Statistics

Problem Statement for "ChartError"

Problem Statement

Given a collection of real values, we want to represent them with a bar chart. Each value will be represented by a number of characters, and the bar chart will also display the value per character. For example, 
   Sales :  XXXXXXXXXX
   Profit:  XXXX
   Costs :  X
   (Each X has a value of 8.8)
In this bar chart, the "bar_value" of the first bar, which contains 10 characters, is 10*8.8 = 88.0

No bar in our chart is allowed to contain more than 15 characters, and each bar must contain an integer number of characters. Unfortunately, we may not be able to represent all the values exactly. We define the "bar_error" for a bar to be the absolute value of the difference between its bar_value and the true value that it is meant to represent. We define the "chart_error" for the bar chart to be the maximum bar_error.

Construct a class ChartError that contains a method minErr that is given a String[] val containing the values we want to represent in our bar chart as decimal strings, and that returns the minimum chart_error that is possible.

Definition

Class:
ChartError
Method:
minErr
Parameters:
String[]
Returns:
double
Method signature:
double minErr(String[] val)
(be sure your method is public)

Constraints

  • val will contain between 1 and 50 elements inclusive.
  • Each element of val will contain between 2 and 10 characters inclusive.
  • Each element of val will consist of digits '0'-'9' and exactly one decimal point.
  • Each element of val will have no more than 2 digits before the decimal point.

Examples

  1. {"88.0","44.0","8.8"}

    Returns: 0.0

    Use 8.8 as the value per character. Then assign 10 characters to 88.0, 5 to 44.0, and 1 to 8.8. The bar chart might appear as in the problem description.

  2. {"9.0","10.","08.9",".1"}

    Returns: 0.1

    Use 1.0 as the value per character. Assign 10 characters to the second bar, 0 characters to the last bar, and 9 characters to the others. Then 0, 0, .1, and .1 are the resulting bar_errors.

  3. {"99.0","7.","74.32"}

    Returns: 0.9923076923076862

  4. {"6.1","6.1","6.1"}

    Returns: 0.0

  5. {"0.","0.0","99.","5.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0."}

    Returns: 1.4999999999999998

  6. {"0.","0.1","99.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0.","0."}

    Returns: 0.09999999999999999

  7. {"1.","2.","3.","4.","5.","6.","7.","8.","9.","10.","11.","12.","13.","14.","15.","16.2","17.","18.","19.","20."}

    Returns: 0.5000000000000009

  8. {".00","0.0"}

    Returns: 0.0

  9. {"12.34"}

    Returns: 0.0

  10. {".2","3.",".4834","4.834"}

    Returns: 0.1417

  11. {".000000002","99.999999"}

    Returns: 2.0E-9

  12. {"1.1","2.2","3.3","4.4","5.2"}

    Returns: 0.03076923076923165

  13. {"3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456"}

    Returns: 0.0

  14. {"3.123456","3.123556","3.123456","3.123456","3.123456","3.123456", "3.123456","3.123456","3.123456","3.123456","3.123456","3.123456", "3.123456","3.123456","3.123456","3.123456","3.123456","3.123456", "3.123456","3.123456","3.123456","3.123456","3.123456","3.123456", "3.123456","3.123456","3.123456","3.123456","3.123456","3.123456", "3.123456","3.123456","3.123456","3.123456","3.123456","3.123456", "3.123456","3.123456","3.123456","3.123456","3.123456","3.123456", "3.123456","3.123456","3.123456","3.123456","3.123456","3.123456", "3.123456","3.123456"}

    Returns: 5.000000000008195E-5

  15. {"3.123456","3.123556","3.123756","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456","3.123456"}

    Returns: 1.4999999999988376E-4

  16. {"71.3467764","2.04007314","21.7766982","61.2222615","96.8432086","71.0441729","76.8441877","77.3020695","61.8594217","57.2637422","24.0778173","27.7422948","10.1623883","50.7098441","9.37998571","98.8305299","78.5542330","1.73221363","57.5473306","48.5470876","13.1774641","18.2523563","92.2844743","86.9656284","30.9302679","81.2398026","74.1381834","14.5163465","84.6252399","36.5033642","17.9638473","13.9277757","81.6382917","37.7638562","75.4620325","53.8702690","87.5326983","48.4942158","32.8735804","90.1562569","18.5065581","58.1575507","79.0975544","43.8094262","89.5002212","32.2431017","45.2970835","94.3969825","38.4135050","94.8946990"}

    Returns: 2.961599599999999

  17. {"3.48395802","51.7261781","91.1208019","37.9457922","38.6236016","59.3383555","66.8355025","60.8196720","76.4778239","39.1907484","48.8633589","72.0230385","57.7035311","8.49833776","61.8977849","24.8555815","97.6514047","86.9150764","3.74829949","17.4778070","60.8592354","65.0658616","76.7566578","60.6238333","9.41050724","23.8975823","52.1434317","5.01544092","55.1295082","78.3997356","79.1411521","24.9281863","57.0100692","68.9519678","20.0083657","74.3798966","57.3258138","38.8881149","51.8822178","68.0564423","42.5455735","17.8231634","26.9155389","90.3591604","48.4784051","76.8717222","23.2575871","2.85287855","2.99842164","34.0935750"}

    Returns: 3.0345046956521906

  18. {"51.1759598","2.91298706","14.2504647","66.3338842","0.98044305","84.5145656","67.4133724","27.0827260","32.3978239","65.8760708","88.8984038","79.0605678","8.66001468","78.0646747","73.2862049","24.9434409","72.8061058","53.6897855","45.3563931","59.9734879","48.5622072","15.4559346","47.2396973","76.1576780","23.6512835","40.6156175","99.0233298","19.3394565","39.4984206","69.2573176","80.0660657","37.6351585","68.0352687","31.8833992","17.8302853","62.5590588","3.67066310","94.8771127","51.2139835","32.6178885","36.4827347","61.2275011","56.1666155","3.23781281","1.30108369","18.2755015","82.7983034","86.5937274","16.5858853","94.2640740"}

    Returns: 3.1535086031250086

  19. {"55.2428367","30.2429230","36.8740542","71.1197544","28.2106090","74.4221015","43.0508883","2.16248515","77.4683937","24.4487508","85.8189343","0.33519501","25.4087346","36.8750182","79.4739957","95.0640703","67.4224282","45.8741231","15.4616209","4.00501556","69.9633432","49.7964717","28.1755577","29.7013235","56.9957222","36.9146350","99.0730393","70.5721176","87.9397209","54.0833902","29.4200116","30.6706500","57.2818804","12.3730275","46.8426639","23.2960684","13.6929045","79.6912372","36.3499807","89.8118136","4.79592394","31.9907913","2.60522440","96.9183124","2.65426215","21.8674063","76.9626139","33.1471939","54.5983882","76.1841155"}

    Returns: 2.9901923200000087

  20. {"80.1487058","98.4887591","34.1876495","52.8155094","39.4562805","69.8339851","37.9030673","70.6873139","37.9317869","29.3068715","84.5932755","76.9937015","42.2757599","62.5824562","26.7465329","30.8068387","16.0387974","69.9303811","75.3373933","63.2501769","75.1840385","83.9934014","73.2975394","20.9890197","84.2003766","55.2047601","26.5859540","11.9989371","22.6888365","48.2679136","16.3844490","50.4046464","74.7079283","91.2665672","71.1203340","40.6389612","6.15200754","32.7425847","72.8187910","50.2535206","99.0499753","91.4737899","8.71327344","95.4199279","5.90991614","28.7032762","56.0931046","3.49210821","72.0985931","33.2163243"}

    Returns: 3.129586100000001

  21. {"6.04313187","22.9575710","49.7329315","85.9305800","90.0311609","22.6874101","92.6739981","62.5596958","72.2246196","59.6018506","78.9521531","40.4300966","9.96870966","96.7001805","54.3154462","98.6751726","65.0340858","21.8609929","28.5815038","39.8006353","69.0428602","51.9006025","85.0865394","15.0093575","7.90753426","6.08460617","82.7632997","5.69351316","92.1682439","98.6195849","40.2431097","99.1464289","22.7894542","30.6089147","91.8654445","97.8160012","45.2780563","58.5387567","96.5917337","18.3161268","8.91060174","78.5672997","62.5583488","68.9321220","12.4081218","93.7223207","22.3670954","42.5006039","22.5728856","24.5692517"}

    Returns: 3.1071035428571467

  22. {"57.1997117","25.3138650","98.2021014","82.9938668","21.4562314","2.09329913","38.0194350","53.4508321","63.8552981","32.0959690","98.4159654","16.3612960","75.7978512","82.0629206","94.4679971","4.29982416","23.2838194","27.9874066","5.99986877","3.19294646","34.7848162","79.5756915","59.3858098","97.9586385","24.2140446","38.7926644","45.3355220","14.8480891","25.4979306","77.0289695","63.0840413","31.2081467","3.24229522","4.19597912","52.2072296","7.46485882","82.5991417","7.44936264","84.7099236","45.8355340","10.6783978","57.2616286","42.0846814","95.6088263","21.7122972","14.2084834","94.7147400","5.78932977","28.6682682","21.1034153"}

    Returns: 3.157610531250002

  23. {"34.2956433","72.4852505","5.11958329","32.0094416","83.8757536","40.6246949","52.9212258","12.1764616","24.6666520","97.4182016","73.6017447","41.0972307","33.9502120","38.4421407","74.3701629","64.6444556","24.2098796","96.2996396","43.2502381","71.6460975","10.0395699","96.5227593","22.0927153","15.2754389","6.43423134","45.7116010","91.0794418","60.2770508","79.7420341","62.8631446","53.8215281","13.3193090","30.8588641","36.4245971","78.2670197","85.6586206","89.1715629","26.8130556","5.37177139","44.8201172","35.3072106","36.9753635","84.8506071","35.1439920","50.9214417","42.0190203","35.3140019","85.8163218","14.5596443","3.02707585"}

    Returns: 3.02707585

  24. {"54.7089013","79.3976387","24.0505843","89.8769546","26.2205274","23.8820918","27.9429150","3.21516772","74.6553117","56.9645901","91.1706301","16.6969514","28.8133752","12.4628030","3.43448222","57.1818562","36.4722783","95.7354480","62.7120316","2.78334555","60.3419905","47.4578571","30.8598581","6.50253494","55.7143916","23.2602737","63.4471988","46.6331842","93.5188098","80.5039336","61.7610901","64.2071152","46.1084451","42.8644842","81.3488500","72.4562427","97.3408053","8.41180367","58.5145240","13.5994724","73.3785100","77.5198770","83.8617104","94.2196832","16.1251581","3.20983940","60.2759524","52.0781217","37.3242166","8.42389818"}

    Returns: 3.0821919000000007

  25. {"31.6656472","94.4205100","98.0871470","72.2473311","58.3312726","0.66122183","55.9803124","60.2402986","45.0083908","0.78892298","9.78842362","62.8107579","98.4308082","24.9190651","50.6856543","9.95427997","2.68595906","69.1257111","97.7837419","50.7060999","52.6853753","38.0171496","55.8897394","21.2952748","78.7489236","5.47680366","83.7943358","77.2603582","28.6022489","81.5729913","2.52493040","31.6804843","47.0126123","85.8480954","4.73599775","24.1953868","7.83916426","5.02975449","48.7724464","43.6322768","8.44940988","56.6636946","33.9300528","40.8271568","32.2544320","89.2498819","57.0503144","97.6226005","21.5412393","24.1706892"}

    Returns: 3.0084672200000018

  26. {"42.6277755","35.4435305","40.7225267","96.6748317","31.6671595","31.8103579","90.3054856","48.0524694","11.1019896","46.6682290","11.3668182","25.1916732","0.11371891","63.3360415","80.8434930","42.2517958","17.7015712","27.7251627","50.0297328","45.6006308","80.6506069","26.9925600","98.9341851","69.4014482","86.7549338","73.1581088","20.1259216","78.9843295","43.1746149","67.9952382","96.0982433","39.1020222","12.0118214","57.2424585","16.6987054","58.7212844","23.0238531","4.54648321","81.3183935","19.1765376","46.8476497","28.5360208","44.3029485","88.3133790","31.1924592","50.0385707","91.4424115","59.6752766","77.1643705","90.6908059"}

    Returns: 3.0733234695652234

  27. {".0","5.","99.0000"}

    Returns: 1.4999999999999998

  28. {"26.4121317","44.8741797","97.4310562","49.4181403","57.2454836","13.2122562","97.7677826","10.4326525","27.1137741","79.9459157","35.5017019","44.3367390","19.3634244","86.3349809","71.7304777","19.6646191","53.9084431","15.1122639"}

    Returns: 2.8402241307692355

  29. {"70.6618883","61.3763060","65.7064670","82.0182189"}

    Returns: 0.8588002791666688

  30. {"98.5650041","76.8198061","76.6747226","21.1045419","0.40185277","56.7450660","25.8708136","19.2811442","30.8359114","17.7707905","24.3424114","12.6083554","92.6850388","72.8529547","62.2620894","57.2367448","41.1630377","66.8239902","31.9141587","30.6451115","94.4785021","66.0548668","70.9143694","55.8922086","58.4035507","77.8959519","65.8426760","26.7119842","98.8365165","73.9841644","59.5416581","1.53400072","99.9959041","20.8984598","41.7589180","9.21775855","40.1212402","66.6652602","79.8625766","49.6216279","1.41969142","92.2599380"}

    Returns: 2.83394082857144

  31. {"9.89420679","8.35171500","32.4023934","52.6601865","32.4750741","17.8172087","80.2552060","52.5831934","94.5398243","58.9122201","6.97043494","41.1715283","24.7074065","74.6411625","9.17189643","3.29312522","68.9872236","38.5409661","73.5406578","20.7176940","21.9010963","63.4234615","94.0160570","81.5885297","87.5827005","0.18820385","26.7150147","9.15327301","66.0480425","17.3337797","6.32758841","24.6493136","61.4905346","76.1120673","50.9693390","47.6182980","39.2395084","93.7113154","63.8187693","28.4282492"}

    Returns: 2.964539515384617

  32. {"14.2126100","7.55774675","93.9759806"}

    Returns: 0.30533765357142867

  33. {"53.4756271","16.4171920"}

    Returns: 0.028177199999999975

  34. {"1.94636363","27.8139150","5.64373783","11.7972213","80.5236141"}

    Returns: 1.9463636299999998

  35. {"95.7544572","38.1636508","68.9615441","2.09401719","68.5436888","33.4801599","22.8026323","87.8924086","69.4562077","29.4606740","93.1948080","94.4596372","16.7277584","64.8554414","73.6002566","69.7820651","98.0382445","25.8206766","59.0222913","57.0244894","0.61258605","33.4318678","87.7177992","26.9699451","82.0565202","89.8618729","24.5983271","10.6663600","92.4528856","33.7151699","45.7222753","39.8514921","25.5290418","69.9509495","2.12830020","31.7314153","72.1162465","7.89425428","38.2327201","86.8168351","72.6569999"}

    Returns: 2.802817573076939

  36. {"2.40089766","31.9983065","18.6787160","96.1619786","65.7453871","61.9619153","72.7185833","3.23967495","50.9517841","75.0959336","34.2240633","38.2426613","25.5517313","77.4474184","21.3277310","95.3318696","26.3799185","51.8663576","70.8496001","51.7370916","79.5153068","45.1220315","97.1244580","86.3776241","18.0606690","94.1059792","16.6927346","24.7475868","95.2610265","30.2482059","11.2089866","33.8116300","75.3249145","61.9177006"}

    Returns: 3.033083359375011

  37. {"94.8799982","95.1848813","35.0862981","79.2634844","35.1223478","13.8209905","58.8315139","5.31030498","15.3626657","26.9043608","11.9325751","12.1630119","68.8800338","15.4425878","38.2523698","95.5561614","69.9791903","78.7749585","56.4927713","91.4687698","49.7346678","61.4575216","27.6916930","24.4907744","11.3413524","31.2537763","19.1298182","88.0461163","43.3899466","26.9839946","41.5299854","49.4930894","31.0459659","19.3026419","39.6548064","61.5014872","94.8960645","4.91478564","97.7557346","52.6099946","45.1356497","85.3087213"}

    Returns: 2.9290580000000004

  38. {"10.2180907","85.0804123","6.86592705","13.7657921","46.7455029","43.6475445","19.6752196","7.64602820","14.0284844","66.0003444","53.4938266"}

    Returns: 1.9051968500000016

  39. {"33.9848699","90.6413230","36.9269394","20.5027700","12.3530183","29.3560667","78.2417104","34.8898852","5.74178789","81.0458308","39.7375387","79.6621240","50.2218704","64.1061634","18.3135958","29.0748267","93.7147705","67.4514071"}

    Returns: 2.7224852521739202

  40. {"88.7457121","88.7664749","80.1019263","50.8410876","82.6248669","4.58599049","78.1678087","28.8237601","26.7207653","4.26093784","11.9609763","13.1389355","10.7233887","57.5787369","28.2921069","12.6370257","36.5541773","79.4097272","85.3628845"}

    Returns: 2.414949700000003

  41. {"33.6581382"}

    Returns: 0.0

  42. {"7.84454403","32.6572200","32.1768250","92.6002720","77.8230233","75.6924128","72.8135011","26.0653386","88.4387910","86.5341887","41.7468357","72.3123876","93.8420754","3.49907168","98.9940340","41.7858081","70.0264434","61.6120890","71.5962400","44.7870462","22.7735878","9.15732588","54.5998156","50.3204623","5.64341971","95.0533868","60.4206574","85.7546631","11.1351148","56.8053636","4.57068332","41.6699865","83.0080176","99.4294025","33.4014098","52.2199282"}

    Returns: 3.050170559999999

  43. {"62.5306745","89.9839424","43.3957143","10.2023770","61.4991265","27.5759988","8.65156017","92.5180865","14.9415839","13.0177027","69.3921583","45.3380371","58.1769212","90.9992190","35.3739477","65.5354364","6.55489858","82.8642682","3.35320729","58.2710304","1.37423103","26.9962344","4.81271671","97.2866416","10.9017524"}

    Returns: 2.9369544626666713

  44. {"29.7443199","1.47677576","26.2103798","86.7094045","27.3073925","57.5574680","3.77220089","72.5043499","70.7509261","73.1455731","8.98255208","60.1743839","42.7736462","14.5196175","20.6695782","51.5885954","42.8558140","8.02900371","23.5752312","93.0581261","47.3998534","58.6722452","13.0361566","93.7131899","78.2729884","59.9148013","53.3134754","18.0741686","98.4926478","39.0977830","85.5095049","27.8808243","80.8463436","73.1207092","15.8728421"}

    Returns: 2.840289144444444

  45. {"98.4163740","17.6884586","50.6894296","53.8237727","58.3677800","5.47493239","90.3123718","71.9318127","37.0547109","41.5820678","68.5240090","43.1443700","52.4784817","57.8345539","18.4901506","66.0662191","65.6294951","38.4998789","18.4143579","85.8327792","36.0061598","96.9501436","63.9964640","14.7855682","90.4326959","93.8736428","71.0494113"}

    Returns: 2.880436199999998

  46. {"49.8802502","16.1896198","82.2609472","30.5405865","10.7575272","6.48226377","87.2523877","31.1057678","44.5960726","82.6255944","35.5942761","85.2705004","38.9077875","8.95148981","92.7745044","86.7241205","97.4970513","14.3545802","21.3271952","74.3403991","24.8643406"}

    Returns: 2.834152737500001

  47. {"69.0679625","55.6600834","92.0461168","26.0753092","43.8117558","72.4947188","3.58733057","79.2965432","32.4563327","75.9210284","41.3018056","99.8267266","87.0748555","18.3187593","97.2490412","75.0314178","82.5035484","25.5997299","72.3245765"}

    Returns: 2.888539863571429

  48. {"45.2410575","45.9430634","44.2651297","67.5158048","59.2374764","44.9712928","6.31613537","4.34063293","97.4896860","76.0457537","95.3966160"}

    Returns: 2.2942105384615448

  49. {"52.1803757","82.4514085","49.7853253","39.9220478","54.6088743","95.7428055","61.7879739","32.4824353","10.1163565","63.5054661","28.8945013","71.5522470","10.5939723","26.9525093","66.1733995","6.86752791","31.0806819","77.7096445"}

    Returns: 2.689423750000001

  50. {"50.3102112"}

    Returns: 0.0

  51. {"22.6406287","94.8121365","24.7189716","32.6198190","78.3660958","61.3008542","17.8800244"}

    Returns: 2.0438486800000013

  52. {"98.5719859","19.7057759","20.8312517","34.3900912","93.6251843","93.7168598","54.2652342","23.0387319","84.1259355","29.0145733","51.4972581","30.6562215","47.8652760","98.6626543","7.02459132","13.2688939","12.8371900","86.7092325","1.04841435","19.7971796","28.9961426","15.7335554","55.2609523","58.5578942","40.5727733","61.9572905","48.1950338","97.5545181"}

    Returns: 2.3490696000000026

  53. {"64.5191854","42.8468619","28.2870045","33.7402351","99.7478777","84.8874856","21.1402392","85.0142728","39.2730145","17.5971444","66.9861141","98.9873380","2.42517168","75.8326034","36.9042458","43.8644728","11.0765987"}

    Returns: 2.5241916090909218

  54. {"7.91173346","8.49812210","2.78999032","20.4802100","76.9965249","35.6010448","89.8287587","47.7913402","93.2795102","0.14473003","47.3690470","27.4093989","35.1640635","36.0816356","33.7552919","36.1078199","18.6312617","45.1857458","92.1231034","64.2764536","84.7362328","68.5573387","54.3738279","1.84195301","21.1511374","92.4498436","13.4685020","95.4319015","48.3364899","88.5560741","30.0232923","18.9610531","75.6294697"}

    Returns: 2.78999032

  55. {"95.1918405","31.3577529","90.1437889","37.4261578","87.8419927","0.90814943","76.4149965","13.5633181","84.6547127","85.8470271"}

    Returns: 2.2189805296296283

  56. {"81.7914759","20.1435316","7.20884948","35.2579560","96.0831570","85.6078617","62.7041956","91.8134414","58.7026367","24.5270776","34.1956820","71.4963607","16.7520419","64.9492807","95.8863288","66.7668877","7.98177799","67.0526384","70.2927534","2.16737184","87.7017331","35.3124484","97.2189999","43.3619734","63.1492088","2.73137089","51.0516320","82.2998174","97.0475143","8.26622070","26.9479730","22.6136147","38.6712993","79.6980712","33.3839158","13.2914491","2.94170088","15.9306138","61.0472734","43.2102761","45.9063871","35.0650697","46.2071649","14.2953592","78.4166424","17.5881638","10.4594597","56.8707503"}

    Returns: 2.94170088

  57. {"31.3514415","30.4695358","73.6976673","14.4043268","38.2262295","37.3895786","80.6075265","63.1933915","23.3189304","81.8756464","96.6900904","31.9962499","58.8611205","60.1176381","14.2820755","77.1752972","44.8496049","27.2962981","24.4085279","8.52931791","36.7086569","36.1828734","53.6293740","4.08680737","38.2576650","14.6930424","13.9834491","29.6753968","22.9755578","54.2975432"}

    Returns: 2.7404251500000063

  58. {"72.3179020","23.7603032","15.0839954","41.9013736","64.6905279","16.8528586","87.9994739","56.4003197","77.5846324","23.5225717"}

    Returns: 2.0727049333333287

  59. {"86.2055529","41.3186628","30.9302933","15.0998150","75.4960747","12.1366804","18.7906655","34.2989250","83.6223294","52.3411314","42.5270516","4.58475148","63.5555609","51.1745681","46.5468497","34.2437047","39.9997913","41.3094434","52.4645443","23.3943000","41.1137689","6.60167606","41.1048351","71.1143925","11.3563739","83.8315827","10.8456138","28.1808519","81.4594810","9.16766267","22.3379654","44.6434693"}

    Returns: 2.3886121909090976

  60. {"79.3346110","96.0896956","9.77878810","45.1527220","61.4064393","60.1203053","73.7454048","62.3407868","23.9436570","44.5684522","49.2703268","34.4514332","57.7903338","62.5373846","75.7904324","44.6587990","63.8524082","30.8896602","42.3547807","53.3206715","15.4070683","18.4825987","78.8625894","40.9693584","72.5114508","39.1002633","63.5317168","5.55261275","72.7934960","2.84232658","17.9996001","0.19472664","8.55234070","82.4060132","92.4156795","98.2362554","1.36512877","33.9980095","39.4663155","63.4240662","2.29168530","36.5391138","38.4803223","84.8616700","78.2880088","77.3750695","58.5951539"}

    Returns: 2.995520349999999

  61. {"54.3268098","30.6918579","46.4325106","53.9170959","83.7209695","47.6341190","27.6982360","65.5679257","28.3429443","72.5548593","67.2230552","48.1341194","62.3002243","97.0056749","55.9935257","5.08268269","47.0639527","87.2553211","17.7322776","91.4616293","53.3783332"}

    Returns: 2.7239258739130494

  62. {"17.6923734","47.2256168","34.0073639","22.3888526","0.40947300","55.0176380","68.1320680","73.0559695","95.0718856","97.0998743"}

    Returns: 2.474064783333335

  63. {"47.7593296","20.1411446","38.3524399","27.8241262","93.2025457","22.3742778","9.82294407","68.9828263","71.2865821","65.3499654","76.2772932","75.7054620","87.4482920","63.0473615","15.3201074","93.2939687","85.4435906","50.3431406","57.9713915","78.9844087","9.34551969","76.5923149","0.30490286"}

    Returns: 2.7093455562500033

  64. {"93.1224815","75.8739251","0.35858731","57.9478361","90.8656236","10.9590961","87.4014267","89.8132147","64.8337929","38.2650591","10.1541817","31.5038783","47.3405313","88.4595913","91.2031004","20.8178351","2.00306448","88.2143316","29.7923684","57.5203131","33.3237695","38.5498037","85.0725727","4.24838102","91.2595952","36.1061952","56.4443823","46.1326407","56.7566262"}

    Returns: 2.5889479344827615

  65. {"11.9298903","16.3488330","90.0637471","54.8661483","65.1148649","92.0805530","89.4854179","67.8455405","79.0596761","71.2907759","8.84658415","55.4090032","37.6668212","39.6064636","14.9718090","28.2685957","77.7927853","10.3011665","6.54534870","42.8885607","28.9627600","82.7760710","34.8661286","32.2042065","47.9302794","62.7354823","40.2621175","68.7154637","31.7273954","59.6603851","87.8586122","5.68566804"}

    Returns: 2.801248474999999

  66. {"84.8845020","3.77062952","94.5400271","52.7614649","89.5413578","4.15308660","50.1500899","18.9622720","22.6316973","8.94533796","32.6055557","23.5554975","90.2779284","1.90466735","4.38161827","74.8824433","86.8883816","73.5433561","34.5049642","12.7079797","77.0365607","73.1413719","6.14092104","71.6928167","42.8529916","51.7362675","78.3970710","31.7856882","72.8970208","49.2305095"}

    Returns: 2.8037737700000007

  67. {"54.7567878","0.22102857","98.1803864","23.8203474","69.0557189","19.1111171","68.5510444","50.7185005","99.4695717","6.05815310","89.4969059","91.0230877","23.8425935","70.2553527","80.7812283","94.1646687","82.2391535","31.8371781","25.8639400","14.9000334","48.8032552","96.2757621","57.1176123","82.6404860","10.3305235","17.4210723","76.6148174","68.5195970","20.6230231","21.8929425","79.6530176","47.9574446","52.9200683","5.91201933","27.9682622","83.9196757","4.04573150","57.1605602","27.4991527","36.6361637","13.3864640","98.8929135","1.59768397","39.2354420","47.4098815","1.26947067","14.7437103"}

    Returns: 3.02401425714286

  68. {"2.85415747","5.76177173","46.1365356","37.6811840","73.3347882","91.6988993","45.0118678","89.4800478","57.3725334"}

    Returns: 2.85415747

  69. {"37.5844777","78.4145644","16.2609995","72.4750894","7.35330771","37.9284486","17.2896943","77.6944861","20.7522190","33.1030698","22.1465407","90.6511704","76.3316073","0.65448978","67.6668104","46.3053125","31.0079443","90.6806141","69.5330970","9.88451080","29.9592876","56.9169701","22.6367185","58.7590760","73.0587993","20.8389961","2.44400050","42.3402192","12.2341306","53.1441883","83.6790834","90.5363392","56.2693566","89.6826010","63.8263456","66.4004070","44.8201247","0.56429707","3.27181769","61.8240114","41.7915285","60.9575956","71.3445533","16.4813138","89.7321778","30.0020070","18.0851448"}

    Returns: 2.7300289333333354

  70. {"81.1326721","15.8374731","21.7117439","78.3718620","68.9404792","94.3294977","46.8263466","80.8108604","66.5800390","54.7200383","71.8867358","10.1787528","43.9447827","97.9594741","84.2885137","71.5595092","42.6356871","45.7226439","14.4084906","6.93030160","83.8149882","64.3056642","64.4020750","33.9904426","91.0712026","93.6654628","42.2662069","17.6064535","35.2931481","30.4209392","3.72212595","81.1395189","66.0701582","3.18555466","57.3043295","62.2848232","67.2802457","8.77686243","6.49912216","6.04057480","63.2974925","48.6492855","86.8581515","66.0378057","6.64446366","16.3222473"}

    Returns: 3.1360096375000057

  71. {"13.7225576","96.6149821","48.6937409","19.5327044","88.8526997","97.4987957","92.9035911","29.1364277","96.7733540","26.7726429","73.6310503"}

    Returns: 2.297602300000006

  72. {"71.5992723","76.4047472","0.58921991","52.6731211","23.9207089","31.0503176","9.35168153","71.8212548","57.3989872","77.5058573","15.6821749","82.9198016","96.8573812","84.7333984","5.98499616","33.8911097","88.3127421","7.06608550","52.3451615","38.1393615","55.4178181","96.7498314","79.8199735","0.31002032","92.1444448","98.3870204","2.63286915","66.6835486","5.78535408","42.5093986","39.6852434","57.9090693","95.9343916","21.6206219","11.6963943","40.7094722","92.3119842","88.7871865","29.8013069"}

    Returns: 2.8747315670000004

  73. {"29.1531380","29.9068550","86.1449123","82.7138383","95.3370822","0.47675951","79.9944814","76.0059419","9.98066539","59.4121000","84.6512198","56.8609979","63.0543898"}

    Returns: 2.4875728799999957

  74. {"42.9583927","52.1306519","11.1616201","25.6163729","8.10373872","37.8717345"}

    Returns: 1.03058899384616

  75. {"74.3638091","73.5393867","53.8659609","32.9277855","79.8238640","34.2851493","4.27477003","54.9395452","7.52850306","43.0668449","40.3823478","52.2202138","87.9618271","68.1992398","53.0992032","13.3617709","8.90148001","0.27082875"}

    Returns: 2.4883178171428613

  76. {"1.41467300","31.0066958","68.2342520","36.9940341","29.5664204","96.4553086","36.4428898","85.1235636","27.3081264","73.6359649","71.3904395","28.5046878","40.3315744","43.8282663","99.9516875","5.71414234","24.3099278","96.3229131","98.3920045","60.7429622","10.7098629","11.4869708","5.04174921","14.0071610","93.9931802","46.8050719","63.8526321","33.8273301","68.4946352","10.0670946","13.3044573","66.6199475","32.0322882","74.6736164","19.2126194","62.6565054","77.7011442","3.45627004","99.6938398","3.48477848","15.3204492","99.4608386","5.87960007","96.9698977","99.6494888","94.8167640","2.92377000","56.4011497"}

    Returns: 3.0067273062500006

  77. {"51.0385591","21.6847485","57.0241737","79.7423401","29.9161700","70.9831435","5.21645409","58.7677788","28.3038194","50.9196753","54.2111144","83.1040262","53.0808027","19.3400665","35.3908887","75.0605780","74.8407767","88.1462272"}

    Returns: 1.8549359235294092

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