999999987,-0.2623999999999998,-0.23199999999999982,-0.20479999999999993,-0.18079999999999991,-0.15999999999999989,-0.14239999999999986,-0.12799999999999986,-0.11679999999999986,-0.10879999999999991,-0.1039999999999999,-0.10239999999999989,-0.1039999999999999,-0.10879999999999991,-0.11679999999999992,-0.12799999999999995,-0.14239999999999997,-0.16,-0.18080000000000002,-0.20479999999999979,-0.23199999999999982,-0.2623999999999998,-0.29599999999999987,-0.33279999999999987,-0.37279999999999991,-0.41599999999999993,-0.46239999999999998,-0.51200000000000012,-0.56480000000000008,-0.62080000000000024,-0.68000000000000027,-0.74240000000000039,-0.80799999999999972,-0.8767999999999998,-0.94879999999999975,-1.0239999999999998,-1.1023999999999998,-1.1839999999999999,-1.2687999999999999,-1.3568,-1.4480000000000002,-1.5424000000000002,-1.6400000000000003,-1.7408000000000006,-1.8448000000000007,-1.9519999999999995,-2.0623999999999998,-2.1759999999999997,-2.2927999999999997,-2.4127999999999998,-2.536,-2.6624000000000003,-2.7920000000000003,-2.9248000000000003,-3.0608000000000004,-3.2000000000000006,-3.3424000000000009,-3.4879999999999991,-3.6367999999999996,-3.7887999999999997,-3.9439999999999995,-4.1024000000000003],[-4.1295999999999999,-3.9711999999999996,-3.8159999999999998,-3.6639999999999997,-3.5152000000000001,-3.3696000000000002,-3.2271999999999998,-3.0879999999999996,-2.9519999999999995,-2.8192000000000004,-2.6896000000000004,-2.5632000000000001,-2.4399999999999999,-2.3199999999999998,-2.2031999999999998,-2.0895999999999995,-1.9791999999999996,-1.8719999999999994,-1.768,-1.6672,-1.5695999999999999,-1.4752000000000003,-1.3840000000000001,-1.296,-1.2112000000000001,-1.1295999999999999,-1.0511999999999999,-0.97599999999999976,-0.9039999999999998,-0.83520000000000005,-0.76960000000000006,-0.70719999999999994,-0.64799999999999991,-0.59199999999999986,-0.53919999999999979,-0.4895999999999997,-0.44319999999999993,-0.39999999999999991,-0.35999999999999988,-0.32319999999999988,-0.28959999999999986,-0.25919999999999982,-0.23199999999999996,-0.20799999999999991,-0.18719999999999992,-0.16959999999999989,-0.15519999999999989,-0.14399999999999988,-0.13599999999999993,-0.1311999999999999,-0.12959999999999991,-0.1311999999999999,-0.13599999999999993,-0.14399999999999993,-0.15519999999999995,-0.16959999999999997,-0.18720000000000001,-0.20800000000000005,-0.23199999999999982,-0.25919999999999982,-0.28959999999999986,-0.32319999999999988,-0.35999999999999988,-0.39999999999999991,-0.44319999999999993,-0.48960000000000004,-0.53920000000000012,-0.59200000000000008,-0.64800000000000024,-0.70720000000000027,-0.76960000000000039,-0.83519999999999972,-0.9039999999999998,-0.97599999999999976,-1.0511999999999999,-1.1295999999999999,-1.2112000000000001,-1.296,-1.3840000000000001,-1.4752000000000003,-1.5696000000000003,-1.6672000000000005,-1.7680000000000007,-1.8720000000000008,-1.9791999999999996,-2.0895999999999995,-2.2031999999999998,-2.3199999999999998,-2.4399999999999999,-2.5632000000000001,-2.6896000000000004,-2.8192000000000004,-2.9520000000000004,-3.0880000000000005,-3.2272000000000007,-3.369600000000001,-3.5151999999999992,-3.6639999999999997,-3.8159999999999998,-3.9711999999999996,-4.1295999999999999],[-4.1600000000000001,-4.0015999999999998,-3.8464,-3.6943999999999999,-3.5456000000000003,-3.4000000000000004,-3.2576000000000001,-3.1183999999999994,-2.9823999999999993,-2.8496000000000006,-2.7200000000000006,-2.5936000000000003,-2.4703999999999997,-2.3503999999999996,-2.2336,-2.1199999999999997,-2.0095999999999998,-1.9023999999999994,-1.7984,-1.6976,-1.5999999999999999,-1.5056000000000003,-1.4144000000000001,-1.3264,-1.2416,-1.1599999999999999,-1.0815999999999999,-1.0063999999999997,-0.93439999999999979,-0.86560000000000004,-0.80000000000000004,-0.73759999999999992,-0.67839999999999989,-0.62239999999999984,-0.56959999999999977,-0.5199999999999998,-0.47359999999999997,-0.43039999999999995,-0.39039999999999991,-0.35359999999999991,-0.31999999999999984,-0.28959999999999986,-0.26239999999999997,-0.23839999999999995,-0.2175999999999999,-0.1999999999999999,-0.1855999999999999,-0.17439999999999989,-0.16639999999999994,-0.16159999999999991,-0.15999999999999992,-0.16159999999999991,-0.16639999999999994,-0.17439999999999994,-0.18559999999999996,-0.19999999999999998,-0.21760000000000002,-0.23840000000000006,-0.2623999999999998,-0.28959999999999986,-0.31999999999999984,-0.35359999999999991,-0.39039999999999991,-0.43039999999999995,-0.47359999999999997,-0.52000000000000002,-0.56960000000000011,-0.62240000000000006,-0.67840000000000023,-0.73760000000000026,-0.80000000000000038,-0.8655999999999997,-0.93439999999999979,-1.0063999999999997,-1.0815999999999999,-1.1599999999999999,-1.2416,-1.3264,-1.4144000000000001,-1.5056000000000003,-1.6000000000000003,-1.6976000000000004,-1.7984000000000007,-1.9024000000000008,-2.0095999999999998,-2.1199999999999997,-2.2336,-2.3503999999999996,-2.4703999999999997,-2.5936000000000003,-2.7200000000000006,-2.8496000000000006,-2.9824000000000002,-3.1184000000000003,-3.2576000000000009,-3.4000000000000012,-3.5455999999999994,-3.6943999999999999,-3.8464,-4.0015999999999998,-4.1600000000000001],[-4.1936,-4.0351999999999997,-3.8799999999999999,-3.7279999999999998,-3.5792000000000002,-3.4336000000000002,-3.2911999999999999,-3.1519999999999997,-3.0159999999999996,-2.8832000000000004,-2.7536000000000005,-2.6272000000000002,-2.504,-2.3839999999999999,-2.2671999999999999,-2.1535999999999995,-2.0431999999999997,-1.9359999999999995,-1.8320000000000001,-1.7312000000000001,-1.6335999999999999,-1.5392000000000003,-1.4480000000000002,-1.3600000000000001,-1.2752000000000001,-1.1936,-1.1152,-1.0399999999999998,-0.96799999999999986,-0.89920000000000011,-0.83360000000000012,-0.7712,-0.71199999999999997,-0.65599999999999992,-0.60319999999999985,-0.55359999999999976,-0.50719999999999998,-0.46399999999999997,-0.42399999999999993,-0.38719999999999993,-0.35359999999999991,-0.32319999999999988,-0.29600000000000004,-0.27199999999999996,-0.25119999999999998,-0.23359999999999995,-0.21919999999999995,-0.20799999999999993,-0.19999999999999998,-0.19519999999999996,-0.19359999999999997,-0.19519999999999996,-0.19999999999999998,-0.20799999999999999,-0.21920000000000001,-0.23360000000000003,-0.25120000000000009,-0.27200000000000013,-0.29599999999999987,-0.32319999999999988,-0.35359999999999991,-0.38719999999999993,-0.42399999999999993,-0.46399999999999997,-0.50719999999999998,-0.55360000000000009,-0.60320000000000018,-0.65600000000000014,-0.7120000000000003,-0.77120000000000033,-0.83360000000000045,-0.89919999999999978,-0.96799999999999986,-1.0399999999999998,-1.1152,-1.1936,-1.2752000000000001,-1.3600000000000001,-1.4480000000000002,-1.5392000000000003,-1.6336000000000004,-1.7312000000000005,-1.8320000000000007,-1.9360000000000008,-2.0431999999999997,-2.1535999999999995,-2.2671999999999999,-2.3839999999999999,-2.504,-2.6272000000000002,-2.7536000000000005,-2.8832000000000004,-3.0160000000000005,-3.1520000000000006,-3.2912000000000008,-3.4336000000000011,-3.5791999999999993,-3.7279999999999998,-3.8799999999999999,-4.0351999999999997,-4.1936],[-4.2304000000000004,-4.0720000000000001,-3.9167999999999998,-3.7647999999999997,-3.6160000000000001,-3.4704000000000002,-3.3279999999999998,-3.1887999999999996,-3.0527999999999995,-2.9200000000000004,-2.7904000000000004,-2.6640000000000001,-2.5407999999999999,-2.4207999999999998,-2.3039999999999998,-2.1903999999999999,-2.0799999999999996,-1.9727999999999994,-1.8688,-1.768,-1.6703999999999999,-1.5760000000000003,-1.4848000000000001,-1.3968,-1.3120000000000001,-1.2303999999999999,-1.1519999999999999,-1.0767999999999998,-1.0047999999999999,-0.93600000000000017,-0.87040000000000006,-0.80800000000000005,-0.74879999999999991,-0.69279999999999986,-0.6399999999999999,-0.59039999999999981,-0.54400000000000004,-0.50080000000000002,-0.46079999999999999,-0.42399999999999993,-0.39039999999999991,-0.35999999999999988,-0.33280000000000004,-0.30880000000000002,-0.28799999999999998,-0.27039999999999997,-0.25599999999999995,-0.24479999999999996,-0.23680000000000001,-0.23199999999999998,-0.23039999999999999,-0.23199999999999998,-0.23680000000000001,-0.24480000000000002,-0.25600000000000006,-0.27040000000000008,-0.28800000000000009,-0.30880000000000013,-0.33279999999999987,-0.35999999999999988,-0.39039999999999991,-0.42399999999999993,-0.46079999999999999,-0.50080000000000002,-0.54400000000000004,-0.59040000000000004,-0.64000000000000012,-0.69280000000000019,-0.74880000000000035,-0.80800000000000027,-0.87040000000000051,-0.93599999999999972,-1.0047999999999999,-1.0767999999999998,-1.1519999999999999,-1.2303999999999999,-1.3120000000000001,-1.3968,-1.4848000000000001,-1.5760000000000003,-1.6704000000000003,-1.7680000000000005,-1.8688000000000007,-1.9728000000000008,-2.0799999999999996,-2.1903999999999999,-2.3039999999999998,-2.4207999999999998,-2.5407999999999999,-2.6640000000000001,-2.7904000000000004,-2.9200000000000004,-3.0528000000000004,-3.1888000000000005,-3.3280000000000007,-3.470400000000001,-3.6159999999999992,-3.7647999999999997,-3.9167999999999998,-4.0720000000000001,-4.2304000000000004],[-4.2704000000000004,-4.1120000000000001,-3.9567999999999999,-3.8047999999999997,-3.6560000000000001,-3.5104000000000002,-3.3679999999999999,-3.2287999999999997,-3.0927999999999995,-2.9600000000000004,-2.8304000000000005,-2.7040000000000002,-2.5808,-2.4607999999999999,-2.3439999999999999,-2.2303999999999999,-2.1199999999999997,-2.0127999999999995,-1.9088000000000001,-1.8080000000000001,-1.7103999999999999,-1.6160000000000003,-1.5248000000000002,-1.4368000000000001,-1.3520000000000001,-1.2704,-1.1919999999999999,-1.1167999999999998,-1.0448,-0.9760000000000002,-0.9104000000000001,-0.84800000000000009,-0.78879999999999995,-0.7327999999999999,-0.67999999999999994,-0.63039999999999985,-0.58400000000000007,-0.54080000000000006,-0.50080000000000002,-0.46399999999999997,-0.43039999999999995,-0.39999999999999991,-0.37280000000000008,-0.34880000000000005,-0.32800000000000001,-0.31040000000000001,-0.29599999999999999,-0.2848,-0.27680000000000005,-0.27200000000000002,-0.27040000000000003,-0.27200000000000002,-0.27680000000000005,-0.28480000000000005,-0.2960000000000001,-0.31040000000000012,-0.32800000000000012,-0.34880000000000017,-0.37279999999999991,-0.39999999999999991,-0.43039999999999995,-0.46399999999999997,-0.50080000000000002,-0.54080000000000006,-0.58400000000000007,-0.63040000000000007,-0.68000000000000016,-0.73280000000000023,-0.78880000000000039,-0.84800000000000031,-0.91040000000000054,-0.97599999999999976,-1.0448,-1.1167999999999998,-1.1919999999999999,-1.2704,-1.3520000000000001,-1.4368000000000001,-1.5248000000000002,-1.6160000000000003,-1.7104000000000004,-1.8080000000000005,-1.9088000000000007,-2.0128000000000008,-2.1199999999999997,-2.2303999999999999,-2.3439999999999999,-2.4607999999999999,-2.5808,-2.7040000000000002,-2.8304000000000005,-2.9600000000000004,-3.0928000000000004,-3.2288000000000006,-3.3680000000000008,-3.5104000000000011,-3.6559999999999993,-3.8047999999999997,-3.9567999999999999,-4.1120000000000001,-4.2704000000000004],[-4.3136000000000001,-4.1551999999999998,-4,-3.8479999999999999,-3.6992000000000003,-3.5536000000000003,-3.4112,-3.2719999999999998,-3.1359999999999997,-3.0032000000000005,-2.8736000000000006,-2.7472000000000003,-2.6240000000000001,-2.504,-2.3872,-2.2735999999999996,-2.1631999999999998,-2.0559999999999996,-1.9520000000000002,-1.8512000000000002,-1.7536,-1.6592000000000005,-1.5680000000000003,-1.4800000000000002,-1.3952000000000002,-1.3136000000000001,-1.2352000000000001,-1.1599999999999999,-1.0879999999999999,-1.0192000000000001,-0.95360000000000023,-0.89119999999999999,-0.83200000000000007,-0.77600000000000002,-0.72319999999999984,-0.67359999999999987,-0.62720000000000009,-0.58400000000000007,-0.54400000000000004,-0.50719999999999998,-0.47359999999999997,-0.44319999999999993,-0.41600000000000009,-0.39200000000000007,-0.37120000000000003,-0.35360000000000003,-0.3392,-0.32800000000000001,-0.32000000000000006,-0.31520000000000004,-0.31360000000000005,-0.31520000000000004,-0.32000000000000006,-0.32800000000000007,-0.33920000000000011,-0.35360000000000014,-0.37120000000000014,-0.39200000000000018,-0.41599999999999993,-0.44319999999999993,-0.47359999999999997,-0.50719999999999998,-0.54400000000000004,-0.58400000000000007,-0.62720000000000009,-0.6736000000000002,-0.72320000000000029,-0.77600000000000025,-0.83200000000000029,-0.89120000000000044,-0.95360000000000045,-1.0191999999999999,-1.0879999999999999,-1.1599999999999999,-1.2352000000000001,-1.3136000000000001,-1.3952000000000002,-1.4800000000000002,-1.5680000000000003,-1.6592000000000005,-1.7536000000000005,-1.8512000000000006,-1.9520000000000008,-2.0560000000000009,-2.1631999999999998,-2.2735999999999996,-2.3872,-2.504,-2.6240000000000001,-2.7472000000000003,-2.8736000000000006,-3.0032000000000005,-3.1360000000000006,-3.2720000000000007,-3.4112000000000009,-3.5536000000000012,-3.6991999999999994,-3.8479999999999999,-4,-4.1551999999999998,-4.3136000000000001],[-4.3600000000000003,-4.2016,-4.0464000000000002,-3.8944000000000001,-3.7456000000000005,-3.6000000000000005,-3.4576000000000002,-3.3183999999999996,-3.1823999999999995,-3.0496000000000008,-2.9200000000000008,-2.7936000000000005,-2.6703999999999999,-2.5503999999999998,-2.4336000000000002,-2.3199999999999998,-2.2096,-2.1023999999999994,-1.9984000000000002,-1.8976000000000002,-1.8,-1.7056000000000004,-1.6144000000000003,-1.5264000000000002,-1.4416000000000002,-1.3600000000000001,-1.2816000000000001,-1.2063999999999999,-1.1343999999999999,-1.0656000000000003,-1.0000000000000002,-0.9376000000000001,-0.87840000000000007,-0.82240000000000002,-0.76959999999999995,-0.71999999999999997,-0.6736000000000002,-0.63040000000000007,-0.59040000000000004,-0.55360000000000009,-0.52000000000000002,-0.48960000000000004,-0.46240000000000014,-0.43840000000000012,-0.41760000000000008,-0.40000000000000008,-0.38560000000000005,-0.37440000000000007,-0.36640000000000011,-0.36160000000000009,-0.3600000000000001,-0.36160000000000009,-0.36640000000000011,-0.37440000000000012,-0.38560000000000016,-0.40000000000000019,-0.41760000000000019,-0.43840000000000023,-0.46239999999999998,-0.48960000000000004,-0.52000000000000002,-0.55360000000000009,-0.59040000000000004,-0.63040000000000007,-0.6736000000000002,-0.7200000000000002,-0.76960000000000028,-0.82240000000000024,-0.8784000000000004,-0.93760000000000043,-1.0000000000000004,-1.0655999999999999,-1.1343999999999999,-1.2063999999999999,-1.2816000000000001,-1.3600000000000001,-1.4416000000000002,-1.5264000000000002,-1.6144000000000003,-1.7056000000000004,-1.8000000000000005,-1.8976000000000006,-1.9984000000000008,-2.1024000000000012,-2.2096,-2.3199999999999998,-2.4336000000000002,-2.5503999999999998,-2.6703999999999999,-2.7936000000000005,-2.9200000000000008,-3.0496000000000008,-3.1824000000000003,-3.3184000000000005,-3.4576000000000011,-3.6000000000000014,-3.7455999999999996,-3.8944000000000001,-4.0464000000000002,-4.2016,-4.3600000000000003],[-4.4096000000000002,-4.2511999999999999,-4.0960000000000001,-3.944,-3.7952000000000004,-3.6496000000000004,-3.5072000000000001,-3.3679999999999999,-3.2319999999999998,-3.0992000000000006,-2.9696000000000007,-2.8432000000000004,-2.7200000000000002,-2.6000000000000001,-2.4832000000000001,-2.3696000000000002,-2.2591999999999999,-2.1519999999999997,-2.048,-1.9472000000000003,-1.8496000000000001,-1.7552000000000005,-1.6640000000000004,-1.5760000000000003,-1.4912000000000003,-1.4096000000000002,-1.3312000000000002,-1.256,-1.1840000000000002,-1.1152000000000002,-1.0496000000000003,-0.98720000000000019,-0.92800000000000016,-0.87200000000000011,-0.81920000000000004,-0.76960000000000006,-0.72320000000000029,-0.68000000000000016,-0.64000000000000012,-0.60320000000000018,-0.56960000000000011,-0.53920000000000012,-0.51200000000000023,-0.48800000000000021,-0.46720000000000017,-0.44960000000000017,-0.43520000000000014,-0.42400000000000015,-0.4160000000000002,-0.41120000000000018,-0.40960000000000019,-0.41120000000000018,-0.4160000000000002,-0.42400000000000021,-0.43520000000000025,-0.44960000000000028,-0.46720000000000028,-0.48800000000000032,-0.51200000000000012,-0.53920000000000012,-0.56960000000000011,-0.60320000000000018,-0.64000000000000012,-0.68000000000000016,-0.72320000000000029,-0.76960000000000028,-0.81920000000000037,-0.87200000000000033,-0.92800000000000049,-0.98720000000000052,-1.0496000000000008,-1.1152,-1.1840000000000002,-1.256,-1.3312000000000002,-1.4096000000000002,-1.4912000000000003,-1.5760000000000003,-1.6640000000000004,-1.7552000000000005,-1.8496000000000006,-1.9472000000000007,-2.0480000000000009,-2.152000000000001,-2.2591999999999999,-2.3696000000000002,-2.4832000000000001,-2.6000000000000001,-2.7200000000000002,-2.8432000000000004,-2.9696000000000007,-3.0992000000000006,-3.2320000000000007,-3.3680000000000008,-3.507200000000001,-3.6496000000000013,-3.7951999999999995,-3.944,-4.0960000000000001,-4.2511999999999999,-4.4096000000000002],[-4.4624000000000006,-4.3040000000000003,-4.1488000000000005,-3.9967999999999999,-3.8480000000000003,-3.7024000000000004,-3.5600000000000001,-3.4207999999999998,-3.2847999999999997,-3.1520000000000006,-3.0224000000000006,-2.8960000000000004,-2.7728000000000002,-2.6528,-2.536,-2.4224000000000001,-2.3119999999999998,-2.2047999999999996,-2.1008000000000004,-2.0000000000000004,-1.9024000000000001,-1.8080000000000005,-1.7168000000000003,-1.6288000000000002,-1.5440000000000003,-1.4624000000000001,-1.3840000000000001,-1.3088,-1.2368000000000001,-1.1680000000000004,-1.1024000000000003,-1.0400000000000003,-0.98080000000000012,-0.92480000000000007,-0.87200000000000011,-0.82240000000000002,-0.77600000000000025,-0.73280000000000023,-0.69280000000000019,-0.65600000000000014,-0.62240000000000006,-0.59200000000000008,-0.56480000000000019,-0.54080000000000017,-0.52000000000000024,-0.50240000000000018,-0.48800000000000016,-0.47680000000000017,-0.46880000000000022,-0.46400000000000019,-0.4624000000000002,-0.46400000000000019,-0.46880000000000022,-0.47680000000000022,-0.48800000000000027,-0.50240000000000029,-0.52000000000000035,-0.54080000000000039,-0.56480000000000008,-0.59200000000000008,-0.62240000000000006,-0.65600000000000014,-0.69280000000000019,-0.73280000000000023,-0.77600000000000025,-0.82240000000000024,-0.87200000000000033,-0.9248000000000004,-0.98080000000000056,-1.0400000000000005,-1.1024000000000007,-1.1679999999999999,-1.2368000000000001,-1.3088,-1.3840000000000001,-1.4624000000000001,-1.5440000000000003,-1.6288000000000002,-1.7168000000000003,-1.8080000000000005,-1.9024000000000005,-2.0000000000000009,-2.1008000000000009,-2.204800000000001,-2.3119999999999998,-2.4224000000000001,-2.536,-2.6528,-2.7728000000000002,-2.8960000000000004,-3.0224000000000006,-3.1520000000000006,-3.2848000000000006,-3.4208000000000007,-3.5600000000000009,-3.7024000000000012,-3.8479999999999994,-3.9967999999999999,-4.1488000000000005,-4.3040000000000003,-4.4624000000000006],[-4.5184000000000006,-4.3600000000000003,-4.2048000000000005,-4.0528000000000004,-3.9040000000000004,-3.7584000000000004,-3.6160000000000001,-3.4767999999999999,-3.3407999999999998,-3.2080000000000006,-3.0784000000000007,-2.9520000000000004,-2.8288000000000002,-2.7088000000000001,-2.5920000000000001,-2.4784000000000002,-2.3679999999999999,-2.2607999999999997,-2.1568000000000005,-2.0560000000000005,-1.9584000000000001,-1.8640000000000008,-1.7728000000000006,-1.6848000000000005,-1.6000000000000005,-1.5184000000000002,-1.4400000000000004,-1.3648000000000002,-1.2928000000000002,-1.2240000000000004,-1.1584000000000003,-1.0960000000000003,-1.0368000000000004,-0.98080000000000023,-0.92800000000000016,-0.87840000000000007,-0.83200000000000029,-0.78880000000000039,-0.74880000000000035,-0.7120000000000003,-0.67840000000000023,-0.64800000000000024,-0.62080000000000035,-0.59680000000000033,-0.57600000000000029,-0.55840000000000023,-0.54400000000000026,-0.53280000000000027,-0.52480000000000027,-0.52000000000000035,-0.51840000000000031,-0.52000000000000035,-0.52480000000000027,-0.53280000000000038,-0.54400000000000037,-0.55840000000000034,-0.5760000000000004,-0.59680000000000044,-0.62080000000000024,-0.64800000000000024,-0.67840000000000023,-0.7120000000000003,-0.74880000000000035,-0.78880000000000039,-0.83200000000000029,-0.8784000000000004,-0.92800000000000049,-0.98080000000000056,-1.0368000000000006,-1.0960000000000005,-1.1584000000000008,-1.2240000000000002,-1.2928000000000002,-1.3648000000000002,-1.4400000000000004,-1.5184000000000002,-1.6000000000000005,-1.6848000000000005,-1.7728000000000006,-1.8640000000000008,-1.9584000000000006,-2.0560000000000009,-2.1568000000000009,-2.260800000000001,-2.3679999999999999,-2.4784000000000002,-2.5920000000000001,-2.7088000000000001,-2.8288000000000002,-2.9520000000000004,-3.0784000000000007,-3.2080000000000006,-3.3408000000000007,-3.4768000000000008,-3.616000000000001,-3.7584000000000013,-3.9039999999999995,-4.0528000000000004,-4.2048000000000005,-4.3600000000000003,-4.5184000000000006],[-4.5776000000000003,-4.4192,-4.2640000000000002,-4.1120000000000001,-3.9632000000000005,-3.8176000000000005,-3.6752000000000002,-3.536,-3.3999999999999999,-3.2672000000000008,-3.1376000000000008,-3.0112000000000005,-2.8880000000000003,-2.7680000000000002,-2.6512000000000002,-2.5376000000000003,-2.4272,-2.3199999999999998,-2.2160000000000002,-2.1152000000000006,-2.0176000000000003,-1.9232000000000007,-1.8320000000000005,-1.7440000000000004,-1.6592000000000005,-1.5776000000000003,-1.4992000000000003,-1.4240000000000002,-1.3520000000000003,-1.2832000000000003,-1.2176000000000005,-1.1552000000000002,-1.0960000000000003,-1.0400000000000003,-0.98720000000000019,-0.93760000000000021,-0.89120000000000044,-0.84800000000000031,-0.80800000000000027,-0.77120000000000033,-0.73760000000000026,-0.70720000000000027,-0.68000000000000038,-0.65600000000000036,-0.63520000000000032,-0.61760000000000037,-0.60320000000000029,-0.5920000000000003,-0.5840000000000003,-0.57920000000000038,-0.57760000000000034,-0.57920000000000038,-0.5840000000000003,-0.59200000000000041,-0.6032000000000004,-0.61760000000000037,-0.63520000000000043,-0.65600000000000047,-0.68000000000000027,-0.70720000000000027,-0.73760000000000026,-0.77120000000000033,-0.80800000000000027,-0.84800000000000031,-0.89120000000000044,-0.93760000000000043,-0.98720000000000052,-1.0400000000000005,-1.0960000000000005,-1.1552000000000007,-1.2176000000000009,-1.2832000000000001,-1.3520000000000003,-1.4240000000000002,-1.4992000000000003,-1.5776000000000003,-1.6592000000000005,-1.7440000000000004,-1.8320000000000005,-1.9232000000000007,-2.0176000000000007,-2.1152000000000006,-2.2160000000000011,-2.3200000000000012,-2.4272,-2.5376000000000003,-2.6512000000000002,-2.7680000000000002,-2.8880000000000003,-3.0112000000000005,-3.1376000000000008,-3.2672000000000008,-3.4000000000000008,-3.5360000000000009,-3.6752000000000011,-3.8176000000000014,-3.9631999999999996,-4.1120000000000001,-4.2640000000000002,-4.4192,-4.5776000000000003],[-4.6400000000000006,-4.4816000000000003,-4.3264000000000005,-4.1744000000000003,-4.0256000000000007,-3.8800000000000008,-3.7376000000000005,-3.5984000000000003,-3.4624000000000001,-3.329600000000001,-3.2000000000000011,-3.0736000000000008,-2.9504000000000006,-2.8304000000000005,-2.7136000000000005,-2.6000000000000001,-2.4896000000000003,-2.3824000000000001,-2.2784000000000004,-2.1776000000000004,-2.0800000000000005,-1.9856000000000007,-1.8944000000000005,-1.8064000000000004,-1.7216000000000005,-1.6400000000000006,-1.5616000000000003,-1.4864000000000002,-1.4144000000000003,-1.3456000000000006,-1.2800000000000007,-1.2176000000000005,-1.1584000000000003,-1.1024000000000003,-1.0496000000000003,-1.0000000000000002,-0.95360000000000045,-0.91040000000000054,-0.87040000000000051,-0.83360000000000045,-0.80000000000000038,-0.76960000000000039,-0.7424000000000005,-0.71840000000000048,-0.69760000000000044,-0.68000000000000038,-0.66560000000000041,-0.65440000000000043,-0.64640000000000042,-0.6416000000000005,-0.64000000000000046,-0.6416000000000005,-0.64640000000000042,-0.65440000000000054,-0.66560000000000052,-0.68000000000000049,-0.69760000000000055,-0.71840000000000059,-0.74240000000000039,-0.76960000000000039,-0.80000000000000038,-0.83360000000000045,-0.87040000000000051,-0.91040000000000054,-0.95360000000000045,-1.0000000000000004,-1.0496000000000008,-1.1024000000000007,-1.1584000000000008,-1.2176000000000009,-1.2800000000000009,-1.3456000000000001,-1.4144000000000003,-1.4864000000000002,-1.5616000000000003,-1.6400000000000006,-1.7216000000000005,-1.8064000000000004,-1.8944000000000005,-1.9856000000000007,-2.080000000000001,-2.1776000000000009,-2.2784000000000013,-2.3824000000000014,-2.4896000000000003,-2.6000000000000001,-2.7136000000000005,-2.8304000000000005,-2.9504000000000006,-3.0736000000000008,-3.2000000000000011,-3.329600000000001,-3.462400000000001,-3.5984000000000012,-3.7376000000000014,-3.8800000000000017,-4.0255999999999998,-4.1744000000000003,-4.3264000000000005,-4.4816000000000003,-4.6400000000000006],[-4.7055999999999996,-4.5471999999999992,-4.3919999999999995,-4.2399999999999993,-4.0911999999999997,-3.9455999999999998,-3.8031999999999995,-3.6639999999999997,-3.5279999999999996,-3.3952,-3.2656000000000001,-3.1391999999999998,-3.016,-2.8959999999999999,-2.7791999999999994,-2.6655999999999995,-2.5551999999999992,-2.4479999999999995,-2.3439999999999999,-2.2431999999999999,-2.1456,-2.0512000000000001,-1.96,-1.8719999999999999,-1.7871999999999999,-1.7055999999999998,-1.6271999999999998,-1.5519999999999996,-1.4799999999999995,-1.4112,-1.3455999999999999,-1.2831999999999999,-1.2239999999999998,-1.1679999999999997,-1.1151999999999997,-1.0655999999999997,-1.0191999999999999,-0.97599999999999976,-0.93599999999999972,-0.89919999999999978,-0.8655999999999997,-0.83519999999999972,-0.80799999999999983,-0.78399999999999981,-0.76319999999999977,-0.74559999999999982,-0.73119999999999974,-0.71999999999999975,-0.71199999999999974,-0.70719999999999983,-0.70559999999999978,-0.70719999999999983,-0.71199999999999974,-0.71999999999999986,-0.73119999999999985,-0.74559999999999982,-0.76319999999999988,-0.78399999999999992,-0.80799999999999972,-0.83519999999999972,-0.8655999999999997,-0.89919999999999978,-0.93599999999999972,-0.97599999999999976,-1.0191999999999999,-1.0655999999999999,-1.1152,-1.1679999999999999,-1.2240000000000002,-1.2832000000000001,-1.3456000000000001,-1.4111999999999996,-1.4799999999999995,-1.5519999999999996,-1.6271999999999998,-1.7055999999999998,-1.7871999999999999,-1.8719999999999999,-1.96,-2.0512000000000001,-2.1456,-2.2432000000000003,-2.3440000000000003,-2.4480000000000004,-2.5551999999999992,-2.6655999999999995,-2.7791999999999994,-2.8959999999999999,-3.016,-3.1391999999999998,-3.2656000000000001,-3.3952,-3.5280000000000005,-3.6640000000000006,-3.8032000000000004,-3.9456000000000007,-4.0911999999999988,-4.2399999999999993,-4.3919999999999995,-4.5471999999999992,-4.7055999999999996],[-4.7744,-4.6159999999999997,-4.4607999999999999,-4.3087999999999997,-4.1600000000000001,-4.0144000000000002,-3.8719999999999999,-3.7327999999999997,-3.5967999999999996,-3.4640000000000004,-3.3344000000000005,-3.2080000000000002,-3.0848,-2.9647999999999999,-2.8479999999999999,-2.7343999999999995,-2.6239999999999997,-2.5167999999999995,-2.4127999999999998,-2.3119999999999998,-2.2143999999999999,-2.1200000000000001,-2.0287999999999999,-1.9407999999999999,-1.8559999999999999,-1.7744,-1.6959999999999997,-1.6207999999999996,-1.5487999999999997,-1.48,-1.4144000000000001,-1.3519999999999999,-1.2927999999999997,-1.2367999999999997,-1.1839999999999997,-1.1343999999999996,-1.0879999999999999,-1.0448,-1.0047999999999999,-0.96799999999999986,-0.93439999999999979,-0.9039999999999998,-0.87679999999999991,-0.85279999999999989,-0.83199999999999985,-0.81439999999999979,-0.79999999999999982,-0.78879999999999983,-0.78079999999999983,-0.77599999999999991,-0.77439999999999987,-0.77599999999999991,-0.78079999999999983,-0.78879999999999995,-0.79999999999999993,-0.8143999999999999,-0.83199999999999996,-0.8528,-0.8767999999999998,-0.9039999999999998,-0.93439999999999979,-0.96799999999999986,-1.0047999999999999,-1.0448,-1.0879999999999999,-1.1343999999999999,-1.1840000000000002,-1.2368000000000001,-1.2928000000000002,-1.3520000000000003,-1.4144000000000003,-1.4799999999999995,-1.5487999999999997,-1.6207999999999996,-1.6959999999999997,-1.7744,-1.8559999999999999,-1.9407999999999999,-2.0287999999999999,-2.1200000000000001,-2.2144000000000004,-2.3120000000000003,-2.4128000000000007,-2.5168000000000008,-2.6239999999999997,-2.7343999999999995,-2.8479999999999999,-2.9647999999999999,-3.0848,-3.2080000000000002,-3.3344000000000005,-3.4640000000000004,-3.5968000000000004,-3.7328000000000006,-3.8720000000000008,-4.0144000000000011,-4.1599999999999993,-4.3087999999999997,-4.4607999999999999,-4.6159999999999997,-4.7744],[-4.8464,-4.6879999999999997,-4.5327999999999999,-4.3807999999999998,-4.2320000000000002,-4.0864000000000003,-3.944,-3.8047999999999993,-3.6687999999999992,-3.5360000000000005,-3.4064000000000005,-3.2800000000000002,-3.1567999999999996,-3.0367999999999995,-2.9199999999999999,-2.8063999999999996,-2.6959999999999997,-2.5887999999999991,-2.4847999999999999,-2.3839999999999999,-2.2863999999999995,-2.1920000000000002,-2.1008,-2.0127999999999999,-1.9279999999999999,-1.8463999999999998,-1.7679999999999998,-1.6927999999999996,-1.6207999999999996,-1.552,-1.4863999999999999,-1.4239999999999999,-1.3647999999999998,-1.3087999999999997,-1.2559999999999998,-1.2063999999999997,-1.1599999999999999,-1.1167999999999998,-1.0767999999999998,-1.0399999999999998,-1.0063999999999997,-0.97599999999999976,-0.94879999999999987,-0.92479999999999984,-0.9039999999999998,-0.88639999999999985,-0.87199999999999978,-0.86079999999999979,-0.85279999999999978,-0.84799999999999986,-0.84639999999999982,-0.84799999999999986,-0.85279999999999978,-0.8607999999999999,-0.87199999999999989,-0.88639999999999985,-0.90399999999999991,-0.92479999999999996,-0.94879999999999975,-0.97599999999999976,-1.0063999999999997,-1.0399999999999998,-1.0767999999999998,-1.1167999999999998,-1.1599999999999999,-1.2063999999999999,-1.256,-1.3088,-1.3648000000000002,-1.4240000000000002,-1.4864000000000002,-1.5519999999999996,-1.6207999999999996,-1.6927999999999996,-1.7679999999999998,-1.8463999999999998,-1.9279999999999999,-2.0127999999999999,-2.1008,-2.1920000000000002,-2.2864000000000004,-2.3840000000000003,-2.4848000000000008,-2.5888000000000009,-2.6959999999999997,-2.8063999999999996,-2.9199999999999999,-3.0367999999999995,-3.1567999999999996,-3.2800000000000002,-3.4064000000000005,-3.5360000000000005,-3.6688000000000001,-3.8048000000000002,-3.9440000000000008,-4.0864000000000011,-4.2319999999999993,-4.3807999999999998,-4.5327999999999999,-4.6879999999999997,-4.8464],[-4.9215999999999998,-4.7631999999999994,-4.6079999999999997,-4.4559999999999995,-4.3071999999999999,-4.1616,-4.0191999999999997,-3.8799999999999999,-3.7439999999999998,-3.6112000000000002,-3.4816000000000003,-3.3552,-3.2320000000000002,-3.1120000000000001,-2.9951999999999996,-2.8815999999999997,-2.7711999999999994,-2.6639999999999997,-2.5600000000000001,-2.4592000000000001,-2.3616000000000001,-2.2672000000000003,-2.1760000000000002,-2.0880000000000001,-2.0032000000000001,-1.9216,-1.8431999999999999,-1.7679999999999998,-1.6959999999999997,-1.6272000000000002,-1.5616000000000001,-1.4992000000000001,-1.4399999999999999,-1.3839999999999999,-1.3311999999999999,-1.2815999999999999,-1.2352000000000001,-1.1919999999999999,-1.1519999999999999,-1.1152,-1.0815999999999999,-1.0511999999999999,-1.024,-1,-0.97919999999999996,-0.96160000000000001,-0.94719999999999993,-0.93599999999999994,-0.92799999999999994,-0.92320000000000002,-0.92159999999999997,-0.92320000000000002,-0.92799999999999994,-0.93600000000000005,-0.94720000000000004,-0.96160000000000001,-0.97920000000000007,-1,-1.0239999999999998,-1.0511999999999999,-1.0815999999999999,-1.1152,-1.1519999999999999,-1.1919999999999999,-1.2352000000000001,-1.2816000000000001,-1.3312000000000002,-1.3840000000000001,-1.4400000000000004,-1.4992000000000003,-1.5616000000000003,-1.6271999999999998,-1.6959999999999997,-1.7679999999999998,-1.8431999999999999,-1.9216,-2.0032000000000001,-2.0880000000000001,-2.1760000000000002,-2.2672000000000003,-2.3616000000000001,-2.4592000000000005,-2.5600000000000005,-2.6640000000000006,-2.7711999999999994,-2.8815999999999997,-2.9951999999999996,-3.1120000000000001,-3.2320000000000002,-3.3552,-3.4816000000000003,-3.6112000000000002,-3.7440000000000007,-3.8800000000000008,-4.0192000000000005,-4.1616000000000009,-4.307199999999999,-4.4559999999999995,-4.6079999999999997,-4.7631999999999994,-4.9215999999999998],[-5,-4.8415999999999997,-4.6863999999999999,-4.5343999999999998,-4.3856000000000002,-4.2400000000000002,-4.0975999999999999,-3.9583999999999997,-3.8223999999999996,-3.6896000000000004,-3.5600000000000005,-3.4336000000000002,-3.3104,-3.1903999999999999,-3.0735999999999999,-2.96,-2.8495999999999997,-2.7423999999999995,-2.6383999999999999,-2.5376000000000003,-2.4399999999999999,-2.3456000000000001,-2.2544000000000004,-2.1664000000000003,-2.0815999999999999,-2,-1.9216,-1.8463999999999998,-1.7744,-1.7056,-1.6400000000000001,-1.5775999999999999,-1.5184,-1.4623999999999999,-1.4095999999999997,-1.3599999999999999,-1.3136000000000001,-1.2704,-1.2303999999999999,-1.1936,-1.1599999999999999,-1.1295999999999999,-1.1024,-1.0784,-1.0576000000000001,-1.04,-1.0256000000000001,-1.0144,-1.0064,-1.0016,-1,-1.0016,-1.0064,-1.0144,-1.0256000000000001,-1.04,-1.0576000000000001,-1.0784000000000002,-1.1023999999999998,-1.1295999999999999,-1.1599999999999999,-1.1936,-1.2303999999999999,-1.2704,-1.3136000000000001,-1.3600000000000001,-1.4096000000000002,-1.4624000000000001,-1.5184000000000002,-1.5776000000000003,-1.6400000000000006,-1.7055999999999998,-1.7744,-1.8463999999999998,-1.9216,-2,-2.0815999999999999,-2.1664000000000003,-2.2544000000000004,-2.3456000000000001,-2.4400000000000004,-2.5376000000000003,-2.6384000000000007,-2.7424000000000008,-2.8495999999999997,-2.96,-3.0735999999999999,-3.1903999999999999,-3.3104,-3.4336000000000002,-3.5600000000000005,-3.6896000000000004,-3.8224000000000005,-3.9584000000000006,-4.0976000000000008,-4.2400000000000011,-4.3855999999999993,-4.5343999999999998,-4.6863999999999999,-4.8415999999999997,-5],[-5.0815999999999999,-4.9231999999999996,-4.7679999999999998,-4.6159999999999997,-4.4672000000000001,-4.3216000000000001,-4.1791999999999998,-4.04,-3.9039999999999999,-3.7712000000000003,-3.6416000000000004,-3.5152000000000001,-3.3920000000000003,-3.2720000000000002,-3.1551999999999998,-3.0415999999999999,-2.9311999999999996,-2.8239999999999998,-2.7200000000000002,-2.6192000000000002,-2.5216000000000003,-2.4272000000000005,-2.3360000000000003,-2.2480000000000002,-2.1632000000000002,-2.0815999999999999,-2.0032000000000001,-1.9279999999999999,-1.8559999999999999,-1.7872000000000003,-1.7216000000000002,-1.6592000000000002,-1.6000000000000001,-1.544,-1.4912000000000001,-1.4416,-1.3952000000000002,-1.3520000000000001,-1.3120000000000001,-1.2752000000000001,-1.2416,-1.2112000000000001,-1.1840000000000002,-1.1600000000000001,-1.1392000000000002,-1.1216000000000002,-1.1072000000000002,-1.0960000000000001,-1.0880000000000001,-1.0832000000000002,-1.0816000000000001,-1.0832000000000002,-1.0880000000000001,-1.0960000000000001,-1.1072000000000002,-1.1216000000000002,-1.1392000000000002,-1.1600000000000001,-1.1839999999999999,-1.2112000000000001,-1.2416,-1.2752000000000001,-1.3120000000000001,-1.3520000000000001,-1.3952000000000002,-1.4416000000000002,-1.4912000000000003,-1.5440000000000003,-1.6000000000000005,-1.6592000000000005,-1.7216000000000005,-1.7871999999999999,-1.8559999999999999,-1.9279999999999999,-2.0032000000000001,-2.0815999999999999,-2.1632000000000002,-2.2480000000000002,-2.3360000000000003,-2.4272000000000005,-2.5216000000000003,-2.6192000000000006,-2.7200000000000006,-2.8240000000000007,-2.9311999999999996,-3.0415999999999999,-3.1551999999999998,-3.2720000000000002,-3.3920000000000003,-3.5152000000000001,-3.6416000000000004,-3.7712000000000003,-3.9040000000000008,-4.0400000000000009,-4.1792000000000007,-4.321600000000001,-4.4671999999999992,-4.6159999999999997,-4.7679999999999998,-4.9231999999999996,-5.0815999999999999],[-5.1664000000000003,-5.008,-4.8528000000000002,-4.7008000000000001,-4.5520000000000005,-4.4064000000000005,-4.2640000000000002,-4.1247999999999996,-3.9887999999999995,-3.8560000000000008,-3.7264000000000008,-3.6000000000000005,-3.4767999999999999,-3.3567999999999998,-3.2400000000000002,-3.1263999999999998,-3.016,-2.9087999999999994,-2.8048000000000002,-2.7040000000000002,-2.6063999999999998,-2.5120000000000005,-2.4208000000000003,-2.3328000000000002,-2.2480000000000002,-2.1664000000000003,-2.0880000000000001,-2.0127999999999999,-1.9407999999999999,-1.8720000000000003,-1.8064000000000002,-1.7440000000000002,-1.6848000000000001,-1.6288,-1.5760000000000001,-1.5264,-1.4800000000000002,-1.4368000000000001,-1.3968,-1.3600000000000001,-1.3264,-1.296,-1.2688000000000001,-1.2448000000000001,-1.2240000000000002,-1.2064000000000001,-1.1920000000000002,-1.1808000000000001,-1.1728000000000001,-1.1680000000000001,-1.1664000000000001,-1.1680000000000001,-1.1728000000000001,-1.1808000000000001,-1.1920000000000002,-1.2064000000000001,-1.2240000000000002,-1.2448000000000001,-1.2687999999999999,-1.296,-1.3264,-1.3600000000000001,-1.3968,-1.4368000000000001,-1.4800000000000002,-1.5264000000000002,-1.5760000000000003,-1.6288000000000002,-1.6848000000000005,-1.7440000000000004,-1.8064000000000004,-1.8719999999999999,-1.9407999999999999,-2.0127999999999999,-2.0880000000000001,-2.1664000000000003,-2.2480000000000002,-2.3328000000000002,-2.4208000000000003,-2.5120000000000005,-2.6064000000000007,-2.7040000000000006,-2.8048000000000011,-2.9088000000000012,-3.016,-3.1263999999999998,-3.2400000000000002,-3.3567999999999998,-3.4767999999999999,-3.6000000000000005,-3.7264000000000008,-3.8560000000000008,-3.9888000000000003,-4.1248000000000005,-4.2640000000000011,-4.4064000000000014,-4.5519999999999996,-4.7008000000000001,-4.8528000000000002,-5.008,-5.1664000000000003],[-5.2544000000000004,-5.0960000000000001,-4.9408000000000003,-4.7888000000000002,-4.6400000000000006,-4.4944000000000006,-4.3520000000000003,-4.2127999999999997,-4.0767999999999995,-3.9440000000000008,-3.8144000000000009,-3.6880000000000006,-3.5648,-3.4447999999999999,-3.3280000000000003,-3.2143999999999999,-3.1040000000000001,-2.9967999999999995,-2.8928000000000003,-2.7920000000000003,-2.6943999999999999,-2.6000000000000005,-2.5088000000000004,-2.4208000000000003,-2.3360000000000003,-2.2544000000000004,-2.1760000000000002,-2.1008,-2.0287999999999999,-1.9600000000000004,-1.8944000000000003,-1.8320000000000003,-1.7728000000000002,-1.7168000000000001,-1.6640000000000001,-1.6144000000000001,-1.5680000000000003,-1.5248000000000002,-1.4848000000000001,-1.4480000000000002,-1.4144000000000001,-1.3840000000000001,-1.3568000000000002,-1.3328000000000002,-1.3120000000000003,-1.2944000000000002,-1.2800000000000002,-1.2688000000000001,-1.2608000000000001,-1.2560000000000002,-1.2544000000000002,-1.2560000000000002,-1.2608000000000001,-1.2688000000000001,-1.2800000000000002,-1.2944000000000002,-1.3120000000000003,-1.3328000000000002,-1.3568,-1.3840000000000001,-1.4144000000000001,-1.4480000000000002,-1.4848000000000001,-1.5248000000000002,-1.5680000000000003,-1.6144000000000003,-1.6640000000000004,-1.7168000000000003,-1.7728000000000006,-1.8320000000000005,-1.8944000000000005,-1.96,-2.0287999999999999,-2.1008,-2.1760000000000002,-2.2544000000000004,-2.3360000000000003,-2.4208000000000003,-2.5088000000000004,-2.6000000000000005,-2.6944000000000008,-2.7920000000000007,-2.8928000000000011,-2.9968000000000012,-3.1040000000000001,-3.2143999999999999,-3.3280000000000003,-3.4447999999999999,-3.5648,-3.6880000000000006,-3.8144000000000009,-3.9440000000000008,-4.0768000000000004,-4.2128000000000005,-4.3520000000000012,-4.4944000000000015,-4.6399999999999997,-4.7888000000000002,-4.9408000000000003,-5.0960000000000001,-5.2544000000000004],[-5.3456000000000001,-5.1871999999999998,-5.032,-4.8799999999999999,-4.7312000000000003,-4.5856000000000003,-4.4432,-4.3040000000000003,-4.1680000000000001,-4.0352000000000006,-3.9056000000000006,-3.7792000000000003,-3.6560000000000006,-3.5360000000000005,-3.4192,-3.3056000000000001,-3.1951999999999998,-3.0880000000000001,-2.9840000000000004,-2.8832000000000004,-2.7856000000000005,-2.6912000000000007,-2.6000000000000005,-2.5120000000000005,-2.4272000000000005,-2.3456000000000001,-2.2672000000000003,-2.1920000000000002,-2.1200000000000001,-2.0512000000000006,-1.9856000000000005,-1.9232000000000005,-1.8640000000000003,-1.8080000000000003,-1.7552000000000003,-1.7056000000000002,-1.6592000000000005,-1.6160000000000003,-1.5760000000000003,-1.5392000000000003,-1.5056000000000003,-1.4752000000000003,-1.4480000000000004,-1.4240000000000004,-1.4032000000000004,-1.3856000000000004,-1.3712000000000004,-1.3600000000000003,-1.3520000000000003,-1.3472000000000004,-1.3456000000000004,-1.3472000000000004,-1.3520000000000003,-1.3600000000000003,-1.3712000000000004,-1.3856000000000004,-1.4032000000000004,-1.4240000000000004,-1.4480000000000002,-1.4752000000000003,-1.5056000000000003,-1.5392000000000003,-1.5760000000000003,-1.6160000000000003,-1.6592000000000005,-1.7056000000000004,-1.7552000000000005,-1.8080000000000005,-1.8640000000000008,-1.9232000000000007,-1.9856000000000007,-2.0512000000000001,-2.1200000000000001,-2.1920000000000002,-2.2672000000000003,-2.3456000000000001,-2.4272000000000005,-2.5120000000000005,-2.6000000000000005,-2.6912000000000007,-2.7856000000000005,-2.8832000000000009,-2.9840000000000009,-3.088000000000001,-3.1951999999999998,-3.3056000000000001,-3.4192,-3.5360000000000005,-3.6560000000000006,-3.7792000000000003,-3.9056000000000006,-4.0352000000000006,-4.168000000000001,-4.3040000000000012,-4.4432000000000009,-4.5856000000000012,-4.7311999999999994,-4.8799999999999999,-5.032,-5.1871999999999998,-5.3456000000000001],[-5.4400000000000004,-5.2816000000000001,-5.1264000000000003,-4.9744000000000002,-4.8256000000000006,-4.6800000000000006,-4.5376000000000003,-4.3984000000000005,-4.2623999999999995,-4.1296000000000008,-4.0000000000000009,-3.8736000000000006,-3.7504000000000004,-3.6304000000000003,-3.5136000000000003,-3.4000000000000004,-3.2896000000000001,-3.1823999999999999,-3.0784000000000002,-2.9776000000000007,-2.8800000000000003,-2.7856000000000005,-2.6944000000000008,-2.6064000000000007,-2.5216000000000003,-2.4400000000000004,-2.3616000000000001,-2.2864000000000004,-2.2144000000000004,-2.1456000000000004,-2.0800000000000005,-2.0176000000000003,-1.9584000000000004,-1.9024000000000003,-1.8496000000000001,-1.8000000000000003,-1.7536000000000005,-1.7104000000000004,-1.6704000000000003,-1.6336000000000004,-1.6000000000000003,-1.5696000000000003,-1.5424000000000004,-1.5184000000000004,-1.4976000000000005,-1.4800000000000004,-1.4656000000000005,-1.4544000000000004,-1.4464000000000004,-1.4416000000000004,-1.4400000000000004,-1.4416000000000004,-1.4464000000000004,-1.4544000000000004,-1.4656000000000005,-1.4800000000000004,-1.4976000000000005,-1.5184000000000006,-1.5424000000000002,-1.5696000000000003,-1.6000000000000003,-1.6336000000000004,-1.6704000000000003,-1.7104000000000004,-1.7536000000000005,-1.8000000000000005,-1.8496000000000006,-1.9024000000000005,-1.9584000000000006,-2.0176000000000007,-2.080000000000001,-2.1456,-2.2144000000000004,-2.2864000000000004,-2.3616000000000001,-2.4400000000000004,-2.5216000000000003,-2.6064000000000007,-2.6944000000000008,-2.7856000000000005,-2.8800000000000008,-2.9776000000000007,-3.0784000000000011,-3.1824000000000012,-3.2896000000000001,-3.4000000000000004,-3.5136000000000003,-3.6304000000000003,-3.7504000000000004,-3.8736000000000006,-4.0000000000000009,-4.1296000000000008,-4.2624000000000013,-4.3984000000000005,-4.5376000000000012,-4.6800000000000015,-4.8255999999999997,-4.9744000000000002,-5.1264000000000003,-5.2816000000000001,-5.4400000000000004],[-5.5376000000000003,-5.3792,-5.2240000000000002,-5.0720000000000001,-4.9232000000000005,-4.7776000000000005,-4.6352000000000002,-4.4960000000000004,-4.3600000000000003,-4.2272000000000007,-4.0976000000000008,-3.9712000000000005,-3.8480000000000008,-3.7280000000000006,-3.6112000000000002,-3.4976000000000003,-3.3872,-3.2800000000000002,-3.1760000000000006,-3.0752000000000006,-2.9776000000000007,-2.8832000000000009,-2.7920000000000007,-2.7040000000000006,-2.6192000000000006,-2.5376000000000003,-2.4592000000000005,-2.3840000000000003,-2.3120000000000003,-2.2432000000000007,-2.1776000000000009,-2.1152000000000006,-2.0560000000000005,-2.0000000000000004,-1.9472000000000005,-1.8976000000000004,-1.8512000000000006,-1.8080000000000005,-1.7680000000000005,-1.7312000000000005,-1.6976000000000004,-1.6672000000000005,-1.6400000000000006,-1.6160000000000005,-1.5952000000000006,-1.5776000000000006,-1.5632000000000006,-1.5520000000000005,-1.5440000000000005,-1.5392000000000006,-1.5376000000000005,-1.5392000000000006,-1.5440000000000005,-1.5520000000000005,-1.5632000000000006,-1.5776000000000006,-1.5952000000000006,-1.6160000000000005,-1.6400000000000003,-1.6672000000000005,-1.6976000000000004,-1.7312000000000005,-1.7680000000000005,-1.8080000000000005,-1.8512000000000006,-1.8976000000000006,-1.9472000000000007,-2.0000000000000009,-2.0560000000000009,-2.1152000000000006,-2.1776000000000009,-2.2432000000000003,-2.3120000000000003,-2.3840000000000003,-2.4592000000000005,-2.5376000000000003,-2.6192000000000006,-2.7040000000000006,-2.7920000000000007,-2.8832000000000009,-2.9776000000000007,-3.075200000000001,-3.176000000000001,-3.2800000000000011,-3.3872,-3.4976000000000003,-3.6112000000000002,-3.7280000000000006,-3.8480000000000008,-3.9712000000000005,-4.0976000000000008,-4.2272000000000007,-4.3600000000000012,-4.4960000000000013,-4.6352000000000011,-4.7776000000000014,-4.9231999999999996,-5.0720000000000001,-5.2240000000000002,-5.3792,-5.5376000000000003],[-5.6384000000000007,-5.4800000000000004,-5.3248000000000006,-5.1728000000000005,-5.0240000000000009,-4.878400000000001,-4.7360000000000007,-4.5968,-4.4608000000000008,-4.3280000000000012,-4.1984000000000012,-4.072000000000001,-3.9488000000000008,-3.8288000000000006,-3.7120000000000006,-3.5984000000000007,-3.4880000000000004,-3.3808000000000002,-3.2768000000000006,-3.176000000000001,-3.0784000000000007,-2.9840000000000009,-2.8928000000000011,-2.8048000000000011,-2.7200000000000006,-2.6384000000000007,-2.5600000000000005,-2.4848000000000008,-2.4128000000000007,-2.3440000000000007,-2.2784000000000009,-2.2160000000000006,-2.1568000000000005,-2.1008000000000004,-2.0480000000000005,-1.9984000000000006,-1.9520000000000008,-1.9088000000000007,-1.8688000000000007,-1.8320000000000007,-1.7984000000000007,-1.7680000000000007,-1.7408000000000008,-1.7168000000000008,-1.6960000000000008,-1.6784000000000008,-1.6640000000000008,-1.6528000000000007,-1.6448000000000007,-1.6400000000000008,-1.6384000000000007,-1.6400000000000008,-1.6448000000000007,-1.6528000000000007,-1.6640000000000008,-1.6784000000000008,-1.6960000000000008,-1.716800000000001,-1.7408000000000006,-1.7680000000000007,-1.7984000000000007,-1.8320000000000007,-1.8688000000000007,-1.9088000000000007,-1.9520000000000008,-1.9984000000000008,-2.0480000000000009,-2.1008000000000009,-2.1568000000000009,-2.2160000000000011,-2.2784000000000013,-2.3440000000000003,-2.4128000000000007,-2.4848000000000008,-2.5600000000000005,-2.6384000000000007,-2.7200000000000006,-2.8048000000000011,-2.8928000000000011,-2.9840000000000009,-3.0784000000000011,-3.176000000000001,-3.2768000000000015,-3.3808000000000016,-3.4880000000000004,-3.5984000000000007,-3.7120000000000006,-3.8288000000000006,-3.9488000000000008,-4.072000000000001,-4.1984000000000012,-4.3280000000000012,-4.4608000000000008,-4.5968000000000018,-4.7360000000000015,-4.8784000000000018,-5.024,-5.1728000000000005,-5.3248000000000006,-5.4800000000000004,-5.6384000000000007],[-5.7424000000000008,-5.5840000000000005,-5.4288000000000007,-5.2768000000000006,-5.128000000000001,-4.9824000000000011,-4.8400000000000007,-4.700800000000001,-4.5648,-4.4320000000000013,-4.3024000000000013,-4.176000000000001,-4.0528000000000013,-3.9328000000000007,-3.8160000000000007,-3.7024000000000008,-3.5920000000000005,-3.4848000000000003,-3.3808000000000007,-3.2800000000000011,-3.1824000000000008,-3.088000000000001,-2.9968000000000012,-2.9088000000000012,-2.8240000000000007,-2.7424000000000008,-2.6640000000000006,-2.5888000000000009,-2.5168000000000008,-2.4480000000000008,-2.382400000000001,-2.3200000000000007,-2.2608000000000006,-2.2048000000000005,-2.1520000000000006,-2.1024000000000007,-2.0560000000000009,-2.0128000000000008,-1.9728000000000008,-1.9360000000000008,-1.9024000000000008,-1.8720000000000008,-1.8448000000000009,-1.8208000000000009,-1.8000000000000009,-1.7824000000000009,-1.7680000000000009,-1.7568000000000008,-1.7488000000000008,-1.7440000000000009,-1.7424000000000008,-1.7440000000000009,-1.7488000000000008,-1.7568000000000008,-1.7680000000000009,-1.7824000000000009,-1.8000000000000009,-1.8208000000000011,-1.8448000000000007,-1.8720000000000008,-1.9024000000000008,-1.9360000000000008,-1.9728000000000008,-2.0128000000000008,-2.0560000000000009,-2.1024000000000012,-2.152000000000001,-2.204800000000001,-2.260800000000001,-2.3200000000000012,-2.3824000000000014,-2.4480000000000004,-2.5168000000000008,-2.5888000000000009,-2.6640000000000006,-2.7424000000000008,-2.8240000000000007,-2.9088000000000012,-2.9968000000000012,-3.088000000000001,-3.1824000000000012,-3.2800000000000011,-3.3808000000000016,-3.4848000000000017,-3.5920000000000005,-3.7024000000000008,-3.8160000000000007,-3.9328000000000007,-4.0528000000000013,-4.176000000000001,-4.3024000000000013,-4.4320000000000013,-4.5648000000000017,-4.700800000000001,-4.8400000000000016,-4.9824000000000019,-5.1280000000000001,-5.2768000000000006,-5.4288000000000007,-5.5840000000000005,-5.7424000000000008],[-5.8495999999999997,-5.6911999999999994,-5.5359999999999996,-5.3839999999999995,-5.2351999999999999,-5.0895999999999999,-4.9471999999999996,-4.8079999999999998,-4.6719999999999988,-4.5392000000000001,-4.4096000000000002,-4.2831999999999999,-4.1600000000000001,-4.0399999999999991,-3.9231999999999996,-3.8095999999999997,-3.6991999999999994,-3.5919999999999992,-3.4879999999999995,-3.3872,-3.2895999999999996,-3.1951999999999998,-3.1040000000000001,-3.016,-2.9311999999999996,-2.8495999999999997,-2.7711999999999994,-2.6959999999999997,-2.6239999999999997,-2.5551999999999997,-2.4895999999999998,-2.4271999999999996,-2.3679999999999994,-2.3119999999999994,-2.2591999999999994,-2.2095999999999996,-2.1631999999999998,-2.1199999999999997,-2.0799999999999996,-2.0431999999999997,-2.0095999999999998,-1.9791999999999996,-1.9519999999999997,-1.9279999999999997,-1.9071999999999998,-1.8895999999999997,-1.8751999999999998,-1.8639999999999997,-1.8559999999999997,-1.8511999999999997,-1.8495999999999997,-1.8511999999999997,-1.8559999999999997,-1.8639999999999997,-1.8751999999999998,-1.8895999999999997,-1.9071999999999998,-1.9279999999999999,-1.9519999999999995,-1.9791999999999996,-2.0095999999999998,-2.0431999999999997,-2.0799999999999996,-2.1199999999999997,-2.1631999999999998,-2.2096,-2.2591999999999999,-2.3119999999999998,-2.3679999999999999,-2.4272,-2.4896000000000003,-2.5551999999999992,-2.6239999999999997,-2.6959999999999997,-2.7711999999999994,-2.8495999999999997,-2.9311999999999996,-3.016,-3.1040000000000001,-3.1951999999999998,-3.2896000000000001,-3.3872,-3.4880000000000004,-3.5920000000000005,-3.6991999999999994,-3.8095999999999997,-3.9231999999999996,-4.0399999999999991,-4.1600000000000001,-4.2831999999999999,-4.4096000000000002,-4.5392000000000001,-4.6720000000000006,-4.8079999999999998,-4.9472000000000005,-5.0896000000000008,-5.235199999999999,-5.3839999999999995,-5.5359999999999996,-5.6911999999999994,-5.8495999999999997],[-5.96,-5.8015999999999996,-5.6463999999999999,-5.4943999999999997,-5.3456000000000001,-5.2000000000000002,-5.0575999999999999,-4.9183999999999992,-4.7823999999999991,-4.6496000000000004,-4.5200000000000005,-4.3936000000000002,-4.2703999999999995,-4.1503999999999994,-4.0335999999999999,-3.9199999999999995,-3.8095999999999997,-3.702399999999999,-3.5983999999999998,-3.4975999999999998,-3.3999999999999995,-3.3056000000000001,-3.2143999999999999,-3.1263999999999998,-3.0415999999999999,-2.96,-2.8815999999999997,-2.8063999999999996,-2.7343999999999995,-2.6656,-2.5999999999999996,-2.5375999999999999,-2.4783999999999997,-2.4223999999999997,-2.3695999999999997,-2.3199999999999994,-2.2735999999999996,-2.2303999999999999,-2.1903999999999999,-2.1535999999999995,-2.1199999999999997,-2.0895999999999995,-2.0623999999999998,-2.0383999999999998,-2.0175999999999998,-1.9999999999999998,-1.9855999999999998,-1.9743999999999997,-1.9663999999999997,-1.9615999999999998,-1.9599999999999997,-1.9615999999999998,-1.9663999999999997,-1.9743999999999997,-1.9855999999999998,-1.9999999999999998,-2.0175999999999998,-2.0383999999999998,-2.0623999999999998,-2.0895999999999995,-2.1199999999999997,-2.1535999999999995,-2.1903999999999999,-2.2303999999999999,-2.2735999999999996,-2.3199999999999998,-2.3696000000000002,-2.4224000000000001,-2.4784000000000002,-2.5376000000000003,-2.6000000000000001,-2.6655999999999995,-2.7343999999999995,-2.8063999999999996,-2.8815999999999997,-2.96,-3.0415999999999999,-3.1263999999999998,-3.2143999999999999,-3.3056000000000001,-3.4000000000000004,-3.4976000000000003,-3.5984000000000007,-3.7024000000000008,-3.8095999999999997,-3.9199999999999995,-4.0335999999999999,-4.1503999999999994,-4.2703999999999995,-4.3936000000000002,-4.5200000000000005,-4.6496000000000004,-4.7824,-4.9184000000000001,-5.0576000000000008,-5.2000000000000011,-5.3455999999999992,-5.4943999999999997,-5.6463999999999999,-5.8015999999999996,-5.96],[-6.0735999999999999,-5.9151999999999996,-5.7599999999999998,-5.6079999999999997,-5.4592000000000001,-5.3136000000000001,-5.1711999999999998,-5.032,-4.895999999999999,-4.7632000000000003,-4.6336000000000004,-4.5072000000000001,-4.3840000000000003,-4.2639999999999993,-4.1471999999999998,-4.0335999999999999,-3.9231999999999996,-3.8159999999999994,-3.7119999999999997,-3.6112000000000002,-3.5135999999999998,-3.4192,-3.3280000000000003,-3.2400000000000002,-3.1551999999999998,-3.0735999999999999,-2.9951999999999996,-2.9199999999999999,-2.8479999999999999,-2.7791999999999999,-2.7136,-2.6511999999999998,-2.5919999999999996,-2.5359999999999996,-2.4831999999999996,-2.4335999999999998,-2.3872,-2.3439999999999999,-2.3039999999999998,-2.2671999999999999,-2.2336,-2.2031999999999998,-2.1760000000000002,-2.1519999999999997,-2.1311999999999998,-2.1135999999999999,-2.0991999999999997,-2.0880000000000001,-2.0800000000000001,-2.0751999999999997,-2.0735999999999999,-2.0751999999999997,-2.0800000000000001,-2.0880000000000001,-2.0991999999999997,-2.1135999999999999,-2.1312000000000002,-2.1520000000000001,-2.1759999999999997,-2.2031999999999998,-2.2336,-2.2671999999999999,-2.3039999999999998,-2.3439999999999999,-2.3872,-2.4336000000000002,-2.4832000000000001,-2.536,-2.5920000000000001,-2.6512000000000002,-2.7136000000000005,-2.7791999999999994,-2.8479999999999999,-2.9199999999999999,-2.9951999999999996,-3.0735999999999999,-3.1551999999999998,-3.2400000000000002,-3.3280000000000003,-3.4192,-3.5136000000000003,-3.6112000000000002,-3.7120000000000006,-3.8160000000000007,-3.9231999999999996,-4.0335999999999999,-4.1471999999999998,-4.2639999999999993,-4.3840000000000003,-4.5072000000000001,-4.6336000000000004,-4.7632000000000003,-4.8960000000000008,-5.032,-5.1712000000000007,-5.313600000000001,-5.4591999999999992,-5.6079999999999997,-5.7599999999999998,-5.9151999999999996,-6.0735999999999999],[-6.1904000000000003,-6.032,-5.8767999999999994,-5.7248000000000001,-5.5760000000000005,-5.4304000000000006,-5.2880000000000003,-5.1487999999999996,-5.0127999999999995,-4.8800000000000008,-4.7504000000000008,-4.6240000000000006,-4.5007999999999999,-4.3807999999999998,-4.2639999999999993,-4.1503999999999994,-4.0399999999999991,-3.9327999999999994,-3.8288000000000002,-3.7279999999999998,-3.6303999999999998,-3.5360000000000005,-3.4447999999999999,-3.3567999999999998,-3.2720000000000002,-3.1903999999999999,-3.1120000000000001,-3.0367999999999995,-2.9647999999999999,-2.8959999999999999,-2.8304,-2.7679999999999998,-2.7088000000000001,-2.6528,-2.5999999999999996,-2.5503999999999998,-2.504,-2.4607999999999999,-2.4207999999999998,-2.3839999999999999,-2.3503999999999996,-2.3199999999999998,-2.2927999999999997,-2.2687999999999997,-2.2479999999999998,-2.2303999999999999,-2.2159999999999997,-2.2048000000000001,-2.1968000000000001,-2.1919999999999997,-2.1903999999999999,-2.1919999999999997,-2.1968000000000001,-2.2048000000000001,-2.2159999999999997,-2.2303999999999999,-2.2480000000000002,-2.2688000000000001,-2.2927999999999997,-2.3199999999999998,-2.3503999999999996,-2.3839999999999999,-2.4207999999999998,-2.4607999999999999,-2.504,-2.5503999999999998,-2.6000000000000001,-2.6528,-2.7088000000000001,-2.7680000000000002,-2.8304000000000005,-2.8959999999999999,-2.9647999999999999,-3.0367999999999995,-3.1120000000000001,-3.1903999999999999,-3.2720000000000002,-3.3567999999999998,-3.4447999999999999,-3.5360000000000005,-3.6304000000000003,-3.7280000000000006,-3.8288000000000006,-3.9328000000000007,-4.0399999999999991,-4.1503999999999994,-4.2639999999999993,-4.3807999999999998,-4.5007999999999999,-4.6240000000000006,-4.7504000000000008,-4.8800000000000008,-5.0128000000000004,-5.1488000000000005,-5.2880000000000003,-5.4304000000000006,-5.5759999999999987,-5.7248000000000001,-5.8767999999999994,-6.032,-6.1904000000000003],[-6.3103999999999996,-6.1519999999999992,-5.9968000000000004,-5.8447999999999993,-5.6959999999999997,-5.5503999999999998,-5.4079999999999995,-5.2687999999999997,-5.1327999999999996,-5,-4.8704000000000001,-4.7439999999999998,-4.6208,-4.5007999999999999,-4.3840000000000003,-4.2703999999999995,-4.1600000000000001,-4.0527999999999995,-3.9488000000000003,-3.8479999999999999,-3.7504,-3.6560000000000006,-3.5648,-3.4767999999999999,-3.3920000000000003,-3.3104,-3.2320000000000002,-3.1567999999999996,-3.0848,-3.016,-2.9504000000000001,-2.8879999999999999,-2.8288000000000002,-2.7728000000000002,-2.7199999999999998,-2.6703999999999999,-2.6240000000000001,-2.5808,-2.5407999999999999,-2.504,-2.4703999999999997,-2.4399999999999999,-2.4127999999999998,-2.3887999999999998,-2.3679999999999999,-2.3504,-2.3359999999999999,-2.3248000000000002,-2.3168000000000002,-2.3119999999999998,-2.3104,-2.3119999999999998,-2.3168000000000002,-2.3248000000000002,-2.3359999999999999,-2.3504,-2.3680000000000003,-2.3888000000000003,-2.4127999999999998,-2.4399999999999999,-2.4703999999999997,-2.504,-2.5407999999999999,-2.5808,-2.6240000000000001,-2.6703999999999999,-2.7200000000000002,-2.7728000000000002,-2.8288000000000002,-2.8880000000000003,-2.9504000000000006,-3.016,-3.0848,-3.1567999999999996,-3.2320000000000002,-3.3104,-3.3920000000000003,-3.4767999999999999,-3.5648,-3.6560000000000006,-3.7504000000000004,-3.8480000000000008,-3.9488000000000008,-4.0528000000000013,-4.1600000000000001,-4.2703999999999995,-4.3840000000000003,-4.5007999999999999,-4.6208,-4.7439999999999998,-4.8704000000000001,-5,-5.1328000000000005,-5.2688000000000006,-5.4080000000000013,-5.5504000000000016,-5.6959999999999997,-5.8447999999999993,-5.9968000000000004,-6.1519999999999992,-6.3103999999999996],[-6.4336000000000002,-6.2751999999999999,-6.1200000000000001,-5.968,-5.8192000000000004,-5.6736000000000004,-5.5312000000000001,-5.3919999999999995,-5.2560000000000002,-5.1232000000000006,-4.9936000000000007,-4.8672000000000004,-4.7439999999999998,-4.6240000000000006,-4.5072000000000001,-4.3936000000000002,-4.2831999999999999,-4.1760000000000002,-4.0720000000000001,-3.9712000000000005,-3.8736000000000002,-3.7792000000000003,-3.6880000000000006,-3.6000000000000005,-3.5152000000000001,-3.4336000000000002,-3.3552,-3.2800000000000002,-3.2080000000000002,-3.1392000000000002,-3.0736000000000003,-3.0112000000000001,-2.952,-2.8959999999999999,-2.8431999999999999,-2.7936000000000001,-2.7472000000000003,-2.7040000000000002,-2.6640000000000001,-2.6272000000000002,-2.5936000000000003,-2.5632000000000001,-2.5360000000000005,-2.512,-2.4912000000000001,-2.4736000000000002,-2.4592000000000001,-2.4480000000000004,-2.4400000000000004,-2.4352,-2.4336000000000002,-2.4352,-2.4400000000000004,-2.4480000000000004,-2.4592000000000001,-2.4736000000000002,-2.4912000000000005,-2.5120000000000005,-2.536,-2.5632000000000001,-2.5936000000000003,-2.6272000000000002,-2.6640000000000001,-2.7040000000000002,-2.7472000000000003,-2.7936000000000005,-2.8432000000000004,-2.8960000000000004,-2.9520000000000004,-3.0112000000000005,-3.0736000000000008,-3.1391999999999998,-3.2080000000000002,-3.2800000000000002,-3.3552,-3.4336000000000002,-3.5152000000000001,-3.6000000000000005,-3.6880000000000006,-3.7792000000000003,-3.8736000000000006,-3.9712000000000005,-4.072000000000001,-4.176000000000001,-4.2831999999999999,-4.3936000000000002,-4.5072000000000001,-4.6240000000000006,-4.7439999999999998,-4.8672000000000004,-4.9936000000000007,-5.1232000000000006,-5.2560000000000002,-5.3920000000000012,-5.531200000000001,-5.6736000000000013,-5.8191999999999995,-5.968,-6.1200000000000001,-6.2751999999999999,-6.4336000000000002],[-6.5600000000000005,-6.4016000000000002,-6.2464000000000004,-6.0944000000000003,-5.9456000000000007,-5.8000000000000007,-5.6576000000000004,-5.5183999999999997,-5.3824000000000005,-5.2496000000000009,-5.120000000000001,-4.9936000000000007,-4.8704000000000001,-4.7504000000000008,-4.6336000000000004,-4.5200000000000005,-4.4096000000000002,-4.3024000000000004,-4.1984000000000004,-4.0976000000000008,-4,-3.9056000000000006,-3.8144000000000009,-3.7264000000000008,-3.6416000000000004,-3.5600000000000005,-3.4816000000000003,-3.4064000000000005,-3.3344000000000005,-3.2656000000000005,-3.2000000000000006,-3.1376000000000004,-3.0784000000000002,-3.0224000000000002,-2.9696000000000002,-2.9200000000000004,-2.8736000000000006,-2.8304000000000005,-2.7904000000000004,-2.7536000000000005,-2.7200000000000006,-2.6896000000000004,-2.6624000000000008,-2.6384000000000003,-2.6176000000000004,-2.6000000000000005,-2.5856000000000003,-2.5744000000000007,-2.5664000000000007,-2.5616000000000003,-2.5600000000000005,-2.5616000000000003,-2.5664000000000007,-2.5744000000000007,-2.5856000000000003,-2.6000000000000005,-2.6176000000000008,-2.6384000000000007,-2.6624000000000003,-2.6896000000000004,-2.7200000000000006,-2.7536000000000005,-2.7904000000000004,-2.8304000000000005,-2.8736000000000006,-2.9200000000000008,-2.9696000000000007,-3.0224000000000006,-3.0784000000000007,-3.1376000000000008,-3.2000000000000011,-3.2656000000000001,-3.3344000000000005,-3.4064000000000005,-3.4816000000000003,-3.5600000000000005,-3.6416000000000004,-3.7264000000000008,-3.8144000000000009,-3.9056000000000006,-4.0000000000000009,-4.0976000000000008,-4.1984000000000012,-4.3024000000000013,-4.4096000000000002,-4.5200000000000005,-4.6336000000000004,-4.7504000000000008,-4.8704000000000001,-4.9936000000000007,-5.120000000000001,-5.2496000000000009,-5.3824000000000005,-5.5184000000000015,-5.6576000000000013,-5.8000000000000016,-5.9455999999999998,-6.0944000000000003,-6.2464000000000004,-6.4016000000000002,-6.5600000000000005],[-6.6896000000000004,-6.5312000000000001,-6.3760000000000003,-6.2240000000000002,-6.0752000000000006,-5.9296000000000006,-5.7872000000000003,-5.6479999999999997,-5.5120000000000005,-5.3792000000000009,-5.2496000000000009,-5.1232000000000006,-5,-4.8800000000000008,-4.7632000000000003,-4.6496000000000004,-4.5392000000000001,-4.4320000000000004,-4.3280000000000003,-4.2272000000000007,-4.1295999999999999,-4.0352000000000006,-3.9440000000000008,-3.8560000000000008,-3.7712000000000003,-3.6896000000000004,-3.6112000000000002,-3.5360000000000005,-3.4640000000000004,-3.3952000000000004,-3.3296000000000006,-3.2672000000000003,-3.2080000000000002,-3.1520000000000001,-3.0992000000000002,-3.0496000000000003,-3.0032000000000005,-2.9600000000000004,-2.9200000000000004,-2.8832000000000004,-2.8496000000000006,-2.8192000000000004,-2.7920000000000007,-2.7680000000000002,-2.7472000000000003,-2.7296000000000005,-2.7152000000000003,-2.7040000000000006,-2.6960000000000006,-2.6912000000000003,-2.6896000000000004,-2.6912000000000003,-2.6960000000000006,-2.7040000000000006,-2.7152000000000003,-2.7296000000000005,-2.7472000000000008,-2.7680000000000007,-2.7920000000000003,-2.8192000000000004,-2.8496000000000006,-2.8832000000000004,-2.9200000000000004,-2.9600000000000004,-3.0032000000000005,-3.0496000000000008,-3.0992000000000006,-3.1520000000000006,-3.2080000000000006,-3.2672000000000008,-3.329600000000001,-3.3952,-3.4640000000000004,-3.5360000000000005,-3.6112000000000002,-3.6896000000000004,-3.7712000000000003,-3.8560000000000008,-3.9440000000000008,-4.0352000000000006,-4.1296000000000008,-4.2272000000000007,-4.3280000000000012,-4.4320000000000013,-4.5392000000000001,-4.6496000000000004,-4.7632000000000003,-4.8800000000000008,-5,-5.1232000000000006,-5.2496000000000009,-5.3792000000000009,-5.5120000000000005,-5.6480000000000015,-5.7872000000000012,-5.9296000000000015,-6.0751999999999997,-6.2240000000000002,-6.3760000000000003,-6.5312000000000001,-6.6896000000000004],[-6.8224,-6.6639999999999997,-6.5088000000000008,-6.3567999999999998,-6.2080000000000002,-6.0624000000000002,-5.9199999999999999,-5.7808000000000002,-5.6448,-5.5120000000000005,-5.3824000000000005,-5.2560000000000002,-5.1328000000000005,-5.0128000000000004,-4.8960000000000008,-4.7824,-4.6720000000000006,-4.5648,-4.4608000000000008,-4.3600000000000003,-4.2624000000000004,-4.168000000000001,-4.0768000000000004,-3.9888000000000003,-3.9040000000000008,-3.8224000000000005,-3.7440000000000007,-3.6688000000000001,-3.5968000000000004,-3.5280000000000005,-3.4624000000000006,-3.4000000000000004,-3.3408000000000007,-3.2848000000000006,-3.2320000000000002,-3.1824000000000003,-3.1360000000000006,-3.0928000000000004,-3.0528000000000004,-3.0160000000000005,-2.9824000000000002,-2.9520000000000004,-2.9248000000000003,-2.9008000000000003,-2.8800000000000003,-2.8624000000000005,-2.8480000000000003,-2.8368000000000007,-2.8288000000000006,-2.8240000000000003,-2.8224000000000005,-2.8240000000000003,-2.8288000000000006,-2.8368000000000007,-2.8480000000000003,-2.8624000000000005,-2.8800000000000008,-2.9008000000000007,-2.9248000000000003,-2.9520000000000004,-2.9824000000000002,-3.0160000000000005,-3.0528000000000004,-3.0928000000000004,-3.1360000000000006,-3.1824000000000003,-3.2320000000000007,-3.2848000000000006,-3.3408000000000007,-3.4000000000000008,-3.462400000000001,-3.5280000000000005,-3.5968000000000004,-3.6688000000000001,-3.7440000000000007,-3.8224000000000005,-3.9040000000000008,-3.9888000000000003,-4.0768000000000004,-4.168000000000001,-4.2624000000000013,-4.3600000000000012,-4.4608000000000008,-4.5648000000000017,-4.6720000000000006,-4.7824,-4.8960000000000008,-5.0128000000000004,-5.1328000000000005,-5.2560000000000002,-5.3824000000000005,-5.5120000000000005,-5.6448000000000009,-5.780800000000001,-5.9200000000000017,-6.062400000000002,-6.2080000000000002,-6.3567999999999998,-6.5088000000000008,-6.6639999999999997,-6.8224],[-6.958400000000001,-6.8000000000000007,-6.6448,-6.4928000000000008,-6.3440000000000012,-6.1984000000000012,-6.0560000000000009,-5.9168000000000003,-5.7808000000000002,-5.6480000000000015,-5.5184000000000015,-5.3920000000000012,-5.2688000000000006,-5.1488000000000005,-5.032,-4.9184000000000001,-4.8079999999999998,-4.7008000000000001,-4.5968000000000009,-4.4960000000000004,-4.3984000000000005,-4.3040000000000012,-4.2128000000000005,-4.1248000000000005,-4.0400000000000009,-3.9584000000000006,-3.8800000000000008,-3.8048000000000002,-3.7328000000000006,-3.6640000000000006,-3.5984000000000007,-3.5360000000000005,-3.4768000000000008,-3.4208000000000007,-3.3680000000000003,-3.3184000000000005,-3.2720000000000007,-3.2288000000000006,-3.1888000000000005,-3.1520000000000006,-3.1184000000000003,-3.0880000000000005,-3.0608000000000004,-3.0368000000000004,-3.0160000000000005,-2.9984000000000006,-2.9840000000000004,-2.9728000000000008,-2.9648000000000008,-2.9600000000000004,-2.9584000000000006,-2.9600000000000004,-2.9648000000000008,-2.9728000000000008,-2.9840000000000004,-2.9984000000000006,-3.0160000000000009,-3.0368000000000008,-3.0608000000000004,-3.0880000000000005,-3.1184000000000003,-3.1520000000000006,-3.1888000000000005,-3.2288000000000006,-3.2720000000000007,-3.3184000000000005,-3.3680000000000008,-3.4208000000000007,-3.4768000000000008,-3.5360000000000009,-3.5984000000000012,-3.6640000000000006,-3.7328000000000006,-3.8048000000000002,-3.8800000000000008,-3.9584000000000006,-4.0400000000000009,-4.1248000000000005,-4.2128000000000005,-4.3040000000000012,-4.3984000000000005,-4.4960000000000013,-4.5968000000000018,-4.700800000000001,-4.8079999999999998,-4.9184000000000001,-5.032,-5.1488000000000005,-5.2688000000000006,-5.3920000000000012,-5.5184000000000015,-5.6480000000000015,-5.780800000000001,-5.9168000000000012,-6.0560000000000009,-6.1984000000000012,-6.3439999999999994,-6.4928000000000008,-6.6448,-6.8000000000000007,-6.958400000000001],[-7.0976000000000008,-6.9392000000000005,-6.7840000000000007,-6.6320000000000006,-6.483200000000001,-6.337600000000001,-6.1952000000000007,-6.0560000000000009,-5.9199999999999999,-5.7872000000000012,-5.6576000000000013,-5.531200000000001,-5.4080000000000013,-5.2880000000000003,-5.1712000000000007,-5.0576000000000008,-4.9472000000000005,-4.8399999999999999,-4.7360000000000007,-4.6352000000000011,-4.5376000000000012,-4.4432000000000009,-4.3520000000000012,-4.2640000000000011,-4.1792000000000007,-4.0976000000000008,-4.0192000000000005,-3.9440000000000008,-3.8720000000000008,-3.8032000000000008,-3.7376000000000009,-3.6752000000000007,-3.6160000000000005,-3.5600000000000005,-3.5072000000000005,-3.4576000000000007,-3.4112000000000009,-3.3680000000000008,-3.3280000000000007,-3.2912000000000008,-3.2576000000000009,-3.2272000000000007,-3.2000000000000011,-3.1760000000000006,-3.1552000000000007,-3.1376000000000008,-3.1232000000000006,-3.112000000000001,-3.104000000000001,-3.0992000000000006,-3.0976000000000008,-3.0992000000000006,-3.104000000000001,-3.112000000000001,-3.1232000000000006,-3.1376000000000008,-3.1552000000000011,-3.176000000000001,-3.2000000000000006,-3.2272000000000007,-3.2576000000000009,-3.2912000000000008,-3.3280000000000007,-3.3680000000000008,-3.4112000000000009,-3.4576000000000011,-3.507200000000001,-3.5600000000000009,-3.616000000000001,-3.6752000000000011,-3.7376000000000014,-3.8032000000000004,-3.8720000000000008,-3.9440000000000008,-4.0192000000000005,-4.0976000000000008,-4.1792000000000007,-4.2640000000000011,-4.3520000000000012,-4.4432000000000009,-4.5376000000000012,-4.6352000000000011,-4.7360000000000015,-4.8400000000000016,-4.9472000000000005,-5.0576000000000008,-5.1712000000000007,-5.2880000000000003,-5.4080000000000013,-5.531200000000001,-5.6576000000000013,-5.7872000000000012,-5.9200000000000017,-6.0560000000000009,-6.1952000000000016,-6.3376000000000019,-6.4832000000000001,-6.6320000000000006,-6.7840000000000007,-6.9392000000000005,-7.0976000000000008],[-7.2400000000000011,-7.0816000000000008,-6.926400000000001,-6.7744000000000009,-6.6256000000000013,-6.4800000000000013,-6.337600000000001,-6.1984000000000012,-6.0624000000000002,-5.9296000000000015,-5.8000000000000016,-5.6736000000000013,-5.5504000000000016,-5.4304000000000006,-5.313600000000001,-5.2000000000000011,-5.0896000000000008,-4.9824000000000002,-4.878400000000001,-4.7776000000000014,-4.6800000000000015,-4.5856000000000012,-4.4944000000000015,-4.4064000000000014,-4.321600000000001,-4.2400000000000011,-4.1616000000000009,-4.0864000000000011,-4.0144000000000011,-3.9456000000000011,-3.8800000000000012,-3.817600000000001,-3.7584000000000009,-3.7024000000000008,-3.6496000000000008,-3.600000000000001,-3.5536000000000012,-3.5104000000000011,-3.470400000000001,-3.4336000000000011,-3.4000000000000012,-3.369600000000001,-3.3424000000000014,-3.3184000000000009,-3.297600000000001,-3.2800000000000011,-3.2656000000000009,-3.2544000000000013,-3.2464000000000013,-3.2416000000000009,-3.2400000000000011,-3.2416000000000009,-3.2464000000000013,-3.2544000000000013,-3.2656000000000009,-3.2800000000000011,-3.2976000000000014,-3.3184000000000013,-3.3424000000000009,-3.369600000000001,-3.4000000000000012,-3.4336000000000011,-3.470400000000001,-3.5104000000000011,-3.5536000000000012,-3.6000000000000014,-3.6496000000000013,-3.7024000000000012,-3.7584000000000013,-3.8176000000000014,-3.8800000000000017,-3.9456000000000007,-4.0144000000000011,-4.0864000000000011,-4.1616000000000009,-4.2400000000000011,-4.321600000000001,-4.4064000000000014,-4.4944000000000015,-4.5856000000000012,-4.6800000000000015,-4.7776000000000014,-4.8784000000000018,-4.9824000000000019,-5.0896000000000008,-5.2000000000000011,-5.313600000000001,-5.4304000000000006,-5.5504000000000016,-5.6736000000000013,-5.8000000000000016,-5.9296000000000015,-6.062400000000002,-6.1984000000000012,-6.3376000000000019,-6.4800000000000022,-6.6256000000000004,-6.7744000000000009,-6.926400000000001,-7.0816000000000008,-7.2400000000000011],[-7.3855999999999993,-7.227199999999999,-7.0719999999999992,-6.919999999999999,-6.7711999999999994,-6.6255999999999995,-6.4831999999999992,-6.3439999999999994,-6.2079999999999984,-6.0751999999999997,-5.9455999999999998,-5.8191999999999995,-5.6959999999999997,-5.5759999999999987,-5.4591999999999992,-5.3455999999999992,-5.235199999999999,-5.1279999999999983,-5.0239999999999991,-4.9231999999999996,-4.8255999999999997,-4.7311999999999994,-4.6399999999999997,-4.5519999999999996,-4.4671999999999992,-4.3855999999999993,-4.307199999999999,-4.2319999999999993,-4.1599999999999993,-4.0911999999999997,-4.025599999999999,-3.9631999999999992,-3.903999999999999,-3.847999999999999,-3.795199999999999,-3.7455999999999992,-3.6991999999999994,-3.6559999999999993,-3.6159999999999992,-3.5791999999999993,-3.5455999999999994,-3.5151999999999992,-3.4879999999999995,-3.4639999999999991,-3.4431999999999992,-3.4255999999999993,-3.4111999999999991,-3.3999999999999995,-3.3919999999999995,-3.3871999999999991,-3.3855999999999993,-3.3871999999999991,-3.3919999999999995,-3.3999999999999995,-3.4111999999999991,-3.4255999999999993,-3.4431999999999996,-3.4639999999999995,-3.4879999999999991,-3.5151999999999992,-3.5455999999999994,-3.5791999999999993,-3.6159999999999992,-3.6559999999999993,-3.6991999999999994,-3.7455999999999996,-3.7951999999999995,-3.8479999999999994,-3.9039999999999995,-3.9631999999999996,-4.0255999999999998,-4.0911999999999988,-4.1599999999999993,-4.2319999999999993,-4.307199999999999,-4.3855999999999993,-4.4671999999999992,-4.5519999999999996,-4.6399999999999997,-4.7311999999999994,-4.8255999999999997,-4.9231999999999996,-5.024,-5.1280000000000001,-5.235199999999999,-5.3455999999999992,-5.4591999999999992,-5.5759999999999987,-5.6959999999999997,-5.8191999999999995,-5.9455999999999998,-6.0751999999999997,-6.2080000000000002,-6.3439999999999994,-6.4832000000000001,-6.6256000000000004,-6.7711999999999986,-6.919999999999999,-7.0719999999999992,-7.227199999999999,-7.3855999999999993],[-7.5343999999999998,-7.3759999999999994,-7.2207999999999997,-7.0687999999999995,-6.9199999999999999,-6.7744,-6.6319999999999997,-6.492799999999999,-6.3567999999999998,-6.2240000000000002,-6.0944000000000003,-5.968,-5.8447999999999993,-5.7248000000000001,-5.6079999999999997,-5.4943999999999997,-5.3839999999999995,-5.2767999999999997,-5.1727999999999996,-5.0720000000000001,-4.9743999999999993,-4.8799999999999999,-4.7888000000000002,-4.7008000000000001,-4.6159999999999997,-4.5343999999999998,-4.4559999999999995,-4.3807999999999998,-4.3087999999999997,-4.2400000000000002,-4.1744000000000003,-4.1120000000000001,-4.0527999999999995,-3.9967999999999995,-3.9439999999999995,-3.8943999999999996,-3.8479999999999999,-3.8047999999999997,-3.7647999999999997,-3.7279999999999998,-3.6943999999999999,-3.6639999999999997,-3.6368,-3.6127999999999996,-3.5919999999999996,-3.5743999999999998,-3.5599999999999996,-3.5488,-3.5407999999999999,-3.5359999999999996,-3.5343999999999998,-3.5359999999999996,-3.5407999999999999,-3.5488,-3.5599999999999996,-3.5743999999999998,-3.5920000000000001,-3.6128,-3.6367999999999996,-3.6639999999999997,-3.6943999999999999,-3.7279999999999998,-3.7647999999999997,-3.8047999999999997,-3.8479999999999999,-3.8944000000000001,-3.944,-3.9967999999999999,-4.0528000000000004,-4.1120000000000001,-4.1744000000000003,-4.2399999999999993,-4.3087999999999997,-4.3807999999999998,-4.4559999999999995,-4.5343999999999998,-4.6159999999999997,-4.7008000000000001,-4.7888000000000002,-4.8799999999999999,-4.9744000000000002,-5.0720000000000001,-5.1728000000000005,-5.2768000000000006,-5.3839999999999995,-5.4943999999999997,-5.6079999999999997,-5.7248000000000001,-5.8447999999999993,-5.968,-6.0944000000000003,-6.2240000000000002,-6.3567999999999998,-6.4928000000000008,-6.6320000000000006,-6.7744000000000009,-6.919999999999999,-7.0687999999999995,-7.2207999999999997,-7.3759999999999994,-7.5343999999999998],[-7.6863999999999999,-7.5279999999999996,-7.3727999999999998,-7.2207999999999997,-7.0720000000000001,-6.9264000000000001,-6.7839999999999998,-6.6448,-6.508799999999999,-6.3760000000000003,-6.2464000000000004,-6.1200000000000001,-5.9968000000000004,-5.8767999999999994,-5.7599999999999998,-5.6463999999999999,-5.5359999999999996,-5.428799999999999,-5.3247999999999998,-5.2240000000000002,-5.1264000000000003,-5.032,-4.9408000000000003,-4.8528000000000002,-4.7679999999999998,-4.6863999999999999,-4.6079999999999997,-4.5327999999999999,-4.4607999999999999,-4.3920000000000003,-4.3263999999999996,-4.2640000000000002,-4.2047999999999996,-4.1487999999999996,-4.0960000000000001,-4.0463999999999993,-4,-3.9567999999999999,-3.9167999999999998,-3.8799999999999999,-3.8464,-3.8159999999999998,-3.7888000000000002,-3.7647999999999997,-3.7439999999999998,-3.7263999999999999,-3.7119999999999997,-3.7008000000000001,-3.6928000000000001,-3.6879999999999997,-3.6863999999999999,-3.6879999999999997,-3.6928000000000001,-3.7008000000000001,-3.7119999999999997,-3.7263999999999999,-3.7440000000000002,-3.7648000000000001,-3.7887999999999997,-3.8159999999999998,-3.8464,-3.8799999999999999,-3.9167999999999998,-3.9567999999999999,-4,-4.0464000000000002,-4.0960000000000001,-4.1488000000000005,-4.2048000000000005,-4.2640000000000002,-4.3264000000000005,-4.3919999999999995,-4.4607999999999999,-4.5327999999999999,-4.6079999999999997,-4.6863999999999999,-4.7679999999999998,-4.8528000000000002,-4.9408000000000003,-5.032,-5.1264000000000003,-5.2240000000000002,-5.3248000000000006,-5.4288000000000007,-5.5359999999999996,-5.6463999999999999,-5.7599999999999998,-5.8767999999999994,-5.9968000000000004,-6.1200000000000001,-6.2464000000000004,-6.3760000000000003,-6.5088000000000008,-6.6448,-6.7840000000000007,-6.926400000000001,-7.0719999999999992,-7.2207999999999997,-7.3727999999999998,-7.5279999999999996,-7.6863999999999999],[-7.8415999999999997,-7.6831999999999994,-7.5279999999999996,-7.3759999999999994,-7.2271999999999998,-7.0815999999999999,-6.9391999999999996,-6.7999999999999989,-6.6639999999999997,-6.5312000000000001,-6.4016000000000002,-6.2751999999999999,-6.1519999999999992,-6.032,-5.9151999999999996,-5.8015999999999996,-5.6911999999999994,-5.5839999999999996,-5.4799999999999995,-5.3792,-5.2815999999999992,-5.1871999999999998,-5.0960000000000001,-5.008,-4.9231999999999996,-4.8415999999999997,-4.7631999999999994,-4.6879999999999997,-4.6159999999999997,-4.5472000000000001,-4.4816000000000003,-4.4192,-4.3599999999999994,-4.3039999999999994,-4.2511999999999999,-4.2015999999999991,-4.1551999999999998,-4.1120000000000001,-4.0720000000000001,-4.0351999999999997,-4.0015999999999998,-3.9711999999999996,-3.944,-3.9199999999999995,-3.8991999999999996,-3.8815999999999997,-3.8671999999999995,-3.8559999999999999,-3.8479999999999999,-3.8431999999999995,-3.8415999999999997,-3.8431999999999995,-3.8479999999999999,-3.8559999999999999,-3.8671999999999995,-3.8815999999999997,-3.8992,-3.9199999999999999,-3.9439999999999995,-3.9711999999999996,-4.0015999999999998,-4.0351999999999997,-4.0720000000000001,-4.1120000000000001,-4.1551999999999998,-4.2016,-4.2511999999999999,-4.3040000000000003,-4.3600000000000003,-4.4192,-4.4816000000000003,-4.5471999999999992,-4.6159999999999997,-4.6879999999999997,-4.7631999999999994,-4.8415999999999997,-4.9231999999999996,-5.008,-5.0960000000000001,-5.1871999999999998,-5.2816000000000001,-5.3792,-5.4800000000000004,-5.5840000000000005,-5.6911999999999994,-5.8015999999999996,-5.9151999999999996,-6.032,-6.1519999999999992,-6.2751999999999999,-6.4016000000000002,-6.5312000000000001,-6.6639999999999997,-6.8000000000000007,-6.9392000000000005,-7.0816000000000008,-7.227199999999999,-7.3759999999999994,-7.5279999999999996,-7.6831999999999994,-7.8415999999999997],[-8,-7.8415999999999997,-7.6863999999999999,-7.5343999999999998,-7.3856000000000002,-7.2400000000000002,-7.0975999999999999,-6.9583999999999993,-6.8224,-6.6896000000000004,-6.5600000000000005,-6.4336000000000002,-6.3103999999999996,-6.1904000000000003,-6.0735999999999999,-5.96,-5.8495999999999997,-5.7423999999999999,-5.6383999999999999,-5.5376000000000003,-5.4399999999999995,-5.3456000000000001,-5.2544000000000004,-5.1664000000000003,-5.0815999999999999,-5,-4.9215999999999998,-4.8464,-4.7744,-4.7056000000000004,-4.6400000000000006,-4.5776000000000003,-4.5183999999999997,-4.4623999999999997,-4.4096000000000002,-4.3599999999999994,-4.3136000000000001,-4.2704000000000004,-4.2304000000000004,-4.1936,-4.1600000000000001,-4.1295999999999999,-4.1024000000000003,-4.0784000000000002,-4.0575999999999999,-4.04,-4.0255999999999998,-4.0144000000000002,-4.0064000000000002,-4.0015999999999998,-4,-4.0015999999999998,-4.0064000000000002,-4.0144000000000002,-4.0255999999999998,-4.04,-4.0575999999999999,-4.0784000000000002,-4.1024000000000003,-4.1295999999999999,-4.1600000000000001,-4.1936,-4.2304000000000004,-4.2704000000000004,-4.3136000000000001,-4.3600000000000003,-4.4096000000000002,-4.4624000000000006,-4.5184000000000006,-4.5776000000000003,-4.6400000000000006,-4.7055999999999996,-4.7744,-4.8464,-4.9215999999999998,-5,-5.0815999999999999,-5.1664000000000003,-5.2544000000000004,-5.3456000000000001,-5.4400000000000004,-5.5376000000000003,-5.6384000000000007,-5.7424000000000008,-5.8495999999999997,-5.96,-6.0735999999999999,-6.1904000000000003,-6.3103999999999996,-6.4336000000000002,-6.5600000000000005,-6.6896000000000004,-6.8224,-6.958400000000001,-7.0976000000000008,-7.2400000000000011,-7.3855999999999993,-7.5343999999999998,-7.6863999999999999,-7.8415999999999997,-8]],"type":"surface","frame":null}],"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- # Marginalization `$$f(x, y) = -x^2 - y^2$$` .pull-left[ <img src="12-multivariate-pdf_files/figure-html/conditional-pdf-1.png" width="432" style="display: block; margin: auto;" /> ] -- .pull-right[ <img src="12-multivariate-pdf_files/figure-html/conditional-pdf-examples-1.gif" style="display: block; margin: auto;" /> ] --- # Why does marginalization work? ### Discrete case Consider jointly distributed discrete random variables, `\(X\)` and `\(Y\)` with joint PMF `$$\Pr(X =x, Y = y) = p(x, y)$$` -- Suppose that the distribution allocates its mass at `\(x_{1}, x_{2}, \ldots, x_{M}\)` and `\(y_{1}, y_{2}, \ldots, y_{N}\)`. Define the conditional mass function `\(\Pr(X= x| Y= y)\)` as, `$$\begin{aligned} \Pr(X=x|Y=y) &\equiv p(x|y) \\ & = \frac{p(x,y)}{p(y)} \end{aligned}$$` -- `$$p(x,y) = p(x|y)p(y)$$` --- # Marginalization (discrete): So, we have: `$$p(x,y) = p(x|y)p(y)$$` -- Marginalizing **over** `\(y\)` to get `\(p(x)\)` is then, `$$p(x_{j}) = \sum_{i=1}^{N} p(x_{j} |y_{i})p(y_{i} )$$` --- # Why does marginalization work? | | `\(Y = 0\)` | `\(Y = 1\)` | | |-------|-------------|-------------|------------| | `\(X = 0\)` | `\(p(0,0)\)` | `\(p(0, 1)\)` | `\(p_{X}(0)\)` | | `\(X = 1\)` | `\(p(1,0)\)` | `\(p(1,1)\)` | `\(p_{X}(1)\)` | | | `\(p_{Y} (0)\)` | `\(p_{Y} (1)\)` | | --- # Why does marginalization work? | | `\(Y = 0\)` | `\(Y = 1\)` | | |-------|-------------|-------------|------------| | `\(X = 0\)` | `\(0.01\)` | `\(0.05\)` | `\(p_{X}(0)\)`? | | `\(X = 1\)` | `\(0.25\)` | `\(0.69\)` | `\(p_{X}(1)\)`? | | | `\(0.26\)` | `\(0.74\)` | | -- `$$p_{X}(0) = \Pr(0|y = 0) *\Pr(y= 0) + \Pr(0|y=1)*\Pr(y=1)$$` -- `$$= \frac{0.01}{0.26} * 0.26 + \frac{0.05}{0.74} * 0.74 \\ = 0.06$$` -- `$$\begin{aligned} p_{X}(1) & = \Pr(1|y = 0) \Pr(y= 0) + \Pr(1|y=1) \Pr(y=1) \\ & = \frac{0.25}{0.26} * 0.26 + \frac{0.69}{0.74} * 0.74 \\ & = 0.94 \end{aligned}$$` --- # Why does marginalization work? | | `\(Y = 0\)` | `\(Y = 1\)` | | |-------|-------------|-------------|------------| | `\(X = 0\)` | `\(0.01\)` | `\(0.05\)` | `\(0.06\)`| | `\(X = 1\)` | `\(0.25\)` | `\(0.69\)` | `\(0.94\)` | | | `\(0.26\)` | `\(0.74\)` | | --- # Why does marginalization work? ### Continuous case For **jointly distributed continuous** random variables `\(X\)` and `\(Y\)` define, `$$f_{X|Y}(x|y) = \frac{f(x,y)}{f_{Y}(y) }$$` -- `$$f_{X}(x) = \int_{-\infty }^{\infty} f_{X|Y}(x|y)f_{Y}(y) \, dy$$` -- * Think of `\(f_{X|Y}(x|y)\)` as the pdf for `\(X\)` at a value of `\(Y\)` * Average over those pdfs to get the final pdf for `\(X\)` * Weighted average --- # A simple(ish) example Suppose `\(X\)` and `\(Y\)` are jointly continuous and that $$ `\begin{aligned} f(x,y) & = x + y \text{ , if } x \in [0,1], y \in [0,1] \\ & = 0 \text{ , otherwise } \end{aligned}` $$ <img src="12-multivariate-pdf_files/figure-html/joint-pdf-plus-dup-1.png" width="864" style="display: block; margin: auto;" /> --- # A simple(-ish) example We want `\(f_{X}(x)\)`. We can find this one of two ways: by either taking the derivative of the original function with respect to y OR by using independence. Option 1: `\(\int_0^1f(x,y) dy = \int_0^1 (x+ y) dy = xy + \frac{y^2}{2} |_0^1 = x + 1/2\)` -- Option 2: we know that `\(f(x|y) = \frac{f(x,y)}{f_Y(y)}\)` -- Suppose you are given: `\(f_{Y}(y) = 1/2 + y\)` -- Then `$$f(x|y) = \frac{x + y}{1/2 + y}$$` `$$f(x) = \int_{0}^{1} f(x|y)f(y)\, dy = 1/2 + x$$` --- # A simple(-ish) example Here are all the possible values for f(x), based on what y might be: <img src="12-multivariate-pdf_files/figure-html/joint-pdf-plus-margin-1.png" width="864" style="display: block; margin: auto;" /> --- # A simple(-ish) example Here's our 'weighted average' for f(x) across all y: <img src="12-multivariate-pdf_files/figure-html/joint-pdf-plus-cond-1.png" width="864" style="display: block; margin: auto;" /> --- # More complex example Suppose `\(X\)` and `\(Y\)` are jointly distributed with pdf `$$f(x,y) = 2 \exp(-x) \exp(-2y), \forall \, x>0, y>0)$$` -- Note: equivalent to : `$$f(x,y) = 2 e^{(-x)} e^{(-2y)}, \forall \, x>0, y>0$$` --- # Verify this is a pdf (e version) `$$\int_{0}^{\infty} \int_{0}^{\infty} f(x, y) = 2\int_{0}^{\infty} \int_{0}^{\infty} e^{(-x)} e^{(-2y)} \, dx\, dy$$` -- `$$2 \int_{0}^{\infty}e^{(-2y)} \, dy \int_{0}^{\infty} e^{(-x)} \, dx$$` -- `$$= 2 (-\frac{1}{2} e^{(-2y)}|_{0}^{\infty} ) ( - e^{(-x)}|_{0}^{\infty} )$$` -- `$$= 2\left[ (-\frac{1}{2}(\lim_{y\rightarrow\infty} e^{(-2y)} - 1))(- (\lim_{x\rightarrow \infty} e^{(-x)} - 1) ) \right]$$` -- `$$= 2 \left[ -\frac{1}{2} (-1) * -1 (-1) \right] = 1$$` --- # Verify this is a pdf (exp version) `$$\int_{0}^{\infty} \int_{0}^{\infty} f(x, y) = 2\int_{0}^{\infty} \int_{0}^{\infty} \exp(-x) \exp(-2y) \, dx\, dy$$` -- `$$2\int_{0}^{\infty}\exp(-2y) \, dy \int_{0}^{\infty} \exp(-x) \, dx$$` -- `$$= 2 (-\frac{1}{2} \exp(-2y)|_{0}^{\infty} ) ( - \exp(-x)|_{0}^{\infty} )$$` -- `$$= 2\left[ (-\frac{1}{2}(\lim_{y\rightarrow\infty} \exp(-2y) - 1))(- (\lim_{x\rightarrow \infty} \exp(-x) - 1) ) \right]$$` -- `$$= 2 \left[ -\frac{1}{2} (-1) * -1 (-1) \right]= 1$$` --- # Calculate CDF `$$F(x,y) \equiv \Pr\{X \leq b, Y \leq a\} = 2 \int_{0}^{a} \int_{0}^{b} \exp(-x) \exp(-2y) \, dx\, dy$$` -- `$$= 2 (\int_{0}^{a} \exp(-2y) \, dy) (\int_{0}^{b} \exp(-x) \, dx)$$` -- $$ = 2 \left[-\frac{1}{2} (\exp(-2a) -1 )\right]\left[ - (\exp(-b) - 1) \right]$$ -- $$ = \left[1 - \exp(-2a) \right] \left[ 1- \exp(-b) \right]$$ -- NOW WHAT? -- Plug in values for a and b, respectively. --- # Calculate `\(f_{X}(x)\)` and `\(f_{Y}(y)\)` `$$\begin{aligned}f_{X}(x) & = \int_{0}^{\infty} 2\exp(-x) \exp(-2y) \, dy \\& = 2 \exp(-x) \int_{0}^{\infty} \exp(-2y) \, dy \\& = 2 \exp(-x) \left[ -\frac{1}{2}(0 - 1) \right] \\& = \exp(-x)\end{aligned}$$` -- `$$\begin{aligned}f_{Y}(y) & = \int_{0}^{\infty} 2 \exp(-x) \exp(-2y) \, dx \\& = 2 \exp(-2y) \int_{0}^{\infty} \exp(-x) \, dx \\& = 2 \exp(-2y) \left[-(0 -1) \right] \\& = 2 \exp(-2y)\end{aligned}$$` --- # Conditional distribution Two random variables `\(X\)` and `\(Y\)` are independent if for any two sets of real numbers `\(A\)` and `\(B\)`, `$$\Pr\{ X \in A , Y \in B \} = \Pr\{X \in A\} \Pr\{Y \in B\}$$` -- `$$f(x,y) = f_{X}(x) f_{Y}(y)$$` -- If `\(X\)` and `\(Y\)` are not independent, we will say they are **dependent**. -- If `\(X\)` and `\(Y\)` are independent, then `$$\begin{aligned}f_{X|Y} (x|y) & = \frac{f(x,y)}{f_{Y}(y)} \\& = \frac{f_{X}(x)f_{Y}(y)}{f_{Y}(y) } \\& = f_{X}(x) \end{aligned}$$` --- # A (simple) example of dependence Suppose `\(X\)` and `\(Y\)` are jointly continuous and that `$$\begin{eqnarray}f(x,y) & = & x + y \text{ , if } x \in [0,1], y \in [0,1] \\& = & 0 \text{ , otherwise } \end{eqnarray}$$` -- Are they dependent? --- # A (simple) example of dependence `$$f_{X}(x) = \int_{0}^{1} \left(x + y \right) \, dy$$` -- `$$xy + \frac{y^2}{2} |^{1}_{0} = x + \frac{1}{2}$$` -- `$$f_{Y}(y) = \int_{0}^{1} \left(x + y \right) \, dx = \frac{x^2}{2} + xy |^{1}_{0} = \frac{1}{2} + y$$` -- `$$\begin{eqnarray}f_{X}(x) f_{Y}(y) & = & (\frac{1}{2} + x) (\frac{1}{2} + y) \\& = & \frac{1}{4} + \frac{x + y}{2} + xy \neq (x+y)\end{eqnarray}$$` --- # Dependence: deep thoughts `$$\begin{eqnarray}f_{X}(x) f_{Y}(y) & = & (\frac{1}{2} + x) (\frac{1}{2} + y) \\& = & \frac{1}{4} + \frac{x + y}{2} + xy \neq (x+y)\end{eqnarray}$$` We can think about this as getting additional INFORMATION from y when we know x and vice versa. --- class: middle # But what to expect? --- # Expectation For jointly continuous random variables `\(X\)` and `\(Y\)`, -- `$$\E[X] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x f(x,y) \, dx\, dy$$` -- `$$E[Y] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} y f(x,y) \, dx\, dy$$` -- `$$E[XY] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x y f(x,y) \, dx\, dy$$` -- Suppose `\(g:\Re^{2} \rightarrow \Re\)`. Then `$$\E[g(X, Y)] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} g(x, y) f(x,y) \, dx\, dy$$` --- # Expectation ex with g(x) `$$\E[g(X, Y)] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} g(x, y) f(x,y) \, dx\, dy$$` Suppose we have the following functions: `\(f(x,y) = xy\)` where `\(0 \leq x \leq 1\)` and `\(0 \leq y \leq 2\)`. 1. Is this a valid pdf? why or why not? 2. Suppose you earn revenue equal to `\(x^3+2\)`. What is your expected utility? --- # Expectation ex with g(x): pdf Suppose we have the following functions: `\(f(x,y) = xy\)` where `\(0 \leq x \leq 1\)` and `\(0 \leq y \leq 2\)`. `$$\int_0^2\int_0^1 xy\, \,dx\,dy$$` -- `$$\int_0^2\frac{x^2y}{2}|_0^1 \, dy= \int_0^2 \frac{y}{2} \, dy$$` `$$=\frac{y^2}{4}|_0^2 = 1$$` -- So, yes it appears to satisfy our requirements! --- # Expectation ex with g(x): expectation > Suppose you earn revenue equal to `\(x^3+2\)`. What is your expected utility? Well, our function is: `\(\int_0^2\int_0^1 xy\, \,dx\,dy\)`, so our expected utility will be: `$$\int_0^2\int_0^1 (x^3+2)*xy\, \,dx\,dy$$` We know we can do this because: `$$\E[g(X, Y)] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} g(x, y) f(x,y) \, dx\, dy$$` --- # Expected value: Math party `$$\int_0^2\int_0^1 (x^3+2)*xy\, \,dx\,dy = \int_0^2\int_0^1 (x^4+2x)y\, \,dx\,dy$$` -- `$$=\int_0^2 y \,dy* \int_0^1 (x^4+2x) \,dx= \frac{y^2}{2}|_0^2*(\frac{x^5}{5}+x^2 )|_0^1$$` -- `$$=2*(1^5/5+1)=2.4$$` -- NOW WHAT? -- This is our expected value! --- class: center, middle, inverse # Examples! --- # Example land: Let's look at what we have here: `\(\int_{1}^{2} \int_{0}^{0.5} (x^2 - \frac{8y}{3}+\frac{1}{3}) \text{ } dy \text{ }dx\)` <img src="12-multivariate-pdf_files/figure-html/multi-cdf-int-1.png" width="864" style="display: block; margin: auto;" /> --- # Example land: Let's look at what we have here: `\(\int_{1}^{2} \int_{0}^{0.5} (x^2 - \frac{8y}{3}+\frac{1}{3}) \text{ } dy \text{ }dx\)` So we will effectively add up all the chunks of our function in one direction, then we can add up along the other. I have this set up for doing y first. I leave doing it in the x direction as an exercise. -- `$$\begin{align}F(x,y) &= \int_{1}^{2} \int_{0}^{0.5} (x^2 - \frac{8y}{3}+\frac{1}{3}) \text{ } dy \text{ }dx \\ &=\int_{1}^{2}(x^2y - \frac{4y^2}{3}+\frac{y}{3}) \text{ } |_0^{0.5} \text{ }dx \\ &= \int_{1}^{2}(0.5x^2 - \frac{1}{3}+\frac{1}{6}) \text{ } \text{ }dx \\ &= \int_{1}^{2}(0.5x^2 - \frac{1}{6}) \text{ } \text{ }dx \\ &= (\frac{x^3}{6} - \frac{x}{6}) \text{ }|_1^2 = (\frac{8}{6}- \frac{2}{6})-(\frac{1}{6}-\frac{1}{6}) \text{ } \\ &= 1 \end{align}$$` -- PHEW! It's a pdf (also need to verify we don't have negative values for f(x)) --- # Example land: Let's look at a slice of it: `\(\int_{1}^{1.5} \int_{0}^{0.5} (x^2 - \frac{8y}{3}+\frac{1}{3}) \text{ } dy \text{ }dx\)` `$$\begin{align}F(x,y) &= \int_{1}^{1.5} \int_{0}^{0.5} (x^2 - \frac{8y}{3}+\frac{1}{3}) \text{ } dy \text{ }dx \\ &=\int_{1}^{1.5}(x^2y - \frac{4y^2}{3}+\frac{y}{3}) \text{ } |_0^0.5 \text{ }dx \\ &= \int_{1}^{1.5}(0.5x^2 - \frac{1}{3}+\frac{1}{6}) \text{ } \text{ }dx \\ &= \int_{1}^{1.5}(0.5x^2 - \frac{1}{6}) \text{ } \text{ }dx \\ &= (\frac{x^3}{6} - \frac{x}{6}) \text{ }|_1^{1.5} \\ &= (\frac{1.5^3}{6}-\frac{3}{12})-(\frac{1}{6}- \frac{1}{6}) \text{ } \\ &= 0.3125 \end{align}$$` -- So....what does this tell us?? --- class: middle # And now, something quite a bit different* *(but also not!)* --- # Covariance and correlation We are interested in how our variables vary with one another. For jointly continuous random variables `\(X\)` and `\(Y\)` we define the covariance of `\(X\)` and `\(Y\)` as, `$$Cov(X,Y) = E[(X-E[X])(Y- E[Y])]$$` -- `$$=E\left[ XY - E[X] Y - E[Y] X + E[X]E[Y] \right]$$` -- `$$=E[XY] - 2E[X]E[Y] + E[E[X]E[Y]]$$` -- `$$=E[XY] - E[X]E[Y]$$` -- Define the correlation of `\(X\)` and `\(Y\)` as, `$$\Cor(X,Y) = \frac{\Cov(X,Y) }{\sqrt{\Var(X) \Var(Y) } }$$` --- # Variance is covariance with itself `$$\begin{eqnarray}\Cov(X,X) & = & E[X X] - E[X]E[X] \\& = & E[X^2] - E[X]^2\end{eqnarray}$$` --- # Correlation measures linear relationship Like covariance, bigger is more, but now we're standardizing relative to variance. Suppose `\(X = Y\)`: `$$\begin{eqnarray}\Cor(X,Y) & = & \frac{\Cov(X,Y)}{\sqrt{\Var(X)\Var(Y)} } \\& = & \frac{\Var(X)}{\Var(X)} \\& = & 1\end{eqnarray}$$` -- Suppose `\(X = -Y\)`: `$$\begin{eqnarray}\Cor(X,Y) & = & \frac{\Cov(X,Y)}{\sqrt{\Var(X)\Var(Y)} } \\& = & \frac{- \Var(X)}{\Var(X)} \\& = & -1 \end{eqnarray}$$` --- # Correlation is between -1 and 1 `$$|\Cor(X,Y)| \leq 1$$` --- # Sums of random variables Suppose we have a sequence of random variables `\(X_{i}\)` , `\(i = 1, 2, \ldots, N\)` Suppose that they have joint pdf `$$f(\boldsymbol{x}) = f(x_{1}, x_{2}, \ldots, x_{n})$$` -- * `\(\E[\sum_{i=1}^{N}X_{i} ] = \sum_{i=1}^{N} \E[X_{i}]\)` -- * `\(\Var(\sum_{i=1}^{N} X_{i} ) = \sum_{i=1}^{N} \Var(X_{i} ) + 2 \sum_{i<j} \Cov(X_{i}, X_{j})\)` --- # Expected value of sums of RVs Suppose we have a sequence of random variables `\(X_{i}\)` , `\(i = 1, 2, \ldots, N\)` Suppose that they have joint pdf, `$$f(\boldsymbol{x}) = f(x_{1}, x_{2}, \ldots, x_{n})$$` Then `$$\E[\sum_{i=1}^{N} X_{i} ] = \sum_{i=1}^{N} \E[X_{i} ]$$` -- $$ `\begin{eqnarray} \E[\sum_{i=1}^{N} X_{i} ] & = & \E[X_{1} + X_{2} + \ldots + X_{N}] \\ & = & \int_{-\infty}^{\infty} \cdot \cdot \cdot \iint_{-\infty}^{\infty} (x_{1} + x_{2} + \ldots + x_{N}) f(x_{1}, x_{2}, \ldots, x_{N}) \, dx_{1}\, dx_{2}\ldots \, dx_{N} \\ & = & \int_{-\infty}^{\infty}x_{1} f_{X_{1}}(x_{1}) \, dx_{1} + \int_{-\infty}^{\infty}x_{2} f_{X_{2}}(x_{2}) \, dx_{2} + \ldots + \int_{-\infty}^{\infty}x_{N} f_{X_{N}}(x_{N}) \, dx_{N} \\ & = & \E[X_{1} ] + \E[X_{2}] + \ldots + \E[X_{N}] \end{eqnarray}` $$ --- # Variance of sums of RVs Suppose `\(X_{i}\)` is a sequence of random variables. Then $$ `\begin{eqnarray} \Var(\sum_{i=1}^{N} X_{i} ) & = & \sum_{i=1}^{N} \Var(X_{i} ) + 2 \sum_{i<j} \Cov(X_{i}, X_{j} ) \end{eqnarray}` $$ -- Consider two random variables, `\(X_{1}\)` and `\(X_{2}\)`. Then, $$ `\begin{eqnarray} \Var(X_{1} + X_{2} ) & = & \E[(X_{1} + X_{2})^2] - \left(\E[X_{1}] + \E[X_{2}] \right)^2 \\ & = & \E[X_{1}^2] + 2 \E[X_{1}X_{2}] + \E[X_{2}^2] \\ && - (\E[X_{1}])^2 - 2 \E[X_{1}] \E[X_{2}] - 2 \E[X_{2}]^2 \\ & = & \underbrace{\E[X_{1}^2] - (\E[X_{1}])^2}_{\Var(X_{1}) } + \underbrace{\E[X_{2}^2] - \E[X_{2}]^{2}}_{\Var(X_{2})} \\ && + 2 \underbrace{(\E[X_{1} X_{2} ] - \E[X_{1}] \E[X_{2} ] )}_{\Cov(X_{1}, X_{2} ) } \\ & = & \Var(X_{1} ) + \Var(X_{2} ) + 2 \Cov(X_{1}, X_{2}) \end{eqnarray}` $$ --- class: middle # Oh good, matrices! -- ### AKA: What happens when you bring multiple variables to the party? -- These are for information -- they haven't featured into my work, but for some people they have been relevant --- # Multivariate normal distribution Suppose `\(\boldsymbol{X} = (X_{1}, X_{2}, \ldots, X_{N})\)` is a vector of random variables. If `\(\boldsymbol{X}\)` has pdf `$$f(\boldsymbol{x}) = (2 \pi)^{-N/2} \text{det}\left(\boldsymbol{\Sigma}\right)^{-1/2} \exp\left(-\frac{1}{2}(\boldsymbol{x} - \boldsymbol{\mu})^{'}\boldsymbol{\Sigma}^{-1} (\boldsymbol{x} - \boldsymbol{\mu} ) \right)$$` where `\(det(\mathbf{\Sigma})\)` is the determinant of the covariance matrix, known as generalized variance -- `\(\boldsymbol{X}\)` is a **Multivariate Normal** Distribution, `$$\boldsymbol{X} \sim \text{Multivariate Normal} (\boldsymbol{\mu}, \boldsymbol{\Sigma})$$` -- * Regularly used for likelihood, Bayesian, and other parametric inferences --- # Bivariate example Consider the (bivariate) **special case** where `\(\boldsymbol{\mu} = (0, 0)\)` and `$$\boldsymbol{\Sigma} = \begin{pmatrix} 1 & 0 \\0 & 1 \\\end{pmatrix}$$` -- `$$\begin{eqnarray}f(x_{1}, x_{2} ) & = & (2\pi)^{-2/2} 1^{-1/2} \exp\left(-\frac{1}{2}\left( (\boldsymbol{x} - \boldsymbol{0} ) ^{'} \begin{pmatrix} 1 & 0 \\0 & 1 \\\end{pmatrix}(\boldsymbol{x} - \boldsymbol{0} ) \right) \right) \\& = & \frac{1}{2\pi} \exp\left(-\frac{1}{2} (x_{1}^{2} + x_{2} ^ 2 ) \right) \\& = & \frac{1}{\sqrt{2\pi}} \exp\left(-\frac{x_{1}^{2}}{2} \right) \frac{1}{\sqrt{2\pi}} \exp\left(-\frac{x_{2}^{2}}{2} \right)\end{eqnarray}$$` -- `\(\leadsto\)` product of univariate standard normally distributed random variables --- # Standard multivariate normal Suppose `\(\boldsymbol{Z} = (Z_{1}, Z_{2}, \ldots, Z_{N})\)` is `$$\boldsymbol{Z} \sim \text{Multivariate Normal}(\boldsymbol{0}, \boldsymbol{I}_{N} )$$` Then we will call `\(\boldsymbol{Z}\)` the standard multivariate normal --- # Properties of the multivariate normal Suppose `\(\boldsymbol{X} = (X_{1}, X_{2}, \ldots, X_{N} )\)` $$ `\begin{eqnarray} \E[\boldsymbol{X} ] & = & \boldsymbol{\mu} \\ \Cov(\boldsymbol{X} ) & = & \boldsymbol{\Sigma} \end{eqnarray}` $$ So that, $$ `\begin{eqnarray} \boldsymbol{\Sigma} & = & \begin{pmatrix} \Var(X_{1}) & \Cov(X_{1}, X_{2}) & \ldots & \Cov(X_{1}, X_{N}) \\ \Cov(X_{2}, X_{1}) & \Var(X_{2}) & \ldots & \Cov(X_{2}, X_{N} ) \\ \vdots & \vdots & \ddots & \vdots \\ \Cov(X_{N}, X_{1} ) & \Cov(X_{N}, X_{2} ) & \ldots & \Var(X_{N} ) \\ \end{pmatrix} \end{eqnarray}` $$ --- # Independence and multivariate normal Suppose `\(X\)` and `\(Y\)` are independent. Then `$$\Cov(X, Y) = 0$$` -- `$$\Cov(X, Y) = \E[XY] - \E[X]\E[Y]$$` -- $$ `\begin{eqnarray} \E[XY] & = & \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x y f(x,y)\, dx\, dy \\ & =& \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x y f_{X}(x) f_{Y}(y)\, dx\, dy \\ & = & \int_{-\infty}^{\infty} x f_{X}(x) \, dx \int_{-\infty}^{\infty} y f_{Y}(y) \, dy \\ & = & \E[X] \E[Y] \end{eqnarray}` $$ -- Then `\(\Cov(X,Y) = 0\)`. --- # Independence and multivariate normal **Zero covariance does not generally imply independence!** -- * Suppose `\(X \in \{-1, 1\}\)` with `\(\Pr(X = 1) = \Pr(X = -1) = 1/2\)` * Suppose `\(Y \in \{-1, 0,1\}\)` with `\(Y = 0\)` if `\(X = -1\)` and `\(\Pr(Y = 1) = \Pr(Y= -1)\)` if `\(X = 1\)` -- $$ `\begin{eqnarray} \E[XY] & = & \sum_{i \in \{-1, 1\} } \sum_{j \in \{-1, 0, 1\}} i j \Pr(X = i, Y = j) \\ & = & -1 * 0 * \Pr(X = -1, Y = 0) + 1 * 1 * \Pr(X = 1, Y = 1) \\ && - 1 * 1 * \Pr(X = 1, Y = -1) \\ &= & 0 + \Pr(X = 1, Y = 1) - \Pr(X = 1, Y = -1 ) \\ & = & 0.25 - 0.25 = 0 \\ \E[X] & = & 0 \\ \E[Y] & = & 0 \end{eqnarray}` $$ --- # Independence, matrices, covariance: why might we care? * we are looking for information * duplication/dependence in variables can be problematic for predicting relationships (recall: determinants and eigenvalues) --- # Recap! * Joint pdf: same concept, integrate over variables * Condition pdfs on other random variables and marginal probability * Covariance and correlation: linear relationship * Matrices: can keep going with many dimensions!