Monte-Carlo estimation of Pi
Statement
Goal
A method to approximate PI is to place N random points in a x-y diagram with x and y between 0 and 1.Then we check which of these points are at a distance smaller or equal to 1 from the origin (0,0). The rate obtained corresponds to PI/4.
From the points you will receive in input, produce the estimation of PI.
Input
N the number of points you will receive to estimate PI.
x the x value of the point
y the y value of the point
x the x value of the point
y the y value of the point
Output
One line which is the estimation of PI. All answers have at most 3 decimal digits, provide them all without trailing zeros.
Constraints
5 < N < 1,000
0 ≤ x ≤ 1
0 ≤ y ≤ 1
0 ≤ x ≤ 1
0 ≤ y ≤ 1
Example
Input
10 0.44665087470084275 0.7814409871720857 0.7041731240004209 0.4788892619817777 0.5886575238238624 0.7324955170095947 0.6565434828324502 0.7039153745498603 0.5775729855984102 0.3079992953472084 0.5172871993693507 0.8574159866720961 0.31215370368367445 0.5742290301153288 0.5068821107488173 0.827249751259953 0.47115127211491314 0.7567791894886847 0.7243752278897876 0.718696681541423
Output
3.2
Game modes
Fastest, Shortest
Test cases
Weak approximation Test
Input
10
0.44665087470084275 0.7814409871720857
0.7041731240004209 0.4788892619817777
0.5886575238238624 0.7324955170095947
0.6565434828324502 0.7039153745498603
0.5775729855984102 0.3079992953472084
0.5172871993693507 0.8574159866720961
0.31215370368367445 0.5742290301153288
0.5068821107488173 0.827249751259953
0.47115127211491314 0.7567791894886847
0.7243752278897876 0.718696681541423
Output
3.2
Weak approximation Validator
Input
10
0.3816348435318292 0.16628762461829172
0.8709965398820737 0.434080621621438
0.9810498355782272 0.6125094703876784
0.37060854184525716 0.3520949596651306
0.15431880930035435 0.633689084990365
0.0669963239639414 0.7931814774932647
0.7697967192600041 0.39645109715981
0.16185410095794428 0.09448270231437961
0.1494901590661205 0.3039946752346987
0.2825277375218066 0.5562984820627004
Output
3.6
More fine but... Test
Input
100
0.7806703833043529 0.8084989914376163
0.03206874409823346 0.284356206903309
0.9052611302828668 0.052136658408795
0.7788956659748854 0.6051567206630364
0.21525182436700574 0.9512450685353645
0.5457083034736901 0.6489310825039813
0.7536536115261395 0.8155871134820206
0.7982153844238143 0.21834768140087968
0.21278362351681135 0.6650720754931843
0.023484624186998482 0.08855159244892774
0.6076624255720021 0.8364239975852418
0.6987082915448508 0.9238307219752703
0.469498847266152 0.1068735866217736
0.7659399101505494 0.7216452275815362
0.4550583445442573 0.3432432327920627
0.05012029817849095 0.2234076022427366
0.6220385069621182 0.5859393209858165
0.9875349928614048 0.2646574938047619
0.5150337983559963 0.6287973098506122
0.6214298087450336 0.034878069948272805
0.957174925891225 0.15149071042635942
0.53502887091356 0.7703567248376597
0.06422465739843686 0.24978621993621186
0.5220732275548385 0.3756679639730752
0.051457531881609175 0.5449876762695847
0.39942983126256004 0.6359794380458825
0.16103825046104236 0.06017499388421743
0.25602550878279107 0.5383751789883052
0.4048945806749279 0.8185328360139665
0.05841807390247222 0.9830199445078641
0.6162406287522352 0.8248973461921485
0.6526140471430726 0.43579346947261943
0.8633433768136013 0.5603412824096353
0.5800308599242608 0.4058318709822111
0.5460645408119965 0.5609563228008656
0.2358297610611011 0.5915740847245444
0.9133004545649154 0.4714520007364197
0.6396120067629244 0.4090579708312637
0.3563396114448044 0.7988779587226329
0.095641081640781 0.7977618503917947
0.5798842365951993 0.21361680467176825
0.8320808512457472 0.18848064569455059
0.24594374266849206 0.6169061404210285
0.07593423049511372 0.1630877143556153
0.7018827718319596 0.545879737929187
0.0942084550119704 0.18595797609619558
0.831818268659658 0.6341345913499243
0.5746886104392517 0.4878211632321844
0.09031148511748144 0.8643812728058017
0.7728278502213185 0.7861947372560779
0.5900412547030306 0.34228679078022195
0.044052214393108025 0.37645114983265304
0.6180786435987371 0.4226216450064383
0.08063659877863338 0.8103559998588484
0.26374031388175234 0.860702690504327
0.7888762125038966 0.9454505172821153
0.322505975557676 0.28724657528789277
0.6733646019145042 0.4488667317245053
0.9478110195915249 0.4120691317299735
0.1284734068142518 0.9871422615405508
0.9793675494536791 0.4588095929168592
0.7426943619917185 0.07365440614478169
0.07124002349360503 0.727291066443477
0.26648123467946216 0.1570932258985691
0.6930152729450726 0.7307452744856143
0.6642709108021155 0.7662350145421832
0.7915378309060739 0.1918930983906073
0.5454909265088611 0.2715350356661337
0.8185088704712207 0.1811256586741119
0.004239130536115132 0.6467074153771353
0.18096722559568845 0.398416756157875
0.23613318692218166 0.7963039198046937
0.5431250168459671 0.39730054191477226
0.8896611065150928 0.6886549029798579
0.8490511592814926 0.5612949500359637
0.23199396424251173 0.3182293383101875
0.8683785899028641 0.712446171756884
0.9231144772159272 0.5720640388186242
0.6276137834449579 0.7481027664814193
0.45727875882632474 0.4482544242889328
0.8842437304648906 0.5337230918893899
0.06912884316770218 0.9856559900403952
0.7740360058184726 0.9240168232985931
0.6469486509365588 0.5600010237814426
0.740297142360706 0.5615778644395544
0.6513478704959393 0.41951877045043107
0.08132049371726868 0.8141251732993725
0.25172027490909044 0.6377996052765251
0.03182223331127776 0.6256414710545986
0.5838361979887665 0.2976486105854279
0.08577554179295899 0.7650273701711886
0.4737886352750176 0.2179719077314336
0.16937690689827767 0.10855640624605523
0.7767508396756595 0.2931710877893937
0.7274465014662997 0.7023952052689755
0.3823050966015743 0.42929519589188236
0.21796605508878553 0.31559585466507467
0.6175296664227613 0.41403592940782363
0.03886625763274565 0.8414853820590136
0.2676478486159267 0.05588516138786537
Output
3.08
More fine but... Validator
Input
100
0.09001796459366085 0.10764857741511491
0.23054842166554168 0.6532818829867145
0.12781635803449487 0.09728982219841431
0.034158858705921946 0.579705587657009
0.27878029331318976 0.7682155622288069
0.30110891825552055 0.4159527267758961
0.9680995354291904 0.25915969222668067
0.12113590800942386 0.9575435703259911
0.016922793024836458 0.19208059635215102
0.2138293655203154 0.40468827734701507
0.7220729330460509 0.5727323056052228
0.9417415434740196 0.4940235532662116
0.4338186335016432 0.5908094656984343
0.8004351229919948 0.1153524632793761
0.5225512130139266 0.9911269685363938
0.04977653742469845 0.23370111920469738
0.4935450914308117 0.8499438483170753
0.8856180056320324 0.8176020193879335
0.7351019834157567 0.30670022380425366
0.46328644586967693 0.39264729240092844
0.6008826613707627 0.5681265298870498
0.28704698410729323 0.30645221083713836
0.07593016095055016 0.18705012726019088
0.25222457903826967 0.04120027593675102
0.8442847055180195 0.09745259567526865
0.8506858082706559 0.3530320866731107
0.7296812218083019 0.8657399956805639
0.7977520024433544 0.768572226610845
0.7160932654526564 0.2488153417165695
0.5039846417847013 0.7247062683970993
0.9671317969519517 0.05364490912345121
0.7044602320608045 0.13047244302660366
0.14399645951543805 0.5017948368194189
0.9918554666983891 0.7360303177022665
0.2782475218045162 0.6455105105931634
0.5749044979827953 0.5957251293835697
0.3125403656552468 0.05077356787792908
0.24848451790775805 0.45368871222288754
0.24252790806197677 0.6458403328153315
0.8751035063862682 0.3689733041344886
0.4401414373860639 0.18999222549706274
0.9302962424922283 0.8187764801401439
0.20817097340539625 0.7248844975821718
0.6294223322469877 0.8620852203570184
0.08324121465031376 0.8049823155270577
0.11194247175300875 0.8441841953677314
0.2516224055710784 0.04140993780278934
0.9100757795417423 0.9552798817686124
0.26550009898918014 0.37358296659195633
0.39413654867611225 0.6220147717047394
0.15906376455224336 0.5615548202759414
0.46755773497428277 0.3234714191571506
0.7500904368570588 0.7006815834011478
0.9532088771978118 0.6066208236156186
0.3086867870020915 0.43922434008688394
0.9803786292206745 0.04294680164720488
0.6977914390530295 0.8947087833758436
0.5139516472381491 0.7104264631638384
0.9242275875594741 0.7125334060535352
0.44831137244750097 0.02010540725558152
0.15261925758504158 0.24377718273125504
0.31403629163230395 0.6325470664506843
0.7179535713062241 0.6588479073353944
0.07425957676370942 0.6438449671751825
0.3349040798918884 0.7701953101176505
0.8876951682849605 0.54095338980839
0.12004066418310222 0.31865566270635615
0.5701227767672258 0.555759952074378
0.49307657891833645 0.7357319200256999
0.0881919391886945 0.7800477028375733
0.8095366830604317 0.12025545790590197
0.8913718889713427 0.5187025100909216
0.06279812733708501 0.5949329247265814
0.8103257317317706 0.10349831693619249
0.935161191486302 0.5030545575732622
0.039628557679908805 0.687208663541056
0.7391797014934814 0.8017304492143208
0.016489344054562594 0.4098950028525842
0.2961220291589728 0.2162229371020985
0.40565019765944466 0.8789498177553231
0.441434523638513 0.9788748425536722
0.11965391380414558 0.9351224021823195
0.7640712188526197 0.9571977657889295
0.08411158945047104 0.095225758889524
0.5849103855067211 0.24957024985652598
0.45340918693151044 0.3241905406048641
0.09981886935465567 0.34484352879285585
0.8548072987847173 0.19928120992872123
0.16623461487392632 0.9367085772843132
0.18430412664792595 0.24434880735842557
0.5302403405624716 0.6117010352208625
0.37594768855581784 0.48372174218355446
0.14859925380364192 0.49136239711963403
0.37153049765283763 0.9998746751760035
0.17171989632506046 0.9379165788054268
0.3744561079601887 0.0881821021828596
0.0753794193356142 0.5093694179197564
0.2987815508541781 0.7628105127718212
0.701603360800742 0.3740066101409303
0.8788351134927926 0.4245174246830551
Output
3.16
That begins to be accurate Test
Input
200
0.2873350590410312 0.260515563697155
0.23963108080076978 0.35623603199816123
0.763771233643995 0.947658561329144
0.3066096525785057 0.34666115204534087
0.4008010219808614 0.4898082269284846
0.7661921125117216 0.44719248457553784
0.030127635333248803 0.5622505706463324
0.9315947336643993 0.18356831343098634
0.6548555455364673 0.40860562031522485
0.13157978603349318 0.567645578443643
0.011869479242873737 0.8364350665986753
0.9181120231615 0.4220552441486677
0.43466495071291966 0.08800276368925863
0.34877776941479766 0.6340898174681953
0.9033127012271979 0.7353534550506943
0.6831030328313213 0.03493868687256141
0.6574383969353051 0.9216408578730283
0.3272886662220089 0.03388894788620822
0.5218328509859861 0.3584565371538295
0.13735808659478033 0.2829148230556038
0.10806804893679611 0.4976846907997272
0.6129962623203215 0.32303211697618683
0.513275026661054 0.5086835375111899
0.7693694264231007 0.16221865144467418
0.6881700694683105 0.6412813386237427
0.6578329282548421 0.9902461037982597
0.6176367327616834 0.13171386934332696
0.27558843754912754 0.4361337469569512
0.8423024847275746 0.4355331734525031
0.5588876525991063 0.9956975721206837
0.3563079459536397 0.5080883870725266
0.01130730643657829 0.6431978381515404
0.3210782640458796 0.8308136267953214
0.2607782903569048 0.1019027744445804
0.4103982124358274 0.41932131118673743
0.5967116599349818 0.1755942614655024
0.4273553071096866 0.11296879678340443
0.2028652115662546 0.2979037296654564
0.6507544297347709 0.06521842026285118
0.4570805983877162 0.149139975817693
0.9767647798783592 0.4354439778548268
0.26032695845320375 0.3739018580988598
0.6869029719640598 0.322609058244012
0.26772387541491094 0.9602986544855923
0.6230549305150939 0.388017027890595
0.5125752742378585 0.24432415602973367
0.6524622099350365 0.7482479124145825
0.11376214454895706 0.04569288394832427
0.9248412561596375 0.12861524457217488
0.945517654018183 0.9890099193602828
0.8840584147499011 0.8373671072648177
0.9306340313563335 0.5103583346299881
0.9728538736784785 0.01985560554292687
0.18371027420735353 0.43892580323179564
0.9940145408419163 0.5183899830354518
0.15078912508722664 0.7784822341554308
0.5962217449599242 0.5244225696800304
0.8034732216717687 0.8271761026643165
0.8425003692581944 0.30066004232891896
0.46018711856338956 0.5435377988969209
0.3226646841448759 0.12921201555239403
0.15116652713048562 0.7119172753736397
0.49012028905275284 0.6128893929638518
0.538745263973043 0.6525222292043532
0.09494946067468368 0.6848539637200527
0.68436494308521 0.13335357273269244
0.9490695346394823 0.2258535672276647
0.6918462581040336 0.8003733661921544
0.06070218605741673 0.9497044620231153
0.9202763759530467 0.1261466150395858
0.643555015339805 0.42158301061928816
0.6803102418173378 0.7137753603883
0.6161184702703779 0.14933431518813622
0.5172832392803672 0.8247096042453492
0.6271135101560027 0.41009793996566457
0.4338159147623418 0.41758950453987886
0.15413921514442708 0.04963715187087203
0.34386549345234085 0.22723280678707447
0.9118368903570984 0.7847291912208402
0.9605855995333763 0.37785388709836853
0.6612257658141574 0.5786155180540878
0.47592486891717256 0.8977293876401531
0.799589365465179 0.6442258486456003
0.6974657828398655 0.2927077890763442
0.11753768881244064 0.6580471513887871
0.7025794142640397 0.619971508476067
0.5629697969671441 0.3394702408615511
0.8387162868197181 0.8434952995299595
0.3839195584357664 0.8709728150430156
0.045376773972189755 0.15918085291048967
0.9022839523389994 0.394306423988503
0.4142623770300151 0.6641861901437925
0.36923138408355494 0.004234416081776771
0.8884901012234488 0.3734192531526064
0.6573169707862873 0.13098340679655618
0.43115433154412497 0.5307819731148533
0.23112945157524067 0.15773817313755478
0.6621714812322933 0.8039556155487063
0.7052733238603722 0.8200104297788734
0.3282512557619919 0.1876430378788414
0.6370943776265046 0.4112700991166912
0.025965309122072955 0.6210934996620735
0.8448063993462231 0.2206429974441666
0.4447248818136311 0.7948260571027698
0.3966500595769311 0.32287695252909565
0.7102435484126305 0.9709883127127436
0.05315462757763745 0.5412882190427548
0.3398213107831729 0.9107626674041368
0.7186600139954222 0.7646958757260323
0.788198616891628 0.3369198771764005
0.6927434005221281 0.45303499272469006
0.24070207753477824 0.6026303974537948
0.06816386009522746 0.9813147601282405
0.19684009065363894 0.5331469124954971
0.5944891154663726 0.7640360448536893
0.48666309934007257 0.30723505543060925
0.7355124925709426 0.17457197405043234
0.3447520360031687 0.9679062793211695
0.8193260211395476 0.404624212463663
0.4675723763393047 0.29352529658636617
0.2945595956591277 0.6714554095119105
0.2037995225014243 0.8592844254479919
0.3458929713859762 0.8066191874396574
0.21815321838968604 0.31909056791123747
0.6958137724842783 0.7666272145448578
0.39302807028969244 0.644731850206595
0.8069238507807726 0.2543466955642725
0.21027648929362852 0.08073855409896524
0.9814861292074912 0.2948407046453664
0.21605188021034838 0.9647750506053521
0.479394448690596 0.6109133862641954
0.718016672943027 0.2400287212256127
0.44533746458725587 0.95574761133558
0.8907114652837841 0.13383418706890993
0.0040054274877079354 0.6285445569110187
0.026191817707080234 0.8998008736582565
0.8616946611413193 0.8328257234041618
0.4113373549373839 0.2903267245754917
0.26996025028197257 0.42813205778924923
0.7452283930477156 0.9445419297348517
0.7691538307379855 0.9311860060648707
0.7841578296868922 0.737284118797798
0.8222728229559179 0.31570826399370966
0.46763199571869096 0.6960791233371784
0.07671031721829946 0.6171640187648696
0.0345842811822934 0.3529480735521612
0.4757788270184956 0.30208637397211113
0.24771336865329419 0.37342065782426104
0.4009074529138601 0.2724872049197419
0.8594042567463762 0.9161631338080404
0.3811819626282862 0.6407881025299794
0.5070631626652036 0.1144659709173963
0.005427634820481142 0.12560536363731734
0.5963668328216505 0.6508461423094682
0.3628986797689824 0.0807926246615982
0.08517732980208614 0.5316719310759743
0.04935745940331504 0.7763240555773383
0.1279390310913795 0.3613479106644639
0.6183859529252509 0.32426863563620656
0.035647851554604704 0.22640319714548585
0.8183388429769421 0.9176507030108718
0.7163280362606592 0.07798875176677322
0.18196832015354203 0.11587625403998036
0.5532542015679515 0.5712526056030693
0.913285597221341 0.8811644955268716
0.4563900131009241 0.7306864248092287
0.3762515614920674 0.19966936660380852
0.09575681057035945 0.5303901596768441
0.7293330720694432 0.05918010694349907
0.374170483423107 0.21624425051920593
0.43483132810463065 0.4100858526375395
0.8883830543169802 0.6447573224261995
0.20694349874134188 0.1779484356658103
0.872320331221993 0.5635182903116988
0.49292172758788144 0.535601923683391
0.02414478589790714 0.2775339452822515
0.3674145620977429 0.06066803270191101
0.4072357688618232 0.5574698342722663
0.7670039333289767 0.5097158663689026
0.8629477419594404 0.1895121539590201
0.8346010456607152 0.937691096847569
0.46607363476625996 0.3034326086275899
0.5104487927603995 0.6492768364156215
0.8344793463733479 0.3981142253264517
0.1232667430415747 0.8426709750658273
0.6830887085730655 0.1315952255493169
0.5147354100696176 0.09623821379939834
0.5094965862174776 0.09173444910804418
0.3312517031377249 0.23371802495117233
0.7760903119464974 0.023582468862756834
0.19216620480236912 0.06555797626545856
0.04224719237552654 0.5307380262491369
0.2374904948225912 0.45381560345221617
0.5383352488949386 0.2573576317857308
0.15601984804894398 0.755241048710642
0.39984516237848333 0.861427925738584
0.8611714892577045 0.5841514287697397
0.7172770165492057 0.7378411132807333
0.38819499129367097 0.4982998146369392
0.7331010592775487 0.9314701619437231
Output
3.22
That begins to be accurate Validator
Input
200
0.2063595765222156 0.6784284274024733
0.9602414010608598 0.9158135406890435
0.8292216717185262 0.27646482426295926
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0.5069753733446735 0.995204352409484
0.8368506370543363 0.9252101546165711
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0.28520500374917956 0.5826138082032831
0.03535997439722238 0.9729111145177604
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0.8562922912882213 0.8819143917351135
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0.502577777428388 0.44178948783856653
0.36876268614508356 0.048763198420158416
0.16564013810889855 0.4258873770340441
0.10583713401307693 0.8405490982255434
0.23886697904106635 0.6915042918133374
0.05096846806788957 0.21235230323324483
0.6881349098593105 0.7954285330351849
0.4346983758924091 0.7113556968277593
0.3862118187354101 0.7232229604199253
0.129451486350047 0.4190453343310223
0.7282937107330045 0.4645209594886982
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0.21356634604499503 0.4725983044839329
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0.4426645693233028 0.2498450517381995
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0.12187280334197836 0.037334844943262335
0.14149124163004956 0.38609127647453967
0.9102468826825738 0.7253960627219073
0.7245107380243458 0.24142474363266497
0.5730876138091096 0.8371311151279287
0.806467142679244 0.3506899886984912
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0.4745514819713118 0.8780905712046534
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0.41300119715711203 0.04005517091613997
0.3936544185234071 0.5937198718335923
0.21378921088050118 0.3241235661391806
0.9256973499869676 0.7343940355625275
0.12514507192415036 0.7601794610633053
0.37903163435714937 0.1116802004738664
0.6161985640702196 0.1752562070852186
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0.5568107516466028 0.47959612031525267
0.04080731046930619 0.13485408580895453
0.7074581932189304 0.0001562868154082464
0.31523435183299464 0.01654811365044795
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0.11657621731076873 0.9866798515233182
0.4215998085082826 0.7025608549029562
0.5301076480152861 0.08468907402023684
0.9054789421368796 0.5025623769490432
0.4214296486609628 0.3088396783171463
0.48344181326083646 0.5166870803358474
0.7439587001682296 0.679065606014209
0.49894640420002967 0.55291165991331
0.613456072244985 0.9867224643432909
0.8868643424109797 0.37323777411788717
0.7031137291792081 0.8695872495968606
0.33929282143714945 0.23451799057082123
0.21358517102029217 0.22200744232166403
0.665969656091488 0.07123445397631911
0.06226566837887226 0.9453506277949795
0.1919229560160829 0.2621787279455564
0.7996064203926888 0.17745848843161205
0.06617498396653154 0.5757907985208967
0.7601974494399285 0.6130390418250546
0.45491777010871226 0.9145370790636558
0.7849846344427551 0.344514920910998
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0.07142538641298124 0.5194761345397964
0.13896255191726348 0.9029152673675616
0.3707856609902477 0.9907855089186541
0.5001499395794772 0.06559166202674183
0.2424511417913049 0.43463310993290005
0.3380812499204833 0.8544806601232565
0.29444587551023216 0.8633666123738727
0.363668437514885 0.9311748299755848
0.7443039056548071 0.5353008677504748
0.9720479958414797 0.12030025991447979
0.3172665402880266 0.7079267522320727
0.21529073241881025 0.26761300917348485
0.19657244833957832 0.029778711974829508
0.7878971175771854 0.03968854430538937
0.7591230690132507 0.6485656787821408
0.4642916007195652 0.0005554407665772088
0.9223978443115646 0.7731577385121905
0.6296006931860847 0.9634043698124272
0.786767747689168 0.39858637206229564
0.5996461876595496 0.7999535413782716
0.06137909736420177 0.32480449125917243
0.35490271022864517 0.267431785144685
0.6963484281328065 0.4899593786490667
0.8522685521576666 0.8277314237111525
0.8696680958721645 0.7436553741722031
0.038041795121297795 0.5219319000018495
0.00726324059178074 0.9352536826853324
0.7780721324985299 0.8851255434477907
0.43515155886463197 0.18437298738677532
0.48335404433643747 0.8007483631990719
0.08080052549281913 0.7380372943845154
0.5883748339171324 0.40909016585653035
0.5536218608733406 0.41726030213213416
0.6581638212249956 0.3915279519039503
0.13342364383292193 0.10676518166074256
0.00504743863882573 0.6794838306446488
0.5012305920559723 0.5099160453925567
0.7517091674863716 0.6605412728520135
0.9717570075918159 0.30747070095047224
0.7224058453842136 0.7203365571917334
0.012620158007891624 0.3625954161308341
0.17438780414971577 0.515807794205365
0.460687759138805 0.6702325519668207
0.41131242856191674 0.7604398972508489
0.18454052962668055 0.9477341578980925
0.0903575457161363 0.8417574190093183
0.14259143725987233 0.09476888483076085
0.34638583647982946 0.16635800182334204
Output
3.16
But sometimes it's not... Test
Input
250
0.5110793179490011 0.6171219757212693
0.5995994660809434 0.16061751005540303
0.10356022589656866 0.7208153125369622
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0.6651209169842104 0.5313153069965532
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0.5699056659065684 0.9162691770852002
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0.0914475006059352 0.6128048654639127
0.40621967531798275 0.3714595288513206
0.15560439150093996 0.3397910766623722
0.9686601154832867 0.7550643984845933
0.9824175948785143 0.2654883659500352
0.09888107716791139 0.1920243244957992
0.5446414697571764 0.8942047109222481
0.20601114121029585 0.6263147679988544
0.10208487948048373 0.7183144057870188
0.6245474323753607 0.38063534064558235
0.5649833443505673 0.8480447584775603
0.6715882182241023 0.3208941772184397
0.9064113381910559 0.8308836184471885
0.917264125516397 0.7975187100954402
0.30828783754604205 0.18621267188056656
0.17475031987101897 0.5584873839394843
0.7676799833258281 0.5982850272799257
0.2813793280617132 0.9824474729545379
0.6537478116099861 0.7308179992509453
0.8563762930991575 0.243645428593098
0.30464107646591854 0.49904665417625194
0.9285623329763217 0.5858761717866113
0.16987499245503324 0.4066837804114032
0.5726176811267961 0.17856410229475428
0.27041544611116175 0.06783510281761707
0.8784994678650164 0.4418168303991147
0.6243466990491703 0.12725351746170255
0.9087542631236801 0.7069718274347152
0.9829359196843331 0.76309048840084
0.9662952124480859 0.25541946824997974
0.39559762830376677 0.3381522781728792
0.8586879197526952 0.3068484893122758
0.5766589711551022 0.40775553476705584
0.3398729030722424 0.47987345370876533
0.9038988518821532 0.7779027849886242
0.4922884920071574 0.49737195704025683
0.7728679363995498 0.16288520349163982
0.7713918092819879 0.27505204130457683
0.32894744557794797 0.5269284360869362
0.2632660505580037 0.4358602259144667
0.4776237299377941 0.9570825345220025
0.3663530242636447 0.8685876235590655
0.7245764443440055 0.22772169898535166
0.4799330963483227 0.18806161544776412
0.9660777656175087 0.6819468011266784
0.31484075507641684 0.2731070824332694
0.5713990286323214 0.8516582993102844
0.5661061762368123 0.8535816260181739
0.9157591852091703 0.08579290921569727
0.5017179517460727 0.9701516920046499
0.8066689809796008 0.46075173112515344
0.7516277796238636 0.542945950314154
0.2254654019642658 0.4627649174938522
0.147426590108526 0.44335122608226674
0.7435956219184461 0.6656602370381128
0.37507229125448993 0.17724607059152997
0.5066291324015348 0.24574692150960742
0.5369758531496133 0.4326098298138047
0.5942280785790511 0.10660059220786677
0.7384006939088095 0.45290251541449533
0.7493442822689415 0.7448926340057966
0.19712129677730905 0.8087105139922699
0.8598880290240979 0.8431287389359811
0.7208114963256085 0.8283143858830938
0.8401662569206902 0.7555514324461549
0.517369610674437 0.8390698541935171
0.7198555825671528 0.4063106914450413
0.870036345146156 0.6440828973952527
0.6478973594092464 0.09622523260319438
0.09960493378714586 0.485051856082665
0.10175974620058514 0.5856290209376008
0.9579525611064484 0.6740207795129943
0.2212790689295222 0.04493030722494373
0.18559552538536817 0.6476228556751981
0.6683491465161221 0.20124891535206846
0.7131638667575172 0.3669731146305326
0.5781081366750942 0.30657307345762685
0.09057709332618469 0.2547765440249239
0.6300843147672294 0.5577902319592806
Output
2.912
But sometimes it's not... Validator
Input
250
0.49917685738212736 0.040341962803060016
0.11074218351690757 0.0278863343047846
0.09132434568006331 0.22690763232929523
0.495198424587905 0.8930110316075999
0.25509017136541 0.5656696314634501
0.4287130275417934 0.6360558493278515
0.2775531581976345 0.12736689201558093
0.0340995526830804 0.08475063049252152
0.9944340836694242 0.46285715159997
0.8474744825863605 0.8645982875652612
0.90254578911704 0.5629388059925584
0.7868684471976768 0.4653578257992993
0.5006398650397627 0.5367052434876699
0.30830535498687694 0.0032770748178968523
0.922729557974296 0.9970683881352842
0.8667698577225313 0.8891063108573186
0.9336259261194652 0.8446691269677309
0.08449682252563329 0.41423363310144345
0.23530968575868227 0.6693567002148888
0.30382053839571954 0.680969712509824
0.04719700723163711 0.6709238564812732
0.9939214082869328 0.617705635795158
0.5182377731429704 0.2865872657218731
0.04733855004177101 0.7051867983524787
0.14170489767377348 0.8944127639913582
0.21429290027597347 0.8207840595125167
0.4570654870635319 0.33715890947962524
0.4059887535990522 0.40016474158790616
0.4465970746532014 0.4093969149252511
0.04192571561827818 0.08782280209911242
0.8332877236158355 0.5077871698230959
0.01171605796613362 0.3944700521660407
0.8518707019975718 0.9519879782258321
0.11001408193418882 0.06242687132621039
0.07499325001076573 0.1750997778400668
0.46406214527693557 0.14650500948524514
0.5356285895420753 0.8105968310139953
0.6768060863885375 0.18611212634928875
0.5456704910026282 0.2540082594667592
0.46070404646350005 0.39575179845924935
0.25309886175958995 0.7910240306915612
0.2081832047822919 0.7808113958014021
0.6509108600212469 0.5388394386561909
0.7407068283608824 0.2338427891572472
0.07954185781080148 0.9948187945519825
0.8629614220097037 0.6417899732869821
0.21870541692863976 0.31993686554095313
0.05514236321451027 0.5959402943069022
0.47421720106712506 0.2974895708626536
0.5212711656782222 0.9450121465363471
0.22501334295820907 0.3261597153521236
0.3596462203354641 0.5349045730332609
0.06722394347854999 0.41549808817721345
0.02698561852798942 0.25354845414623306
0.658132050703567 0.45866566912219486
0.5465018183701431 0.4464125566925222
0.2893381635004475 0.09232263329565904
0.7231854715455142 0.18818862860018348
0.7988198841215457 0.882642419746477
0.2796550911121072 0.3160923338388708
0.1352254712676455 0.5367858738153273
0.48847010578672934 0.9710065820187075
0.31105966294215226 0.8979861863975044
0.651281289121559 0.9689931353522658
0.0922871878767193 0.9860194351092422
0.31329334989731183 0.1715874547104037
0.25396984211609175 0.06745526010401681
0.884951488756979 0.8268044331726407
0.07223789179203355 0.022393647219742463
0.7699041504762444 0.8153892130476558
0.8301683675676106 0.31656469931443265
0.9311914534957803 0.18694172506489515
0.49165368643323126 0.1291187641733721
0.5341269834475932 0.1534507974567818
0.8355184742466902 0.6221202076644825
0.9691615254395533 0.58664361305026
0.6459936981006982 0.4657221348046925
0.07390708475250407 0.6604222795842261
0.4226037338470505 0.5727556332390744
0.05556112791691148 0.03404544902549944
0.9694597192311002 0.6438518011314561
0.8443023662139877 0.5823218303479951
0.5506030503644505 0.5826598157400904
0.9364356781822332 0.9824486661081966
0.9592836347888348 0.6643972247008116
0.8200416771245366 0.7457469363145415
0.5043915158834973 0.8410651043422283
0.835452148179403 0.6178632463577257
0.5818281516658598 0.5549629619339622
0.08358572959654009 0.38822196372558393
0.748982935560893 0.5385052862867922
0.62971329411305 0.3023777099920726
0.751220751660933 0.9737059270525407
0.18015789005539484 0.603532974882254
0.059111983704168036 0.7141089184975852
0.25744220435934495 0.3139985653113605
0.3105972251797511 0.831077250341577
0.6076367015275328 0.18517774705491674
0.3107044100668205 0.6463225346983945
0.9588348434327452 0.3263179478034205
0.6777516843864494 0.7928936274417401
0.11593452407407068 0.47621728389827656
0.7613459221779527 0.10028148704090534
0.029977281492401642 0.010892861316356917
0.6995029264146897 0.2736109056416651
0.232440850709983 0.1043982156339901
0.7229973053611811 0.6551906650685342
0.6239857871100959 0.11344853467480975
0.4741529423844415 0.95006389385701
0.7273090558717491 0.9172420649791099
0.8601477865419705 0.910858697488333
0.13966722374048868 0.16085577228852477
0.7501351035791413 0.5251759597387474
0.23846386724462654 0.8021906359351487
0.21226322974944833 0.10276005584077552
0.17133880261027634 0.33509993545732253
0.8709198905287621 0.6062159162124473
0.5860422448315749 0.10243385338855004
0.15738440668168052 0.5857481882230805
0.182029871283664 0.5601303586179016
0.6120064948998477 0.015892897327251965
0.9133658450564649 0.6975424684975218
0.5689211347771784 0.09701288996880808
0.13820104419442603 0.10172928772729939
0.8289784192346576 0.28385792395033205
0.3518877938271603 0.9391270923756043
0.737126442774975 0.2640296263779206
0.7250180471285105 0.9627167083862017
0.6365333962367481 0.34514946246088984
0.3671611367178106 0.7925803219191337
0.3555824568100556 0.7430832860153427
0.4106897845671462 0.44410995494657524
0.9160712911456429 0.9892105431136902
0.9719100826520151 0.6132153972250488
0.38404774139428766 0.7867424840270308
0.7971669875370746 0.36046288634706214
0.10585985711763879 0.7974206000941508
0.03697740231446356 0.5971751535671793
0.532326840060492 0.7685454817573686
0.9829297476594079 0.8308015633561757
0.08177010063695644 0.9125638259490138
0.8120772731250361 0.09145560867294944
0.632801677049461 0.28112700999559725
0.6272826013125171 0.9778841127476512
0.9174294033828069 0.47103222209471574
0.6175200701268038 0.8978006296299088
0.980272630026352 0.44046148200030444
0.7434702221332268 0.983051894244619
0.11100849843184057 0.12073406344721904
0.5876495354587183 0.6845554829130397
0.23751157470663198 0.5930800827061815
0.11545956056225737 0.15276825615146006
0.5148676545910901 0.37052505078558307
0.7644493523494253 0.4355386732152364
0.860055109360721 0.054244353568590586
0.27182759749542773 0.7678966363686257
0.5269325841673955 0.009001669428023718
0.6365681763259976 0.5798996895883757
0.6884671449848637 0.26558627697813053
0.925436098378929 0.5125059120638912
0.2957476575508561 0.2595437212422179
0.18218278763971396 0.21754709084971335
0.21012051937045384 0.993787875234787
0.341022243717204 0.3338650168396724
0.29969085289480235 0.39642603322303804
0.7782251296911039 0.6539924313755463
0.9652647711858814 0.9998539602015409
0.08499203057107929 0.8745015387891498
0.5910500865148515 0.20206961821470093
0.42128566849574 0.9380483254733514
0.15499129446773385 0.26331357302395775
0.1788695067546684 0.3314028189728512
0.4076642911400148 0.8149623007270228
0.014264873549665547 0.6073978574014011
0.12804940031184409 0.7066654999730728
0.7810309282028114 0.6460749319825904
0.977719045115606 0.8676925711582655
0.5016240288228063 0.4086922636437539
0.3040030313351362 0.9213300027981988
0.9770453754415079 0.7221919289037826
6.18668464470451e-05 0.2354072929965132
0.14369050014638018 0.8173412473069999
0.3308450875568165 0.9254629473169763
0.49050468633521727 0.4631444254822906
0.7053887979872916 0.7496257786845015
0.7176602498125431 0.3305404061908531
0.6298980445895832 0.20554875636534042
0.10174129132537868 0.8381521140297638
0.36830221844854283 0.2521946590097528
0.315878572086559 0.37577241474846457
0.09892770313111443 0.6369861628561522
0.1339664786644511 0.5490838362764687
0.5901077288067882 0.0923582057594301
0.021071668368175533 0.6499322648142551
0.24487411348247534 0.7221250677996317
0.5616846548784346 0.15549733324098558
0.809123858357413 0.8420745825111213
0.8952945625803105 0.38230113585085934
0.8821843831813834 0.8406722636237391
0.007257289741517736 0.40977662305995344
0.8177785175440019 0.08710947644120903
0.6946303984439812 0.8602725206802916
0.19659455279323446 0.6090335414845361
0.6560276305599129 0.7099975237549777
0.3106244657037669 0.13304157701878416
0.8291695211850906 0.9132896740014311
0.3477510138857167 0.4891929212018511
0.041591951426148355 0.9752733430459597
0.3523575946483476 0.21538564137949512
0.555222494892471 0.7387329121982911
0.18704993626501976 0.16358837465225795
0.5625380814389408 0.3710356087935197
0.8244875871334577 0.6727692275738466
0.5385351890222239 0.7080390776723756
0.9778305213406046 0.04908263168860749
0.3036978938061543 0.9824312815533951
0.9452235927549071 0.940396094367047
0.6978213958676598 0.915191197240632
0.9124026683216985 0.6739450494717454
0.08359147818164392 0.5223191162658133
0.4183012424899585 0.9351612252957571
0.6389295976340622 0.9349803794841762
0.8782788118741016 0.5311900200087623
0.5424051399013254 0.8684031665965318
0.43961048750981224 0.046010965730857833
0.4330725286143221 0.7413468010547744
0.012018405088829565 0.1207544596503125
0.6935400622173776 0.6065747817811245
0.8248590657654327 0.3320479530404645
0.19986838078692304 0.7592292976579955
0.8093107937889978 0.10565192607422036
0.8635771759272167 0.1362955603999042
0.31920221448039343 0.9029363231569963
0.45726465475935796 0.13828646221634
0.05528855247826192 0.0016114808307186035
0.22039303822185963 0.39615436895033485
0.5962983749750997 0.6245955827788826
0.9457682765163207 0.8535616954682461
0.0004986600695164878 0.6069519867214048
0.5128500571123153 0.4485768715775287
0.24386600474623255 0.6214321976114803
0.5805823807435218 0.7013457384256306
0.4351752567375735 0.6472408925661622
0.4032856277390151 0.5660315178511655
0.07226520789552471 0.22371294738477743
0.07663012442505568 0.4772830056739028
0.07615556866751405 0.7710435339629067
0.942661961099663 0.16429246772490325
0.9157098691278708 0.1661754893274211
0.0834085879187153 0.13338460255303586
Output
2.96
Solution language
Solution
Stub generator input