class3

55
CSE 592: Data Mining Instructor: Pedro Domingos

description

dm

Transcript of class3

  • CSE 592: Data MiningInstructor: Pedro Domingos

  • Program for TodayRule inductionPropositionalFirst-orderFirst project

  • Rule Induction

  • First Project:Clickstream Mining

  • OverviewThe Gazelle siteData collectionData pre-processingKDD CupHints and findings

  • The Gazelle SiteGazelle.com was a legwear and legcare web retailer.Soft-launch: Jan 30, 2000Hard-launch: Feb 29, 2000 with an Ally McBeal TV ad on 28th and strong $10 off promotionTraining set: 2 monthsTest sets: one month (split into two test sets)

  • Data CollectionSite was running Blue Martinis Customer Interaction System version 2.0Data collected includes:ClickstreamsSession: date/time, cookie, browser, visit count, referrerPage views: URL, processing time, product, assortment (assortment is a collection of products, such as back to school)Order informationOrder header: customer, date/time, discount, tax, shipping.Order line: quantity, price, assortmentRegistration form: questionnaire responses

  • Data Pre-ProcessingAcxiom enhancements: age, gender, marital status, vehicle type, own/rent home, etc.Keynote records (about 250,000) removed. They hit the home page 3 times a minute, 24 hours.Personal information removed, including: Names, addresses, login, credit card, phones, host name/IP, verification question/answer. Cookie, e-mail obfuscated.Test users removed based on multiple criteria (e.g., credit card) not available to participantsOriginal data and aggregated data (to session level) were provided

  • KDD Cup QuestionsWill visitor leave after this page?Which brands will visitor view?Who are the heavy spenders?Insights on Question 1Insights on Question 2

  • KDD Cup Statistics170 requests for data31 submissions200 person/hours per submission (max 900)Teams of 1-13 people (typically 2-3)

  • Decision trees most widely tried and by far the most commonly submittedNote: statistics from final submitters only

    Data Sheet

    QuestionsArchitectureOSSystemData LoadingData ProcessingTriedData SourcePeopleTimeQuestionsQ1Q2Q3Q4Q5

    EntryOrg12345Unix WorkstationDesktop PCUnixLinuxWin95/98WinNTWin2kRAM (M)DISK (G)CPUPrice ($)TypeNameBuilt inProprietaryOtherUnknownProprietaryBuilt inOtherUnix ToolsSQLUnknownDecision TreesNeural NetNave BayesBayesion Belief NetNearest NeighbourClusteringSequence AnalysisAssociation RulesDecision RulesDecision TableMarkovLogistic RegressionLinear RegressionSVMGenetic ProgrammingBaggingBoostingExploratoryDatabaseFlatTechNon-TechTotalLoadingTransformingRunningOtherTotalAlgorithmTypeDecision TreeNeural NetworkNearest NeighbourNave BayesDecision RulesSequence AnalysisAssociation RulesLogistic RegressionLinear RegressionSVMGenetic ProgrammingBoostingReasonAggregated or UnaggregatedSampledAttributes builtMissing Value HandlingMultiple ModelsTrain TimeTest Set TimeSamplingAlgorithmTrain TimeTest TimeSamplingAlgorithmTrain TimeTest TimeSamplingAlgorithmTrain TimeSamplingAlgorithmTrain TimeSamplingAlgorithmTrain Time

    11University of Minnesota1111181.949507Decision Tree114096101ResearchC4.51AWK111122204080140C4.5Decision Tree1UnaggregatedNoSomeNone11

    12Angoss11111281.46348Decision Tree1119211.217500CommercialKnowledgeSTUDIOSQLServer1VB + SQLServer11111KnowledgeSTUDIO13385012020198KnowledgeSEEKERDecision Tree1Better than others triedAggregatedNoBy hand3

    18Seoul National University111844.754962Decision Tree, NN111282012000CommercialSASSAS + Excel1SAS1111554012040200Decision Tree, NN11Better than others triedAggregatedYesBuilt in152

    19LLSoft1111975.671662Decision Forest11256121CommercialKernel Miner111111221614120150Kernel MinerDecision Forest1BothSomeYes300020No1080Yes1260

    21University of Helsinki112140.502228Nave Bayes1112821Proprietary1Proprietary111115403075Nave Bayes1Past performanceAggregatedNoSomeSeparate ValueYes100

    26IDAC01Nearest Neighbour116441ProprietaryProprietaryProprietary1Proprietary112248161640ProprietaryNearest Neighbour1Past performanceAggregatedAcxiom onlyNoneMean for NULL540

    27Rudjer Boskovic Institute01Rules1111641ResearchILLMProprietary11111110305030120ILLMRules1Algorithm TestingBothNoNoneBuilt in10

    36Imperial College113663.831511Sequence Analysis + Decision Tree + Nave Bayes1111ProprietaryKensington + ProprietaryNone1Python + Perl111111Kensington15162020012080420ProprietarySequence Analysis + Decision Tree + Nave Bayes111AvailabilityBothNoSomeDeleted attributes

    37,53Salford1113780.869448Decision Tree1111768500215000CommercialCARTDBMSCopy1SAS111CART16632360250300942CARTDecision Tree1RobustnessUnaggregatedYesManyBuilt in15030

    50Accrue1115083.488592111CommercialDecision SeriesOracle1DecisionAccess + Oracle + Perl11111111111221004022074434Decision Series111BothYesSomeBuilt inDecision Tree41Boosted Nave Bayes + Decision Tree151YesSQL code10

    52WizSoft015382.422033Association11128113995CommercialWizWhyWizWhy1WizWhy11441012ProprietaryAssociation1UnaggregatedNoNoneBuilt in60

    54Panapo15479.384366Nearest Neighbour111128310Public DomainMineThis111133120113Nearest Neighbour1SimpleAggregatedYes1200

    55Russians1115581.530984Decision Tree11258101ResearchPergamentProprietary1Foxbase for DOS11133516322477PergamentDecision Tree1RobustnessBothSomeCount as all valuesNo303No303No1

    64Humboldt University16435.601458Sequence Analysis11125621ResearchWUMWUM1Perl11115510644024138WUMSequence Analysis1Algorithm TestingUnaggregatedYesNoneNone8025

    66SAS111116683.3535841118192134180000CommercialSASSAS1SAS111111111SAS111010484030038811BothSomeBuilt inYesYesSequence Analysis21YesDecision Tree41NoDecision Tree2YesDecision Tree2

    71Fujistu Labs117186.296746Nearest Neighbour111536504CommercialSymfoWARE Mining Server1AWK + Perl11122202060100MBRNearest Neighbour1Past performanceBothNoSomeBuilt inNo4No1

    74NUS17488.092345SVM11128201Proprietary111133108010025215SVM1FamiliarityAggregatedYesNone60000120

    76FEG111117685.0951811130601CommercialSAS11111SAS1131351013014511BothSomeNoneYesDecision Tree3015YesDecision Tree12060NoDecision Tree60NoDecision Tree30NoDecision Tree + Association Rules120

    77BroadBase17780.801944Decision Rules11512181200000CommercialBroadBase Foundation11111133109080180C5.0Decision Rules1IntrepretabilityUnaggregatedYesSome3030

    85SGI11118567.584717Decision Tree11111819210016CommercialSGI MineSet11111111554163248100Decision Tree1IntrepretabilityBothNoSomeBuilt inYesNo15110155

    89Quadstone11118986.26974511204875480000CommercialQuadstone SystemQuadstone System1Quadstone System1111155147020070354111FastBothNoManyYesNoLogistic Regression11NoLogistic Regression11NoLogistic Regression + Decision Tree1

    91Franklin Mint119186.53976Genetic Programming112565423000CommercialSASSAS1SAS1111SAS111245050124Genetic Programming1Algorithm TestingAggregatedYesManySeparate Value720019001

    103National Taiwan University110353.503443SVM117681Public DomainBSVM11113313020070301BSVMSVM1Algorithm TestingAggregatedYesNoneSeparate Value1100225

    106eSteam111110686.310247Boosted Decision Trees11650501Proprietary1Perl1111133120100200321Boosted Decision Trees11Provides probablity estimatesBothYesSomeBuilt inYes

    111Potchefstroom University111181.665992Hybrid Decision Tree Neural Network11128101100000CommercialSASSAS1SAS11111188244080Hybrid Decision Tree Neural Network11FamiliarityAggregatedYesManySeparate ValueYes11

    114Austrian Research Institute for AI0111128281Public DomainWEKAWEKA1VI + AWK + SQLServer1111111111111124124884ManyInsightAggregatedYesSomeBuilt inYes15

    115Tel-Aviv University01Decision Tree1CommercialS-Plus11133102010125165Decision Tree1IntrepretabilityAggregatedNoSomeNo

    125Amdocs111112585.905225Decision Tree, Decision Rules1110242.52ProprietaryCMSSAS1SAS11111661535150200400C4.5Decision Tree, Decision Rules111AvailabilityAggregatedManyBuilt inNoYesDecision Tree + Association Rules60060NoDecision Tree + Decision Rules300YesDecision Tree + Association Rules180YesDecision Tree + Decision Rules180

    128JCB112882.921561Boosted Decision Trees11128101CommercialSAS10322355Boosted Decision Trees11AggregatedNoNoneYes240010

    170,171SAS117086.121237Decision Tree111181922564180000CommercialSASSAS1SAS1111122860100168Decision Tree1RobustnessUnaggregatedYesSomeSeparate Value105

    QuestionsArchitectureOSData LoadingData ProcessingTechniques TriedData SourceAlgorithms in submission

    Entries12345Unix WorkstationDesktop PCUnixLinuxWin95/98WinNTWin2kRAM (M)DISK (G)CPUBuilt inProprietaryOtherUnknownProprietaryBuilt inOtherUnix ToolsSQLUnknownDecision TreesNeural NetNave BayesBayesion Belief NetNearest NeighbourClusteringSequence AnalysisAssociation RulesDecision RulesDecision TableMarkovLogistic RegressionLinear RegressionSVMGenetic ProgrammingBaggingBoostingDatabaseFlat FilesPeopleData LoadingData TransformationsLearning AlgorithmsOtherTotalDecision TreeNeural NetworkNearest NeighbourNave BayesDecision RulesSequence AnalysisAssociation RulesLogistic RegressionLinear RegressionSVMGenetic ProgrammingBoostingAggregated1324

    TOTALS3025131610410271165132Commercial17107582114837186415335511622125112310817.366666666752.466666666793.241379310388.6666666667204.31823333311213Unaggregated617

    Research4Load TotalTrans TotalRun TotalOther TotalTotalBoth11

    Proprietary65211574270413306129

    Public Domain3TriedSubmitted

    Decision Trees1818

    Nearest Neighbor53

    Association Rules53

    q1 scoreq2 scoreq3 scoreq4 scoreq5 scoreentryTotal timeall12345Decision Rules53

    74.929784608457311140Decision TreeBoosting53

    74.718145606821244412198Decision TreeNave Bayes43

    63.2145264718200Decision Tree, NNSequence Analysis33

    72.498912967919150Decision ForestNeural Network62

    62.6745522175Nave BayesSVM22

    1272640Nearest NeighbourLogistic Regression61

    10127120RulesLinear Regression21

    65.576176536420Sequence Analysis + Decision Tree + Nave BayesGenetic Programming11

    75.80204960181 6006924037,53942Decision TreeClustering3

    75.598323604055550434Decision TreeBoosted Nave Bayes + Decision TreeSQL codeBagging2

    40522AssociationBayesion Belief Net1

    73.0309745413Nearest NeighbourDecision Table1

    75.196804608765577Decision TreeMarkov Models1

    59.56525264138Sequence Analysis

    76.38751560764106876266388Sequence AnalysisDecision TreeDecision TreeDecision Tree

    76.8325495976771100Nearest Neighbour

    76.96309274215SVM

    76.76925560124133725376145Decision TreeDecision TreeDecision TreeDecision TreeDecision Tree + Association Rules

    75.67150677180Decision Rules

    72.70461660673934485100Decision Tree

    76.167966602221387089354Logistic RegressionLogistic RegressionLogistic Regression + Decision Tree

    76.6327786019491124Genetic Programming

    35.992326103301SVM

    76.76727760829119108106321Boosted Decision Trees

    74.09509911180Hybrid Decision Tree Neural Network

    6311484

    191115165Decision Tree

    77.06198818083102125400Decision Tree, Decision RulesDecision Tree + Association RulesDecision Tree + Decision RulesDecision Tree + Association RulesDecision Tree + Decision Rules

    75.96423912855Boosted Decision Trees

    76.668381170,171168Decision Tree

    Interesting Numbers

    Competitors who submitted30

    Total person-hours spent6129

    Average person-hours spent204.3

    Average computer RAM1425.1

    Longest algorithm training time1000 hrs

    Top four entries in question 1 used various algorithms (two decision tree based, svm and nearest neighbour)

    Top four entries in question 2 all used algorithms based on decision trees

    Winners and honourable mentions for questions 3, 4 and 5 all used algorithms based on decision trees

    Graphs ->

    Entries

    25

    13

    16

    10

    4

    Question

    Entries

    Entries by Question

    Hardware

    10

    27

    Hardware

    Entries

    Hardware Used

    OS

    11

    6

    5

    13

    2

    Operating System

    Entries

    Operating Systems Used

    Software Type

    17

    4

    6

    3

    Software Type Used

    Data Processing

    2

    11

    4

    8

    3

    7

    Data Processing Tools Used

    Data Source

    11

    23

    Data Source

    Data Source Used

    Algorithms

    1818

    53

    53

    53

    53

    43

    33

    62

    22

    61

    21

    11

    3Clustering

    2Bagging

    1Bayesion Belief Net

    1Decision Table

    1Markov Models

    Tried

    Submitted

    Algorithm

    Entries

    Algorithms Tried vs Submitted

    Aggregation

    24

    17

    Aggregated vs Unaggregated Data

    Average Time Spent Relative

    17.3666666667

    52.4666666667

    93.2413793103

    88.6666666667

    Average Time Spent Relative

    Average Time Spent

    17.3666666667

    52.4666666667

    93.2413793103

    88.6666666667

    Hours

    Average Time Spent

  • Evaluation CriteriaAccuracy (or score) was measured for the two questions with test setsInsight questions judged with help of retail experts from Gazelle and Blue MartiniCreated a list of insights from all participantsEach insight was given a weightEach participant was scored on all insightsAdditional factors: presentation quality, correctness

  • Question: Who Will LeaveGiven set of page views, will visitor view another page on site or leave? Hard prediction task because most sessions are of length 1. Gains chart for sessions longer than 5 is excellent.

    Q1 - long sessions

    0.00073909830.00073909830.00013500740.0007390983

    0.00073909830.00147819660.00027001490.0014781966

    0.00147819660.00221729490.00040502230.0022172949

    0.00147819660.00295639320.00054002970.0029563932

    0.00221729490.00369549150.00067503710.0036954915

    0.00221729490.00369549150.00081004460.0044345898

    0.00221729490.00443458980.0009450520.0051736881

    0.00295639320.00443458980.00108005940.0059127864

    0.00295639320.00517368810.00121506680.0066518847

    0.00369549150.00591278640.00135007430.007390983

    0.00369549150.00665188470.00148508170.0081300813

    0.00443458980.0073909830.00162008910.0088691796

    0.00443458980.00813008130.00175509650.0096082779

    0.00443458980.00886917960.0018901040.0103473762

    0.00443458980.00960827790.00202511140.0110864745

    0.00517368810.00960827790.00216011880.0118255728

    0.00591278640.01034737620.00229512620.0125646711

    0.00665188470.01108647450.00243013370.0133037694

    0.00665188470.01182557280.00256514110.0140428677

    0.0073909830.01256467110.00270014850.014781966

    0.00813008130.01330376940.00283515590.0155210643

    0.00886917960.01404286770.00297016340.0162601626

    0.00960827790.0147819660.00310517080.0169992609

    0.01034737620.01552106430.00324017820.0177383592

    0.01108647450.01626016260.00337518560.0184774575

    0.01108647450.01699926090.00351019310.0192165558

    0.01182557280.01773835920.00364520050.0199556541

    0.01256467110.01847745750.00378020790.0206947524

    0.01330376940.01921655580.00391521530.0214338507

    0.01330376940.01995565410.00405022280.022172949

    0.01404286770.02069475240.00418523020.0229120473

    0.01404286770.02069475240.00432023760.0236511456

    0.0147819660.02143385070.0044552450.0243902439

    0.01552106430.0221729490.00459025250.0251293422

    0.01626016260.0221729490.00472525990.0258684405

    0.01699926090.02291204730.00486026730.0266075388

    0.01773835920.02365114560.00499527470.0273466371

    0.01847745750.02439024390.00513028220.0280857354

    0.01921655580.02512934220.00526528960.0288248337

    0.01921655580.02512934220.0054002970.029563932

    0.01921655580.02586844050.00553530440.0303030303

    0.01995565410.02586844050.00567031190.0310421286

    0.01995565410.02660753880.00580531930.0317812269

    0.02069475240.02660753880.00594032670.0325203252

    0.02069475240.02734663710.00607533410.0332594235

    0.02143385070.02808573540.00621034160.0339985218

    0.0221729490.02882483370.0063453490.0347376201

    0.02291204730.0295639320.00648035640.0354767184

    0.02365114560.03030303030.00661536380.0362158167

    0.02439024390.03104212860.00675037130.036954915

    0.02439024390.03178122690.00688537870.0376940133

    0.02512934220.03252032520.00702038610.0384331116

    0.02512934220.03325942350.00715539350.0391722099

    0.02586844050.03399852180.0072904010.0399113082

    0.02660753880.03473762010.00742540840.0406504065

    0.02660753880.03547671840.00756041580.0413895048

    0.02660753880.03621581670.00769542320.0421286031

    0.02734663710.0369549150.00783043070.0428677014

    0.02734663710.03769401330.00796543810.0436067997

    0.02808573540.03769401330.00810044550.044345898

    0.02882483370.03843311160.00823545290.0450849963

    0.0295639320.03917220990.00837046040.0458240946

    0.03030303030.03991130820.00850546780.0465631929

    0.03030303030.04065040650.00864047520.0473022912

    0.03104212860.04138950480.00877548270.0480413895

    0.03104212860.04212860310.00891049010.0487804878

    0.03178122690.04212860310.00904549750.0495195861

    0.03178122690.04212860310.00918050490.0502586844

    0.03252032520.04286770140.00931551240.0509977827

    0.03252032520.04360679970.00945051980.051736881

    0.03325942350.0443458980.00958552720.0524759793

    0.03325942350.04508499630.00972053460.0532150776

    0.03399852180.04582409460.00985554210.0539541759

    0.03473762010.04656319290.00999054950.0546932742

    0.03473762010.04730229120.01012555690.0554323725

    0.03547671840.04804138950.01026056430.0561714708

    0.03621581670.04804138950.01039557180.0569105691

    0.0369549150.04878048780.01053057920.0576496674

    0.0369549150.04951958610.01066558660.0583887657

    0.03769401330.05025868440.0108005940.059127864

    0.03843311160.05099778270.01093560150.0598669623

    0.03917220990.0517368810.01107060890.0606060606

    0.03917220990.05247597930.01120561630.0613451589

    0.03991130820.05321507760.01134062370.0620842572

    0.04065040650.05395417590.01147563120.0628233555

    0.04138950480.05395417590.01161063860.0635624538

    0.04212860310.05469327420.0117456460.0643015521

    0.04286770140.05543237250.01188065340.0650406504

    0.04286770140.05617147080.01201566090.0657797487

    0.04286770140.05691056910.01215066830.066518847

    0.04360679970.05764966740.01228567570.0672579453

    0.04360679970.05838876570.01242068310.0679970436

    0.0443458980.0591278640.01255569060.0687361419

    0.0443458980.05986696230.0126906980.0694752402

    0.04508499630.06060606060.01282570540.0702143385

    0.04582409460.06060606060.01296071280.0709534368

    0.04656319290.06134515890.01309572030.0716925351

    0.04730229120.06208425720.01323072770.0724316334

    0.04804138950.06282335550.01336573510.0731707317

    0.04804138950.06356245380.01350074250.07390983

    0.04878048780.06430155210.013635750.0746489283

    0.04951958610.06504065040.01377075740.0753880266

    0.05025868440.06504065040.01390576480.0761271249

    0.05099778270.06577974870.01404077220.0768662232

    0.0517368810.0665188470.01417577970.0776053215

    0.0517368810.06725794530.01431078710.0783444198

    0.0517368810.06799704360.01444579450.0790835181

    0.0517368810.06799704360.01458080190.0798226164

    0.0517368810.06873614190.01471580940.0805617147

    0.0517368810.06947524020.01485081680.081300813

    0.05247597930.07021433850.01498582420.0820399113

    0.05321507760.07095343680.01512083160.0827790096

    0.05321507760.07169253510.01525583910.0835181079

    0.05321507760.07243163340.01539084650.0842572062

    0.05395417590.07317073170.01552585390.0849963045

    0.05395417590.073909830.01566086130.0857354028

    0.05469327420.07464892830.01579586880.0864745011

    0.05543237250.07464892830.01593087620.0872135994

    0.05617147080.07464892830.01606588360.0879526977

    0.05617147080.07538802660.0162008910.088691796

    0.05691056910.07538802660.01633589850.0894308943

    0.05764966740.07538802660.01647090590.0901699926

    0.05764966740.07612712490.01660591330.0909090909

    0.05838876570.07686622320.01674092080.0916481892

    0.0591278640.07760532150.01687592820.0923872875

    0.0591278640.07834441980.01701093560.0931263858

    0.05986696230.07908351810.0171459430.0938654841

    0.05986696230.07982261640.01728095050.0946045824

    0.06060606060.08056171470.01741595790.0953436807

    0.06134515890.0813008130.01755096530.096082779

    0.06134515890.0813008130.01768597270.0968218773

    0.06208425720.0813008130.01782098020.0975609756

    0.06282335550.08203991130.01795598760.0983000739

    0.06356245380.08277900960.0180909950.0990391722

    0.06356245380.08351810790.01822600240.0997782705

    0.06356245380.08425720620.01836100990.1005173688

    0.06430155210.08499630450.01849601730.1012564671

    0.06430155210.08573540280.01863102470.1019955654

    0.06504065040.08647450110.01876603210.1027346637

    0.06577974870.08647450110.01890103960.103473762

    0.06577974870.08721359940.0190360470.1042128603

    0.06577974870.08795269770.01917105440.1049519586

    0.0665188470.0886917960.01930606180.1056910569

    0.0665188470.08943089430.01944106930.1064301552

    0.06725794530.09016999260.01957607670.1071692535

    0.06725794530.09090909090.01971108410.1079083518

    0.06799704360.09164818920.01984609150.1086474501

    0.06799704360.09238728750.0199810990.1093865484

    0.06873614190.09238728750.02011610640.1101256467

    0.06947524020.09238728750.02025111380.110864745

    0.07021433850.09312638580.02038612120.1116038433

    0.07095343680.09386548410.02052112870.1123429416

    0.07095343680.09386548410.02065613610.1130820399

    0.07169253510.09386548410.02079114350.1138211382

    0.07243163340.09386548410.02092615090.1145602365

    0.07243163340.09460458240.02106115840.1152993348

    0.07317073170.09534368070.02119616580.1160384331

    0.073909830.0960827790.02133117320.1167775314

    0.073909830.0960827790.02146618060.1175166297

    0.07464892830.09682187730.02160118810.118255728

    0.07538802660.09682187730.02173619550.1189948263

    0.07538802660.09756097560.02187120290.1197339246

    0.07538802660.09756097560.02200621030.1204730229

    0.07612712490.09830007390.02214121780.1212121212

    0.07686622320.09903917220.02227622520.1219512195

    0.07686622320.09903917220.02241123260.1226903178

    0.07760532150.09903917220.022546240.1234294161

    0.07760532150.09977827050.02268124750.1241685144

    0.07834441980.09977827050.02281625490.1249076127

    0.07908351810.09977827050.02295126230.125646711

    0.07908351810.10051736880.02308626970.1263858093

    0.07908351810.10125646710.02322127720.1271249076

    0.07982261640.10125646710.02335628460.1278640059

    0.07982261640.10125646710.0234912920.1286031042

    0.07982261640.10125646710.02362629940.1293422025

    0.08056171470.10199556540.02376130690.1300813008

    0.0813008130.10199556540.02389631430.1308203991

    0.08203991130.10273466370.02403132170.1315594974

    0.08203991130.1034737620.02416632910.1322985957

    0.08277900960.10421286030.02430133660.133037694

    0.08277900960.10495195860.0244363440.1337767923

    0.08351810790.10569105690.02457135140.1345158906

    0.08425720620.10643015520.02470635880.1352549889

    0.08499630450.10716925350.02484136630.1359940872

    0.08573540280.10790835180.02497637370.1367331855

    0.08573540280.10790835180.02511138110.1374722838

    0.08573540280.10864745010.02524638860.1382113821

    0.08573540280.10864745010.0253813960.1389504804

    0.08647450110.10938654840.02551640340.1396895787

    0.08721359940.11012564670.02565141080.140428677

    0.08795269770.1108647450.02578641830.1411677753

    0.0886917960.11160384330.02592142570.1419068736

    0.0886917960.11234294160.02605643310.1426459719

    0.08943089430.11308203990.02619144050.1433850702

    0.08943089430.11382113820.0263264480.1441241685

    0.09016999260.11456023650.02646145540.1448632668

    0.09090909090.11529933480.02659646280.1456023651

    0.09090909090.11603843310.02673147020.1463414634

    0.09164818920.11677753140.02686647770.1470805617

    0.09238728750.11677753140.02700148510.14781966

    0.09238728750.11677753140.02713649250.1485587583

    0.09312638580.11751662970.02727149990.1492978566

    0.09312638580.1182557280.02740650740.1500369549

    0.09386548410.11899482630.02754151480.1507760532

    0.09386548410.11973392460.02767652220.1515151515

    0.09460458240.12047302290.02781152960.1522542498

    0.09534368070.12121212120.02794653710.1529933481

    0.0960827790.12195121950.02808154450.1537324464

    0.09682187730.12269031780.02821655190.1544715447

    0.09756097560.12342941610.02835155930.155210643

    0.09830007390.12342941610.02848656680.1559497413

    0.09903917220.12416851440.02862157420.1566888396

    0.09977827050.12490761270.02875658160.1574279379

    0.10051736880.1256467110.0288915890.1581670362

    0.10125646710.12638580930.02902659650.1589061345

    0.10199556540.12638580930.02916160390.1596452328

    0.10273466370.12712490760.02929661130.1603843311

    0.1034737620.12786400590.02943161870.1611234294

    0.10421286030.12860310420.02956662620.1618625277

    0.10495195860.12934220250.02970163360.162601626

    0.10569105690.13008130080.0298366410.1633407243

    0.10643015520.13008130080.02997164840.1640798226

    0.10716925350.13082039910.03010665590.1648189209

    0.10790835180.13155949740.03024166330.1655580192

    0.10864745010.13229859570.03037667070.1662971175

    0.10938654840.1330376940.03051167810.1670362158

    0.11012564670.13377679230.03064668560.1677753141

    0.1108647450.13451589060.0307816930.1685144124

    0.11160384330.13525498890.03091670040.1692535107

    0.11234294160.13599408720.03105170780.169992609

    0.11308203990.13673318550.03118671530.1707317073

    0.11382113820.13747228380.03132172270.1714708056

    0.11456023650.13821138210.03145673010.1722099039

    0.11529933480.13895048040.03159173750.1729490022

    0.11603843310.13968957870.0317267450.1736881005

    0.11677753140.1404286770.03186175240.1744271988

    0.11751662970.14116777530.03199675980.1751662971

    0.11751662970.14190687360.03213176720.1759053954

    0.1182557280.14190687360.03226677470.1766444937

    0.11899482630.14264597190.03240178210.177383592

    0.11973392460.14338507020.03253678950.1781226903

    0.12047302290.14412416850.03267179690.1788617886

    0.12121212120.14412416850.03280680440.1796008869

    0.12195121950.14412416850.03294181180.1803399852

    0.12269031780.14412416850.03307681920.1810790835

    0.12342941610.14486326680.03321182670.1818181818

    0.12416851440.14486326680.03334683410.1825572801

    0.12490761270.14560236510.03348184150.1832963784

    0.1256467110.14634146340.03361684890.1840354767

    0.12638580930.14708056170.03375185640.184774575

    0.12712490760.147819660.03388686380.1855136733

    0.12786400590.14855875830.03402187120.1862527716

    0.12860310420.14855875830.03415687860.1869918699

    0.12934220250.14929785660.03429188610.1877309682

    0.13008130080.15003695490.03442689350.1884700665

    0.13008130080.15077605320.03456190090.1892091648

    0.13082039910.15151515150.03469690830.1899482631

    0.13155949740.15225424980.03483191580.1906873614

    0.13229859570.15299334810.03496692320.1914264597

    0.1330376940.15373244640.03510193060.192165558

    0.13377679230.15447154470.0352369380.1929046563

    0.13451589060.15447154470.03537194550.1936437546

    0.13451589060.15447154470.03550695290.1943828529

    0.13525498890.1552106430.03564196030.1951219512

    0.13599408720.15594974130.03577696770.1958610495

    0.13673318550.15668883960.03591197520.1966001478

    0.13747228380.15742793790.03604698260.1973392461

    0.13821138210.15816703620.036181990.1980783444

    0.13821138210.15890613450.03631699740.1988174427

    0.13895048040.15964523280.03645200490.199556541

    0.13968957870.16038433110.03658701230.2002956393

    0.1404286770.16038433110.03672201970.2010347376

    0.14116777530.16112342940.03685702710.2017738359

    0.14190687360.16112342940.03699203460.2025129342

    0.14264597190.16112342940.0371270420.2032520325

    0.14338507020.16186252770.03726204940.2039911308

    0.14412416850.16186252770.03739705680.2047302291

    0.14486326680.1626016260.03753206430.2054693274

    0.14560236510.16334072430.03766707170.2062084257

    0.14634146340.16407982260.03780207910.206947524

    0.14708056170.16481892090.03793708650.2076866223

    0.147819660.16555801920.0380720940.2084257206

    0.14855875830.16629711750.03820710140.2091648189

    0.14929785660.16703621580.03834210880.2099039172

    0.15003695490.16777531410.03847711620.2106430155

    0.15077605320.16851441240.03861212370.2113821138

    0.15151515150.16851441240.03874713110.2121212121

    0.15151515150.16925351070.03888213850.2128603104

    0.15151515150.1699926090.03901714590.2135994087

    0.15225424980.17073170730.03915215340.214338507

    0.15299334810.17147080560.03928716080.2150776053

    0.15373244640.17147080560.03942216820.2158167036

    0.15447154470.17220990390.03955717560.2165558019

    0.1552106430.17220990390.03969218310.2172949002

    0.15594974130.17220990390.03982719050.2180339985

    0.15668883960.17220990390.03996219790.2187730968

    0.15742793790.17294900220.04009720530.2195121951

    0.15816703620.17368810050.04023221280.2202512934

    0.15890613450.17442719880.04036722020.2209903917

    0.15964523280.17516629710.04050222760.22172949

    0.16038433110.17590539540.0406372350.2224685883

    0.16112342940.17590539540.04077224250.2232076866

    0.16186252770.17664449370.04090724990.2239467849

    0.1626016260.1773835920.04104225730.2246858832

    0.16334072430.1773835920.04117726470.2254249815

    0.16407982260.17812269030.04131227220.2261640798

    0.16481892090.17886178860.04144727960.2269031781

    0.16555801920.17960088690.0415822870.2276422764

    0.16629711750.18033998520.04171729450.2283813747

    0.16703621580.18107908350.04185230190.229120473

    0.16777531410.18181818180.04198730930.2298595713

    0.16851441240.18255728010.04212231670.2305986696

    0.16925351070.18329637840.04225732420.2313377679

    0.1699926090.18403547670.04239233160.2320768662

    0.17073170730.18403547670.0425273390.2328159645

    0.17147080560.1847745750.04266234640.2335550628

    0.17220990390.18551367330.04279735390.2342941611

    0.17294900220.18625277160.04293236130.2350332594

    0.17368810050.18699186990.04306736870.2357723577

    0.17442719880.18773096820.04320237610.236511456

    0.17516629710.18847006650.04333738360.2372505543

    0.17590539540.18920916480.0434723910.2379896526

    0.17664449370.18994826310.04360739840.2387287509

    0.1773835920.19068736140.04374240580.2394678492

    0.17812269030.19142645970.04387741330.2402069475

    0.17886178860.1921655580.04401242070.2409460458

    0.17960088690.19290465630.04414742810.2416851441

    0.18033998520.19364375460.04428243550.2424242424

    0.18107908350.19364375460.0444174430.2431633407

    0.18181818180.19364375460.04455245040.243902439

    0.18255728010.19364375460.04468745780.2446415373

    0.18329637840.19364375460.04482246520.2453806356

    0.18403547670.19364375460.04495747270.2461197339

    0.1847745750.19438285290.04509248010.2468588322

    0.18551367330.19512195120.04522748750.2475979305

    0.18625277160.19586104950.04536249490.2483370288

    0.18699186990.19660014780.04549750240.2490761271

    0.18773096820.19733924610.04563250980.2498152254

    0.18847006650.19733924610.04576751720.2505543237

    0.18920916480.19807834440.04590252460.251293422

    0.18994826310.19807834440.04603753210.2520325203

    0.19068736140.19881744270.04617253950.2527716186

    0.19142645970.19881744270.04630754690.2535107169

    0.1921655580.1995565410.04644255430.2542498152

    0.19290465630.20029563930.04657756180.2549889135

    0.19364375460.20103473760.04671256920.2557280118

    0.19438285290.20177383590.04684757660.2564671101

    0.19512195120.20177383590.0469825840.2572062084

    0.19586104950.20251293420.04711759150.2579453067

    0.19660014780.20325203250.04725259890.258684405

    0.19733924610.20325203250.04738760630.2594235033

    0.19807834440.20399113080.04752261370.2601626016

    0.19881744270.20473022910.04765762120.2609016999

    0.1995565410.20473022910.04779262860.2616407982

    0.20029563930.20546932740.0479276360.2623798965

    0.20103473760.20620842570.04806264340.2631189948

    0.20177383590.2069475240.04819765090.2638580931

    0.20251293420.20768662230.04833265830.2645971914

    0.20325203250.20842572060.04846766570.2653362897

    0.20399113080.20916481890.04860267310.266075388

    0.20399113080.20916481890.04873768060.2668144863

    0.20473022910.20916481890.0488726880.2675535846

    0.20546932740.20916481890.04900769540.2682926829

    0.20620842570.20990391720.04914270280.2690317812

    0.2069475240.21064301550.04927771030.2697708795

    0.20768662230.21138211380.04941271770.2705099778

    0.20842572060.21212121210.04954772510.2712490761

    0.20916481890.21286031040.04968273260.2719881744

    0.20990391720.21359940870.049817740.2727272727

    0.21064301550.2143385070.04995274740.273466371

    0.21064301550.21507760530.05008775480.2742054693

    0.21138211380.21581670360.05022276230.2749445676

    0.21212121210.21655580190.05035776970.2756836659

    0.21286031040.21655580190.05049277710.2764227642

    0.21359940870.21729490020.05062778450.2771618625

    0.2143385070.21729490020.0507627920.2779009608

    0.21507760530.21729490020.05089779940.2786400591

    0.21581670360.21803399850.05103280680.2793791574

    0.21655580190.21877309680.05116781420.2801182557

    0.21729490020.21877309680.05130282170.280857354

    0.21803399850.21951219510.05143782910.2815964523

    0.21877309680.22025129340.05157283650.2823355506

    0.21951219510.22099039170.05170784390.2830746489

    0.21951219510.221729490.05184285140.2838137472

    0.22025129340.221729490.05197785880.2845528455

    0.22099039170.22246858830.05211286620.2852919438

    0.221729490.22246858830.05224787360.2860310421

    0.22246858830.22246858830.05238288110.2867701404

    0.22320768660.22320768660.05251788850.2875092387

    0.22394678490.22320768660.05265289590.288248337

    0.22468588320.22320768660.05278790330.2889874353

    0.22542498150.22394678490.05292291080.2897265336

    0.22616407980.22468588320.05305791820.2904656319

    0.22616407980.22468588320.05319292560.2912047302

    0.22690317810.22468588320.0533279330.2919438285

    0.22764227640.22542498150.05346294050.2926829268

    0.22838137470.22616407980.05359794790.2934220251

    0.2291204730.22616407980.05373295530.2941611234

    0.2291204730.22690317810.05386796270.2949002217

    0.22985957130.22764227640.05400297020.29563932

    0.23059866960.22764227640.05413797760.2963784183

    0.23133776790.22838137470.0542729850.2971175166

    0.23207686620.2291204730.05440799240.2978566149

    0.23281596450.22985957130.05454299990.2985957132

    0.23355506280.23059866960.05467800730.2993348115

    0.23429416110.23133776790.05481301470.3000739098

    0.23503325940.23207686620.05494802210.3008130081

    0.23503325940.23281596450.05508302960.3015521064

    0.23577235770.23355506280.0552180370.3022912047

    0.2365114560.23429416110.05535304440.303030303

    0.23725055430.23429416110.05548805180.3037694013

    0.23798965260.23503325940.05562305930.3045084996

    0.23872875090.23577235770.05575806670.3052475979

    0.23946784920.2365114560.05589307410.3059866962

    0.24020694750.23725055430.05602808150.3067257945

    0.24094604580.23798965260.0561630890.3074648928

    0.24168514410.23872875090.05629809640.3082039911

    0.24242424240.23946784920.05643310380.3089430894

    0.24316334070.23946784920.05656811120.3096821877

    0.2439024390.24020694750.05670311870.310421286

    0.24464153730.24094604580.05683812610.3111603843

    0.24538063560.24168514410.05697313350.3118994826

    0.24611973390.24242424240.05710814090.3126385809

    0.24685883220.24242424240.05724314840.3133776792

    0.24759793050.24242424240.05737815580.3141167775

    0.24833702880.24316334070.05751316320.3148558758

    0.24907612710.2439024390.05764817060.3155949741

    0.24981522540.24464153730.05778317810.3163340724

    0.25055432370.24538063560.05791818550.3170731707

    0.2512934220.24538063560.05805319290.317812269

    0.2512934220.24611973390.05818820040.3185513673

    0.25203252030.24685883220.05832320780.3192904656

    0.25203252030.24685883220.05845821520.3200295639

    0.25277161860.24685883220.05859322260.3207686622

    0.25351071690.24759793050.05872823010.3215077605

    0.25424981520.24833702880.05886323750.3222468588

    0.25498891350.24907612710.05899824490.3229859571

    0.25572801180.24981522540.05913325230.3237250554

    0.25572801180.24981522540.05926825980.3244641537

    0.25572801180.25055432370.05940326720.325203252

    0.25572801180.25055432370.05953827460.3259423503

    0.25572801180.25055432370.0596732820.3266814486

    0.25572801180.25055432370.05980828950.3274205469

    0.25572801180.2512934220.05994329690.3281596452

    0.25646711010.2512934220.06007830430.3288987435

    0.25720620840.25203252030.06021331170.3296378418

    0.25794530670.25277161860.06034831920.3303769401

    0.2586844050.25351071690.06048332660.3311160384

    0.25942350330.25424981520.0606183340.3318551367

    0.26016260160.25424981520.06075334140.332594235

    0.26016260160.25424981520.06088834890.3333333333

    0.26090169990.25424981520.06102335630.3340724316

    0.26164079820.25498891350.06115836370.3348115299

    0.26237989650.25498891350.06129337110.3355506282

    0.26311899480.25572801180.06142837860.3362897265

    0.26385809310.25572801180.0615633860.3370288248

    0.26459719140.25646711010.06169839340.3377679231

    0.26533628970.25720620840.06183340080.3385070214

    0.2660753880.25794530670.06196840830.3392461197

    0.26681448630.2586844050.06210341570.339985218

    0.26755358460.25942350330.06223842310.3407243163

    0.26829268290.25942350330.06237343050.3414634146

    0.26903178120.26016260160.0625084380.3422025129

    0.26977087950.26090169990.06264344540.3429416112

    0.27050997780.26090169990.06277845280.3436807095

    0.27124907610.26164079820.06291346020.3444198078

    0.27198817440.26237989650.06304846770.3451589061

    0.27272727270.26311899480.06318347510.3458980044

    0.2734663710.26385809310.06331848250.3466371027

    0.2734663710.26459719140.06345348990.347376201

    0.2734663710.26533628970.06358849740.3481152993

    0.27420546930.26533628970.06372350480.3488543976

    0.27494456760.2660753880.06385851220.3495934959

    0.27568366590.2660753880.06399351960.3503325942

    0.27642276420.26681448630.06412852710.3510716925

    0.27716186250.26755358460.06426353450.3518107908

    0.27790096080.26755358460.06439854190.3525498891

    0.27864005910.26829268290.06453354930.3532889874

    0.27937915740.26903178120.06466855680.3540280857

    0.28011825570.26903178120.06480356420.354767184

    0.2808573540.26977087950.06493857160.3555062823

    0.2808573540.26977087950.0650735790.3562453806

    0.28159645230.27050997780.06520858650.3569844789

    0.28233555060.27124907610.06534359390.3577235772

    0.28307464890.27198817440.06547860130.3584626755

    0.28381374720.27272727270.06561360870.3592017738

    0.28455284550.2734663710.06574861620.3599408721

    0.28529194380.27420546930.06588362360.3606799704

    0.28603104210.27420546930.0660186310.3614190687

    0.28677014040.27494456760.06615363850.362158167

    0.28750923870.27568366590.06628864590.3628972653

    0.2882483370.27642276420.06642365330.3636363636

    0.2882483370.27642276420.06655866070.3643754619

    0.28898743530.27642276420.06669366820.3651145602

    0.28972653360.27642276420.06682867560.3658536585

    0.28972653360.27716186250.0669636830.3665927568

    0.29046563190.27790096080.06709869040.3673318551

    0.29046563190.27790096080.06723369790.3680709534

    0.29120473020.27864005910.06736870530.3688100517

    0.29194382850.27937915740.06750371270.36954915

    0.29268292680.28011825570.06763872010.3702882483

    0.29342202510.2808573540.06777372760.3710273466

    0.29416112340.28159645230.0679087350.3717664449

    0.29490022170.28233555060.06804374240.3725055432

    0.295639320.28233555060.06817874980.3732446415

    0.29637841830.28307464890.06831375730.3739837398

    0.29711751660.28381374720.06844876470.3747228381

    0.29785661490.28455284550.06858377210.3754619364

    0.29859571320.28529194380.06871877950.3762010347

    0.29859571320.28529194380.0688537870.376940133

    0.29933481150.28603104210.06898879440.3776792313

    0.30007390980.28677014040.06912380180.3784183296

    0.30007390980.28750923870.06925880920.3791574279

    0.30081300810.2882483370.06939381670.3798965262

    0.30081300810.28898743530.06952882410.3806356245

    0.30081300810.28972653360.06966383150.3813747228

    0.30155210640.28972653360.06979883890.3821138211

    0.30229120470.29046563190.06993384640.3828529194

    0.3030303030.29046563190.07006885380.3835920177

    0.30376940130.29120473020.07020386120.384331116

    0.30450849960.29194382850.07033886860.3850702143

    0.30450849960.29268292680.07047387610.3858093126

    0.30524759790.29342202510.07060888350.3865484109

    0.30524759790.29416112340.07074389090.3872875092

    0.30524759790.29490022170.07087889830.3880266075

    0.30598669620.295639320.07101390580.3887657058

    0.30672579450.29637841830.07114891320.3895048041

    0.30672579450.29711751660.07128392060.3902439024

    0.30746489280.29785661490.0714189280.3909830007

    0.30820399110.29785661490.07155393550.391722099

    0.30820399110.29859571320.07168894290.3924611973

    0.30820399110.29933481150.07182395030.3932002956

    0.30820399110.30007390980.07195895770.3939393939

    0.30894308940.30081300810.07209396520.3946784922

    0.30968218770.30155210640.07222897260.3954175905

    0.3104212860.30229120470.072363980.3961566888

    0.31116038430.3030303030.07249898740.3968957871

    0.31189948260.30376940130.07263399490.3976348854

    0.31189948260.30450849960.07276900230.3983739837

    0.31263858090.30524759790.07290400970.399113082

    0.31263858090.30524759790.07303901710.3998521803

    0.31263858090.30598669620.07317402460.4005912786

    0.31337767920.30672579450.0733090320.4013303769

    0.31411677750.30746489280.07344403940.4020694752

    0.31485587580.30820399110.07357904680.4028085735

    0.31559497410.30894308940.07371405430.4035476718

    0.31559497410.30968218770.07384906170.4042867701

    0.31633407240.3104212860.07398406910.4050258684

    0.31707317070.31116038430.07411907650.4057649667

    0.31707317070.31116038430.0742540840.406504065

    0.3178122690.31116038430.07438909140.4072431633

    0.3178122690.31116038430.07452409880.4079822616

    0.31855136730.31189948260.07465910630.4087213599

    0.31929046560.31189948260.07479411370.4094604582

    0.31929046560.31263858090.07492912110.4101995565

    0.32002956390.31337767920.07506412850.4109386548

    0.32076866220.31411677750.0751991360.4116777531

    0.32076866220.31485587580.07533414340.4124168514

    0.32076866220.31559497410.07546915080.4131559497

    0.32076866220.31633407240.07560415820.413895048

    0.32150776050.31707317070.07573916570.4146341463

    0.32224685880.3178122690.07587417310.4153732446

    0.32298595710.31855136730.07600918050.4161123429

    0.32372505540.31929046560.07614418790.4168514412

    0.32446415370.31929046560.07627919540.4175905395

    0.3252032520.32002956390.07641420280.4183296378

    0.3252032520.32076866220.07654921020.4190687361

    0.32594235030.32150776050.07668421760.4198078344

    0.32594235030.32150776050.07681922510.4205469327

    0.32668144860.32224685880.07695423250.421286031

    0.32742054690.32298595710.07708923990.4220251293

    0.32815964520.32372505540.07722424730.4227642276

    0.32889874350.32372505540.07735925480.4235033259

    0.32963784180.32446415370.07749426220.4242424242

    0.32963784180.3252032520.07762926960.4249815225

    0.33037694010.32594235030.0777642770.4257206208

    0.33111603840.32668144860.07789928450.4264597191

    0.33185513670.32668144860.07803429190.4271988174

    0.33185513670.32742054690.07816929930.4279379157

    0.33185513670.32815964520.07830430670.428677014

    0.3325942350.32889874350.07843931420.4294161123

    0.33333333330.32963784180.07857432160.4301552106

    0.33407243160.32963784180.0787093290.4308943089

    0.33481152990.33037694010.07884433640.4316334072

    0.33555062820.33111603840.07897934390.4323725055

    0.33628972650.33185513670.07911435130.4331116038

    0.33702882480.3325942350.07924935870.4338507021

    0.33776792310.33333333330.07938436610.4345898004

    0.33850702140.33407243160.07951937360.4353288987

    0.33924611970.33481152990.0796543810.436067997

    0.3399852180.33481152990.07978938840.4368070953

    0.34072431630.33555062820.07992439580.4375461936

    0.34146341460.33628972650.08005940330.4382852919

    0.34220251290.33702882480.08019441070.4390243902

    0.34294161120.33776792310.08032941810.4397634885

    0.34368070950.33850702140.08046442550.4405025868

    0.34441980780.33924611970.0805994330.4412416851

    0.34441980780.3399852180.08073444040.4419807834

    0.34441980780.34072431630.08086944780.4427198817

    0.34515890610.34146341460.08100445520.44345898

    0.34589800440.34146341460.08113946270.4441980783

    0.34663710270.34220251290.08127447010.4449371766

    0.3473762010.34294161120.08140947750.4456762749

    0.34811529930.34368070950.08154448490.4464153732

    0.34885439760.34441980780.08167949240.4471544715

    0.34885439760.34515890610.08181449980.4478935698

    0.34959349590.34589800440.08194950720.4486326681

    0.35033259420.34589800440.08208451460.4493717664

    0.35107169250.34663710270.08221952210.4501108647

    0.35181079080.3473762010.08235452950.450849963

    0.35254988910.34811529930.08248953690.4515890613

    0.35254988910.34885439760.08262454430.4523281596

    0.35328898740.34959349590.08275955180.4530672579

    0.35328898740.35033259420.08289455920.4538063562

    0.35402808570.35107169250.08302956660.4545454545

    0.3547671840.35181079080.08316457410.4552845528

    0.35550628230.35254988910.08329958150.4560236511

    0.35624538060.35328898740.08343458890.4567627494

    0.35698447890.35328898740.08356959630.4575018477

    0.35698447890.35328898740.08370460380.458240946

    0.35698447890.35328898740.08383961120.4589800443

    0.35772357720.35402808570.08397461860.4597191426

    0.35772357720.3547671840.0841096260.4604582409

    0.35772357720.35550628230.08424463350.4611973392

    0.35846267550.35624538060.08437964090.4619364375

    0.35920177380.35698447890.08451464830.4626755358

    0.35994087210.35772357720.08464965570.4634146341

    0.36067997040.35846267550.08478466320.4641537324

    0.36141906870.35920177380.08491967060.4648928307

    0.3621581670.35920177380.0850546780.465631929

    0.36289726530.35994087210.08518968540.4663710273

    0.36289726530.36067997040.08532469290.4671101256

    0.36363636360.36141906870.08545970030.4678492239

    0.36437546190.3621581670.08559470770.4685883222

    0.36437546190.36289726530.08572971510.4693274205

    0.36511456020.36363636360.08586472260.4700665188

    0.36585365850.36437546190.085999730.4708056171

    0.36659275680.36511456020.08613473740.4715447154

    0.36733185510.36585365850.08626974480.4722838137

    0.36807095340.36659275680.08640475230.473022912

    0.36881005170.36733185510.08653975970.4737620103

    0.369549150.36807095340.08667476710.4745011086

    0.37028824830.36881005170.08680977450.4752402069

    0.37102734660.36881005170.0869447820.4759793052

    0.37176644490.369549150.08707978940.4767184035

    0.37250554320.37028824830.08721479680.4774575018

    0.37324464150.37102734660.08734980420.4781966001

    0.37398373980.37102734660.08748481170.4789356984

    0.37472283810.37176644490.08761981910.4796747967

    0.37472283810.37250554320.08775482650.480413895

    0.37546193640.37324464150.08788983390.4811529933

    0.37620103470.37324464150.08802484140.4818920916

    0.3769401330.37398373980.08815984880.4826311899

    0.3769401330.37472283810.08829485620.4833702882

    0.37767923130.37546193640.08842986360.4841093865

    0.37841832960.37620103470.08856487110.4848484848

    0.37915742790.37620103470.08869987850.4855875831

    0.37989652620.3769401330.08883488590.4863266814

    0.38063562450.37767923130.08896989330.4870657797

    0.38137472280.37841832960.08910490080.487804878

    0.38137472280.37841832960.08923990820.4885439763

    0.38211382110.37915742790.08937491560.4892830746

    0.38285291940.37989652620.0895099230.4900221729

    0.38359201770.38063562450.08964493050.4907612712

    0.3843311160.38137472280.08977993790.4915003695

    0.38507021430.38211382110.08991494530.4922394678

    0.38580931260.38285291940.09004995270.4929785661

    0.38654841090.38359201770.09018496020.4937176644

    0.38728750920.3843311160.09031996760.4944567627

    0.38802660750.38507021430.0904549750.495195861

    0.38876570580.38580931260.09058998240.4959349593

    0.38950480410.38654841090.09072498990.4966740576

    0.39024390240.38728750920.09085999730.4974131559

    0.39098300070.38802660750.09099500470.4981522542

    0.3917220990.38876570580.09113001220.4988913525

    0.39246119730.38950480410.09126501960.4996304508

    0.39246119730.39024390240.0914000270.5003695492

    0.39320029560.39024390240.09153503440.5011086475

    0.39393939390.39098300070.09167004190.5018477458

    0.39467849220.3917220990.09180504930.5025868441

    0.39467849220.39246119730.09194005670.5033259424

    0.39541759050.39320029560.09207506410.5040650407

    0.39541759050.39393939390.09221007160.504804139

    0.39615668880.39467849220.0923450790.5055432373

    0.39689578710.39541759050.09248008640.5062823356

    0.39763488540.39615668880.09261509380.5070214339

    0.39837398370.39689578710.09275010130.5077605322

    0.39837398370.39763488540.09288510870.5084996305

    0.3991130820.39837398370.09302011610.5092387288

    0.3991130820.39837398370.09315512350.5099778271

    0.3991130820.39837398370.0932901310.5107169254

    0.3991130820.3991130820.09342513840.5114560237

    0.39985218030.3991130820.09356014580.512195122

    0.40059127860.39985218030.09369515320.5129342203

    0.40059127860.40059127860.09383016070.5136733186

    0.40133037690.40133037690.09396516810.5144124169

    0.40206947520.40206947520.09410017550.5151515152

    0.40280857350.40280857350.09423518290.5158906135

    0.40280857350.40354767180.09437019040.5166297118

    0.40354767180.40428677010.09450519780.5173688101

    0.40428677010.40502586840.09464020520.5181079084

    0.40428677010.40576496670.09477521260.5188470067

    0.40502586840.40576496670.09491022010.519586105

    0.40502586840.4065040650.09504522750.5203252033

    0.40576496670.40724316330.09518023490.5210643016

    0.40576496670.40798226160.09531524230.5218033999

    0.40576496670.40872135990.09545024980.5225424982

    0.40576496670.40872135990.09558525720.5232815965

    0.4065040650.40946045820.09572026460.5240206948

    0.4065040650.41019955650.0958552720.5247597931

    0.40724316330.41093865480.09599027950.5254988914

    0.40724316330.41167775310.09612528690.5262379897

    0.40724316330.41241685140.09626029430.526977088

    0.40798226160.41315594970.09639530170.5277161863

    0.40872135990.41315594970.09653030920.5284552846

    0.40872135990.4138950480.09666531660.5291943829

    0.40872135990.41463414630.0968003240.5299334812

    0.40946045820.41537324460.09693533140.5306725795

    0.41019955650.41611234290.09707033890.5314116778

    0.41093865480.41685144120.09720534630.5321507761

    0.41093865480.41759053950.09734035370.5328898744

    0.41167775310.41832963780.09747536110.5336289727

    0.41241685140.41906873610.09761036860.534368071

    0.41315594970.41980783440.0977453760.5351071693

    0.41315594970.42054693270.09788038340.5358462676

    0.4138950480.4212860310.09801539080.5365853659

    0.41463414630.4212860310.09815039830.5373244642

    0.41463414630.42202512930.09828540570.5380635625

    0.41537324460.42202512930.09842041310.5388026608

    0.41537324460.42276422760.09855542050.5395417591

    0.41611234290.42350332590.0986904280.5402808574

    0.41611234290.42424242420.09882543540.5410199557

    0.41685144120.42498152250.09896044280.541759054

    0.41759053950.42572062080.09909545020.5424981523

    0.41832963780.42645971910.09923045770.5432372506

    0.41906873610.42719881740.09936546510.5439763489

    0.41906873610.42793791570.09950047250.5447154472

    0.41980783440.4286770140.099635480.5454545455

    0.42054693270.4286770140.09977048740.5461936438

    0.42054693270.42941611230.09990549480.5469327421

    0.42054693270.43015521060.10004050220.5476718404

    0.4212860310.43089430890.10017550970.5484109387

    0.42202512930.43163340720.10031051710.549150037

    0.42276422760.43237250550.10044552450.5498891353

    0.42276422760.43311160380.10058053190.5506282336

    0.42276422760.43311160380.10071553940.5513673319

    0.42350332590.43385070210.10085054680.5521064302

    0.42350332590.43458980040.10098555420.5528455285

    0.42350332590.43532889870.10112056160.5535846268

    0.42350332590.4360679970.10125556910.5543237251

    0.42350332590.43680709530.10139057650.5550628234

    0.42350332590.43754619360.10152558390.5558019217

    0.42424242420.43828529190.10166059130.55654102

    0.42424242420.43902439020.10179559880.5572801183

    0.42424242420.43976348850.10193060620.5580192166

    0.42424242420.44050258680.10206561360.5587583149

    0.42424242420.44050258680.1022006210.5594974132

    0.42424242420.44124168510.10233562850.5602365115

    0.42424242420.44124168510.10247063590.5609756098

    0.42424242420.44198078340.10260564330.5617147081

    0.42424242420.44271988170.10274065070.5624538064

    0.42424242420.443458980.10287565820.5631929047

    0.42498152250.443458980.10301066560.563932003

    0.42572062080.443458980.1031456730.5646711013

    0.42572062080.44419807830.10328068040.5654101996

    0.42572062080.44493717660.10341568790.5661492979

    0.42572062080.44567627490.10355069530.5668883962

    0.42572062080.44641537320.10368570270.5676274945

    0.42572062080.44641537320.10382071010.5683665928

    0.42572062080.44715447150.10395571760.5691056911

    0.42572062080.44789356980.1040907250.5698447894

    0.42572062080.44789356980.10422573240.5705838877

    0.42572062080.44863266810.10436073980.571322986

    0.42645971910.44937176640.10449574730.5720620843

    0.42719881740.45011086470.10463075470.5728011826

    0.42793791570.4508499630.10476576210.5735402809

    0.42793791570.45158906130.10490076950.5742793792

    0.42793791570.45232815960.1050357770.5750184775

    0.42793791570.45306725790.10517078440.5757575758

    0.42793791570.45380635620.10530579180.5764966741

    0.42793791570.45454545450.10544079920.5772357724

    0.4286770140.45454545450.10557580670.5779748707

    0.4286770140.45454545450.10571081410.578713969

    0.4286770140.45528455280.10584582150.5794530673

    0.4286770140.45602365110.10598082890.5801921656

    0.42941611230.45676274940.10611583640.5809312639

    0.42941611230.45750184770.10625084380.5816703622

    0.42941611230.4582409460.10638585120.5824094605

    0.42941611230.4582409460.10652085860.5831485588

    0.42941611230.4582409460.10665586610.5838876571

    0.42941611230.45898004430.10679087350.5846267554

    0.43015521060.45898004430.10692588090.5853658537

    0.43015521060.45971914260.10706088830.586104952

    0.43089430890.46045824090.10719589580.5868440503

    0.43089430890.46119733920.10733090320.5875831486

    0.43089430890.46193643750.10746591060.5883222469

    0.43089430890.46267553580.10760091810.5890613452

    0.43089430890.46341463410.10773592550.5898004435

    0.43163340720.46415373240.10787093290.5905395418

    0.43163340720.46489283070.10800594030.5912786401

    0.43237250550.4656319290.10814094780.5920177384

    0.43311160380.46637102730.10827595520.5927568367

    0.43311160380.46711012560.10841096260.593495935

    0.43385070210.46711012560.108545970.5942350333

    0.43385070210.46784922390.10868097750.5949741316

    0.43458980040.46858832220.10881598490.5957132299

    0.43458980040.46932742050.10895099230.5964523282

    0.43458980040.47006651880.10908599970.5971914265

    0.43532889870.47080561710.10922100720.5979305248

    0.43532889870.47154471540.10935601460.5986696231

    0.43532889870.47154471540.1094910220.5994087214

    0.43532889870.47228381370.10962602940.6001478197

    0.43532889870.47228381370.10976103690.600886918

    0.43532889870.4730229120.10989604430.6016260163

    0.43532889870.47376201030.11003105170.6023651146

    0.4360679970.47450110860.11016605910.6031042129

    0.4360679970.47524020690.11030106660.6038433112

    0.4360679970.47597930520.1104360740.6045824095

    0.43680709530.47671840350.11057108140.6053215078

    0.43680709530.47671840350.11070608880.6060606061

    0.43754619360.47671840350.11084109630.6067997044

    0.43828529190.47671840350.11097610370.6075388027

    0.43828529190.47671840350.11111111110.608277901

    0.43828529190.47671840350.11124611850.6090169993

    0.43828529190.47671840350.1113811260.6097560976

    0.43828529190.47671840350.11151613340.6104951959

    0.43828529190.47745750180.11165114080.6112342942

    0.43902439020.47745750180.11178614820.6119733925

    0.43902439020.47745750180.11192115570.6127124908

    0.43976348850.47745750180.11205616310.6134515891

    0.43976348850.47745750180.11219117050.6141906874

    0.43976348850.47745750180.11232617790.6149297857

    0.43976348850.47745750180.11246118540.615668884

    0.44050258680.47745750180.11259619280.6164079823

    0.44050258680.47745750180.11273120020.6171470806

    0.44124168510.47745750180.11286620760.6178861789

    0.44198078340.47745750180.11300121510.6186252772

    0.44198078340.47745750180.11313622250.6193643755

    0.44198078340.47745750180.11327122990.6201034738

    0.44198078340.47745750180.11340623730.6208425721

    0.44271988170.47745750180.11354124480.6215816704

    0.44271988170.47745750180.11367625220.6223207687

    0.44271988170.47745750180.11381125960.623059867

    0.44271988170.47745750180.1139462670.6237989653

    0.443458980.47745750180.11408127450.6245380636

    0.443458980.47745750180.11421628190.6252771619

    0.443458980.47745750180.11435128930.6260162602

    0.443458980.47745750180.11448629670.6267553585

    0.443458980.47745750180.11462130420.6274944568

    0.443458980.47745750180.11475631160.6282335551

    0.443458980.47745750180.1148913190.6289726534

    0.443458980.47745750180.11502632640.6297117517

    0.443458980.47745750180.11516133390.63045085

    0.443458980.47745750180.11529634130.6311899483

    0.44419807830.47819660010.11543134870.6319290466

    0.44419807830.47893569840.11556635610.6326681449

    0.44419807830.47893569840.11570136360.6334072432

    0.44419807830.47893569840.1158363710.6341463415

    0.44419807830.47893569840.11597137840.6348854398

    0.44419807830.47893569840.11610638590.6356245381

    0.44419807830.47893569840.11624139330.6363636364

    0.44419807830.47967479670.11637640070.6371027347

    0.44419807830.47967479670.11651140810.637841833

    0.44419807830.47967479670.11664641560.6385809313

    0.44493717660.47967479670.1167814230.6393200296

    0.44493717660.47967479670.11691643040.6400591279

    0.44493717660.47967479670.11705143780.6407982262

    0.44493717660.47967479670.11718644530.6415373245

    0.44493717660.47967479670.11732145270.6422764228

    0.44493717660.47967479670.11745646010.6430155211

    0.44493717660.47967479670.11759146750.6437546194

    0.44567627490.4804138950.1177264750.6444937177

    0.44567627490.4804138950.11786148240.645232816

    0.44567627490.4804138950.11799648980.6459719143

    0.44567627490.48115299330.11813149720.6467110126

    0.44641537320.48189209160.11826650470.6474501109

    0.44715447150.48189209160.11840151210.6481892092

    0.44715447150.48189209160.11853651950.6489283075

    0.44715447150.48189209160.11867152690.6496674058

    0.44715447150.48189209160.11880653440.6504065041

    0.44715447150.48189209160.11894154180.6511456024

    0.44715447150.48263118990.11907654920.6518847007

    0.44789356980.48263118990.11921155660.652623799

    0.44863266810.48263118990.11934656410.6533628973

    0.44863266810.48263118990.11948157150.6541019956

    0.44863266810.48263118990.11961657890.6548410939

    0.44863266810.48263118990.11975158630.6555801922

    0.44863266810.48337028820.11988659380.6563192905

    0.44937176640.48337028820.12002160120.6570583888

    0.44937176640.48337028820.12015660860.6577974871

    0.44937176640.48337028820.1202916160.6585365854

    0.45011086470.48337028820.12042662350.6592756837

    0.4508499630.48337028820.12056163090.660014782

    0.4508499630.48337028820.12069663830.6607538803

    0.45158906130.48410938650.12083164570.6614929786

    0.45232815960.48410938650.12096665320.6622320769

    0.45232815960.48410938650.12110166060.6629711752

    0.45232815960.48410938650.1212366680.6637102735

    0.45232815960.48484848480.12137167540.6644493718

    0.45232815960.48484848480.12150668290.6651884701

    0.45232815960.48484848480.12164169030.6659275684

    0.45232815960.48484848480.12177669770.6666666667

    0.45232815960.48484848480.12191170510.667405765

    0.45232815960.48484848480.12204671260.6681448633

    0.45306725790.48484848480.122181720.6688839616

    0.45380635620.48484848480.12231672740.6696230599

    0.45380635620.48558758310.12245173480.6703621582

    0.45380635620.48558758310.12258674230.6711012565

    0.45454545450.48558758310.12272174970.6718403548

    0.45528455280.48558758310.12285675710.6725794531

    0.45528455280.48558758310.12299176450.6733185514

    0.45528455280.48558758310.1231267720.6740576497

    0.45528455280.48558758310.12326177940.674796748

    0.45602365110.48558758310.12339678680.6755358463

    0.45602365110.48558758310.12353179420.6762749446

    0.45602365110.48558758310.12366680170.6770140429

    0.45602365110.48558758310.12380180910.6777531412

    0.45602365110.48558758310.12393681650.6784922395

    0.45602365110.48632668140.1240718240.6792313378

    0.45602365110.48706577970.12420683140.6799704361

    0.45602365110.48706577970.12434183880.6807095344

    0.45602365110.48706577970.12447684620.6814486327

    0.45602365110.48706577970.12461185370.682187731

    0.45602365110.48706577970.12474686110.6829268293

    0.45602365110.48706577970.12488186850.6836659276

    0.45676274940.48706577970.12501687590.6844050259

    0.45676274940.48706577970.12515188340.6851441242

    0.45676274940.48706577970.12528689080.6858832225

    0.45750184770.48706577970.12542189820.6866223208

    0.45750184770.48706577970.12555690560.6873614191

    0.45750184770.48706577970.12569191310.6881005174

    0.4582409460.48706577970.12582692050.6888396157

    0.4582409460.48706577970.12596192790.689578714

    0.4582409460.48706577970.12609693530.6903178123

    0.4582409460.48706577970.12623194280.6910569106

    0.45898004430.48706577970.12636695020.6917960089

    0.45971914260.48706577970.12650195760.6925351072

    0.45971914260.48706577970.1266369650.6932742055

    0.45971914260.48706577970.12677197250.6940133038

    0.45971914260.4878048780.12690697990.6947524021

    0.45971914260.4878048780.12704198730.6954915004

    0.46045824090.4878048780.12717699470.6962305987

    0.46045824090.4878048780.12731200220.696969697

    0.46045824090.4878048780.12744700960.6977087953

    0.46045824090.4878048780.1275820170.6984478936

    0.46045824090.4878048780.12771702440.6991869919

    0.46045824090.4878048780.12785203190.6999260902

    0.46045824090.4878048780.12798703930.7006651885

    0.46045824090.48854397630.12812204670.7014042868

    0.46045824090.48928307460.12825705410.7021433851

    0.46119733920.48928307460.12839206160.7028824834

    0.46119733920.48928307460.1285270690.7036215817

    0.46119733920.48928307460.12866207640.70436068

    0.46119733920.48928307460.12879708380.7050997783

    0.46193643750.48928307460.12893209130.7058388766

    0.46267553580.48928307460.12906709870.7065779749

    0.46267553580.48928307460.12920210610.7073170732

    0.46267553580.48928307460.12933711350.7080561715

    0.46341463410.48928307460.1294721210.7087952698

    0.46341463410.48928307460.12960712840.7095343681

    0.46415373240.48928307460.12974213580.7102734664

    0.46415373240.48928307460.12987714320.7110125647

    0.46415373240.48928307460.13001215070.711751663

    0.46415373240.48928307460.13014715810.7124907613

    0.46415373240.48928307460.13028216550.7132298596

    0.46415373240.48928307460.13041717290.7139689579

    0.46415373240.48928307460.13055218040.7147080562

    0.46489283070.48928307460.13068718780.7154471545

    0.46489283070.48928307460.13082219520.7161862528

    0.46489283070.48928307460.13095720260.7169253511

    0.46489283070.48928307460.13109221010.7176644494

    0.46489283070.48928307460.13122721750.7184035477

    0.4656319290.49002217290.13136222490.719142646

    0.4656319290.49002217290.13149723230.7198817443

    0.4656319290.49002217290.13163223980.7206208426

    0.4656319290.49002217290.13176724720.7213599409

    0.46637102730.49002217290.13190225460.7220990392

    0.46637102730.49002217290.1320372620.7228381375

    0.46637102730.49002217290.13217226950.7235772358

    0.46637102730.49002217290.13230727690.7243163341

    0.46637102730.49076127120.13244228430.7250554324

    0.46637102730.49076127120.13257729180.7257945307

    0.46637102730.49076127120.13271229920.726533629

    0.46637102730.49076127120.13284730660.7272727273

    0.46637102730.49076127120.1329823140.7280118256

    0.46637102730.49076127120.13311732150.7287509239

    0.46637102730.49076127120.13325232890.7294900222

    0.46637102730.49076127120.13338733630.7302291205

    0.46711012560.49076127120.13352234370.7309682188

    0.46784922390.49076127120.13365735120.7317073171

    0.46784922390.49076127120.13379235860.7324464154

    0.46858832220.49076127120.1339273660.7331855137

    0.46858832220.49076127120.13406237340.733924612

    0.46858832220.49076127120.13419738090.7346637103

    0.46858832220.49076127120.13433238830.7354028086

    0.46932742050.49076127120.13446739570.7361419069

    0.46932742050.49076127120.13460240310.7368810052

    0.46932742050.49076127120.13473741060.7376201035

    0.46932742050.49076127120.1348724180.7383592018

    0.46932742050.49076127120.13500742540.7390983001

    0.47006651880.49076127120.13514243280.7398373984

    0.47006651880.49076127120.13527744030.7405764967

    0.47080561710.49076127120.13541244770.741315595

    0.47080561710.49150036950.13554745510.7420546933

    0.47080561710.49150036950.13568246250.7427937916

    0.47080561710.49150036950.135817470.7435328899

    0.47154471540.49150036950.13595247740.7442719882

    0.47228381370.49150036950.13608748480.7450110865

    0.47228381370.49150036950.13622249220.7457501848

    0.4730229120.49150036950.13635749970.7464892831

    0.47376201030.49150036950.13649250710.7472283814

    0.47450110860.49223946780.13662751450.7479674797

    0.47450110860.49297856610.13676252190.748706578

    0.47450110860.49371766440.13689752940.7494456763

    0.47450110860.49371766440.13703253680.7501847746

    0.47450110860.49371766440.13716754420.7509238729

    0.47524020690.49371766440.13730255160.7516629712

    0.47524020690.49445676270.13743755910.7524020695

    0.47524020690.49445676270.13757256650.7531411678

    0.47524020690.49445676270.13770757390.7538802661

    0.47524020690.49445676270.13784258130.7546193644

    0.47597930520.49445676270.13797758880.7553584627

    0.47597930520.49445676270.13811259620.756097561

    0.47597930520.49445676270.13824760360.7568366593

    0.47597930520.49445676270.1383826110.7575757576

    0.47597930520.49445676270.13851761850.7583148559

    0.47597930520.4951958610.13865262590.7590539542

    0.47597930520.4951958610.13878763330.7597930525

    0.47597930520.4951958610.13892264070.7605321508

    0.47671840350.4951958610.13905764820.7612712491

    0.47745750180.4951958610.13919265560.7620103474

    0.47745750180.4951958610.1393276630.7627494457

    0.47819660010.4951958610.13946267040.763488544

    0.47819660010.4951958610.13959767790.7642276423

    0.47893569840.4951958610.13973268530.7649667406

    0.47967479670.4951958610.13986769270.7657058389

    0.47967479670.49593495930.14000270010.7664449372

    0.4804138950.49593495930.14013770760.7671840355

    0.4804138950.49667405760.1402727150.7679231338

    0.4804138950.49667405760.14040772240.7686622321

    0.4804138950.49667405760.14054272990.7694013304

    0.4804138950.49667405760.14067773730.7701404287

    0.48115299330.49667405760.14081274470.770879527

    0.48189209160.49667405760.14094775210.7716186253

    0.48189209160.49667405760.14108275960.7723577236

    0.48189209160.49667405760.1412177670.7730968219

    0.48189209160.49667405760.14135277440.7738359202

    0.48263118990.49667405760.14148778180.7745750185

    0.48263118990.49667405760.14162278930.7753141168

    0.48263118990.49667405760.14175779670.7760532151

    0.48337028820.49667405760.14189280410.7767923134

    0.48337028820.49667405760.14202781150.7775314117

    0.48337028820.49667405760.1421628190.77827051

    0.48337028820.49667405760.14229782640.7790096083

    0.48337028820.49667405760.14243283380.7797487066

    0.48337028820.49667405760.14256784120.7804878049

    0.48337028820.49667405760.14270284870.7812269032

    0.48337028820.49667405760.14283785610.7819660015

    0.48337028820.49667405760.14297286350.7827050998

    0.48337028820.49667405760.14310787090.7834441981

    0.48337028820.49667405760.14324287840.7841832964

    0.48337028820.49667405760.14337788580.7849223947

    0.48337028820.49741315590.14351289320.785661493

    0.48337028820.49741315590.14364790060.7864005913

    0.48337028820.49741315590.14378290810.7871396896

    0.48337028820.49741315590.14391791550.7878787879

    0.48337028820.49741315590.14405292290.7886178862

    0.48410938650.49741315590.14418793030.7893569845

    0.48410938650.49741315590.14432293780.7900960828

    0.48410938650.49741315590.14445794520.7908351811

    0.48410938650.49741315590.14459295260.7915742794

    0.48410938650.49815225420.144727960.7923133777

    0.48410938650.49815225420.14486296750.793052476

    0.48410938650.49815225420.14499797490.7937915743

    0.48410938650.49815225420.14513298230.7945306726

    0.48410938650.49815225420.14526798970.7952697709

    0.48410938650.49815225420.14540299720.7960088692

    0.48410938650.49889135250.14553800460.7967479675

    0.48410938650.49889135250.1456730120.7974870658

    0.48410938650.49889135250.14580801940.7982261641

    0.48410938650.49889135250.14594302690.7989652624

    0.48410938650.49889135250.14607803430.7997043607

    0.48410938650.49889135250.14621304170.800443459

    0.48410938650.49889135250.14634804910.8011825573

    0.48484848480.49889135250.14648305660.8019216556

    0.48484848480.49963045080.1466180640.8026607539

    0.48484848480.49963045080.14675307140.8033998522

    0.48484848480.49963045080.14688807880.8041389505

    0.48484848480.49963045080.14702308630.8048780488

    0.48484848480.50036954920.14715809370.8056171471

    0.48484848480.50036954920.14729310110.8063562454

    0.48484848480.50036954920.14742810850.8070953437

    0.48558758310.50036954920.1475631160.807834442

    0.48558758310.50036954920.14769812340.8085735403

    0.48558758310.50036954920.14783313080.8093126386

    0.48558758310.50036954920.14796813820.8100517369

    0.48558758310.50036954920.14810314570.8107908352

    0.48558758310.50036954920.14823815310.8115299335

    0.48632668140.50036954920.14837316050.8122690318

    0.48632668140.50036954920.14850816790.8130081301

    0.48632668140.50036954920.14864317540.8137472284

    0.48706577970.50036954920.14877818280.8144863267

    0.4878048780.50110864750.14891319020.815225425

    0.48854397630.50110864750.14904819770.8159645233

    0.48928307460.50110864750.14918320510.8167036216

    0.49002217290.50110864750.14931821250.8174427199

    0.49002217290.50184774580.14945321990.8181818182

    0.49002217290.50184774580.14958822740.8189209165

    0.49002217290.50184774580.14972323480.8196600148

    0.49002217290.50184774580.14985824220.8203991131

    0.49002217290.50184774580.14999324960.8211382114

    0.49002217290.50184774580.15012825710.8218773097

    0.49002217290.50184774580.15026326450.822616408

    0.49002217290.50184774580.15039827190.8233555063

    0.49002217290.50184774580.15053327930.8240946046

    0.49002217290.50184774580.15066828680.8248337029

    0.49002217290.50184774580.15080329420.8255728012

    0.49076127120.50184774580.15093830160.8263118995

    0.49150036950.50184774580.1510733090.8270509978

    0.49150036950.50184774580.15120831650.8277900961

    0.49150036950.50258684410.15134332390.8285291944

    0.49150036950.50258684410.15147833130.8292682927

    0.49150036950.50258684410.15161333870.830007391

    0.49150036950.50258684410.15174834620.8307464893

    0.49150036950.50332594240.15188335360.8314855876

    0.49150036950.50332594240.1520183610.8322246859

    0.49223946780.50332594240.15215336840.8329637842

    0.49223946780.50406504070.15228837590.8337028825

    0.49223946780.50406504070.15242338330.8344419808

    0.49223946780.50406504070.15255839070.8351810791

    0.49223946780.50406504070.15269339810.8359201774

    0.49223946780.50406504070.15282840560.8366592757

    0.49223946780.50406504070.1529634130.837398374

    0.49223946780.50406504070.15309842040.8381374723

    0.49223946780.50406504070.15323342780.8388765706

    0.49297856610.50406504070.15336843530.8396156689

    0.49371766440.5048041390.15350344270.8403547672

    0.49445676270.5048041390.15363845010.8410938655

    0.49445676270.5048041390.15377345750.8418329638

    0.4951958610.5048041390.1539084650.8425720621

    0.4951958610.5048041390.15404347240.8433111604

    0.4951958610.5048041390.15417847980.8440502587

    0.4951958610.50554323730.15431348720.844789357

    0.4951958610.50554323730.15444849470.8455284553

    0.4951958610.50554323730.15458350210.8462675536

    0.4951958610.50554323730.15471850950.8470066519

    0.4951958610.50554323730.15485351690.8477457502

    0.4951958610.50554323730.15498852440.8484848485

    0.4951958610.50554323730.15512353180.8492239468

    0.4951958610.50628233560.15525853920.8499630451

    0.4951958610.50628233560.15539354660.8507021434

    0.49593495930.50628233560.15552855410.8514412417

    0.49667405760.50628233560.15566356150.85218034

    0.49667405760.50702143390.15579856890.8529194383

    0.49667405760.50702143390.15593357630.8536585366

    0.49667405760.50702143390.15606858380.8543976349

    0.49667405760.50702143390.15620359120.8551367332

    0.49667405760.50702143390.15633859860.8558758315

    0.49667405760.50702143390.1564736060.8566149298

    0.49667405760.50702143390.15660861350.8573540281

    0.49667405760.50702143390.15674362090.8580931264

    0.49667405760.50702143390.15687862830.8588322247

    0.49741315590.50702143390.15701363570.859571323

    0.49741315590.50702143390.15714864320.8603104213

    0.49741315590.50702143390.15728365060.8610495196

    0.49741315590.50776053220.1574186580.8617886179

    0.49741315590.50776053220.15755366550.8625277162

    0.49815225420.50849963050.15768867290.8632668145

    0.49815225420.50849963050.15782368030.8640059128

    0.49815225420.50849963050.15795868770.8647450111

    0.49815225420.50849963050.15809369520.8654841094

    0.49815225420.50849963050.15822870260.8662232077

    0.49815225420.50849963050.158363710.866962306

    0.49889135250.50849963050.15849871740.8677014043

    0.49889135250.50849963050.15863372490.8684405026

    0.49889135250.50849963050.15876873230.8691796009

    0.49889135250.50849963050.15890373970.8699186992

    0.49889135250.50849963050.15903874710.8706577975

    0.49889135250.50849963050.15917375460.8713968958

    0.49889135250.50849963050.1593087620.8721359941

    0.49889135250.50849963050.15944376940.8728750924

    0.49889135250.50849963050.15957877680.8736141907

    0.49889135250.50849963050.15971378430.874353289

    0.49889135250.50849963050.15984879170.8750923873

    0.49889135250.50849963050.15998379910.8758314856

    0.49889135250.50923872880.16011880650.8765705839

    0.49889135250.50923872880.1602538140.8773096822

    0.49963045080.50923872880.16038882140.8780487805

    0.50036954920.50923872880.16052382880.8787878788

    0.50036954920.50923872880.16065883620.8795269771

    0.50036954920.50923872880.16079384370.8802660754

    0.50036954920.50923872880.16092885110.8810051737

    0.50036954920.50923872880.16106385850.881744272

    0.50110864750.50923872880.16119886590.8824833703

    0.50110864750.50923872880.16133387340.8832224686

    0.50184774580.50997782710.16146888080.8839615669

    0.50184774580.51071692540.16160388820.8847006652

    0.50258684410.51071692540.16173889560.8854397635

    0.50258684410.51071692540.16187390310.8861788618

    0.50258684410.51145602370.16200891050.8869179601

    0.50258684410.51145602370.16214391790.8876570584

    0.50258684410.51145602370.16227892530.8883961567

    0.50332594240.51145602370.16241393280.889135255

    0.50406504070.51145602370.16254894020.8898743533

    0.50406504070.51145602370.16268394760.8906134516

    0.50406504070.5121951220.1628189550.8913525499

    0.50406504070.5121951220.16295396250.8920916482

    0.50406504070.51293422030.16308896990.8928307465

    0.50406504070.51293422030.16322397730.8935698448

    0.50406504070.51367331860.16335898470.8943089431

    0.50406504070.51367331860.16349399220.8950480414

    0.50406504070.51367331860.16362899960.8957871397

    0.5048041390.51367331860.1637640070.896526238

    0.5048041390.51367331860.16389901440.8972653363

    0.5048041390.51367331860.16403402190.8980044346

    0.5048041390.51367331860.16416902930.8987435329

    0.5048041390.51441241690.16430403670.8994826312

    0.50554323730.51441241690.16443904410.9002217295

    0.50628233560.51441241690.16457405160.9009608278

    0.50702143390.51441241690.1647090590.9016999261

    0.50776053220.51441241690.16484406640.9024390244

    0.50776053220.51441241690.16497907380.9031781227

    0.50776053220.51441241690.16511408130.903917221

    0.50776053220.51441241690.16524908870.9046563193

    0.50776053220.51441241690.16538409610.9053954176

    0.50776053220.51441241690.16551910360.9061345159

    0.50776053220.51441241690.1656541110.9068736142

    0.50849963050.51441241690.16578911840.9076127125

    0.50923872880.51441241690.16592412580.9083518108

    0.50923872880.51441241690.16605913330.9090909091

    0.50923872880.51515151520.16619414070.9098300074

    0.50997782710.51515151520.16632914810.9105691057

    0.50997782710.51515151520.16646415550.911308204

    0.51071692540.51515151520.1665991630.9120473023

    0.51071692540.51589061350.16673417040.9127864006

    0.51145602370.51589061350.16686917780.9135254989

    0.5121951220.51589061350.16700418520.9142645972

    0.5121951220.51589061350.16713919270.9150036955

    0.5121951220.51589061350.16727420010.9157427938

    0.5121951220.51589061350.16740920750.9164818921

    0.5121951220.51589061350.16754421490.9172209904

    0.5121951220.51589061350.16767922240.9179600887

    0.51293422030.51589061350.16781422980.918699187

    0.51367331860.51589061350.16794923720.9194382853

    0.51441241690.51589061350.16808424460.9201773836

    0.51441241690.51589061350.16821925210.9209164819

    0.51515151520.51589061350.16835425950.9216555802

    0.51589061350.51589061350.16848926690.9223946785

    0.51662971180.51589061350.16862427430.9231337768

    0.51662971180.51662971180.16875928180.9238728751

    0.51662971180.51662971180.16889428920.9246119734

    0.51736881010.51662971180.16902929660.9253510717

    0.51736881010.51662971180.1691643040.92609017

    0.51810790840.51662971180.16929931150.9268292683

    0.51810790840.51662971180.16943431890.9275683666

    0.51810790840.51662971180.16956932630.9283074649

    0.51810790840.51662971180.16970433370.9290465632

    0.51884700670.51662971180.16983934120.9297856615

    0.51884700670.51662971180.16997434860.9305247598

    0.51884700670.51662971180.1701093560.9312638581

    0.51884700670.51662971180.17024436340.9320029564

    0.51884700670.51662971180.17037937090.9327420547

    0.51884700670.51662971180.17051437830.933481153

    0.51884700670.51736881010.17064938570.9342202513

    0.51884700670.51736881010.17078439310.9349593496

    0.51884700670.51736881010.17091940060.9356984479

    0.5195861050.51810790840.1710544080.9364375462

    0.5195861050.51884700670.17118941540.9371766445

    0.5195861050.51884700670.17132442280.9379157428

    0.52032520330.51884700670.17145943030.9386548411

    0.52032520330.51884700670.17159443770.9393939394

    0.52032520330.5195861050.17172944510.9401330377

    0.52032520330.5195861050.17186445250.940872136

    0.52032520330.5195861050.171999460.9416112343

    0.52032520330.5195861050.17213446740.9423503326

    0.52106430160.52032520330.17226947480.9430894309

    0.52106430160.52032520330.17240448220.9438285292

    0.52106430160.52032520330.17253948970.9445676275

    0.52106430160.52032520330.17267449710.9453067258

    0.52106430160.52032520330.17280950450.9460458241

    0.52180339990.52032520330.17294451190.9467849224

    0.52180339990.52032520330.17307951940.9475240207

    0.52180339990.52032520330.17321452680.948263119

    0.52180339990.52032520330.17334953420.9490022173

    0.52254249820.52032520330.17348454160.9497413156

    0.52328159650.52032520330.17361954910.9504804139

    0.52328159650.52032520330.17375455650.9512195122

    0.52328159650.52032520330.17388956390.9519586105

    0.52328159650.52106430160.17402457140.9526977088

    0.52402069480.52106430160.17415957880.9534368071

    0.52402069480.52106430160.17429458620.9541759054

    0.52402069480.52106430160.17442959360.9549150037

    0.52402069480.52180339990.17456460110.955654102

    0.52402069480.52254249820.17469960850.9563932003

    0.52402069480.52328159650.17483461590.9571322986

    0.52475979310.52328159650.17496962330.9578713969

    0.52475979310.52328159650.17510463080.9586104952

    0.52475979310.52328159650.17523963820.9593495935

    0.52475979310.52328159650.17537464560.9600886918

    0.52475979310.52328159650.1755096530.9608277901

    0.52549889140.52328159650.17564466050.9615668884

    0.52549889140.52328159650.17577966790.9623059867

    0.52549889140.52328159650.17591467530.963045085

    0.52549889140.52328159650.17604968270.9637841833

    0.52549889140.52328159650.17618469020.9645232816

    0.52549889140.52328159650.17631969760.9652623799

    0.52549889140.52328159650.1764547050.9660014782

    0.52549889140.52328159650.17658971240.9667405765

    0.52623798970.52328159650.17672471990.9674796748

    0.52623798970.52328159650.17685972730.9682187731

    0.52623798970.52328159650.17699473470.9689578714

    0.5269770880.52328159650.17712974210.9696969697

    0.5269770880.52402069480.17726474960.970436068

    0.5269770880.52402069480.1773997570.9711751663

    0.5269770880.52402069480.17753476440.9719142646

    0.5269770880.52402069480.17766977180.9726533629

    0.5269770880.52402069480.17780477930.9733924612

    0.5269770880.52402069480.17793978670.9741315595

    0.5269770880.52402069480.17807479410.9748706578

    0.5269770880.52475979310.17820980150.9756097561

    0.5269770880.52475979310.1783448090.9763488544

    0.5269770880.52475979310.17847981640.9770879527

    0.52771618630.52549889140.17861482380.977827051

    0.52771618630.52549889140.17874983120.9785661493

    0.52771618630.52549889140.17888483870.9793052476

    0.52845528460.52549889140.17901984610.9800443459

    0.52919438290.52549889140.17915485350.9807834442

    0.52919438290.52549889140.17928986090.9815225425

    0.52993348120.52549889140.17942486840.9822616408

    0.52993348120.52549889140.17955987580.9830007391

    0.52993348120.52549889140.17969488320.9837398374

    0.52993348120.52549889140.17982989060.9844789357

    0.52993348120.52549889140.17996489810.985218034

    0.52993348120.52623798970.18009990550.9859571323

    0.52993348120.52623798970.18023491290.9866962306

    0.52993348120.52623798970.18036992030.9874353289

    0.52993348120.52623798970.18050492780.9881744272

    0.53067257950.52623798970.18063993520.9889135255

    0.53141167780.5269770880.18077494260.9896526238

    0.53141167780.5269770880.180909950.9903917221

    0.53215077610.5269770880.18104495750.9911308204

    0.53288987440.5269770880.18117996490.9918699187

    0.53288987440.5269770880.18131497230.992609017

    0.53288987440.5269770880.18144997970.9933481153

    0.53362897270.5269770880.18158498720.9940872136

    0.5343680710.5269770880.18171999460.9948263119

    0.5343680710.5269770880.1818550020.9955654102

    0.5343680710.5269770880.18199000950.9963045085

    0.5343680710.5269770880.18212501690.9970436068

    0.5343680710.5269770880.18226002430.9977827051

    0.5343680710.5269770880.18239503170.9985218034

    0.5343680710.5269770880.18253003920.9992609017

    0.5343680710.5269770880.18266504661

    0.5343680710.5269770880.1828000541

    0.5343680710.5269770880.18293506141

    0.53510716930.52771618630.18307006891

    0.53510716930.52771618630.18320507631

    0.53510716930.52845528460.18334008371

    0.53510716930.52845528460.18347509111

    0.53510716930.52845528460.18361009861

    0.53510716930.52845528460.1837451061

    0.53584626760.52845528460.18388011341

    0.53584626760.52845528460.18401512081

    0.53584626760.52845528460.18415012831

    0.53584626760.52845528460.18428513571

    0.53584626760.52845528460.18442014311

    0.53658536590.52845528460.18455515051

    0.53658536590.52845528460.1846901581

    0.53732446420.52845528460.18482516541

    0.53806356250.52845528460.18496017281

    0.53806356250.52845528460.18509518021

    0.53880266080.52845528460.18523018771

    0.53880266080.52845528460.18536519511

    0.53880266080.52845528460.18550020251

    0.53880266080.52845528460.18563520991

    0.53880266080.52845528460.18577021741

    0.53880266080.52845528460.18590522481

    0.53880266080.52845528460.18604023221

    0.53954175910.52845528460.18617523961

    0.53954175910.52845528460.18631024711

    0.54028085740.52845528460.18644525451

    0.54028085740.52845528460.18658026191

    0.54028085740.52919438290.18671526931

    0.54101995570.52919438290.18685027681

    0.54101995570.52919438290.18698528421

    0.54101995570.52919438290.18712029161

    0.54101995570.52919438290.1872552991

    0.54101995570.52919438290.18739030651

    0.54101995570.52919438290.18752531391

    0.54101995570.52919438290.18766032131

    0.54101995570.52919438290.18779532871

    0.54101995570.52919438290.18793033621

    0.54101995570.52919438290.18806534361

    0.5417590540.52919438290.1882003511

    0.5417590540.52919438290.18833535841

    0.54249815230.52919438290.18847036591

    0.54249815230.52919438290.18860537331

    0.54249815230.52919438290.18874038071

    0.54249815230.52919438290.18887538811

    0.54249815230.52919438290.18901039561

    0.54249815230.52919438290.1891454031

    0.54249815230.52919438290.18928041041

    0.54249815230.52919438290.18941541781

    0.54249815230.52919438290.18955042531

    0.54249815230.52919438290.18968543271

    0.54249815230.52919438290.18982044011

    0.54249815230.52919438290.18995544751

    0.54249815230.52919438290.1900904551

    0.54249815230.52919438290.19022546241

    0.5424