{
  "provenance": "New exact implementation of printed manuscript recipes; absent historical helper not recovered",
  "python": "3.12.13",
  "platform": "Linux-5.15.0-1118-azure-x86_64-with-glibc2.39",
  "assertions_enabled": true,
  "script_sha256": "50a857b18f4ef6ead7a2bf4a7cb43e2de112c5f2fd6724d8e78e7426f039a95a",
  "checks": [
    {
      "name": "J residual positive",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "77654719505791076791505219934011999",
        "denominator": "1000000000000000000000000000000000000",
        "display": 0.07765471950579107
      },
      "positive_margin": {
        "numerator": "77654719505791076791505219934011999",
        "denominator": "1000000000000000000000000000000000000",
        "display": 0.07765471950579107
      }
    },
    {
      "name": "J maximal modulus unique",
      "left": {
        "numerator": "77654719505791076791505219934011999",
        "denominator": "1000000000000000000000000000000000000",
        "display": 0.07765471950579107
      },
      "right": {
        "numerator": "988065780494208923208494780065988001",
        "denominator": "1000000000000000000000000000000000000",
        "display": 0.9880657804942089
      },
      "positive_margin": {
        "numerator": "455205530494208923208494780065988001",
        "denominator": "500000000000000000000000000000000000",
        "display": 0.9104110609884178
      }
    },
    {
      "name": "N first cap is filled",
      "left": {
        "numerator": "2812664781782894485727281",
        "denominator": "14551915228366851806640625",
        "display": 0.19328485203789614
      },
      "right": {
        "numerator": "556631",
        "denominator": "2000000",
        "display": 0.2783155
      },
      "positive_margin": {
        "numerator": "158381923962577927457767407",
        "denominator": "1862645149230957031250000000",
        "display": 0.08503064796210387
      }
    },
    {
      "name": "N at most two caps",
      "left": {
        "numerator": "556631",
        "denominator": "2000000",
        "display": 0.2783155
      },
      "right": {
        "numerator": "5625329563565788971454562",
        "denominator": "14551915228366851806640625",
        "display": 0.3865697040757923
      },
      "positive_margin": {
        "numerator": "201639168105632566715324561",
        "denominator": "1862645149230957031250000000",
        "display": 0.10825420407579227
      }
    },
    {
      "name": "rho0 J ratio",
      "left": {
        "numerator": "77654719505791076791505219934011999",
        "denominator": "1000000000000000000000000000000000000",
        "display": 0.07765471950579107
      },
      "right": {
        "numerator": "47925108233510925035515355350169375626225899492518649562157349285681",
        "denominator": "244140625000000000000000000000000000000000000000000000000000000000000",
        "display": 0.19630124332446075
      },
      "positive_margin": {
        "numerator": "28966436479167400428214276264717227432866524492518649562157349285681",
        "denominator": "244140625000000000000000000000000000000000000000000000000000000000000",
        "display": 0.11864652381866968
      }
    },
    {
      "name": "rho0 N ratio",
      "left": {
        "numerator": "109",
        "denominator": "125",
        "display": 0.872
      },
      "right": {
        "numerator": "436563",
        "denominator": "500000",
        "display": 0.873126
      },
      "positive_margin": {
        "numerator": "563",
        "denominator": "500000",
        "display": 0.001126
      }
    },
    {
      "name": "D32 J cube root",
      "left": {
        "numerator": "77654719505791076791505219934011999",
        "denominator": "1000000000000000000000000000000000000",
        "display": 0.07765471950579107
      },
      "right": {
        "numerator": "621240026860783",
        "denominator": "8000000000000000",
        "display": 0.07765500335759787
      },
      "positive_margin": {
        "numerator": "283851806798208494780065988001",
        "denominator": "1000000000000000000000000000000000000",
        "display": 2.838518067982085e-07
      }
    },
    {
      "name": "D32 N cube root",
      "left": {
        "numerator": "158381923962577927457767407",
        "denominator": "1862645149230957031250000000",
        "display": 0.08503064796210387
      },
      "right": {
        "numerator": "166075704649063",
        "denominator": "1953125000000000",
        "display": 0.08503076078032025
      },
      "positive_margin": {
        "numerator": "840561214016487289747",
        "denominator": "7450580596923828125000000000",
        "display": 1.1281821639021467e-07
      }
    },
    {
      "name": "D32 upper",
      "left": {
        "numerator": "42758886913391604424504111846390830684628973616309754708090134978320968147583935226790855835648",
        "denominator": "968491075759526836634315583440965937270477795138368452063880004201714935049990659955040495968001",
        "display": 0.04415000611116472
      },
      "right": {
        "numerator": "221",
        "denominator": "5000",
        "display": 0.0442
      },
      "positive_margin": {
        "numerator": "242093175897408773663184708499318713630724644030654365666806036974159908128259716109670430688221",
        "denominator": "4842455378797634183171577917204829686352388975691842260319400021008574675249953299775202479840005000",
        "display": 4.99938888352792e-05
      }
    },
    {
      "name": "D120 upper",
      "left": {
        "numerator": "218390227667622733626292388531183614626095820046842806625789727805805284953108455856213710850102000109603590670990977466124229507746414073634129301666866596664693356776834345602043517714118106570149674863217429265239725532588561277223644529965930913053835316942608066496908171311019069636461236419309892893554372533081777936967702068549540901620191214657",
        "denominator": "886867187586063811316277629828650019273089009872265201315198179374263048660011680353985980985181590472593242155370327651967791922105263855517397466724885020545353836125061120209275253003364094018183723782702413375749882669065521064161785431517662063402733865383112845641842281677689744904764495063034747681210198871446840155126308267078634890190289167139880001",
        "display": 2.4624907846918125e-07
      },
      "right": {
        "numerator": "1",
        "denominator": "4000000",
        "display": 2.5e-07
      },
      "positive_margin": {
        "numerator": "13306276915572876811108075703915560768705729684893974812039268151041908847577856929131137584773590034178879471406417787470873891119607560980880260057418633886580409017723737801101182146891667737585024329832696314790980538711275955267207311653938411187392597612680579654209596433613466358919549385795176106992708739119728407255499992880471283709524308511880001",
        "denominator": "3547468750344255245265110519314600077092356039489060805260792717497052194640046721415943923940726361890372968621481310607871167688421055422069589866899540082181415344500244480837101012013456376072734895130809653502999530676262084256647141726070648253610935461532451382567369126710758979619057980252138990724840795485787360620505233068314539560761156668559520004000000",
        "display": 3.7509215308187286e-09
      }
    },
    {
      "name": "b1 dominant mass from purity",
      "left": {
        "numerator": "151249",
        "denominator": "2500000",
        "display": 0.0604996
      },
      "right": {
        "numerator": "968",
        "denominator": "15625",
        "display": 0.061952
      },
      "positive_margin": {
        "numerator": "3631",
        "denominator": "2500000",
        "display": 0.0014524
      }
    },
    {
      "name": "b1 dominant root lower",
      "left": {
        "numerator": "12771044244318001756635136",
        "denominator": "14551915228366851806640625",
        "display": 0.8776194778418376
      },
      "right": {
        "numerator": "214358881",
        "denominator": "244140625",
        "display": 0.878013976576
      },
      "positive_margin": {
        "numerator": "5740712137228956255489",
        "denominator": "14551915228366851806640625",
        "display": 0.0003944987341623781
      }
    },
    {
      "name": "tail32 upper",
      "left": {
        "numerator": "515307961597135121107804032114997546621115125052857564790485790363077226601965476056618329573725907064961073016164475552872540918520092547188847868154809400317069485672439206687210519388711257623652573306643045892303292728931544649803930934980891428129322049963603485179688562642494812743518061574876277816359236257831811685081",
        "denominator": "2464000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.20913472467416197
      },
      "right": {
        "numerator": "523",
        "denominator": "2500",
        "display": 0.2092
      },
      "positive_margin": {
        "numerator": "160838402864878892195967885002453378884874947142435209514209636922773398034523943381670426274092935038926983835524447127459081479907452811152131845190599682930514327560793312789480611288742376347426693356954107696707271068455350196069065019108571870677950036396514820311437357505187256481938425123722183640763742168188314919",
        "denominator": "2464000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 6.527532583801903e-05
      }
    },
    {
      "name": "rho1 residual bound",
      "left": {
        "numerator": "523",
        "denominator": "2500",
        "display": 0.2092
      },
      "right": {
        "numerator": "38868628949944800881608934764397388050618136873235494570144290223850691363507154561",
        "denominator": "184467440737095516160000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.21070725974531562
      },
      "positive_margin": {
        "numerator": "278040347744418900936934764397388050618136873235494570144290223850691363507154561",
        "denominator": "184467440737095516160000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.0015072597453156206
      }
    },
    {
      "name": "periodic R positive",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "725525598007280878214648582489761697742236403212298833119726716853433837779924227767974301108333666187900565039051130676699083392185064655864495481444491259714925467457812517472521512798741006688140066819943225805032984763367217366313488062361678922195284810125125967455229145252562522118678417125331608782633863396715816689934468150465501756953856936971622432079779432590299556252382243013339708036211939014332275986773161421411726721793058441617741306905274792359095178575717555412453663610201664132782125506564590917342098521321771230584691120282215357593851709501802511945901607840889840294804020567201",
        "denominator": "4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.18138139950182022
      },
      "positive_margin": {
        "numerator": "725525598007280878214648582489761697742236403212298833119726716853433837779924227767974301108333666187900565039051130676699083392185064655864495481444491259714925467457812517472521512798741006688140066819943225805032984763367217366313488062361678922195284810125125967455229145252562522118678417125331608782633863396715816689934468150465501756953856936971622432079779432590299556252382243013339708036211939014332275986773161421411726721793058441617741306905274792359095178575717555412453663610201664132782125506564590917342098521321771230584691120282215357593851709501802511945901607840889840294804020567201",
        "denominator": "4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.18138139950182022
      }
    },
    {
      "name": "periodic spatial seed",
      "left": {
        "numerator": "4501",
        "denominator": "5000",
        "display": 0.9002
      },
      "right": {
        "numerator": "1766847064778384329583297500742918515827483896875618958121606201292619776000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "denominator": "1962589713600800007743291420164709730148027119543982976358510098819083830398054776156687361033689995140641564632533857162194678590519151660645198454082429799174783939134745628706757426718342591564330130487538145004641504051951918269246020760046292255043112804341286821872248651159079228290595826945304737441941601",
        "display": 0.9002630822601821
      },
      "positive_margin": {
        "numerator": "619022974720813063932821553234083741149419310627414018377051678402559378355452518750187987361331871972317588965108912961751664073298375435961758174983473914297489954509925190884822340739995368950082675590809334108590262164415870123660559031638560050949267659868014753008821132984393464028182919183376773820853899",
        "denominator": "9812948568004000038716457100823548650740135597719914881792550494095419151990273880783436805168449975703207823162669285810973392952595758303225992270412148995873919695673728143533787133591712957821650652437690725023207520259759591346230103800231461275215564021706434109361243255795396141452979134726523687209708005000",
        "display": 6.308226018214271e-05
      }
    },
    {
      "name": "periodic physical seed",
      "left": {
        "numerator": "2343",
        "denominator": "2500",
        "display": 0.9372
      },
      "right": {
        "numerator": "256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "denominator": "273121480275534680629714575384758451399330949168230991711568574967884855529654395786479152232264981605910589316632715286226707531691105742502370809141462122582288302404915234522982890495931514141302088414273877270603909447354482372204460748308008231005820538934115807351976405073938418783172388999850283905717418688660358427972476527197418595589037788563389750927404335471296516126204676102586571789396535560087096288274280433580344643702585704406087435709806223407860225104657478854956060598396386172786583218252552069566078383174867591137145529884564358999745924683291593557407588303411203240402125440473396812700634798335387580929984251316056234076041340890041075329288359821429340748640780238288495194473507170598006696181633873472350802998794215389185477332537614636590567157496909457530452449912272356598424858133135727521450439775736951483641053634636267396652734326484240663172753509195389768364942936296536078483465626504875184836629601274261632115087696976343050786999362656626033162002609058280230687474780452429264479105610280418004077146541791433547653608201595366426664474313376045512730325260092852268688792825068141614474727724892850390533086825093706839871631541152971013086838181254855847347279298995349077911126137161353905703402749752415490202988017183290183330641709590160961077082872989417624939088159047189131664763683862477445663108531308765978930672896662357932754719575369443954395783033483097634586671025876488500182925235671582243460374989908500749341903747044515407003810499382137057085862129414646167624633040419940977823978920748795114884405731303590358659718299050489110794692768494175074738837497917159375909686546809825043368889291787261588966743296562403506782835009791931121457054591544729321740360735321543199981989590257815533606868916060978204822884567157121915154768462479722244981522418284660638046442312887067927584711211975835877678819568003013161070730639945966758091367676325312681720192492686532737291149806308322861885011298577763434736342546801202215318026440116569093862616773560039141350671492965458091342761867269389159945961133937364636289592151775359743985164844704891222285176559546870077798720328238755375927891025153882180578605132789271792047415576309001058396839278826148646121317785902575560524880430708585045615622135471667036389521151328956632534299383541460930407160130420731940934588800719064505121523278956694266875201961490431574763526485724181129240277769308801",
        "display": 0.9373118501764786
      },
      "positive_margin": {
        "numerator": "76371714422243284578749873510948371367586098834786419794828850245783494019750672279346319803148097351489231129548084370824253247739245316945194181554246789698507465283605512651087568032462366929206845356305554975040164848447801924948466714336714753362477277366663374319282911762284791027092573350784808904088012468780203260487496776448230534884461395977813577091641990752262716302443891639662297443917182715933396573360944121252499804841694576537138131924018555383492579787527042837950017957267197161035519634270501006678348221285233965668023480465706863595298467047796294994020605107550807737820092970831267842412667500186897881046899166480243559835138294633760503477372938391054625934651901690055759348572699288870310846431834454282068573825153343138426609864368906468301149984741141006149909855545868489890557394062990417241619605448322673829011334047225489642643473047424126186238527955201772720938700257215968113240037099077441927776844214404995954349525984428232006060493295525204301427886976449419499246589399958233325455555112980616447245652582671197847595983662056462325136683759925363672847915602447134462158410865344197285712940576051534980977568805444874180767299078588916337538141319872749665324602453897110454231460630947798936927357330090506454399075739551100456306474430252868196394828585794504767716443352435864509458688710215344811336711143561311365433403120095363555692034909392814850680352549102242163429786371387444071406172821482803572341398644382744291919520674700401390071999947652875247825030781484029255484786296078288958417388685573045825837371555687789660280025324704013408034843418147799886903742380095582243604420824579923386692389342446097050920456154288583607817572057505382426121092010699199162334797141624282442198390025938204759106129669128066099981459150863352792377492410010780008292973959040125057185660905599845669021630340616538598525752168940163611278110606599885791925534369792386729588989635453796526836003819599534603418527432300272412749412844783209509864050806878613079888899548828291815376691981931691983908944987821198246613063184754657173485588390332119842758768856439866185831320981683407717598270936596154200951328064454050904328173874736191232905304708010520176205569710333722137752427630265461690205150849785238122597336589884133739351942436254609972136544362357040056023814424225062390258439915231864500270957404465332711401804227918820329057443948243614190029186509479257",
        "denominator": "682803700688836701574286438461896128498327372920577479278921437419712138824135989466197880580662454014776473291581788215566768829227764356255927022853655306455720756012288086307457226239828785353255221035684693176509773618386205930511151870770020577514551347335289518379941012684846046957930972499625709764293546721650896069931191317993546488972594471408474377318510838678241290315511690256466429473491338900217740720685701083950861609256464261015218589274515558519650562761643697137390151495990965431966458045631380173915195957937168977842863824711410897499364811708228983893518970758528008101005313601183492031751586995838468952324960628290140585190103352225102688323220899553573351871601950595721237986183767926495016740454084683680877007496985538472963693331344036591476417893742273643826131124780680891496062145332839318803626099439342378709102634086590668491631835816210601657931883772988474420912357340741340196208664066262187962091574003185654080287719242440857626967498406641565082905006522645700576718686951131073161197764025701045010192866354478583869134020503988416066661185783440113781825813150232130671721982062670354036186819312232125976332717062734267099679078852882427532717095453137139618368198247488372694777815342903384764258506874381038725507470042958225458326604273975402402692707182473544062347720397617972829161909209656193614157771328271914947326682241655894831886798938423609885989457583707744086466677564691221250457313089178955608650937474771251873354759367611288517509526248455342642714655323536615419061582601049852444559947301871987787211014328258975896649295747626222776986731921235437686847093744792898439774216367024562608422223229468153972416858241406008766957087524479827803642636478861823304350901838303857999954973975644538834017172290152445512057211417892804787886921156199305612453806045711651595116105782217669818961778029939589694197048920007532902676826599864916895228419190813281704300481231716331843227874515770807154712528246444408586840856367003005538295066100291422734656541933900097853376678732413645228356904668173472899864902834843411590723980379438399359962912111762228055712941398867175194496800820596888439819727562884705451446512831973179480118538940772502645992098197065371615303294464756438901312201076771462614039055338679167590973802878322391581335748458853652326017900326051829852336472001797661262803808197391735667188004903726078936908816214310452823100694423272002500",
        "display": 0.00011185017647853516
      }
    },
    {
      "name": "periodic first coupled output",
      "left": {
        "numerator": "225995919339172671649",
        "denominator": "4506201674428345343298",
        "display": 0.05015219816317751
      },
      "right": {
        "numerator": "251",
        "denominator": "5000",
        "display": 0.0502
      },
      "positive_margin": {
        "numerator": "538511792825661461399",
        "denominator": "11265504186070863358245000",
        "display": 4.780183682249213e-05
      }
    },
    {
      "name": "periodic second coupled output",
      "left": {
        "numerator": "26828845591358296201",
        "denominator": "1359325578807716592402",
        "display": 0.019736879824545236
      },
      "right": {
        "numerator": "99",
        "denominator": "5000",
        "display": 0.0198
      },
      "positive_margin": {
        "numerator": "214502172586230821399",
        "denominator": "3398313947019291481005000",
        "display": 6.312017545476447e-05
      }
    },
    {
      "name": "periodic G endpoint",
      "left": {
        "numerator": "989224080031250",
        "denominator": "177210755074809",
        "display": 5.58218985982906
      },
      "right": {
        "numerator": "5583",
        "denominator": "1000",
        "display": 5.583
      },
      "positive_margin": {
        "numerator": "143565551408647",
        "denominator": "177210755074809000",
        "display": 0.0008101401709396319
      }
    },
    {
      "name": "periodic invariant interval",
      "left": {
        "numerator": "39",
        "denominator": "125",
        "display": 0.312
      },
      "right": {
        "numerator": "1",
        "denominator": "1",
        "display": 1.0
      },
      "positive_margin": {
        "numerator": "86",
        "denominator": "125",
        "display": 0.688
      }
    },
    {
      "name": "rho2 bound",
      "left": {
        "numerator": "13",
        "denominator": "461",
        "display": 0.028199566160520606
      },
      "right": {
        "numerator": "29262241416262156805796671937492796271464866582650938204342044054918729627502537896039186797250532278178483657243190226905165618740392096297037774710267534946294534904704823275533507892233932302529777997034862930933309898010186584086069870398777203548344399468258684908315129347909523570751437399470415942366216823557030445532021173147459798533999982701962401",
        "denominator": "1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.029262241416262158
      },
      "positive_margin": {
        "numerator": "489893292896854287472265763184179081145303494602082512201682309317534358278669970074065113532495380240280965989110694603281350239320756392934414141433333610241780591068923530020947138319842791466227656633071811160255862982696015263678210253836290835786768154867253742733274629386290366116412641155861749430825955659791035390261760820978967124173992025604666861",
        "denominator": "461000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.0010626752557415494
      }
    },
    {
      "name": "P factorization at U",
      "equal_value": {
        "numerator": "683536128491619",
        "denominator": "1000000000000000",
        "display": 0.683536128491619
      }
    },
    {
      "name": "P positive at left endpoint",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "677462859",
        "denominator": "1000000000",
        "display": 0.677462859
      },
      "positive_margin": {
        "numerator": "677462859",
        "denominator": "1000000000",
        "display": 0.677462859
      }
    },
    {
      "name": "4P-xPprime positive at left endpoint",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "178281",
        "denominator": "1000000",
        "display": 0.178281
      },
      "positive_margin": {
        "numerator": "178281",
        "denominator": "1000000",
        "display": 0.178281
      }
    },
    {
      "name": "derivative of positive quadratic on interval",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "859",
        "denominator": "500",
        "display": 1.718
      },
      "positive_margin": {
        "numerator": "859",
        "denominator": "500",
        "display": 1.718
      }
    },
    {
      "name": "boundary leading coefficient",
      "left": {
        "numerator": "2040776659725170230600124129957784731965315100108018011256911486023199211445596298812907466487081041334736707568370406979477009371099530810526547112336652005045954105776988672029636860207870304234924302287390561715358746301559808565079852904866144597789260242291672467981404836529124950877657916089361380903207053455664109863485641573038476622903490209494545305056597738500587861640007458171428713802278491312204568523165191902227919753847645177443113838187777",
        "denominator": "1800856852276933040030907595570710029212312587929318843036777373040260317286047380019963207235207485598461813779757242834640257631101881679872000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 1.1332253627737774
      },
      "right": {
        "numerator": "566613",
        "denominator": "500000",
        "display": 1.133226
      },
      "positive_margin": {
        "numerator": "1147553209490621941160940428711598837044660772263962283589317722826871202029457595358995244196740065779814008774289051031223163530158028079959663347994954045894223011327970363139792129695765075697712609438284641253698440191434920147095133855402210739757708327532018595163470875049122342083910638619096792946544335890136514358426961523377096509790505454694943402261499412138359992541828571286197721508687795431476834808097772080246152354822556886161812223",
        "denominator": "1800856852276933040030907595570710029212312587929318843036777373040260317286047380019963207235207485598461813779757242834640257631101881679872000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 6.372262226393511e-07
      }
    },
    {
      "name": "exponential lower",
      "left": {
        "numerator": "285277",
        "denominator": "250000",
        "display": 1.141108
      },
      "right": {
        "numerator": "19104748366473276644582027502879407009537571474339676126792205510330881590414372434855071623306263471985286760452440195800356816689199972481208019073412646066651193015345923330499897687469762710869307344624215650069864473668136789579682451998063701805773665572438367473469266287615078811",
        "denominator": "16742274194216222765405243199386739013198538758705840842860498813714165288954778379232248702868091072559764143079519271850585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 1.141108319267235
      },
      "positive_margin": {
        "numerator": "5345259591117195981246113604027664613308470371494277347430011137865865763188086118770473861804358759418671256118537478398720449972481208019073412646066651193015345923330499897687469762710869307344624215650069864473668136789579682451998063701805773665572438367473469266287615078811",
        "denominator": "16742274194216222765405243199386739013198538758705840842860498813714165288954778379232248702868091072559764143079519271850585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 3.192672350906645e-07
      }
    },
    {
      "name": "leading coefficient under exponential",
      "left": {
        "numerator": "2040776659725170230600124129957784731965315100108018011256911486023199211445596298812907466487081041334736707568370406979477009371099530810526547112336652005045954105776988672029636860207870304234924302287390561715358746301559808565079852904866144597789260242291672467981404836529124950877657916089361380903207053455664109863485641573038476622903490209494545305056597738500587861640007458171428713802278491312204568523165191902227919753847645177443113838187777",
        "denominator": "1800856852276933040030907595570710029212312587929318843036777373040260317286047380019963207235207485598461813779757242834640257631101881679872000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 1.1332253627737774
      },
      "right": {
        "numerator": "19104748366473276644582027502879407009537571474339676126792205510330881590414372434855071623306263471985286760452440195800356816689199972481208019073412646066651193015345923330499897687469762710869307344624215650069864473668136789579682451998063701805773665572438367473469266287615078811",
        "denominator": "16742274194216222765405243199386739013198538758705840842860498813714165288954778379232248702868091072559764143079519271850585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 1.141108319267235
      },
      "positive_margin": {
        "numerator": "397110267434976069602073907485631764229241464110879231642065117895524372031432407418495066547873482660832457814968495656844947473698276029761471476377918123779260517556669350597991993508930501439573739732794061762438764917371873666947044078737252366254495204348164968451951127666075449844809015244031170903116203641610298059448789881088851377818015641138752030772918045191561541842854938410269491371398731572331478635910623933582362721877520487265321396855090631196060283",
        "denominator": "50375803515413053069912434154859823649011629754867798617436383818637834884053684213695747626751883281293623664609495702789127573082589082988132588387827712000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.00788295649345773
      }
    },
    {
      "name": "positive R upper m34",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "5755236007119735863373644749654590483998186873165981212980862743187177862108611866944186353126031068391531471273838498348158426441824395642840199329385474839436350090831932260263444018506430820059342443382269050845303795684072941860414872914895754906216080784152393505223928931601479522251469105387070318374847774055389205781876889595422820347399619955628181488967496126896320219373628482630158676907804384629672074144341128307326025909251607806387329985618161121642987331321198959655766236942199194251740640167574140040788088600976041232532344549190236313993026018995294901063883020299268034756997556271497126935308164908200807900118239302873233956863225027812764405971668163733447116824143809000939074309941",
        "denominator": "19913223458725108599825349766258763756091555411115608384393609312221901319209101523764629728483622632884446975158240723133792256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.289015789886998
      },
      "positive_margin": {
        "numerator": "5755236007119735863373644749654590483998186873165981212980862743187177862108611866944186353126031068391531471273838498348158426441824395642840199329385474839436350090831932260263444018506430820059342443382269050845303795684072941860414872914895754906216080784152393505223928931601479522251469105387070318374847774055389205781876889595422820347399619955628181488967496126896320219373628482630158676907804384629672074144341128307326025909251607806387329985618161121642987331321198959655766236942199194251740640167574140040788088600976041232532344549190236313993026018995294901063883020299268034756997556271497126935308164908200807900118239302873233956863225027812764405971668163733447116824143809000939074309941",
        "denominator": "19913223458725108599825349766258763756091555411115608384393609312221901319209101523764629728483622632884446975158240723133792256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.289015789886998
      }
    },
    {
      "name": "positive R upper m78",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "3078306128266372462807940088870394533294105905183432623822057432469255115148538233541600655291718833908596503684444454594324831697330042781707502212750820717611827295050939789376806561034158238516592065372104024794056990210061054150192678138670841520525484243642318484988655519788316779505920977557973564938815053478225309727109038561473020644087931912327309047027385438594730736415108286211193595861542325208143205152238323279601968468777465645205949989312760032399633620620410177507770844771403349937371430681525218966139922615055197934914466039364523337915502344097587745632865876612624192408961678592622737553446572040456500529351600283022037447789283847414731743169384776199782060039774232430961563142754538045541080526734762996289810577319129828463849976556835998697665017271737868006482161208067003679005614991911405915906207293202962369109560635313596869897221380084191841154029373664687165635200747705429910060067450731289615709925549425882734143041666515154128061134810342768617872201541638130251730076080066446338069639520754224874528341",
        "denominator": "11319357019331794503969689325378319470071093866815549736425969804384920575562944988953762349685588692912260157276160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.2719506172487606
      },
      "positive_margin": {
        "numerator": "3078306128266372462807940088870394533294105905183432623822057432469255115148538233541600655291718833908596503684444454594324831697330042781707502212750820717611827295050939789376806561034158238516592065372104024794056990210061054150192678138670841520525484243642318484988655519788316779505920977557973564938815053478225309727109038561473020644087931912327309047027385438594730736415108286211193595861542325208143205152238323279601968468777465645205949989312760032399633620620410177507770844771403349937371430681525218966139922615055197934914466039364523337915502344097587745632865876612624192408961678592622737553446572040456500529351600283022037447789283847414731743169384776199782060039774232430961563142754538045541080526734762996289810577319129828463849976556835998697665017271737868006482161208067003679005614991911405915906207293202962369109560635313596869897221380084191841154029373664687165635200747705429910060067450731289615709925549425882734143041666515154128061134810342768617872201541638130251730076080066446338069639520754224874528341",
        "denominator": "11319357019331794503969689325378319470071093866815549736425969804384920575562944988953762349685588692912260157276160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.2719506172487606
      }
    },
    {
      "name": "positive R upper m142",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "23926136922700479529526145074253732290785079433596976764175962477988583609587236235818537682297080014086415686063432674913374279114879375045694260495963062315753976132441648300231010610804644876081479161829839745168118554763397768196092710377605281775809249631592015156111491374755577931006785201341412958543375827011642253518546174330628559523306078924118837233187361517151319838999846630782531699556266704441621980692206522364049866139175058472400845484713707981206244996648402732689644372099824653925667497795289675530064724289091949636268522938416861252485685920746396938950647172141538812250523593566464698125464945262818705795508554746906242969965704043920455335971739804451988372521102664862746864064546220914600690388136385551662891951728078952771855855860682636020585581564008600540199389951262911139727528828756742982295463289444637360217261083127553519066905077557860803262619830419501746133583896354364045863367481845373185942885866798081058348673791077326539586062898667453967574912049642921577131250326520435788897603690129271792696028032417045976458423783662087414362528452242308235994441159893223930921012158620037047973127943881973612683293993899693379603936529388805345883179881991705006730685019651848008329807512014779099281351285270405322223452680430006411506265356488699696734732719039283094123713507443587335980434571218282550735630715152287547007705693639351993893661731313639597561501660281535290675061734395340659727254481066266712813024561780245543378631943735678632189745134835776364324412973278829498178961478741",
        "denominator": "61362357357492878064302853257176801379753642319903385535120799649214934354663977621320062020376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.38991554355235164
      },
      "positive_margin": {
        "numerator": "23926136922700479529526145074253732290785079433596976764175962477988583609587236235818537682297080014086415686063432674913374279114879375045694260495963062315753976132441648300231010610804644876081479161829839745168118554763397768196092710377605281775809249631592015156111491374755577931006785201341412958543375827011642253518546174330628559523306078924118837233187361517151319838999846630782531699556266704441621980692206522364049866139175058472400845484713707981206244996648402732689644372099824653925667497795289675530064724289091949636268522938416861252485685920746396938950647172141538812250523593566464698125464945262818705795508554746906242969965704043920455335971739804451988372521102664862746864064546220914600690388136385551662891951728078952771855855860682636020585581564008600540199389951262911139727528828756742982295463289444637360217261083127553519066905077557860803262619830419501746133583896354364045863367481845373185942885866798081058348673791077326539586062898667453967574912049642921577131250326520435788897603690129271792696028032417045976458423783662087414362528452242308235994441159893223930921012158620037047973127943881973612683293993899693379603936529388805345883179881991705006730685019651848008329807512014779099281351285270405322223452680430006411506265356488699696734732719039283094123713507443587335980434571218282550735630715152287547007705693639351993893661731313639597561501660281535290675061734395340659727254481066266712813024561780245543378631943735678632189745134835776364324412973278829498178961478741",
        "denominator": "61362357357492878064302853257176801379753642319903385535120799649214934354663977621320062020376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.38991554355235164
      }
    },
    {
      "name": "positive R upper m240",
      "left": {
        "numerator": "0",
        "denominator": "1",
        "display": 0.0
      },
      "right": {
        "numerator": "1147425894540262046529781532105799375280386602950858665500673934826944621670220588674625236023951050988484192671317358246428853922417819182613880433637071990363996801507034488446894565797764850772870072923034163005306373668141803435250387321422837026859764227015846015624014576750090129501794254031979602308800994877743069660311182443588080627610031400821018128718128180078929885993355010270626297560502909546037558733727563935065172434118765289389873092135765757472141038221913329313209943455640760982590563090676930284012677614574534447743232011298515286955344510731476593771356245734380319717485703163259915256466640657174996061815071491213266432004461232750074876034497179772114897138420515270215756463529000116727632128321206537550378850283330390485135777149148227305957226966770458409905394810864189839839905113591545606295512357603846349167599773849200405926916604769839708566713831637462815065226781358342302181451557392823942528830617982533368885757980632554048326820611572061240588375288706207744657571196432880585976963190727163879277737436624910103912767307817872165875531997947539762248823737825608030202733534718624766386795458096187674173921009564119381490960732514143497938850880744100341667296874140912476745711159738322449176287358696749692910996556300655611173497936794774257667973601060855901888866528524305206852994237575415083992004340040980431104624859782266091170795067781889628894783025338326124032749752806775789874027399090459124093250308715350447851832018505019024281479644906675101861091820954034274812719482510383207444529523027371744963893619684404292707660052846258334381446259156707235180061134106870815286727963458496024181010302911949310434912990134256165279595374574662044057006862056066867350765842079907477412474372771961132813715761781178936903898692603232118884964213597411283615333848411175363685453395973017247446123442262609201360944010476156388980181889850238705070731188570454735551339894275604481834359270394813483375147703521447761943856943863012563181627139714100229889811182952410907761629447047718279677925179228755869729201845566326384328243809699481690943154990136548237327031512553644313502377393276954329996999428619715606716613039994320611079586101692741892448395921249762446432901691857013665522019676346974089729073461902046891334448504709",
        "denominator": "1936254590861081828190390545093813332423088890410353619944778043912590107354677093016378521527930947719929923057879635802519535658916538523044437170028686523437500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.5926007354384034
      },
      "positive_margin": {
        "numerator": "1147425894540262046529781532105799375280386602950858665500673934826944621670220588674625236023951050988484192671317358246428853922417819182613880433637071990363996801507034488446894565797764850772870072923034163005306373668141803435250387321422837026859764227015846015624014576750090129501794254031979602308800994877743069660311182443588080627610031400821018128718128180078929885993355010270626297560502909546037558733727563935065172434118765289389873092135765757472141038221913329313209943455640760982590563090676930284012677614574534447743232011298515286955344510731476593771356245734380319717485703163259915256466640657174996061815071491213266432004461232750074876034497179772114897138420515270215756463529000116727632128321206537550378850283330390485135777149148227305957226966770458409905394810864189839839905113591545606295512357603846349167599773849200405926916604769839708566713831637462815065226781358342302181451557392823942528830617982533368885757980632554048326820611572061240588375288706207744657571196432880585976963190727163879277737436624910103912767307817872165875531997947539762248823737825608030202733534718624766386795458096187674173921009564119381490960732514143497938850880744100341667296874140912476745711159738322449176287358696749692910996556300655611173497936794774257667973601060855901888866528524305206852994237575415083992004340040980431104624859782266091170795067781889628894783025338326124032749752806775789874027399090459124093250308715350447851832018505019024281479644906675101861091820954034274812719482510383207444529523027371744963893619684404292707660052846258334381446259156707235180061134106870815286727963458496024181010302911949310434912990134256165279595374574662044057006862056066867350765842079907477412474372771961132813715761781178936903898692603232118884964213597411283615333848411175363685453395973017247446123442262609201360944010476156388980181889850238705070731188570454735551339894275604481834359270394813483375147703521447761943856943863012563181627139714100229889811182952410907761629447047718279677925179228755869729201845566326384328243809699481690943154990136548237327031512553644313502377393276954329996999428619715606716613039994320611079586101692741892448395921249762446432901691857013665522019676346974089729073461902046891334448504709",
        "denominator": "1936254590861081828190390545093813332423088890410353619944778043912590107354677093016378521527930947719929923057879635802519535658916538523044437170028686523437500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.5926007354384034
      }
    },
    {
      "name": "boundary initial overlap",
      "left": {
        "numerator": "41628400904943031577212967800811683127141977060413341554149890856375069119390624224446117668037729557387387292907428632466760250657250830220194066350537337072149902416929526604537178259329483168706679325372798195301552983605666236671736276186243434555070620993030765604897676871180475880745069844196095553021099193172488007626074804627003094685454121691665989506187431553892278991142306126819818534884174077366072824416405306037493318747583171573417805506091940189621594286150140597882472644782703412000127857202252221353299845702031708094617169987941756039887272185129998814319408619827693767364075036025622050264708248116512369294457463795522814105335378630965439932111418718227868503",
        "denominator": "448952983208195750114893423949644409817287648712375655589822130689847187192473297444849735905732248731648000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.09272329723141284
      },
      "right": {
        "numerator": "58",
        "denominator": "625",
        "display": 0.0928
      },
      "positive_margin": {
        "numerator": "34435936777534033449141941715318103902316740095119284585602871642749852070897778435937824014223124909547107092571367533239749342749169779805933649462662927850097583070473395462821740670516831293320674627201804698447016394333763328263723813756565444929379006969234395102323128819524119254930155803904446978900806827511992373925195372996905314545878308334010493812568446107721008857693873180181465115825922633927175583594693962506681252416828426582194493908059810378405713849859402117527355217296587999872142797747778646700154297968291905382830012058243960112727814870001185680591380172306232635924963974377949735291751883487630705542536204477185894664621369034560067888581281772131497",
        "denominator": "448952983208195750114893423949644409817287648712375655589822130689847187192473297444849735905732248731648000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 7.670276858716148e-05
      }
    },
    {
      "name": "boundary purity78",
      "left": {
        "numerator": "309",
        "denominator": "500",
        "display": 0.618
      },
      "right": {
        "numerator": "128127843331095967255859940049805402833444100559540472431404948642114380619460212570330260845870538470064932806805795855738311212065810849411890288761926291914612182656834987408571006435117660626940967413252228918964178990504345600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "denominator": "207292704111706356596011900443247762208179669834699250419936052430904323156251335651805625477311122841553183958701061217695885789767220817990538920044275165389569390336555661485822575745588213582936378972888950757522113349288798686025176272104726979913984638256485996171300104379387779188616562743442162226462620971717742660748326465706409172932533077159688713956962114635985849100148677736500594878649613956946097950505174268006664330376370174729388047286056598693792258555946500984814533396633926836916308936207382639405509242707142896858065449061284524324009212593675493557514189293779313961642012184758482963876112362737152963104635951092602320108542330321235721927685949604542025217548456232044358141077952370970136966720842179588800165916971139917212568795952353172011184593369508865047864776616821957716340998813348324339027160789539174846445247749271381316554302644949019548915987362758314290809436741134879110671866534510460552556974884363150486963095467352535644034453890866925949361448899022854635159328255753829801061300763496395490519181660369462815300954798485097493840665053981487462535388947170493221658703097319427739911639023588824026012168652339496226747942944186864797972725365911001280282819101236002918200967107556390064684828104413234236303378922966748953328768851710515374693047666616653912508005871521677176393017579662259914223652030287089273935928344196029336381845884556728277160664620914224289660008310388316340565043404020502032724812993570055276472768745513105070381976272569734289943579495078341069638556541315338952033064247519622292061820656765919483159433610796219235601103099535507730578946859723731122425331367937030735573674373768972212138952152475242480803780606197759313979211275209609319282872754729233755562305215627436648071601169272285786374600616338052216551881541928882583415934959016775390566406182471653185382254879676522405658857346443854417920780563693181607036761331615116943922304720587056244341444840265093442818948502551396272078792848165255774970237704094626414460037697256789174811286226900603828704237099273590367798948629931724587212212281",
        "display": 0.6181010753858956
      },
      "positive_margin": {
        "numerator": "10476095030719439762292787939142894394532300848167835942234119907754454448443568757192150446132276992532560164270011601126896994834191946868618087282119851929149714421794305166327312172072316343142604003428675407756470321934006018220531919639363206578746778745827183068267746769176230717482112276371872023050119739217517828767122096719565563847279157656187387298706577480372628054058579421316182497269287303655733293901151185940721913701616008619093388608511003618192106212531195692309180440116607392860538711918764423697644003492844870857776240063081983881153308554272490728115508222191985852618234909628764162281279914219734400667491112385883086460419930738161924345041572196514207777527024298293334406912717370227677283259766507060748731655917765581316242050722869848543960648821760700209784025402015065650631366675367779240607316032394972448418445475143173184720482710752959384959904907680884139884046989322354802393240836267689259894760731786499528403500588066485993353747722119881647312290201937917735767568972066591472058064079613793429572866945835990072004967268104874403234498319720374076564815324317594507460742928296828367303541711053375962239886427095665934885630246258777426427861933500604392608897718075098275901163765075470012388115736310620982255912803274573421410424821450749219848271015453941035026185699801752494557567884361686504891522641289414353798141643426935058009621671970962357354632137504694495057432090010250765401588157664871888032784986852919569914457636450533251969331775952104407433936020792609481686028733560263821783147516436711752897417059330879703735014263968256199259142243528111251105420345367083170572607307457502707734618505387586449063784885150073431631792684892371980423715960230720341592318788666769531247688371122075745875238694863692010248409551541865085468603543975281724476097663816404314980489616259165716883242179954576651413079948848984862478805818806883425640748530928864328007841338599620498493544358086126168944912711618551927653009916935965534196549434760437931848351547652144983312555887713416930390736324460576350124873351097102551426405171",
        "denominator": "103646352055853178298005950221623881104089834917349625209968026215452161578125667825902812738655561420776591979350530608847942894883610408995269460022137582694784695168277830742911287872794106791468189486444475378761056674644399343012588136052363489956992319128242998085650052189693889594308281371721081113231310485858871330374163232853204586466266538579844356978481057317992924550074338868250297439324806978473048975252587134003332165188185087364694023643028299346896129277973250492407266698316963418458154468103691319702754621353571448429032724530642262162004606296837746778757094646889656980821006092379241481938056181368576481552317975546301160054271165160617860963842974802271012608774228116022179070538976185485068483360421089794400082958485569958606284397976176586005592296684754432523932388308410978858170499406674162169513580394769587423222623874635690658277151322474509774457993681379157145404718370567439555335933267255230276278487442181575243481547733676267822017226945433462974680724449511427317579664127876914900530650381748197745259590830184731407650477399242548746920332526990743731267694473585246610829351548659713869955819511794412013006084326169748113373971472093432398986362682955500640141409550618001459100483553778195032342414052206617118151689461483374476664384425855257687346523833308326956254002935760838588196508789831129957111826015143544636967964172098014668190922942278364138580332310457112144830004155194158170282521702010251016362406496785027638236384372756552535190988136284867144971789747539170534819278270657669476016532123759811146030910328382959741579716805398109617800551549767753865289473429861865561212665683968515367786837186884486106069476076237621240401890303098879656989605637604804659641436377364616877781152607813718324035800584636142893187300308169026108275940770964441291707967479508387695283203091235826592691127439838261202829428673221927208960390281846590803518380665807558471961152360293528122170722420132546721409474251275698136039396424082627887485118852047313207230018848628394587405643113450301914352118549636795183899474314965862293606106140500",
        "display": 0.00010107538589562764
      }
    },
    {
      "name": "boundary purity142",
      "left": {
        "numerator": "7533",
        "denominator": "10000",
        "display": 0.7533
      },
      "right": {
        "numerator": "14177777035382540058157054571319419403685896235867616572720331951259262335085717912085617113978053179253227660053374847123703093783115486782129734122431520403758231006412873732043068275931414297564121822697150666913405873727378122196679568491546817545326935671042332060339255641794239061693788203509676342951974830498199973470449949353925375423792610552108505216611122764225253376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "denominator": "18816499544203945983901339190207453873109660507348475617658615271377337923766430776754249703762864717220596977638169441498067659593585728047517436880448067442162379060233495129039837321557177171312044214807211955466288843865527786789711035017711472288248748255221074885633412095114052104413008544640983912429635701850775485397207405015110220166749761477535644049871072496147222905981463300120104583856548185341905997854556677460233140117853277069302474149498750391468276487617631630249689155847258468174532415500652410309987873830075578239898831424687487795584221232364516809938608671835616864889711106248389715741603649595352355950169933049722220352474604176225951500993553633198637562810369235206715341095994691990467702984355388281082006696289455731039090908473295608336947239916942069621312190751522895397111458790476124605810350250032121099258666837045791048901909754433515178185453584577976349480182092279916678749459979041692049481441688514424589604351758827699852527642262515392226705981825534705007679739473896112113353559203909655316611715456603032060240169204206875238141659378683620274323916500542862749879955624556154487307058110273911944930828815690801947804842276992150968431947887713672456446928746601743900792064427707044946525217639940057548563948590891428131106513053411893651400045867785212846115709457827269961640454988015706174891038730122289319350104466474631053074501204577630826521725806109552488964812871105737493162009661118189709880874347487131611297078238435963256439263799865467365759763345528719459751025698384677968808517218337477806583151898300438316564470159421244124342363798943379641220074486666448310236115445906888222474599789553975811442154311394242799480149492374934831876436517627254969459845491501557916427979002433658758971026561052952461056581890746867827323703738560293761026652221137196109256993194789193631149214898344729909082126489381913166554618750373974368285899920897089961974692791018761981910510324134391062254363232780830328696062648754334189293500817334028624629510161123818089526774985526636427751953761558337463790257954101139431114051762138348599300949093852319893267252051954240168751599746501516697281983786466487731479668445453555950583972901905081013420695858928868574877085634640808195424613730121492532747583130815531515614287759333783751149662169576218755665780940292793197439108532280207588231394432855571810253148642503595385387404016952105309444934088138197781758942028935976984793975759400798690222405339337991895651622653533196227044830878954693937490644330066201082513380460816058716929740443486509945968976614157058541934233214970291751995895047918903919424177748487333897937010963742919325771943689779106707086094008293083952555640189869771122459400993918814032512118656417791428451843544810747006431764414025382824833950883996285571672425709936509084467603462428066806599937703060322155023891620129373361738335419179495466650780666505017203039424500085040447884233012477297488136565285947827378576384333398096554894461431279237004554533711974886148784501343156347097897063027443977249624652003015712054242309625111559885541321878353047379835902619875892152014458239544928533606897585139184138935492453734166428900966278901889873667276060869076363292595455005835023532848465498493155597217752459762733064312200842842448398616610429165276846811335778081320628452907674932730692178411717978625779551614597702826512211869821724251842147638342521454635114959223736794943878449527695045751405493853313332879648937757980230758520172737588316951162844707576580583052252013117167162878556524762100908408278548293098129458143628413311616080875855959138097168774846703038027065061895020173855446258469431823371114266310523360024405651987472895949620469640785535062494789924111884462149642366435670946311654424452104541457978297512036911481862401771602518759907862925670312553651711550568151549326657516429773508572174072869358255867027655878985240583863903288178713379721142095257240474234868008037708796110707874123941232991378514669339164881198883123596526422534547153873666291313106455008915177444086636089020527068766015417026934732428354976737054429281972905453638257190506664165685550526268533480092844380278405459338933569144168091445460742853598000497862816781387496448670123144628525239211512323356322687913001474347845811904976497257516719240220649388245504746773872327213509508606841543968838727749953776178823300556286758548038418748624897667480336990615570602969880479819115449684996489238883821881589101525498635763280868923932264952835076997432180767669925882055978985881498899591910603537765291009877492412651134689683988673391536231141446712145999170316072374135180839640455289885591012481822249957272673217734041973173716148223816281375982808987472441427493225844873027481225228662801671067031207370058581956917609894632643944913132674084907569477925950594116187524965270052430078601686913856945955411116458243525994223613101132468137054381226177658415982581883793569394135698871840907169849298194226620598830246078150372962723293595887147176133745536113937389679127025043623051254262157319788702050961485481414123970030538808091620101900110309252403582480021661611995038141535228624502664482698994598128037606479117927454090941071062789489712749836785109475182247801822268706493239110742801413402219118542339362530350751688151037634139311372540531030330282466531761527064901299452623195404727262130208578043209731932635399454217273889412631688065995139998762957717988505689393039879025473661541250637243322604957199371558624788244033817052920425870017632285885175148369275681768021199940517748575607467721773873203185756364436811093111095055334593987772711976531544152228569157336377815351118181902671115845698346813862687303501914363854840513402745246120849458035217707124446683985351179335977648876141597833113682795459697956857389007860286644453563737287677208990313149193182242694611319991085690866286605006592778373598192733708230331439021324830687275324296491319798291695785526857875795910013226510442293960444117718869277890133086221029507377566135439591792569456275877344897934240801891026547327428888708008105655730672390993197396384115363465861557044021113116347006096561",
        "display": 0.7534757993683117
      },
      "positive_margin": {
        "numerator": "33079287337075484841757593361444010723889756820098899380970673307136771124656079566408121334871877709519567985418068432087258112673578439348489203899911995773108603389818513373588216023927344147589156828779008606504876434760404079902458127047654705891536103842963489916063105448236114394688668316231617187302562940108003207336111560428465721800152310809045538432438528775503609241636960195252169808622519819422118161624548692063755492211263836944462231825913301069473218776380929329091589002601959241247314033585393134861346438040669118842102877829154435864061456598094870732460875062298156785806236630880271318499707598210702627369894336442514084808806740489907343015560481114663239349488551187813335523871985235806793418850860078609243556851529978082528186470664182397776441705675389542655267068778028973559380931343353344430631566508031759284462716534056028621913819852330162728978147374104159365788298855387658980317977878933791256299760420839566510418200750937010909270836471550356223838908247067177148522543140587450107638516948566499963947465409359490210805384709608831078879900376288473517937001410614905154294280218488247115931255306621318836066531401188927186123127418126754802136561852905385585285751849063195333378666082830417825535518331546486667775264814871888374637168648205124003454477973991630210360654187175378962452575277685384545805245988794557335663054046604277189782425916706983811839502576741100628064641960479464010581222796676915467373540379437572099109629861888789243025795613434333731702718132156309695523414068220860965439794263779683009116750102798161319846289079768011328973502559521162689178891941644878991342345983411020098839785289900212406251572267168991516033873939615911474803712713888315058983912518764215548034174667248568671256915588109110860768617003844656770539737425307098186228818173501708967070263653004376552964170769149594884341155486048116344056953432851083702315895882221316444639205255665990268125728295632128037881767462005133932560066933600552052058343022762370665899956254278331594804034027847789744532314181043885267986831756116665417848075811820001465950476010474244017790292628708808794199109604074719374816136547947918763657600398363024250932129949024725901898094688833025450913914250791863866384770994796750812456275566601092877570308938607002589594876582344113569672176774388843691195426333196237852905737298977553363031276020415961876685540299790703951311514054956110009889696025285373546980604433783466554620578766907050056326550934432821671288988834290568882976261611307245426704988672629685368265239216120577015699165554878003609421191628792232214922604026896774977669020644913746840496410124588718959948184893989175520453835528198585398362449711014134513332312809573893086210161204777169472262576940642800549518669146791180525847990855980788591617127048277066705543117529372745882669282846593206205024425565430466025119287320860649719669239217705409504015240859390306088072717008518021867253700955016357184096816512138651980022038173507644690697547693182641206351382003237311541424214264519378577496461282641095392681594034619382217222290366494087696145564474904418875086081508053356339240491146525881398935346020524291089021021032063581664409433473247755316878437441044767727052509399851058886158670720607331826536191050867836213221073637097969512970207583713411705864246484731739695820024528467012002637687235504607883507984632951210873101840365785882233679012167590723687763639707873220354662414802990663417604551869134921696067538767747208406890290817825618467867385585188379762035833698967093856960437695708091790791804047162523596062762177059812714027619079786014542118888744813030346923334949770074545396231882827528936152223578366674811509002195962564374226747501665174346626744053640090761434307220602296489197049484841825945807130527454518226181614068580925535533341656889570114378922288928734516159925812709075124258553680668263604182681753216530149752110560636596427207507588739295451939638898037584224350691875945648995868070949928813429947366459047256289869671827538369074417841968313695370341408369590985605863536100660617201960239768984218898103217743008583913298839890747885619137294460603283362771674799813423636981767141344224083846262249599401185807989252167962351513319373019677668156821191951359893737677498919812046159126553963417848158346612742552419759100632871664662649282737863859598204044924076909491847857626591566608645870870621449692906647827890345522603317522921446563488169765989298208418776795205214396018248110293364978343382277142448330472310299354668789374137423550014062822592849655499002382610513323341557570811481917404188250009026805639682734988450301291842902974432991071864952650809461816082396255429991952394721499897370098726693529710571483983930352483115011852053914881348702118539644663732293162969371566118391279122783814174522759374436620695044217893492477915626117888059720051518685513522509169117523569346223203699152403210669383041753975780398422446289525236702890867029011756293293240471805429342182120322184494876453709643547136120346387554901643168910031707450107129868507404133759951158645825772386469040401643813177996823076841377679815122771621428451828473692301492710392804652488332940911684006773993855479497770323452127308872849833986429778774476952841083380020557582058867787533158233502028567430652179748521982179616240416620098511223389469016189534373138781600501089351457535911381275791054645493798858610389318639510392586641802230591301106907609758949646050816857417134048879470157693256140350431921157175990426975607334246289241496300848079799979948945651877413160401697306697502035594120948164503490108160680787877901262188537785065916960026735727178484334354353451172376542720079097081486412537120060971641032620705012231543129538349566062080371016025343523154627501802095290993288603788460707331304367011927584675971047127758165781492926507151490704263004485336600511684814136975900913269852360050432754982074530887959468655647626179621629409870364696838199595974461223757729653627461496984720924794301733555026574285873815960883861364039354897018982478181362574940095380844878648244013038458967011664890787388954894558003074605987",
        "denominator": "188164995442039459839013391902074538731096605073484756176586152713773379237664307767542497037628647172205969776381694414980676595935857280475174368804480674421623790602334951290398373215571771713120442148072119554662888438655277867897110350177114722882487482552210748856334120951140521044130085446409839124296357018507754853972074050151102201667497614775356440498710724961472229059814633001201045838565481853419059978545566774602331401178532770693024741494987503914682764876176316302496891558472584681745324155006524103099878738300755782398988314246874877955842212323645168099386086718356168648897111062483897157416036495953523559501699330497222203524746041762259515009935536331986375628103692352067153410959946919904677029843553882810820066962894557310390909084732956083369472399169420696213121907515228953971114587904761246058103502500321210992586668370457910489019097544335151781854535845779763494801820922799166787494599790416920494814416885144245896043517588276998525276422625153922267059818255347050076797394738961121133535592039096553166117154566030320602401692042068752381416593786836202743239165005428627498799556245561544873070581102739119449308288156908019478048422769921509684319478877136724564469287466017439007920644277070449465252176399400575485639485908914281311065130534118936514000458677852128461157094578272699616404549880157061748910387301222893193501044664746310530745012045776308265217258061095524889648128711057374931620096611181897098808743474871316112970782384359632564392637998654673657597633455287194597510256983846779688085172183374778065831518983004383165644701594212441243423637989433796412200744866664483102361154459068882224745997895539758114421543113942427994801494923749348318764365176272549694598454915015579164279790024336587589710265610529524610565818907468678273237037385602937610266522211371961092569931947891936311492148983447299090821264893819131665546187503739743682858999208970899619746927910187619819105103241343910622543632327808303286960626487543341892935008173340286246295101611238180895267749855266364277519537615583374637902579541011394311140517621383485993009490938523198932672520519542401687515997465015166972819837864664877314796684454535559505839729019050810134206958589288685748770856346408081954246137301214925327475831308155315156142877593337837511496621695762187556657809402927931974391085322802075882313944328555718102531486425035953853874040169521053094449340881381977817589420289359769847939757594007986902224053393379918956516226535331962270448308789546939374906443300662010825133804608160587169297404434865099459689766141570585419342332149702917519958950479189039194241777484873338979370109637429193257719436897791067070860940082930839525556401898697711224594009939188140325121186564177914284518435448107470064317644140253828248339508839962855716724257099365090844676034624280668065999377030603221550238916201293733617383354191794954666507806665050172030394245000850404478842330124772974881365652859478273785763843333980965548944614312792370045545337119748861487845013431563470978970630274439772496246520030157120542423096251115598855413218783530473798359026198758921520144582395449285336068975851391841389354924537341664289009662789018898736672760608690763632925954550058350235328484654984931555972177524597627330643122008428424483986166104291652768468113357780813206284529076749327306921784117179786257795516145977028265122118698217242518421476383425214546351149592237367949438784495276950457514054938533133328796489377579802307585201727375883169511628447075765805830522520131171671628785565247621009084082785482930981294581436284133116160808758559591380971687748467030380270650618950201738554462584694318233711142663105233600244056519874728959496204696407855350624947899241118844621496423664356709463116544244521045414579782975120369114818624017716025187599078629256703125536517115505681515493266575164297735085721740728693582558670276558789852405838639032881787133797211420952572404742348680080377087961107078741239412329913785146693391648811988831235965264225345471538736662913131064550089151774440866360890205270687660154170269347324283549767370544292819729054536382571905066641656855505262685334800928443802784054593389335691441680914454607428535980004978628167813874964486701231446285252392115123233563226879130014743478458119049764972575167192402206493882455047467738723272135095086068415439688387277499537761788233005562867585480384187486248976674803369906155706029698804798191154496849964892388838218815891015254986357632808689239322649528350769974321807676699258820559789858814988995919106035377652910098774924126511346896839886733915362311414467121459991703160723741351808396404552898855910124818222499572726732177340419731737161482238162813759828089874724414274932258448730274812252286628016710670312073700585819569176098946326439449131326740849075694779259505941161875249652700524300786016869138569459554111164582435259942236131011324681370543812261776584159825818837935693941356988718409071698492981942266205988302460781503729627232935958871471761337455361139373896791270250436230512542621573197887020509614854814141239700305388080916201019001103092524035824800216616119950381415352286245026644826989945981280376064791179274540909410710627894897127498367851094751822478018222687064932391107428014134022191185423393625303507516881510376341393113725405310303302824665317615270649012994526231954047272621302085780432097319326353994542172738894126316880659951399987629577179885056893930398790254736615412506372433226049571993715586247882440338170529204258700176322858851751483692756817680211999405177485756074677217738732031857563644368110931110950553345939877727119765315441522285691573363778153511181819026711158456983468138626873035019143638548405134027452461208494580352177071244466839853511793359776488761415978331136827954596979568573890078602866444535637372876772089903131491931822426946113199910856908662866050065927783735981927337082303314390213248306872753242964913197982916957855268578757959100132265104422939604441177188692778901330862210295073775661354395917925694562758773448979342408018910265473274288887080081056557306723909931973963841153634658615570440211131163470060965610000",
        "display": 0.00017579936831165236
      }
    },
    {
      "name": "boundary purity240",
      "left": {
        "numerator": "7923",
        "denominator": "10000",
        "display": 0.7923
      },
      "right": {
        "numerator": "197560303125938742053562298833771733080847529191071259262683176827668431327060820155082904500012927407288455830556973581747673493636674475636566606407657524970885023846175168521178118855695160939469752106242911870428620737861721419666756683792797579620838634724987750342300175179412386293842325610635476009307565358301066190906750517172254789718083272680880728786290279588210753026742125725942238562264708899756148758805792801787358131705612889061764421358801462320249602071012469540829322490067768548371683365336784082833289431296295252286577701147923584475930588920923071157173074604031208141486459363712208168593543553317532333720912445134964870858810888860849133947830386955502479912093210652453029887069572058196439473057064332871164015974507047919779502687676884367887332051588581626714278736601881621085674282396534621626034867609093426521032593639318908859125044882090192778341010048944545459780720443965174591975231490935386551557905075615593613153378419636384798589172275647460451549659895412547010098644079613786098459452227362583231121242972628160353002384200413502536317540255069517241311427321060101599360852624252266438933261780416660808667691293329953246562327726416835419834861510747228884501802774599765037378106620060905099581227695182406023377552628517150878906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "denominator": "249292957604819442802581425186925138378532890128260137348530512017538710529995420202882965931236118978329836517936363198268267337967250681997416730294595416292771866912768004486826402529994761139777098864672398570396726771835221683635650549672645922124271476666870419311322918748993495101519929583479173421335066354734081858253979228526272510571207441767003817623189202959866331772112884703583530966404486369045687388080046650065262026741285870395746239519670959890567993156503791675494732938303131237314852126311942054702741716008306677883105369265450930356726661468202549590432920980650969329844787497049663158456057990169341885703704085509235728167118308967102949738361191053320453601901344603868743101025490460439716006183053316540834767672543557579016344978621161746804397994358599676636201904794546754124390578211143640405222941486166246540648283539481582171458810257267887430243983208473182587617799240805269871586143670477716818756111297644280015410648278577654620151779475767658248248696719732452705218548860602141457999713065020926499457887190109292193914108169426091819876925940327673374366378886917964228278739817971417615682113347417938079079070751842843326072386726184952666658176159887390669748397512805236758797728989468766922749582151735389932412929746900738447006708531042416472612547977340737685287224934919753104791167994578621144007142303607282766165289123240827081443271906810792118726416363251400904209784936032868622228691426521425188012854074610752809524446264280891456452313581506054300486241384743083869543009351233894931218911439427054057100974364979065796482727161687751682577612473571844566484721374016568901238388692260476847724818457859464030358555373216505225348074566934819047816943190850510637413305785712979340345693838990300890678026092357660830192028978340696560037839539928646306513380250800447080702213950677722513546056398844788725582866353124256382848669506996802290224431930379796029391921085154531740279121862857947392312670948391730496766656297859383035066320297893987438490774126214747182585321505508024633691825125877181066791978120584454994083150920354346415487073525085955484929507528075329746404902370635144389801981154695818562342860997126959244203640047799127581949443251543437715519880460388815218242563164772792650556008654804834164167978139096442328055331615511305645761377460570585567470072667428367296371704299850899909484349358302382538526800956200892986581653094888777766249499521427160703460793754391603040158524718419688306199267807578222071079015803939484219685787935351819418714125428912322321465750946392635318631340341387831432971883312281409741717065164915086304994325153529019846371268749442338079977266408453948231835906774538176862133620045800351594583564315195162341664234003608434561421997030651193900560224176703877431374425501876061854277373362135389953006802323931691708084464574383658313044556880495333846696776151312203000940309491423385434238667042776648386272583660326346398480896708951548245987355778887508494582185315520802117254720003636754549914496013803300465544628144630887141003104748624906978569144115441814867216944082484228590762956215491814058315457520975990796220620232446338006858532555507474633472598934685373120056609315937266485309643969940747088958434208120748299027059931536326865515911978398006828309927538527999845170836193338386270863088017968331520046505099280763562265112069683181438089770745854416310526409215625218550520091892137706127921966009588989308570172685000779870816538973806842315213227781713839857416780534805899677022235136066146563876998665065027724143069113732182165147818056428411062493689539566352397317417447967390874350691428104455913853336380083142244701041888340215678625026371470324076787708890099151583333587830742263543135986242302613950905063576762672103438807034982397326838742572094055500988564935065595235085726227091074967238229277195435874188359499737462947013779687069849409623025304788228938275525934886546531567489444518255373210008467273302336071029146328563430082846033820506570721265980178368947910640496987657247460681274979395330359901653866968410343880571882361982828230169067598273268334510608826845818482196912602201395852636576074903199786975998772362547858480335626361797838626975509699939126874005866504052566329631030012205418539410965810098583613781832689749318575341924249548168846476480657621554902494012238414644740665068484413604313056225196001087018142663818292345013767105054794928582913898513936913893108133770549170453772468886480615138593313954265643157579255444764276479470277717719528431565793207664664046919467040956221268562312775812962366560898266520556157502271780711855575624308225578125221011643191706325280716112253837742291119438868717188636694214690028986852793814028016782119240920272160878518188013859857287741798509707346927728822490153644579837776251236092180914373530171539355598542299573734039741485478389989828561490984257566221781071098830697201074394137615562847644686995416687576959298991829134780279947070500470198035721127965779105936751351785221155505573617730533142150167458613822416951742218741554660254140240788408690917844621171793221031211502353102718705170160756491179312807237409661466496759432307759787106848566234031624339817176248581624545501146152416731189165099949305854970551900225711394484460311500515828767100092301783180777934605492503723318394335334538008311265451835913186076378563544664802700572981928806800082906751304204913421223606881533038006823025473630293415501747334879877623448565472890758061621064071074568743532307700532195868067091850451760808777045974333572841860756434185315044573567445147336903085485508605060743732995283788116410307114485642004405226698945778067836238508197601056901368842322391109741679027883518600166827519054422462473219939365655426077306309729636974065757938728742075693331269402925322241783410216083032773019667303343909632238098444301219635340140835988215015746789606655792892904167315578462286128490462637250757417661906570591781781563160203658111447151326568901004381468853029914532419521644990031638110534561884191589306360006313831045358473833340239037217235142725557419854968353894142218825903276996492563377804732083130755126807076477907021760877525589790794199927206045125505017841233651277114511181294064444390809724081585412669462766617065757273626935042920624158101601940448628142942651817031850892547269484460042207520649425417974743780791951422806191599488300336139650131864483133635071987684933309950794564662429588163955093994856847485003191135640767491286955171507858111601600784631606677370577556570355328228033178689206673404155901209503238573164253887478900859480107855617356866813901342062398944124032921906252690511021833904155760161494795722444138757179412913776119836183684595054803457830064948477139314244637301262423824848504966080329133193743791795697842300995851988360054418491888958988377634513111248710328342629797448664884618150817066959882619614923925444861075618929711013675300106586732442808089280313149909039371511180000548704460685189985209827886362707442181336301921795103694720860296137888065600640515811155626349604067887126797755795710032434979261741626763102936718850803458948466440607124422494615379729856928175289076765788076070396890115842376658107179731934114463948214987980659364080170984459564782068733434043216067443125674966828727123988282660511094976191463317899519206196703455882554886405957369171897045085240425206775537527617000688282334350681891236886391666578388344009507917097509162736774124683393573054796501318095235737294956868568817929856399710857874269573603106733766474203935751546014939356313795801942891541412179449142355208783459206450390666213563550774080095779525403174473160434892887883013911714116910180875898057325080027006486160108507874677534450177195954667710141136085088715296936026307735899915326038022500489527322352416438833832872926249469728187364388039709744727969401987672162396398589623759759407150327420277777324765206103415870704187257533297960677618962501475787517975089553009130901213874354675442618821910412227124791309513541952302553364448972387428420578649242893773324060949044265476204657621582160286100190952868695714945447552544608668897938685053810644468857064129171853992976297111920192614547553593757153658044774422769705023115844531278098838274845512930584577395043393526258760652139262351641726389376918982431667721418923997064223392086732112917728173077225306782492278776350414208069055124359578875451861126073464794830199516047520860870925665576288302518300603648821760654945376212410803405013396693554926224138855045890980657707430331598946181866209457562744957387353195286088507987193694806371176984964899063549135540931536451928869975027908121029640060257525782294700733601670182167030800934614514056887444659343720203123976093458433962007773016916803034278103312572374116052941990951626988552789512723103623689731040005726399159462750295533467390096771325502777024085048843842758479903116817612528804212563658729299525613760304888928653247082646037259911864228299463622926361325647528130993478163690656133312394525251866385741734584266976830372055782157353411022316417974845613369995234601198276441064909086152590235567489105557463939957392965108977911103099875209391805689921660229672932916363484365045032048073855384524786925962606123642195125187452868185550641693025410740421503429323620862034872710839393174006722936774888157792232835002715425977947180433207207378138001200407478891102004582864939720585879860918187524942146491502744158486222767760836742188011929874389856512568174982428058636253013468670108881693188417288298692145759597690056988965863325322249545037875712206692560487631517277671432984728152193872005456842259670100819056750771973671536562316548057853019138015310648380722944202691831534614858880870865590432932525285937761912939029144662784932933848101544073128356034974943431103597643879574264637516421935896053554566264665321457305843838717171515545943595191218998419010262485529850052794160570229689756458779169248936807142533464116975034231156980377758292872906165484822460252197166198016199908610556211971072502245732998400230227154147471547923075270756442440898185490819101394376683250130131074903715755389391749586549593352535338747025320086403484139595294879108550504229627242544275839819645191973206837462040572821866608547768566958308695280114648144302250646149816306823779697965602214747888565979438285051487090194294787054102094128774344674549483350846967988698439116118681112833923349139769380788333813397816199939427875596857010034415268950904028253777571540500523229162832512774843059009970316827042911129639932659989600774518077219386178954944203739494448847795838666306805096901940065255113329358009029142113013432565431590701204628499040114565461167255053864849887704188032112280330147957955118685636838307641161133745879958547190182968041329913213515870180088827293106232327633710525676467967537019450566919719511175910501642525491041152811708054024845943555515632296702945661052058859054589181468044637651876956408437530196591992885415277545541160979100528616302587133575026499186639343865730564512103258289826318006467596617676283221365308305864704398175211607579004720474400026326685389447637151088490778525830416658259246422215380487489806113716492999265567896862883418130807743604883352916491192603685877218864966125837975031544331269969376804071516531406723448746123409420704906055279621760628832906335524989981555719619317729768396678283551177292119419678005605426600178003653116233499022979567179821451976707601589740138600200178589975225577065100460275657075137951189262178544645582664138133215556408319305760891634543819913045594653044914184255378186431054149479125350045786666814068036963546827965083485915148536228283641035936258944898795223371407626935306452244990500007818754771594738138117680274263909623003567389321450676881826231119564068536380495267741993900990751506884016622007884539951238695872639191181804918235945920906395173876585565139340099700456656525430914844075038829075040916713722092089705892027465376176236180655074880384449419145909243408251798309260590095155670665691279266777330454976538980255033073208375109076000313434288671521628956625123422057062656741142006758737515706258121716532416798004415138084509742316771473467540765429175762296179612160497013092659017378830106430499299867794876069965860110750263285468834427294064899609482297736191883587548276452764212990459871986651176490765283047013414985262671536463900199542502252680691115532783865108174848299661410855604058431764029339539684728870959632811212545076447793020980566850151526177236505751270410041362232818094656003608085755367059152750777890979591118600689173135700076181541902770714523386210675388911374773274379024606629043277124624620980634963729926867776119530517780741162306778562382530687185659139636217291887249156208232007749784789262149663814800589438092594733966393652143377430996176725209244778905495461882955110196410105557724255726743928894883925511476090525627856714857963641367105009047427733678014094097781858986563294639043695211651511538172067688974315856033009386849972172383732833346902895665022613363027367225219472895008150232415292301749581471719588089150068796574891383082954793432615745915920752580662270488600310073341152330605028066991014652082200694848434697955446152298892927157686947808227022727761417814408230916932514805099539430158943421176987441959315737853080489153447207879897996910150896734074612079944616433113755749268109609901768737474372048290711355258342091242976023469864525202125649275597345854126501063678382923906615458162586587077612989905717393758431359379332310902426138810610113733285759695837140364426301487013072475102442015493446790447330054977213523441386171993950501307125251796985632585109292157233532073080842767640498774511643447347841746349439091946046268096260460735837563889720623182090893001065812678153563814932700908271251345741886118854650449551757910709215841972884426803946556302167337549145391995775561327545950866749366770620860243554757656975333465848317026061426319521061563541919312635091070550071810922145686484850580991436452265783952540495557326537888853209660938100990699115398848058688455151758300276732650605181662313494279332731933572107512497634775139677873070284955265172823041669919904984600173486711653359739738355861957993830473531345861743297419023590893566741168820375633440711367680813683272153651399666927281170104539852794374757696519808583340860519211277573844143538959277436576542489441477551742184774540575032065136023405204178835129412021045999611444538871145867478301437331072905681164643000868425183377489876929134261322269558934742113945534939453128318415867462656567224063435062285320345832534779054774828451974407521726666385295001979251418995099715477057261734321228586309601254814872987911547445441226208258459903610369323172730195323996361190185197593317975594805920857191288861297903931035237928956058023317688154141734525709005033365606907662292311130105546084958651818815512849513437406477104253251720242670163636369405760537412047783583575804521676368309668468405948341085585544266365946603391233717105843550775072118600285424125408248568318747431093385825519139452431712145279881071864809652102772633235181045579629442721658132031125339665903108202264440193342860084834528641453224341120115785522305249411579182298731240071512111052388434729392884421185331243509963403483788265978234763482304547553744722421628648158119860215453612930010368652029701407024720193800073369453836957504798502301690624373990156328553786716708551032002639897307192207776510032778057293049890831026611684155378485663578162876216242756860205050629180443951065157063824062215758568849920084346555774337454303486613799224070936236098091301000785849154906811353003842163023680741389482797316576918902181837824907539986133332269896272153182416281721070496428803735768633427130932620472734068251171691443623529576039405422159634040593141352182714208726793942726162466963103240340761026437765710625996370435933874787003586165471997561360953164573541127315163867386804444727113199254789674694788604606926386461757785254695411671736245048044289783881235667311970504878553124972649749739405937398813173527441158490502661661278761059865268838985596533122481449096503442758356944019496156984241611112560330922755665903848138515162073367112450267474947293855227105817064768789796406781371482264697253278296731913170689994630304288924686386446817665040416981699194786364232952611063573738511171229803599682952236564251794799177362136063084690839086340727605408446433761177518482803370388585633162273438467513977391331676215431952956115401794688615669302431999193857223961279457420936872434878837188882119867905973571203385176877300752783066587076598658273412933806310326786735502038506322762411627292705408188098515904035019342514452791306343715796643378248800183527209954786926903284038442013688011933320396950033935775365387335062765442764806806191847370973322713815426603061468043006898743174451394728413028996898325299959095429747992296244428992610994727329630303432838151778289630521727049335310850777858497101997722706672259616605335653198066329858836073725510597508021955528075695205791471458147518909132571305875863014417879350045855993430027129484174007079168607665441513106170427459249582996410835287285136933345239586595817027656693156702068536392549274779897777185417465485193314918421654811595276053876145700755543276749539197115575762058460600798999737969061391742238027810921007807363011397645335020861357954887535347427587925135537757539045704576749218168933977594303112093123308379561316759628172031925500735686763990951203793912965184553395664632988487048885455983220313918441798701379837622328230421978633492172875868933424435815347680554121644095913213451940483457809905718819862527944009478879131351401340361562763062117303183296897851538837675421609660986920066038834299224366947672022264625794281980957476143284865355295842431544804501971907644115703409523289898749050960801516605883419608909384472776525522239926343278452379893368841986778905623785248144119589565282890207986161748878356187594797813543780729488610396653106298972468450909789397761262872712798537982983196280139234608579196313565859432941413078185087830992158454957176626251861407424870241345693864079547938105859959525824891323701638900261329929194680795675624135500912277622017101966006218378068299712576662010054001121",
        "display": 0.7924824873677836
      },
      "positive_margin": {
        "numerator": "454928156402975210770356581709459435359203424507524414424521561725109741454487283387305926945503407577263573959930197597252817652217602900133309952495766421218736911890785662655601311803116884243566757629704831032941165366752797222307532871602155217783437618263171219390266545848401249080854016449269075837922854452531346121227744108890795925156165688836040834374740831086583636970871752930069775824343495612506412299718409406510279184920939472146757873661607989525810931145153963348455830501976690471260256598323928923071697029138713997933170789068123542960550396661911166730713110614451414504342297997600481488088077063627576778676981859974034320030526662134668701268152839566845233067753228078247281270759663900524813582311901758606295475507872499248525611153379158942075206582631029154159674331622277929196272798455153329767310696039093868769585909876513046782295152568455673587021528712428956111381054751592727175298608158915160574380944920305569435217885193090430429173969967448214622174843685247317539878173587094212862795659465031656007589519045681477642362977772099874290518325479016268009453289549985412956070664735122620283233752574284686133435366448684793151757232604974220415885392684492568601474252041759533826659417048010666867337563624565799267883900476958073428348308550934287490782375529335319469316840630796150739575978953584676031411528519498643672414276562927033724956682338094043330603153959150635945873951811581906082077827670748235374157166859005490137812248102496990528319493727531777247509508680546501610736910173850459952564665419450705588980106270861694467352697947943418937576371890275499741552553666724595488246391220241935476263358379466487469165778005629099567205206175428684146359098891404219774378259796064686441067713679846043157999270250253242388554404606661154820197325145335313494488272908057779596358868780404525174595151952738927206949884196516678689991496064335454551825815600876059127809242320645021768517480576482810706708075892319274117782152060108213169544279785937524837596598000558072376497711859920827259669527675094407807157350609363081879195258032513350095916460743974692903511855059162419233958517457750999598903311345029530557512319763101908174559901287512168214561118021342979935987112339417025864172045505163829644743427981298917297109203938887434817607610303925368632606379899250548934614255965045910846986832281320017155500034170223147252156024020324867313562529196213758005215291732605746480131083955329112824008655960809549983201160557746530840957785387466527429502188207534745527984226727670247026855251731150370483890475184211556563768516794390616375692698377771205529961808589575757200437698168355392340118245819368159164110625334024721315328377123814316114419930708728766994273989410372969853517526150590725861343847975179111220426748635961928560370851801305402327105187489206596846787177158275185747975835835469932621442553153415623549927899452517204527041020080614835562319659234357484835855374976883247042180163874270197425345745128684824990853411185993701027448082636450411489911210089481181832401076644862008796671173354500807040152034477456875385097904658357215966630061307224921544025898327663971659846562714278478996598640487788769791484389829037636891690826159460814182325769059311226808604162437682244517429395152591899300444112242657226711464840179965575951753633636909366671540098398510296173517071900153466014746380595459571699259784601393424229311938592954348474263306026437708198521816738821083520561710528388336565596285481246809686847822732856858952831016947920774402539576689785341614463411899920705533837538917699151862497778015789956054101559754362102519471815128395794540015860601263995233645118680471178253916058840622339610982463744422005247983617029045947733581002236389666979181281309348924454331861834465979456642601298798265667600019475288952415791102757413034571509436780561568805627683580081070809823539345583127556770510162862122043008017893891830390781131081862678057102913793625591309236073638791943453610874040126440175409639046782825703995342366791628369022258338250797558499196412009284845434228976046010051932370477418880894985672446264900580165553861452758340659560407758541948087789161726571533317260300832335475724558473036647382297777251519688391516970333349213296468912246917886588922028006539599116148927565934170829858229366843749664420507539941035040769719710662397991013027655527772083387555255674567669750455923226650859780837573182074077831224904256135938922494760729012414086256925173540353309262499559111132637453156989642508176236704220415672866756257062634503858889180795877233899169738003034357633564109500681419968274328605928744513873924750992110784800886242612843567827460685843153714431471737010900337165314611456023035269254188683669359500396366188350709221730407588690291604539410512673993945298761456441650615418520450893685592749360477305203128210554716110588307306931727302824828573683964386075887575247671895558111144935313584327751474087737765135841979360424774620962981503127132143663119039805692784929340226720985914744223225402684990491346400910662426806446872233437941857917066455882309769711266856367159698936816326320386304628258003252200946175017825619206752438809727767440355628512582487788725994419034402238788244913101649711068317294511688621499620951981413088678265968692971858696424120682893000148361681144455360149843825104059826716852641035620768203360264178063722943129809416784470963645362677613739871941169172427185268979655865746729589417015758286523877776309364876191844993526088683412137304431268870699112059464745355102373937226771949748901843625132097649716853698315322103727403478366546753681136731930258399097388864252600368533482299550406826170454662279695237516677062078882130878225566531810829824678420405912059189502108012086254476999851452176534281736352520622671878350040857974131339365175955606203983777546025801436829200064156465372430238185946466152909520282358671843307003970064525062248979864714241201312944675081706416783004220039594597342285622277443987159640130006743979331250234666191550037925709669975516627624811818445286108127845964185408562489085732096711200242368336356789420357653107705355027130307533065542666588567364752087537553976746504470623743643905780931421727910607127407091614556101598775419846500092988005121053793654939894795361007825825519223465369653656645378347983874623085589813894602413386105024785368877106543957254196436765552005237700132209324641572273385259854664179570372976983790278749197376319716632318199166533454176143240181780516983363780295192914019293074734449293125245415526618872794717105840784819616449504668490339105459943681544233459666839613165705287159736759933081174009977373912240476733491075088626867511484151802537916666953380792203612395413215625213239738662097816035725295153745552277705967937602685995449209864696223288842288763777935084001752619576468068541344114814228119170391076378476850004790957738700365697871219899638650597255513318855631508632078913270681059516920855652614557991239747182533656348268935597272479873617393426726623873699512856246125193228213972432086970130294381380830589413017659309221091155935432376545084194751300391069753200575162346400343558067184644784661073294245439612180849737816814983886011102138292650229235858392805290126868231669425002075599097648115277237815994996640836480770594503635036132282109329303518519042517635005599764051059711789640111086717416168690503546739064939547375730149118825699429150412668772836434903636538610133472720686847320056731447253412056730329255541747745090873062162168342585348368224882217040500923635479925795861206470317391302224445119680808652707293554751589935987216963401138820230648649149874343649302880777489051720636920259691813390946027610153460292108929894551246076451167732551778797842108702375863563808464970871800747728621475025001804555119542147805325451343571511953561379692520298428051673457333333974410951426217147955849139170255885272042636056410724358563680257551224960100807335495083365471508655869682473487906468131074003803924490278454724207111906869693470791774404623755362048552633953465100722284632030497664204544053228187080421323850487219041189065516321631798318658263873245480904571400813648797982256313914939732876662071567311252248395627101853163778683622904348399001050978393299071193091451839353100624387942601816966670902193896643197865171260158064496821469352839684709143894362313675254975668229468876249699056569794904298119938430560329234355492219319655951639067779147504317290385190330867784269069204622078857996964319526147851471405760248984029482741549401074022467730371702620000633748320751217464356049121164748123104719500199109199436691367563187853883957082161802579623226879086087673967146690614964195049205127280775964019704830648737411528827719012414386968169559414587454489079878512540605690259369696248690694849989506260970034629739459576629408488337868263280788041497638174158010233824563727605454055934284223858131887759858562177104365018280323364195446789718299719183349715554439216894634618138672509078931455765898176429462625768236888852742572962202037967288924470187020385298205269527756254706055757442725310413027563598783816668213203717575537441568010330139688715988723518750686000301352503652113375748211083110843788410113185598271682382888023139810925365882265866159670703640428329468951910097703512019487882344734171932561125812139248273485679976724489427699295943012616489171544745798817689961082593798073861945200239883373347823758032313657011030890491644381479605209166850922349614222491424967374287726727330344868169824809462129146707501678476423464873471816854664910732186374843256495488609009236461998850167952100765438776633791210613363633652600415816765989737630529369504693732879532113082072618751246473086860131926999875602159515112363784072086836754976365121491466308604035134893523195366195867542133101276957389001895567687171485056658093765799265843850082329488895299971875526181690327146998031711865802070168059577092642040673677009707363801206803786543244467021045567964450863751647421841852213117648124078563132553192564707057453674975910257689582925805474629796706540763676356240259652353538609218971493537860070049849168025767571867862511107318388955425195161986478672822954354988663357321702521108951143996282226788252541532350860476029643989320207295651642752693268130555005401035193453018533652552478891744910467537067784390602402170349108217720867143544443411239472625542266882991689543016825304765607196014031196449102247879912941646101909497327824101987384145320300684614354455342878001284918443464005179779339015119862813534902393063493274190803304139977073771985481778913570246851183217245928862983737091496494462107038594573784085506874355728402105172297851171838208228794339719718221574402944237729121594653699330088559080337331393088430612180344208543097609313760563156221356719321268158111505065344293204194893158295062312953261095486270534480946272837087961145589209649645313222561527484537659710489915228682335884178874375949448252401640368854756006677381562586511773034602140685065046944256478551816737370605884569706082434757231998150808037122662292633947053257798433151545599681328591413671659406370851925887561739845608816611990596787540397618266161024225966818905553155374678149610247418509194842640281000996794794932873384985723825074263348032627581341374521664530115584464227159755029324019556790537756883103635504376134033456145627044993117959424022314537837891161588205046789677056360081987240932889234274635988545672604488881870613985031626287752913209053235968993682012727475759390773048552033570533146576886140456455579509314828939753563925144918144638628906757973676889851587232238832138943137818482032643541094278147463308712072277020379566845445228337371791566978862940268438052005944654889731693619187007044056942735574406146287065290770839693884986257335993680182322450275810957936303831530789966335812601079688266559632816600468658631037375812567401008390073281910349010861690393467357238450816877179864373260217466391824555680740669841722714007252106961064476421001995728344676081621315727994369323210805220881659439372960970044010790849516660130855534133776659147127041892570639931880450522663059316901639913661709411018860956429311624219615716674515504640435327368932852382165266862605307529066751154047147461196897660490342525663989230424832549123800394071755036151706335855005664749140476586434249762728663666662418512713071763853416596518719024754652010884291633753436747930676921782641791049045045133595542827077893155386829236763005359304135894770968846249458097755164932684541242287029382236040483413136560226790332755586769768699567326739681245848296413643504347628831211052818893655177671347094988041678090115341599127970429182367789426609804959707623187771043393450243209365428022636662250396377324935362177802598455114675988213595334929881992371922784263094068020614217291806167153616731759455501346661913842733666150721877007851365834658172574934765450491248180354069448427013317230066069094332463274331249459016574856802838085074083062707700256495472650466627987670478203684761392488357646025834324734169474586116252850425708573639093238065999565703569664004924737135571833749171633385445108159877303412830918819743288918050084616362625230190911552723894715851888099000135335871338129646312515417298927946286656443586445143685199196349094850691274014728497356341408990043284437237771967568170480874445175926848490598804000439713198548767560748286292990550261392693932288155611081900966048263366823558480789442228797755732072476172093887885724977826470584072280977001089251948339637550100720077702203536068891176925929882336892650413318395426779763351911245421079285803974415537253773897359291930178143646630012482833028179078238238725384980482751984328209544248966663049843673394074511475417873328369589958981301743502528293854752555566150989313894288210703766875587687036280314604488201422073450882884048836686432331434417928184598121059217470227601853431282744767076370924290315655083784432950083784202515319270434629232057373285992173448031781042063839725980528846804848988698193744021653699301840306616019856387425850690908694926831011369832618986907447209255145689490184824846764890308192178481239676568332211664132299434035723040849224592807012825464783570430782053006505706814881158211146737407854549076089350270709719436163856249243833864913187434726619960438935151289261730746310168794770473556594190362106289047782432850740825644870004053856155173357546670031315024020947927286560567291089269668557252545078524918523911291969417712025909368288132533504119467272100147705090469247543658284560038231209526674712864333191082093372017883745404001513406899968826945549019034175006769205359622229307699318391007301824954275275315278972905910669029258101761316776809589769164751968222183695043852502458662447976830290162679468141679362352689048473418351936707154407809888881152281253956754735037352807553120644296470591658018916173758368872601639524691693305035428481903001486620517324293509045198159262084345410667328900774758133882496724819671293578905732777582605061331255259370401547209103604329938584654390446593210564103447104104411858118383544672947502267615113126389732426877660575872595925316302619917393933827049673713458840348144519547856029573766103545305322631306775508912058138647152384913409544131926431639020176730948620557670559954197945568654445968929701069731680564253436220643216347512961024755527849169968675752143141904522018693817249785689481466263705183084875991408868347843518150173443084093635116137786711010299452067165714945776155626436936258087470215531738708637396595383865003342575710760583321955064544859002083171722238599924349553475558868747685972201394822622170773717145673333650150558542363377485971127796860761071538013298913257560689865608425611835730335715799923958456794588001505117356841620847994527977245966688692170775169039790840229219496380541066656355324257611591780614774251333026780150387533582274710230757036095910062570586810965363321337168077083833648281956678694348384427082122304301407393189885699322240063493067427048253324833730484345092042308969807887257689847223590841696032814686757989203226142083701279747411657688376122687474988717118668070579478808403223025537932533531948213853715155184498099006859043811198544370892712368056530795992590785035640611395836878443069071193746016803662276054993051948623172544099118849709760181863639884776253997279707636182316462543305269775990346266079711969429701433029806117759795972179994481918922415182348878905310190521060748896411236028455307547021886757128479129345132636728697671580682098052116831270387069214554782858853917159698454972952486964286580971395355579243601146135699763430592108830499749325452603280868694617348914404753412676959895050925695458492330541749257990534479838739743194514134756145913915528223178145280563423925549881452302494964881126851780036144297709396974435674541993279778364138440375023943988695256341257828821599566783571257574568648424086910106657036855389091543088775367339105901623323460611257376356588116332129287027127460872042995035687057635925619711720468528441787872779535943942046351056266884514171637097207682942637543545537336767141909586682964053895053096889341911747121466706891659811703240365553919436952018839860077105666755401341689876020119449510986161832095918869911359937420960813365901345228927730627825139297612913830618313400941253293237210816659869525076071126593226248105654072855142262860696456010629715460923426057442331220869151134347018140882638415944447536095520336442886184027708735687313465992991054257671153768899693612340827576842783446149112832217111680532244945452824185628888967546518293430366663286841514304490440478195035000326969694213828079609820275549563772116989790229191099612898840642302847180315338228258844606878738678322257789097634586656000632316774315847245340673594567597369831903864873916516754011789991040414870513930876575735671281886346974132211269237569583931585666438610946822191588287293063582204821794104838664938750730742749478954140491874263660882125640463636783925686416923292625280261739827317438793241132463441738601537514259496497183560824135872456844196227027607617695712805184181539549115049128561374289590206502068972753077818067514897741686387271540676889386042311914993229482970990544055862029974426272024400758501123332731790564861377255106894342149118317",
        "denominator": "2492929576048194428025814251869251383785328901282601373485305120175387105299954202028829659312361189783298365179363631982682673379672506819974167302945954162927718669127680044868264025299947611397770988646723985703967267718352216836356505496726459221242714766668704193113229187489934951015199295834791734213350663547340818582539792285262725105712074417670038176231892029598663317721128847035835309664044863690456873880800466500652620267412858703957462395196709598905679931565037916754947329383031312373148521263119420547027417160083066778831053692654509303567266614682025495904329209806509693298447874970496631584560579901693418857037040855092357281671183089671029497383611910533204536019013446038687431010254904604397160061830533165408347676725435575790163449786211617468043979943585996766362019047945467541243905782111436404052229414861662465406482835394815821714588102572678874302439832084731825876177992408052698715861436704777168187561112976442800154106482785776546201517794757676582482486967197324527052185488606021414579997130650209264994578871901092921939141081694260918198769259403276733743663788869179642282787398179714176156821133474179380790790707518428433260723867261849526666581761598873906697483975128052367587977289894687669227495821517353899324129297469007384470067085310424164726125479773407376852872249349197531047911679945786211440071423036072827661652891232408270814432719068107921187264163632514009042097849360328686222286914265214251880128540746107528095244462642808914564523135815060543004862413847430838695430093512338949312189114394270540571009743649790657964827271616877516825776124735718445664847213740165689012383886922604768477248184578594640303585553732165052253480745669348190478169431908505106374133057857129793403456938389903008906780260923576608301920289783406965600378395399286463065133802508004470807022139506777225135460563988447887255828663531242563828486695069968022902244319303797960293919210851545317402791218628579473923126709483917304967666562978593830350663202978939874384907741262147471825853215055080246336918251258771810667919781205844549940831509203543464154870735250859554849295075280753297464049023706351443898019811546958185623428609971269592442036400477991275819494432515434377155198804603888152182425631647727926505560086548048341641679781390964423280553316155113056457613774605705855674700726674283672963717042998508999094843493583023825385268009562008929865816530948887777662494995214271607034607937543916030401585247184196883061992678075782220710790158039394842196857879353518194187141254289123223214657509463926353186313403413878314329718833122814097417170651649150863049943251535290198463712687494423380799772664084539482318359067745381768621336200458003515945835643151951623416642340036084345614219970306511939005602241767038774313744255018760618542773733621353899530068023239316917080844645743836583130445568804953338466967761513122030009403094914233854342386670427766483862725836603263463984808967089515482459873557788875084945821853155208021172547200036367545499144960138033004655446281446308871410031047486249069785691441154418148672169440824842285907629562154918140583154575209759907962206202324463380068585325555074746334725989346853731200566093159372664853096439699407470889584342081207482990270599315363268655159119783980068283099275385279998451708361933383862708630880179683315200465050992807635622651120696831814380897707458544163105264092156252185505200918921377061279219660095889893085701726850007798708165389738068423152132277817138398574167805348058996770222351360661465638769986650650277241430691137321821651478180564284110624936895395663523973174174479673908743506914281044559138533363800831422447010418883402156786250263714703240767877088900991515833335878307422635431359862423026139509050635767626721034388070349823973268387425720940555009885649350655952350857262270910749672382292771954358741883594997374629470137796870698494096230253047882289382755259348865465315674894445182553732100084672733023360710291463285634300828460338205065707212659801783689479106404969876572474606812749793953303599016538669684103438805718823619828282301690675982732683345106088268458184821969126022013958526365760749031997869759987723625478584803356263617978386269755096999391268740058665040525663296310300122054185394109658100985836137818326897493185753419242495481688464764806576215549024940122384146447406650684844136043130562251960010870181426638182923450137671050547949285829138985139369138931081337705491704537724688864806151385933139542656431575792554447642764794702777177195284315657932076646640469194670409562212685623127758129623665608982665205561575022717807118555756243082255781252210116431917063252807161122538377422911194388687171886366942146900289868527938140280167821192409202721608785181880138598572877417985097073469277288224901536445798377762512360921809143735301715393555985422995737340397414854783899898285614909842575662217810710988306972010743941376155628476446869954166875769592989918291347802799470705004701980357211279657791059367513517852211555055736177305331421501674586138224169517422187415546602541402407884086909178446211717932210312115023531027187051701607564911793128072374096614664967594323077597871068485662340316243398171762485816245455011461524167311891650999493058549705519002257113944844603115005158287671000923017831807779346054925037233183943353345380083112654518359131860763785635446648027005729819288068000829067513042049134212236068815330380068230254736302934155017473348798776234485654728907580616210640710745687435323077005321958680670918504517608087770459743335728418607564341853150445735674451473369030854855086050607437329952837881164103071144856420044052266989457780678362385081976010569013688423223911097416790278835186001668275190544224624732199393656554260773063097296369740657579387287420756933312694029253222417834102160830327730196673033439096322380984443012196353401408359882150157467896066557928929041673155784622861284904626372507574176619065705917817815631602036581114471513265689010043814688530299145324195216449900316381105345618841915893063600063138310453584738333402390372172351427255574198549683538941422188259032769964925633778047320831307551268070764779070217608775255897907941999272060451255050178412336512771145111812940644443908097240815854126694627666170657572736269350429206241581016019404486281429426518170318508925472694844600422075206494254179747437807919514228061915994883003361396501318644831336350719876849333099507945646624295881639550939948568474850031911356407674912869551715078581116016007846316066773705775565703553282280331786892066734041559012095032385731642538874789008594801078556173568668139013420623989441240329219062526905110218339041557601614947957224441387571794129137761198361836845950548034578300649484771393142446373012624238248485049660803291331937437917956978423009958519883600544184918889589883776345131112487103283426297974486648846181508170669598826196149239254448610756189297110136753001065867324428080892803131499090393715111800005487044606851899852098278863627074421813363019217951036947208602961378880656006405158111556263496040678871267977557957100324349792617416267631029367188508034589484664406071244224946153797298569281752890767657880760703968901158423766581071797319341144639482149879806593640801709844595647820687334340432160674431256749668287271239882826605110949761914633178995192061967034558825548864059573691718970450852404252067755375276170006882823343506818912368863916665783883440095079170975091627367741246833935730547965013180952357372949568685688179298563997108578742695736031067337664742039357515460149393563137958019428915414121794491423552087834592064503906662135635507740800957795254031744731604348928878830139117141169101808758980573250800270064861601085078746775344501771959546677101411360850887152969360263077358999153260380225004895273223524164388338328729262494697281873643880397097447279694019876721623963985896237597594071503274202777773247652061034158707041872575332979606776189625014757875179750895530091309012138743546754426188219104122271247913095135419523025533644489723874284205786492428937733240609490442654762046576215821602861001909528686957149454475525446086688979386850538106444688570641291718539929762971119201926145475535937571536580447744227697050231158445312780988382748455129305845773950433935262587606521392623516417263893769189824316677214189239970642233920867321129177281730772253067824922787763504142080690551243595788754518611260734647948301995160475208608709256655762883025183006036488217606549453762124108034050133966935549262241388550458909806577074303315989461818662094575627449573873531952860885079871936948063711769849648990635491355409315364519288699750279081210296400602575257822947007336016701821670308009346145140568874446593437202031239760934584339620077730169168030342781033125723741160529419909516269885527895127231036236897310400057263991594627502955334673900967713255027770240850488438427584799031168176125288042125636587292995256137603048889286532470826460372599118642282994636229263613256475281309934781636906561333123945252518663857417345842669768303720557821573534110223164179748456133699952346011982764410649090861525902355674891055574639399573929651089779111030998752093918056899216602296729329163634843650450320480738553845247869259626061236421951251874528681855506416930254107404215034293236208620348727108393931740067229367748881577922328350027154259779471804332072073781380012004074788911020045828649397205858798609181875249421464915027441584862227677608367421880119298743898565125681749824280586362530134686701088816931884172882986921457595976900569889658633253222495450378757122066925604876315172776714329847281521938720054568422596701008190567507719736715365623165480578530191380153106483807229442026918315346148588808708655904329325252859377619129390291446627849329338481015440731283560349749434311035976438795742646375164219358960535545662646653214573058438387171715155459435951912189984190102624855298500527941605702296897564587791692489368071425334641169750342311569803777582928729061654848224602521971661980161999086105562119710725022457329984002302271541474715479230752707564424408981854908191013943766832501301310749037157553893917495865495933525353387470253200864034841395952948791085505042296272425442758398196451919732068374620405728218666085477685669583086952801146481443022506461498163068237796979656022147478885659794382850514870901942947870541020941287743446745494833508469679886984391161186811128339233491397693807883338133978161999394278755968570100344152689509040282537775715405005232291628325127748430590099703168270429111296399326599896007745180772193861789549442037394944488477958386663068050969019400652551133293580090291421130134325654315907012046284990401145654611672550538648498877041880321122803301479579551186856368383076411611337458799585471901829680413299132135158701800888272931062323276337105256764679675370194505669197195111759105016425254910411528117080540248459435555156322967029456610520588590545891814680446376518769564084375301965919928854152775455411609791005286163025871335750264991866393438657305645121032582898263180064675966176762832213653083058647043981752116075790047204744000263266853894476371510884907785258304166582592464222153804874898061137164929992655678968628834181308077436048833529164911926036858772188649661258379750315443312699693768040715165314067234487461234094207049060552796217606288329063355249899815557196193177297683966782835511772921194196780056054266001780036531162334990229795671798214519767076015897401386002001785899752255770651004602756570751379511892621785446455826641381332155564083193057608916345438199130455946530449141842553781864310541494791253500457866668140680369635468279650834859151485362282836410359362589448987952233714076269353064522449905000078187547715947381381176802742639096230035673893214506768818262311195640685363804952677419939009907515068840166220078845399512386958726391911818049182359459209063951738765855651393400997004566565254309148440750388290750409167137220920897058920274653761762361806550748803844494191459092434082517983092605900951556706656912792667773304549765389802550330732083751090760003134342886715216289566251234220570626567411420067587375157062581217165324167980044151380845097423167714734675407654291757622961796121604970130926590173788301064304992998677948760699658601107502632854688344272940648996094822977361918835875482764527642129904598719866511764907652830470134149852626715364639001995425022526806911155327838651081748482996614108556040584317640293395396847288709596328112125450764477930209805668501515261772365057512704100413622328180946560036080857553670591527507778909795911186006891731357000761815419027707145233862106753889113747732743790246066290432771246246209806349637299268677761195305177807411623067785623825306871856591396362172918872491562082320077497847892621496638148005894380925947339663936521433774309961767252092447789054954618829551101964101055577242557267439288948839255114760905256278567148579636413671050090474277336780140940977818589865632946390436952116515115381720676889743158560330093868499721723837328333469028956650226133630273672252194728950081502324152923017495814717195880891500687965748913830829547934326157459159207525806622704886003100733411523306050280669910146520822006948484346979554461522988929271576869478082270227277614178144082309169325148050995394301589434211769874419593157378530804891534472078798979969101508967340746120799446164331137557492681096099017687374743720482907113552583420912429760234698645252021256492755973458541265010636783829239066154581625865870776129899057173937584313593793323109024261388106101137332857596958371403644263014870130724751024420154934467904473300549772135234413861719939505013071252517969856325851092921572335320730808427676404987745116434473478417463494390919460462680962604607358375638897206231820908930010658126781535638149327009082712513457418861188546504495517579107092158419728844268039465563021673375491453919957755613275459508667493667706208602435547576569753334658483170260614263195210615635419193126350910705500718109221456864848505809914364522657839525404955573265378888532096609381009906991153988480586884551517583002767326506051816623134942793327319335721075124976347751396778730702849552651728230416699199049846001734867116533597397383558619579938304735313458617432974190235908935667411688203756334407113676808136832721536513996669272811701045398527943747576965198085833408605192112775738441435389592774365765424894414775517421847745405750320651360234052041788351294120210459996114445388711458674783014373310729056811646430008684251833774898769291342613222695589347421139455349394531283184158674626565672240634350622853203458325347790547748284519744075217266663852950019792514189950997154770572617343212285863096012548148729879115474454412262082584599036103693231727301953239963611901851975933179755948059208571912888612979039310352379289560580233176881541417345257090050333656069076622923111301055460849586518188155128495134374064771042532517202426701636363694057605374120477835835758045216763683096684684059483410855855442663659466033912337171058435507750721186002854241254082485683187474310933858255191394524317121452798810718648096521027726332351810455796294427216581320311253396659031082022644401933428600848345286414532243411201157855223052494115791822987312400715121110523884347293928844211853312435099634034837882659782347634823045475537447224216286481581198602154536129300103686520297014070247201938000733694538369575047985023016906243739901563285537867167085510320026398973071922077765100327780572930498908310266116841553784856635781628762162427568602050506291804439510651570638240622157585688499200843465557743374543034866137992240709362360980913010007858491549068113530038421630236807413894827973165769189021818378249075399861333322698962721531824162817210704964288037357686334271309326204727340682511716914436235295760394054221596340405931413521827142087267939427261624669631032403407610264377657106259963704359338747870035861654719975613609531645735411273151638673868044447271131992547896746947886046069263864617577852546954116717362450480442897838812356673119705048785531249726497497394059373988131735274411584905026616612787610598652688389855965331224814490965034427583569440194961569842416111125603309227556659038481385151620733671124502674749472938552271058170647687897964067813714822646972532782967319131706899946303042889246863864468176650404169816991947863642329526110635737385111712298035996829522365642517947991773621360630846908390863407276054084464337611775184828033703885856331622734384675139773913316762154319529561154017946886156693024319991938572239612794574209368724348788371888821198679059735712033851768773007527830665870765986582734129338063103267867355020385063227624116272927054081880985159040350193425144527913063437157966433782488001835272099547869269032840384420136880119333203969500339357753653873350627654427648068061918473709733227138154266030614680430068987431744513947284130289968983252999590954297479922962444289926109947273296303034328381517782896305217270493353108507778584971019977227066722596166053356531980663298588360737255105975080219555280756952057914714581475189091325713058758630144178793500458559934300271294841740070791686076654415131061704274592495829964108352872851369333452395865958170276566931567020685363925492747798977771854174654851933149184216548115952760538761457007555432767495391971155757620584606007989997379690613917422380278109210078073630113976453350208613579548875353474275879251355377575390457045767492181689339775943031120931233083795613167596281720319255007356867639909512037939129651845533956646329884870488854559832203139184417987013798376223282304219786334921728758689334244358153476805541216440959132134519404834578099057188198625279440094788791313514013403615627630621173031832968978515388376754216096609869200660388342992243669476720222646257942819809574761432848653552958424315448045019719076441157034095232898987490509608015166058834196089093844727765255222399263432784523798933688419867789056237852481441195895652828902079861617488783561875947978135437807294886103966531062989724684509097893977612628727127985379829831962801392346085791963135658594329414130781850878309921584549571766262518614074248702413456938640795479381058599595258248913237016389002613299291946807956756241355009122776220171019660062183780682997125766620100540011210000",
        "display": 0.00018248736778362178
      }
    },
    {
      "name": "boundary e78 output",
      "left": {
        "numerator": "12252159289398784158906480998176076044103620424484555105862387031516523353180529863707101814724018857794218475076951181688286970834995822771210990477389021244352315302262537274692427554836392055891765052405073777545107606725070322918815465752112449409499305975669260686943760813839943100864464112089706330687332898512410924475405973055716904481445994713233213166168193413768108426383543530587643619082774131863008566186240351647686047246288999146400899195185541449882422022706667830553947373833095310753362382695162827193959936965382661720511585279202254848079373421692546104751398246272874545160916160203035913637733001875469141564761764503462322903728568221123091137729350045705797945029390078449424124335362650644854500129061457610489809670767167403741830075359229183781493982128557083967789217960838644946677553563103900106269575166051259239698251523211825929952487564921314502297057320129413498623483568238291969117307281517450424951609520809602361090920859559581125529713014734565401264327159536791541873037442840692810170238614222934703633541497927328873761326364698581812162215339626808994108388246923537026970077255024672125017612746357975695109654581380468437594259783311151043859633324214148965510167766478912380647847823334733945975308685873679038620058517397625409281358467774352336222180079736076108357948365543191080004283560095878013320880519748898990295266401268616763852279809266681651141583011026166213082726614763703174417005192305366883346182445136503544529167117910308707627612597661029886695750121901031042393722357132412266426844365078798328138865752230915709623626445569283848826563657005345036057752458961894571001499279068386829486701882303201660352766400676431654408512432252146872767926516363827162562666460225303657067479205208884541990924431606070913000712987386671672117569732235578070684462105635561783738464327433496211998936113189806379685119349138281978259940940795292676139414218888753390691337775198904684024185145621335267092402314923034954585489688865500959775254272097275433837389860819768360718728152720989946227180415165987517745379646217213309400156718709708185076267769577986026126987015564480043470478705908155585084274024693897022674444988478581271250114627904917153833738030563161",
        "denominator": "92729307846606113938255098539608987517965456436889209262945041746617647430030195093101867886677269213241850418778782849721770681319381276475268320360019352010068626461227499991319244922059203203786355131141550610062656759927649228094426738881051002605045676995123521081979434794166432618689011937731975124431667303338348858457680876785391492736119788894064133904793600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.13212822972502336
      },
      "right": {
        "numerator": "132129",
        "denominator": "1000000",
        "display": 0.132129
      },
      "positive_margin": {
        "numerator": "71427065435069641226916763919867657637369065179224841278389422319784101929783749354887274762046082213978905870617462600867517052705908189737423459975717386042243432991071660592957470368404221322264717528163011861168307410041940073044829501938513702774280019415030097099926078473474610296346230881810528698870610381771843748943513060088062284776873550586782538280160631891573616456469412356380917225868136991433813759648352313952753711000853599100804814458550117577977293332169446052626166904689246637617304837172806040063034617338279488414720797745151920626578307453895248601753727125454839083839796964086362266998124530858435238235496537677096271431778876908862270649954294202054970609921550575875664637349355145499870938542389510190329232832596258169924640770816218506017871442916032210782039161355053322446436896099893730424833948740760301748476788174070047512435078685497702942679870586501376516431761708030882692718482549575048390479190397638909079140440418874470286985265434598735672840463208458126962557159307189829761385777065296366458502072671126238673635301418187837784660373191005891611753076462973029922744975327874982387253642024304890345418619531562405740216688848956140366675785851034489832233521087619352152176665266054024691314126320961379941482602374590718641532225647663777819920263923891642051634456808919995716439904121986679119480251101009704733598731383236147720190733318348858416988973833786917273385236296825582994807694633116653817554863496455470832882089691292372387402338970113304249878098968957606277642867587733573155634921201671861134247769084290376373554430716151173436342994654963942247541038105428998500720931613170513298117696798339647233599323568345591487567747853127232073483636172837437333539774696342932520794791115458009075568393929086999287012613328327882430267764421929315537894364438216261535672566503788001063886810193620314880650861718021740059059204707323860585781111246609308662224801095315975814854378664732907597685076965045414510311134499040224745727902724566162610139180231639281271847279010053772819584834012482254620353782786690599843281290291814923732230422013973873012984435519956529521294091844414915725975306102977325555011521418728749885372095082846166261969436839",
        "denominator": "92729307846606113938255098539608987517965456436889209262945041746617647430030195093101867886677269213241850418778782849721770681319381276475268320360019352010068626461227499991319244922059203203786355131141550610062656759927649228094426738881051002605045676995123521081979434794166432618689011937731975124431667303338348858457680876785391492736119788894064133904793600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 7.702749766365679e-07
      }
    },
    {
      "name": "boundary e142 output",
      "left": {
        "numerator": "1240736001976095577036574270447904546949891316560359681837473990519199206074298752775339236970585234096961897995611106366025355165288401457493634495001962259926851195992459839176247717444745855793308814153606463024728355323747249259459763568988042421481903478842480490602940714565592593090840216257009495829153248568789950585256310162466970208865229473775887396641104565230684903883688092086715610546819948797194735693387662548465530555865480831351622494776243459098740923993140418693287837984550516369226738625312521142355119948146976599357312926914103269627312600210228264122327848640886737528866823432776045777220976338367409981468250309335667464359424172933413520201555125193551356419400121560711836331013332386507191694361137553292115210842904595216596081780189997970968743354921131815780174619260058991322753801208641737980364033793844475340598233841148845083168815433228088844343062105058367590886543649949169392343626205561813216735212845986466214985193644184414379732466589122716179847116718305721860175853952965993393689766024103157371542112591532478472047347745204605890031298840310295121432617669636163094818978906178476816030004731971598412068402457898971158341528938543721603071485676228456875199456884535703686980458295818516594984624951953101991951452714320564247296693755670580239503651487278352210138289886169874846219112150365426626021082692716561210849347003809667816174587005543135009635905121932744366007355733534620838469223189638179442653753839188939682805614580063396219881181847727974521852991529169677219967795542286621035673129554020918761150182707911128619912794605264218836516830404942493102110348383709265561260280399916897580229259303326007005024428000123890207227697409396312879929455442865755557424750205185510525828260982218119283646131551996671710157395872546382198517983028035329344155149116823556230499792308015745888547650797227221935598393340572802318057822325522814938471993500474903358593590573375156001532982677002428752116480362421629445592162560177099862865661754317965372052832496893140137107484199923861047898060192442451847236968840122830164661533195990391107980617870371125807077706062720913794084710812817370926514573391724973337813998075566526572596534320784420456753751189952114205393937528434260808994797245618849641969660537973046758641063033785012860479037497986144297763473823878046993828864044467697942783833368838817578679112794428230315677079992538639113322932182376407781456392227679112652239187892154965911145269742386766558695224506484708001978997259680797162370474795175810008058779959290450990092628217571562178840016662283882881916710688587792708894589200046489229461392370774425388918531940497273596290073112029040043547857097411812093642089810337260172757155784491565957977829801939189613764807875870972650065293587152661435919932100090723282672296767740918774224496061621056807793635502304956030788361810270188668080840532744549787528895526818785992357970895742756807408535776689792064766375036193368065607307712826461191354732280737597350563503292442845891940388674344221949231256816270697640349269876056992198956871926444810028419146989533725268917899203336781503638774849458592818428086782739215774760475672149111300018844970892952321916347981031338269380509827371917143218314072671955835203727159968176459533544852387692574186210378579560264588559263236523939450915155996871919952607886188422849196936160849392226752328170499705965006150728685378456981696855707994323945342828360518910044536169318020598520800421026774075733550286904934808632095436805712992100915462876361879112012263465454489093167560996189087149169091049477981440986756660495720511157885302690446189165041328694026353910779317896118526565609584262575776197409862416721600940941005572441666716780410442927266243799594519123328124867219438349406300525364879823211704077081091725862538110625939422586620633014559118124372516133484032778898876479391609665316854460002250510635258811032552240307258582630120324355411692485120508079837993487933874171463522030515755362354797212044672916060015787436144261095988052772403220644150945945211198833173458847809546127326907878840646490866006420678499435692844146746139061590652737114118372386726724925055478543202033471901227606053408102204797001603966347636261314000364265535875091168936251322044550472390122993803483348980904301636447097730746851598866139102450847763198269319295711598564408618858780188566732768774856414976608398695805496762436673796963806422795457155276514625064832199458360653511371207077864136037216455805932154939196001941842387284951092608110972094322591534667095017224536406074945319797972403111079323965124466469037583001055211757540299819418260205733931825566923472531771830314973790265081850266246889628810265220213305172720163692685997039658110925102242810169714275741859771456028370603912591184150032296591812950009879572097115260049722336149573709254852437700484774071587053833395661516113757537301412324708098337027748530931775819369786078984364729963094348451387435127730407454242971018276592942992377235491383082058521850528509977791696121852862351182167530941957040558146737665637931641168660605748022302048482698003667528195993838434335184630406415105416638753630724976301838208476595785158704696749861318715562640204451823765746692801829967763632220019893545715998024127701924163039295065562725964681998521434437878147988088331601549858607482974100271308383423278654641007820891821592943821442894146778290396242713068309765693808364441480511828933375045595524864736245127125503286871044062972810542138032300845826161689841109521827391838057665886775068657817722197614645096759086529759728151688864879608484658399811642926899705484711623591206003230693166791436359029730625484482507766934896549445969192416221870721145012487580316511699284613052660877516539873398744531601641063644054617003039641752451319165786030673610565050968448885093140269348356276970175687233894031897219912085784074197347454104376400215239524464914131961210816098607248620609818926803464989241872530627131216529328970214354776954744169572477382357593560853588448270115930015539377637553337772308840768524992013490597558933951102763512962755519364693418300091858421324225306957122167197827748863641188311212747668930790271325588132890196764217344263710790810615770281278659170454520436057156294018805791279743318664499338239916983908767309586369709136909224661073841",
        "denominator": "9036674501748924326118743282479919742588523630925287854908409093805389881671709455039753262359945824418238995829152863979291360102132604462285011378371581712173305024354089831313292933645438003357062708996536001657396533029618398784171779790934962698168219395539718032302022736852524044555251697267581103697573737601298519781433811896888299242274979184206139750449307814076132157272971466503934630072128526925878222185135939127506083268106162779227819119265003558814590772048974336933924464982455653564250177374514481432516202253741270307837301336761874975788192809199970185216000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 0.1373000656088662
      },
      "right": {
        "numerator": "137301",
        "denominator": "1000000",
        "display": 0.137301
      },
      "positive_margin": {
        "numerator": "8443788533481863855300979870913627255566489313265929305486469374630069108627111073925704697687541486734370727411011195327868094507267782559852259834280736255757156381048752898715637706427505619252854326926538833846057752386512005805968087118891939291212384518334950159309226995810750640397029526657289627323177605937479254333644787690165398367443194799797235335846949782117442048163235741118096713370078255270090853687029680182182928763424399136298117960794530061203599955806742076924982005627320798374978385691672810787137493953555179056383924638926423382060685736842278014167359113262471133176567223954222779023661632590018531749690664332535640575827066586479798444874806448643580599878439288163668986667613492808305638862446707884789157095404783403918219810002029031256645078868184219825380739941008677246198791358262019635966206155524659401766158851154916831184566771911155656937894941632409113456350050830607656373794438186783264787154013533785014806355815585620267533410877283820152883281694278139824146047034006606310233975896842628457887408467521527952652254795394109968701159689704878567382330363836905181021093821523183969995268028401587931597542101028841658471061456278396928514323771543124800543115464296313019541704181483405015375048046898008048547285679435752703306244329419760496348512721647789861710113830125153780887849634573373978917307283438789150652996190332183825412994456864990364094878067255633992644266465379161530776810361820557346246160811060317194385419936603780118818152272025478147008470830322780032204457713378964326870445979081238849817292088871380087205394735781163483169595057506897889651616290734438739719600083102419770740696673992994975571999876109792772302590603687120070544557134244442575249794814489474171739017781880716353868448003328289842604127453617801482016971964670655844850883176443769500207691984254111452349202772778064401606659427197681942177674477185061528006499525096641406409426624843998467017322997571247883519637578370554407837439822900137134338245682034627947167503106859862892515800076138952101939807557548152763031159877169835338466804009608892019382129628874192922293937279086205915289187182629073485426608275026662186001924433473427403465679215579543246248810047885794606062471565739191005202754381150358030339462026953241358936966214987139520962502013855702236526176121953006171135955532302057216166631161182421320887205571769684322920007461360886677067817623592218543607772320887347760812107845034088854730257613233441304775493515291998021002740319202837629525204824189991941220040709549009907371782428437821159983337716117118083289311412207291105410799953510770538607629225574611081468059502726403709926887970959956452142902588187906357910189662739827242844215508434042022170198060810386235192124129027349934706412847338564080067899909276717327703232259081225775503938378943192206364497695043969211638189729811331919159467255450212471104473181214007642029104257243192591464223310207935233624963806631934392692287173538808645267719262402649436496707557154108059611325655778050768743183729302359650730123943007801043128073555189971580853010466274731082100796663218496361225150541407181571913217260784225239524327850888699981155029107047678083652018968661730619490172628082856781685927328044164796272840031823540466455147612307425813789621420439735411440736763476060549084844003128080047392113811577150803063839150607773247671829500294034993849271314621543018303144292005676054657171639481089955463830681979401479199578973225924266449713095065191367904563194287007899084537123638120887987736534545510906832439003810912850830908950522018559013243339504279488842114697309553810834958671305973646089220682103881473434390415737424223802590137583278399059058994427558333283219589557072733756200405480876671875132780561650593699474635120176788295922918908274137461889374060577413379366985440881875627483866515967221101123520608390334683145539997749489364741188967447759692741417369879675644588307514879491920162006512066125828536477969484244637645202787955327083939984212563855738904011947227596779355849054054788801166826541152190453872673092121159353509133993579321500564307155853253860938409347262885881627613273275074944521456797966528098772393946591897795202998396033652363738685999635734464124908831063748677955449527609877006196516651019095698363552902269253148401133860897549152236801730680704288401435591381141219811433267231225143585023391601304194503237563326203036193577204542844723485374935167800541639346488628792922135863962783544194067845060803998058157612715048907391889027905677408465332904982775463593925054680202027596888920676034875533530962416998944788242459700180581739794266068174433076527468228169685026209734918149733753110371189734779786694827279836307314002960341889074897757189830285724258140228543971629396087408815849967703408187049990120427902884739950277663850426290745147562299515225928412946166604338483886242462698587675291901662972251469068224180630213921015635270036905651548612564872269592545757028981723407057007622764508616917941478149471490022208303878147137648817832469058042959441853262334362068358831339394251977697951517301996332471804006161565664815369593584894583361246369275023698161791523404214841295303250138681284437359795548176234253307198170032236367779980106454284001975872298075836960704934437274035318001478565562121852011911668398450141392517025899728691616576721345358992179108178407056178557105853221709603757286931690234306191635558519488171066624954404475135263754872874496713128955937027189457861967699154173838310158890478172608161942334113224931342182277802385354903240913470240271848311135120391515341600188357073100294515288376408793996769306833208563640970269374515517492233065103450554030807583778129278854987512419683488300715386947339122483460126601255468398358936355945382996960358247548680834213969326389434949031551114906859730651643723029824312766105968102780087914215925802652545895623599784760475535085868038789183901392751379390181073196535010758127469372868783470671029785645223045255830427522617642406439146411551729884069984460622362446662227691159231475007986509402441066048897236487037244480635306581699908141578675774693042877832802172251136358811688787252331069209728674411867109803235782655736289209189384229718721340829545479563942843705981194208720256681335500661760083016091232690413630290863090775338926159",
        "denominator": "9036674501748924326118743282479919742588523630925287854908409093805389881671709455039753262359945824418238995829152863979291360102132604462285011378371581712173305024354089831313292933645438003357062708996536001657396533029618398784171779790934962698168219395539718032302022736852524044555251697267581103697573737601298519781433811896888299242274979184206139750449307814076132157272971466503934630072128526925878222185135939127506083268106162779227819119265003558814590772048974336933924464982455653564250177374514481432516202253741270307837301336761874975788192809199970185216000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 9.343911338012323e-07
      }
    },
    {
      "name": "boundary eta240 output",
      "left": {
        "numerator": "51732654478880700749019126353153405297685360937188878085847335189870279202934600047800061431223191571041380687379389616520593844330576206360850123886937891321886843066592835965648283674299600200307346758429486699968106033973500263968893865879848342503432841941882668969022743569581108807677603972843697412027500996433015667347228711354017720853124169086123088836898923371655578745370758977641292404139777469289538629274253848277903895035672981333981818160869497570318391085491322134665410448235362688943168760975157971869452284712011425596527668117527345880796072547279478433259846376619761188358328133337454989862514436851809551982791640374270857308307420106253815790530804097817973689808133951415713213955918402243276533125988983669670751698036509659236842290944277378917065942770018049921923168192665133038716295814609018779188073877072820019615689900162673312333765375177694651902973159528637127837078796840095279610912179542330267198206222028686402257269858941269821562607200120197796699036824319905695119904780988355359540260837658343268336644217481131840911723969012589283559385685258156133054951565857862628917887193719151176748851567001277270411379458512890079510058999768117246823314649140161785246594738205471721419622369407861823168354456552983909035377118383587568100458531042416472612547977340737685287224934919753104791167994578621144007142303607282766165289123240827081443271906810792118726416363251400904209784936032868622228691426521425188012854074610752809524446264280891456452313581506054300486241384743083869543009351233894931218911439427054057100974364979065796482727161687751682577612473571844566484721374016568901238388692260476847724818457859464030358555373216505225348074566934819047816943190850510637413305785712979340345693838990300890678026092357660830192028978340696560037839539928646306513380250800447080702213950677722513546056398844788725582866353124256382848669506996802290224431930379796029391921085154531740279121862857947392312670948391730496766656297859383035066320297893987438490774126214747182585321505508024633691825125877181066791978120584454994083150920354346415487073525085955484929507528075329746404902370635144389801981154695818562342860997126959244203640047799127581949443251543437715519880460388815218242563164772792650556008654804834164167978139096442328055331615511305645761377460570585567470072667428367296371704299850899909484349358302382538526800956200892986581653094888777766249499521427160703460793754391603040158524718419688306199267807578222071079015803939484219685787935351819418714125428912322321465750946392635318631340341387831432971883312281409741717065164915086304994325153529019846371268749442338079977266408453948231835906774538176862133620045800351594583564315195162341664234003608434561421997030651193900560224176703877431374425501876061854277373362135389953006802323931691708084464574383658313044556880495333846696776151312203000940309491423385434238667042776648386272583660326346398480896708951548245987355778887508494582185315520802117254720003636754549914496013803300465544628144630887141003104748624906978569144115441814867216944082484228590762956215491814058315457520975990796220620232446338006858532555507474633472598934685373120056609315937266485309643969940747088958434208120748299027059931536326865515911978398006828309927538527999845170836193338386270863088017968331520046505099280763562265112069683181438089770745854416310526409215625218550520091892137706127921966009588989308570172685000779870816538973806842315213227781713839857416780534805899677022235136066146563876998665065027724143069113732182165147818056428411062493689539566352397317417447967390874350691428104455913853336380083142244701041888340215678625026371470324076787708890099151583333587830742263543135986242302613950905063576762672103438807034982397326838742572094055500988564935065595235085726227091074967238229277195435874188359499737462947013779687069849409623025304788228938275525934886546531567489444518255373210008467273302336071029146328563430082846033820506570721265980178368947910640496987657247460681274979395330359901653866968410343880571882361982828230169067598273268334510608826845818482196912602201395852636576074903199786975998772362547858480335626361797838626975509699939126874005866504052566329631030012205418539410965810098583613781832689749318575341924249548168846476480657621554902494012238414644740665068484413604313056225196001087018142663818292345013767105054794928582913898513936913893108133770549170453772468886480615138593313954265643157579255444764276479470277717719528431565793207664664046919467040956221268562312775812962366560898266520556157502271780711855575624308225578125221011643191706325280716112253837742291119438868717188636694214690028986852793814028016782119240920272160878518188013859857287741798509707346927728822490153644579837776251236092180914373530171539355598542299573734039741485478389989828561490984257566221781071098830697201074394137615562847644686995416687576959298991829134780279947070500470198035721127965779105936751351785221155505573617730533142150167458613822416951742218741554660254140240788408690917844621171793221031211502353102718705170160756491179312807237409661466496759432307759787106848566234031624339817176248581624545501146152416731189165099949305854970551900225711394484460311500515828767100092301783180777934605492503723318394335334538008311265451835913186076378563544664802700572981928806800082906751304204913421223606881533038006823025473630293415501747334879877623448565472890758061621064071074568743532307700532195868067091850451760808777045974333572841860756434185315044573567445147336903085485508605060743732995283788116410307114485642004405226698945778067836238508197601056901368842322391109741679027883518600166827519054422462473219939365655426077306309729636974065757938728742075693331269402925322241783410216083032773019667303343909632238098444301219635340140835988215015746789606655792892904167315578462286128490462637250757417661906570591781781563160203658111447151326568901004381468853029914532419521644990031638110534561884191589306360006313831045358473833340239037217235142725557419854968353894142218825903276996492563377804732083130755126807076477907021760877525589790794199927206045125505017841233651277114511181294064444390809724081585412669462766617065757273626935042920624158101601940448628142942651817031850892547269484460042207520649425417974743780791951422806191599488300336139650131864483133635071987684933309950794564662429588163955093994856847485003191135640767491286955171507858111601600784631606677370577556570355328228033178689206673404155901209503238573164253887478900859480107855617356866813901342062398944124032921906252690511021833904155760161494795722444138757179412913776119836183684595054803457830064948477139314244637301262423824848504966080329133193743791795697842300995851988360054418491888958988377634513111248710328342629797448664884618150817066959882619614923925444861075618929711013675300106586732442808089280313149909039371511180000548704460685189985209827886362707442181336301921795103694720860296137888065600640515811155626349604067887126797755795710032434979261741626763102936718850803458948466440607124422494615379729856928175289076765788076070396890115842376658107179731934114463948214987980659364080170984459564782068733434043216067443125674966828727123988282660511094976191463317899519206196703455882554886405957369171897045085240425206775537527617000688282334350681891236886391666578388344009507917097509162736774124683393573054796501318095235737294956868568817929856399710857874269573603106733766474203935751546014939356313795801942891541412179449142355208783459206450390666213563550774080095779525403174473160434892887883013911714116910180875898057325080027006486160108507874677534450177195954667710141136085088715296936026307735899915326038022500489527322352416438833832872926249469728187364388039709744727969401987672162396398589623759759407150327420277777324765206103415870704187257533297960677618962501475787517975089553009130901213874354675442618821910412227124791309513541952302553364448972387428420578649242893773324060949044265476204657621582160286100190952868695714945447552544608668897938685053810644468857064129171853992976297111920192614547553593757153658044774422769705023115844531278098838274845512930584577395043393526258760652139262351641726389376918982431667721418923997064223392086732112917728173077225306782492278776350414208069055124359578875451861126073464794830199516047520860870925665576288302518300603648821760654945376212410803405013396693554926224138855045890980657707430331598946181866209457562744957387353195286088507987193694806371176984964899063549135540931536451928869975027908121029640060257525782294700733601670182167030800934614514056887444659343720203123976093458433962007773016916803034278103312572374116052941990951626988552789512723103623689731040005726399159462750295533467390096771325502777024085048843842758479903116817612528804212563658729299525613760304888928653247082646037259911864228299463622926361325647528130993478163690656133312394525251866385741734584266976830372055782157353411022316417974845613369995234601198276441064909086152590235567489105557463939957392965108977911103099875209391805689921660229672932916363484365045032048073855384524786925962606123642195125187452868185550641693025410740421503429323620862034872710839393174006722936774888157792232835002715425977947180433207207378138001200407478891102004582864939720585879860918187524942146491502744158486222767760836742188011929874389856512568174982428058636253013468670108881693188417288298692145759597690056988965863325322249545037875712206692560487631517277671432984728152193872005456842259670100819056750771973671536562316548057853019138015310648380722944202691831534614858880870865590432932525285937761912939029144662784932933848101544073128356034974943431103597643879574264637516421935896053554566264665321457305843838717171515545943595191218998419010262485529850052794160570229689756458779169248936807142533464116975034231156980377758292872906165484822460252197166198016199908610556211971072502245732998400230227154147471547923075270756442440898185490819101394376683250130131074903715755389391749586549593352535338747025320086403484139595294879108550504229627242544275839819645191973206837462040572821866608547768566958308695280114648144302250646149816306823779697965602214747888565979438285051487090194294787054102094128774344674549483350846967988698439116118681112833923349139769380788333813397816199939427875596857010034415268950904028253777571540500523229162832512774843059009970316827042911129639932659989600774518077219386178954944203739494448847795838666306805096901940065255113329358009029142113013432565431590701204628499040114565461167255053864849887704188032112280330147957955118685636838307641161133745879958547190182968041329913213515870180088827293106232327633710525676467967537019450566919719511175910501642525491041152811708054024845943555515632296702945661052058859054589181468044637651876956408437530196591992885415277545541160979100528616302587133575026499186639343865730564512103258289826318006467596617676283221365308305864704398175211607579004720474400026326685389447637151088490778525830416658259246422215380487489806113716492999265567896862883418130807743604883352916491192603685877218864966125837975031544331269969376804071516531406723448746123409420704906055279621760628832906335524989981555719619317729768396678283551177292119419678005605426600178003653116233499022979567179821451976707601589740138600200178589975225577065100460275657075137951189262178544645582664138133215556408319305760891634543819913045594653044914184255378186431054149479125350045786666814068036963546827965083485915148536228283641035936258944898795223371407626935306452244990500007818754771594738138117680274263909623003567389321450676881826231119564068536380495267741993900990751506884016622007884539951238695872639191181804918235945920906395173876585565139340099700456656525430914844075038829075040916713722092089705892027465376176236180655074880384449419145909243408251798309260590095155670665691279266777330454976538980255033073208375109076000313434288671521628956625123422057062656741142006758737515706258121716532416798004415138084509742316771473467540765429175762296179612160497013092659017378830106430499299867794876069965860110750263285468834427294064899609482297736191883587548276452764212990459871986651176490765283047013414985262671536463900199542502252680691115532783865108174848299661410855604058431764029339539684728870959632811212545076447793020980566850151526177236505751270410041362232818094656003608085755367059152750777890979591118600689173135700076181541902770714523386210675388911374773274379024606629043277124624620980634963729926867776119530517780741162306778562382530687185659139636217291887249156208232007749784789262149663814800589438092594733966393652143377430996176725209244778905495461882955110196410105557724255726743928894883925511476090525627856714857963641367105009047427733678014094097781858986563294639043695211651511538172067688974315856033009386849972172383732833346902895665022613363027367225219472895008150232415292301749581471719588089150068796574891383082954793432615745915920752580662270488600310073341152330605028066991014652082200694848434697955446152298892927157686947808227022727761417814408230916932514805099539430158943421176987441959315737853080489153447207879897996910150896734074612079944616433113755749268109609901768737474372048290711355258342091242976023469864525202125649275597345854126501063678382923906615458162586587077612989905717393758431359379332310902426138810610113733285759695837140364426301487013072475102442015493446790447330054977213523441386171993950501307125251796985632585109292157233532073080842767640498774511643447347841746349439091946046268096260460735837563889720623182090893001065812678153563814932700908271251345741886118854650449551757910709215841972884426803946556302167337549145391995775561327545950866749366770620860243554757656975333465848317026061426319521061563541919312635091070550071810922145686484850580991436452265783952540495557326537888853209660938100990699115398848058688455151758300276732650605181662313494279332731933572107512497634775139677873070284955265172823041669919904984600173486711653359739738355861957993830473531345861743297419023590893566741168820375633440711367680813683272153651399666927281170104539852794374757696519808583340860519211277573844143538959277436576542489441477551742184774540575032065136023405204178835129412021045999611444538871145867478301437331072905681164643000868425183377489876929134261322269558934742113945534939453128318415867462656567224063435062285320345832534779054774828451974407521726666385295001979251418995099715477057261734321228586309601254814872987911547445441226208258459903610369323172730195323996361190185197593317975594805920857191288861297903931035237928956058023317688154141734525709005033365606907662292311130105546084958651818815512849513437406477104253251720242670163636369405760537412047783583575804521676368309668468405948341085585544266365946603391233717105843550775072118600285424125408248568318747431093385825519139452431712145279881071864809652102772633235181045579629442721658132031125339665903108202264440193342860084834528641453224341120115785522305249411579182298731240071512111052388434729392884421185331243509963403483788265978234763482304547553744722421628648158119860215453612930010368652029701407024720193800073369453836957504798502301690624373990156328553786716708551032002639897307192207776510032778057293049890831026611684155378485663578162876216242756860205050629180443951065157063824062215758568849920084346555774337454303486613799224070936236098091301000785849154906811353003842163023680741389482797316576918902181837824907539986133332269896272153182416281721070496428803735768633427130932620472734068251171691443623529576039405422159634040593141352182714208726793942726162466963103240340761026437765710625996370435933874787003586165471997561360953164573541127315163867386804444727113199254789674694788604606926386461757785254695411671736245048044289783881235667311970504878553124972649749739405937398813173527441158490502661661278761059865268838985596533122481449096503442758356944019496156984241611112560330922755665903848138515162073367112450267474947293855227105817064768789796406781371482264697253278296731913170689994630304288924686386446817665040416981699194786364232952611063573738511171229803599682952236564251794799177362136063084690839086340727605408446433761177518482803370388585633162273438467513977391331676215431952956115401794688615669302431999193857223961279457420936872434878837188882119867905973571203385176877300752783066587076598658273412933806310326786735502038506322762411627292705408188098515904035019342514452791306343715796643378248800183527209954786926903284038442013688011933320396950033935775365387335062765442764806806191847370973322713815426603061468043006898743174451394728413028996898325299959095429747992296244428992610994727329630303432838151778289630521727049335310850777858497101997722706672259616605335653198066329858836073725510597508021955528075695205791471458147518909132571305875863014417879350045855993430027129484174007079168607665441513106170427459249582996410835287285136933345239586595817027656693156702068536392549274779897777185417465485193314918421654811595276053876145700755543276749539197115575762058460600798999737969061391742238027810921007807363011397645335020861357954887535347427587925135537757539045704576749218168933977594303112093123308379561316759628172031925500735686763990951203793912965184553395664632988487048885455983220313918441798701379837622328230421978633492172875868933424435815347680554121644095913213451940483457809905718819862527944009478879131351401340361562763062117303183296897851538837675421609660986920066038834299224366947672022264625794281980957476143284865355295842431544804501971907644115703409523289898749050960801516605883419608909384472776525522239926343278452379893368841986778905623785248144119589565282890207986161748878356187594797813543780729488610396653106298972468450909789397761262872712798537982983196280139234608579196313565859432941413078185087830992158454957176626251861407424870241345693864079547938105859959525824891323701638900261329929194680795675624135500912277622017101966006218378068299712576662010054001121",
        "denominator": "249292957604819442802581425186925138378532890128260137348530512017538710529995420202882965931236118978329836517936363198268267337967250681997416730294595416292771866912768004486826402529994761139777098864672398570396726771835221683635650549672645922124271476666870419311322918748993495101519929583479173421335066354734081858253979228526272510571207441767003817623189202959866331772112884703583530966404486369045687388080046650065262026741285870395746239519670959890567993156503791675494732938303131237314852126311942054702741716008306677883105369265450930356726661468202549590432920980650969329844787497049663158456057990169341885703704085509235728167118308967102949738361191053320453601901344603868743101025490460439716006183053316540834767672543557579016344978621161746804397994358599676636201904794546754124390578211143640405222941486166246540648283539481582171458810257267887430243983208473182587617799240805269871586143670477716818756111297644280015410648278577654620151779475767658248248696719732452705218548860602141457999713065020926499457887190109292193914108169426091819876925940327673374366378886917964228278739817971417615682113347417938079079070751842843326072386726184952666658176159887390669748397512805236758797728989468766922749582151735389932412929746900738447006708531042416472612547977340737685287224934919753104791167994578621144007142303607282766165289123240827081443271906810792118726416363251400904209784936032868622228691426521425188012854074610752809524446264280891456452313581506054300486241384743083869543009351233894931218911439427054057100974364979065796482727161687751682577612473571844566484721374016568901238388692260476847724818457859464030358555373216505225348074566934819047816943190850510637413305785712979340345693838990300890678026092357660830192028978340696560037839539928646306513380250800447080702213950677722513546056398844788725582866353124256382848669506996802290224431930379796029391921085154531740279121862857947392312670948391730496766656297859383035066320297893987438490774126214747182585321505508024633691825125877181066791978120584454994083150920354346415487073525085955484929507528075329746404902370635144389801981154695818562342860997126959244203640047799127581949443251543437715519880460388815218242563164772792650556008654804834164167978139096442328055331615511305645761377460570585567470072667428367296371704299850899909484349358302382538526800956200892986581653094888777766249499521427160703460793754391603040158524718419688306199267807578222071079015803939484219685787935351819418714125428912322321465750946392635318631340341387831432971883312281409741717065164915086304994325153529019846371268749442338079977266408453948231835906774538176862133620045800351594583564315195162341664234003608434561421997030651193900560224176703877431374425501876061854277373362135389953006802323931691708084464574383658313044556880495333846696776151312203000940309491423385434238667042776648386272583660326346398480896708951548245987355778887508494582185315520802117254720003636754549914496013803300465544628144630887141003104748624906978569144115441814867216944082484228590762956215491814058315457520975990796220620232446338006858532555507474633472598934685373120056609315937266485309643969940747088958434208120748299027059931536326865515911978398006828309927538527999845170836193338386270863088017968331520046505099280763562265112069683181438089770745854416310526409215625218550520091892137706127921966009588989308570172685000779870816538973806842315213227781713839857416780534805899677022235136066146563876998665065027724143069113732182165147818056428411062493689539566352397317417447967390874350691428104455913853336380083142244701041888340215678625026371470324076787708890099151583333587830742263543135986242302613950905063576762672103438807034982397326838742572094055500988564935065595235085726227091074967238229277195435874188359499737462947013779687069849409623025304788228938275525934886546531567489444518255373210008467273302336071029146328563430082846033820506570721265980178368947910640496987657247460681274979395330359901653866968410343880571882361982828230169067598273268334510608826845818482196912602201395852636576074903199786975998772362547858480335626361797838626975509699939126874005866504052566329631030012205418539410965810098583613781832689749318575341924249548168846476480657621554902494012238414644740665068484413604313056225196001087018142663818292345013767105054794928582913898513936913893108133770549170453772468886480615138593313954265643157579255444764276479470277717719528431565793207664664046919467040956221268562312775812962366560898266520556157502271780711855575624308225578125221011643191706325280716112253837742291119438868717188636694214690028986852793814028016782119240920272160878518188013859857287741798509707346927728822490153644579837776251236092180914373530171539355598542299573734039741485478389989828561490984257566221781071098830697201074394137615562847644686995416687576959298991829134780279947070500470198035721127965779105936751351785221155505573617730533142150167458613822416951742218741554660254140240788408690917844621171793221031211502353102718705170160756491179312807237409661466496759432307759787106848566234031624339817176248581624545501146152416731189165099949305854970551900225711394484460311500515828767100092301783180777934605492503723318394335334538008311265451835913186076378563544664802700572981928806800082906751304204913421223606881533038006823025473630293415501747334879877623448565472890758061621064071074568743532307700532195868067091850451760808777045974333572841860756434185315044573567445147336903085485508605060743732995283788116410307114485642004405226698945778067836238508197601056901368842322391109741679027883518600166827519054422462473219939365655426077306309729636974065757938728742075693331269402925322241783410216083032773019667303343909632238098444301219635340140835988215015746789606655792892904167315578462286128490462637250757417661906570591781781563160203658111447151326568901004381468853029914532419521644990031638110534561884191589306360006313831045358473833340239037217235142725557419854968353894142218825903276996492563377804732083130755126807076477907021760877525589790794199927206045125505017841233651277114511181294064444390809724081585412669462766617065757273626935042920624158101601940448628142942651817031850892547269484460042207520649425417974743780791951422806191599488300336139650131864483133635071987684933309950794564662429588163955093994856847485003191135640767491286955171507858111601600784631606677370577556570355328228033178689206673404155901209503238573164253887478900859480107855617356866813901342062398944124032921906252690511021833904155760161494795722444138757179412913776119836183684595054803457830064948477139314244637301262423824848504966080329133193743791795697842300995851988360054418491888958988377634513111248710328342629797448664884618150817066959882619614923925444861075618929711013675300106586732442808089280313149909039371511180000548704460685189985209827886362707442181336301921795103694720860296137888065600640515811155626349604067887126797755795710032434979261741626763102936718850803458948466440607124422494615379729856928175289076765788076070396890115842376658107179731934114463948214987980659364080170984459564782068733434043216067443125674966828727123988282660511094976191463317899519206196703455882554886405957369171897045085240425206775537527617000688282334350681891236886391666578388344009507917097509162736774124683393573054796501318095235737294956868568817929856399710857874269573603106733766474203935751546014939356313795801942891541412179449142355208783459206450390666213563550774080095779525403174473160434892887883013911714116910180875898057325080027006486160108507874677534450177195954667710141136085088715296936026307735899915326038022500489527322352416438833832872926249469728187364388039709744727969401987672162396398589623759759407150327420277777324765206103415870704187257533297960677618962501475787517975089553009130901213874354675442618821910412227124791309513541952302553364448972387428420578649242893773324060949044265476204657621582160286100190952868695714945447552544608668897938685053810644468857064129171853992976297111920192614547553593757153658044774422769705023115844531278098838274845512930584577395043393526258760652139262351641726389376918982431667721418923997064223392086732112917728173077225306782492278776350414208069055124359578875451861126073464794830199516047520860870925665576288302518300603648821760654945376212410803405013396693554926224138855045890980657707430331598946181866209457562744957387353195286088507987193694806371176984964899063549135540931536451928869975027908121029640060257525782294700733601670182167030800934614514056887444659343720203123976093458433962007773016916803034278103312572374116052941990951626988552789512723103623689731040005726399159462750295533467390096771325502777024085048843842758479903116817612528804212563658729299525613760304888928653247082646037259911864228299463622926361325647528130993478163690656133312394525251866385741734584266976830372055782157353411022316417974845613369995234601198276441064909086152590235567489105557463939957392965108977911103099875209391805689921660229672932916363484365045032048073855384524786925962606123642195125187452868185550641693025410740421503429323620862034872710839393174006722936774888157792232835002715425977947180433207207378138001200407478891102004582864939720585879860918187524942146491502744158486222767760836742188011929874389856512568174982428058636253013468670108881693188417288298692145759597690056988965863325322249545037875712206692560487631517277671432984728152193872005456842259670100819056750771973671536562316548057853019138015310648380722944202691831534614858880870865590432932525285937761912939029144662784932933848101544073128356034974943431103597643879574264637516421935896053554566264665321457305843838717171515545943595191218998419010262485529850052794160570229689756458779169248936807142533464116975034231156980377758292872906165484822460252197166198016199908610556211971072502245732998400230227154147471547923075270756442440898185490819101394376683250130131074903715755389391749586549593352535338747025320086403484139595294879108550504229627242544275839819645191973206837462040572821866608547768566958308695280114648144302250646149816306823779697965602214747888565979438285051487090194294787054102094128774344674549483350846967988698439116118681112833923349139769380788333813397816199939427875596857010034415268950904028253777571540500523229162832512774843059009970316827042911129639932659989600774518077219386178954944203739494448847795838666306805096901940065255113329358009029142113013432565431590701204628499040114565461167255053864849887704188032112280330147957955118685636838307641161133745879958547190182968041329913213515870180088827293106232327633710525676467967537019450566919719511175910501642525491041152811708054024845943555515632296702945661052058859054589181468044637651876956408437530196591992885415277545541160979100528616302587133575026499186639343865730564512103258289826318006467596617676283221365308305864704398175211607579004720474400026326685389447637151088490778525830416658259246422215380487489806113716492999265567896862883418130807743604883352916491192603685877218864966125837975031544331269969376804071516531406723448746123409420704906055279621760628832906335524989981555719619317729768396678283551177292119419678005605426600178003653116233499022979567179821451976707601589740138600200178589975225577065100460275657075137951189262178544645582664138133215556408319305760891634543819913045594653044914184255378186431054149479125350045786666814068036963546827965083485915148536228283641035936258944898795223371407626935306452244990500007818754771594738138117680274263909623003567389321450676881826231119564068536380495267741993900990751506884016622007884539951238695872639191181804918235945920906395173876585565139340099700456656525430914844075038829075040916713722092089705892027465376176236180655074880384449419145909243408251798309260590095155670665691279266777330454976538980255033073208375109076000313434288671521628956625123422057062656741142006758737515706258121716532416798004415138084509742316771473467540765429175762296179612160497013092659017378830106430499299867794876069965860110750263285468834427294064899609482297736191883587548276452764212990459871986651176490765283047013414985262671536463900199542502252680691115532783865108174848299661410855604058431764029339539684728870959632811212545076447793020980566850151526177236505751270410041362232818094656003608085755367059152750777890979591118600689173135700076181541902770714523386210675388911374773274379024606629043277124624620980634963729926867776119530517780741162306778562382530687185659139636217291887249156208232007749784789262149663814800589438092594733966393652143377430996176725209244778905495461882955110196410105557724255726743928894883925511476090525627856714857963641367105009047427733678014094097781858986563294639043695211651511538172067688974315856033009386849972172383732833346902895665022613363027367225219472895008150232415292301749581471719588089150068796574891383082954793432615745915920752580662270488600310073341152330605028066991014652082200694848434697955446152298892927157686947808227022727761417814408230916932514805099539430158943421176987441959315737853080489153447207879897996910150896734074612079944616433113755749268109609901768737474372048290711355258342091242976023469864525202125649275597345854126501063678382923906615458162586587077612989905717393758431359379332310902426138810610113733285759695837140364426301487013072475102442015493446790447330054977213523441386171993950501307125251796985632585109292157233532073080842767640498774511643447347841746349439091946046268096260460735837563889720623182090893001065812678153563814932700908271251345741886118854650449551757910709215841972884426803946556302167337549145391995775561327545950866749366770620860243554757656975333465848317026061426319521061563541919312635091070550071810922145686484850580991436452265783952540495557326537888853209660938100990699115398848058688455151758300276732650605181662313494279332731933572107512497634775139677873070284955265172823041669919904984600173486711653359739738355861957993830473531345861743297419023590893566741168820375633440711367680813683272153651399666927281170104539852794374757696519808583340860519211277573844143538959277436576542489441477551742184774540575032065136023405204178835129412021045999611444538871145867478301437331072905681164643000868425183377489876929134261322269558934742113945534939453128318415867462656567224063435062285320345832534779054774828451974407521726666385295001979251418995099715477057261734321228586309601254814872987911547445441226208258459903610369323172730195323996361190185197593317975594805920857191288861297903931035237928956058023317688154141734525709005033365606907662292311130105546084958651818815512849513437406477104253251720242670163636369405760537412047783583575804521676368309668468405948341085585544266365946603391233717105843550775072118600285424125408248568318747431093385825519139452431712145279881071864809652102772633235181045579629442721658132031125339665903108202264440193342860084834528641453224341120115785522305249411579182298731240071512111052388434729392884421185331243509963403483788265978234763482304547553744722421628648158119860215453612930010368652029701407024720193800073369453836957504798502301690624373990156328553786716708551032002639897307192207776510032778057293049890831026611684155378485663578162876216242756860205050629180443951065157063824062215758568849920084346555774337454303486613799224070936236098091301000785849154906811353003842163023680741389482797316576918902181837824907539986133332269896272153182416281721070496428803735768633427130932620472734068251171691443623529576039405422159634040593141352182714208726793942726162466963103240340761026437765710625996370435933874787003586165471997561360953164573541127315163867386804444727113199254789674694788604606926386461757785254695411671736245048044289783881235667311970504878553124972649749739405937398813173527441158490502661661278761059865268838985596533122481449096503442758356944019496156984241611112560330922755665903848138515162073367112450267474947293855227105817064768789796406781371482264697253278296731913170689994630304288924686386446817665040416981699194786364232952611063573738511171229803599682952236564251794799177362136063084690839086340727605408446433761177518482803370388585633162273438467513977391331676215431952956115401794688615669302431999193857223961279457420936872434878837188882119867905973571203385176877300752783066587076598658273412933806310326786735502038506322762411627292705408188098515904035019342514452791306343715796643378248800183527209954786926903284038442013688011933320396950033935775365387335062765442764806806191847370973322713815426603061468043006898743174451394728413028996898325299959095429747992296244428992610994727329630303432838151778289630521727049335310850777858497101997722706672259616605335653198066329858836073725510597508021955528075695205791471458147518909132571305875863014417879350045855993430027129484174007079168607665441513106170427459249582996410835287285136933345239586595817027656693156702068536392549274779897777185417465485193314918421654811595276053876145700755543276749539197115575762058460600798999737969061391742238027810921007807363011397645335020861357954887535347427587925135537757539045704576749218168933977594303112093123308379561316759628172031925500735686763990951203793912965184553395664632988487048885455983220313918441798701379837622328230421978633492172875868933424435815347680554121644095913213451940483457809905718819862527944009478879131351401340361562763062117303183296897851538837675421609660986920066038834299224366947672022264625794281980957476143284865355295842431544804501971907644115703409523289898749050960801516605883419608909384472776525522239926343278452379893368841986778905623785248144119589565282890207986161748878356187594797813543780729488610396653106298972468450909789397761262872712798537982983196280139234608579196313565859432941413078185087830992158454957176626251861407424870241345693864079547938105859959525824891323701638900261329929194680795675624135500912277622017101966006218378068299712576662010054001121",
        "display": 0.20751751263221638
      },
      "right": {
        "numerator": "103759",
        "denominator": "500000",
        "display": 0.207518
      },
      "positive_margin": {
        "numerator": "60748678110191243482919393462784175513678223704548222509801492659464414494780930902946447532683551835163574864300828820228554855860332944900575167980138178294605705477394724478862959926320948458621884800053281740956132100634687904532443559896981975863176536473352812182941686261654399804387230366849010554651684345765856960275095648648997795828407241004694315026824084981345657281315138477387473274366521042163062670636225169575114812589959401324985886790342126248859180015853124952770827713249580967361286421809719175635355300179792209295950850250142485565393639489126323806259721483332516201239237648504726984902576075968727334812021217361264738318566990727066637216773592490100375614639044960308441344663563126226522552937236125098809917192161222735793164614432228144560111644918887134089343244810141834494097305543595211490247126713565003280301691732828361512005895011405923198873963650388190095833006666356800450591333932285798212241117929648990358525266303954951024886566077553830518110782766712680819020733039915770461809084334678488928808217984128292471965045187219358917116013380995123405323998789735903030167913320732011134615314099201941475572884016540914915274438165880328128375603674875879126608428422700146282377514358875553396666205420369479544618416879936472739804951221854475531376910528758844104704562462110004442802660172579277465926476346669451899672517931436421836496373384920083726053808901654315010607161400104259481080463723962076598688622160696001223887795075288403878814150459537921031227468015704448408431657730238558887312329984673360252816646329989735887706725683585543764255859418737131527518038300722004399626190016393380670209439308113146695660361318753002853585523180365673966613114202814520714302163303353202081927544644184776848263138108114983880245593304054354046422859133258860831696042580048295474041969508553509997066465342070586319453371691526603660345878080063719180867474379241517715797297283188700060473939304067322634950738312316230683341879900206802286178842188523384977169454542361625209621335994811121317520297299896913279797521494968689498196167873421980986499346415912696047007567903265954775079757159751840473185282174157038702415637416542117505463820025887800770656565176696164687046495075469108348529027263867351036574611477705955916174186286595489027345338184739617866033646050604160090936185516314118379516522779568966011925916905640551601862314001962103899196028175809123532060130180415699991621966116819764546007048664285863295924657397708333579698831214833307483702708259721709296225922352491020089379250435788710199071788144285167787984458301922532288381988881287422743606840507647054002099452218516851727981047799098669108463750218261971312259432022883810613892182753678576622254176190280947586474577740277648116211998678902714766264711127374799279301614110949630631640362982545896903672581644846380911737115648421251022721027901370704410826808906332151836332303138066774965177848628176719531007148329571461724158817834746598260308392721848256872491038968740387330184994566420232130999343312648361788771300118233904783766553219835199090859812366778967495466217308105719024796430952430914745218475230581824368201673162743758183925521333069535649068043701590594421363706708432724021070940026573245218745668114306481109521767595376343646002206126813349662695915404485646939140672210350165252772955890965324509728396666503789871149891900226700705085991447776323368268567463186166072266394449287382846205122605983207783780479802994177595410545926381057317464107975506077032527450014019382814171955968349557826151305646406699663425502749972186437963152688959734549192999953072556407677836462284238840139419475633817414461122184599285940925542227317489561441678222077468315824358854751404253675363769945479426703279982043061303661651539900816089804490879354232790041564673478454396754051205363906556792974803293775730243464527944412312923015755800081562830205407377268767328034619915785166415014641972663893034919159409052879340029623697900543004712928655910834846748142909710939898833113704608932190920889414902862208770098570116930418316761005562159249578485792601881865181847841786038795813153591116705955430459504281213208843270440291674007893331074774862624608597060986420428317041450567707064980671036933712752525259496440727130291472833181040258387940593434784028103312827743377463880870096638342753314132598667469013390288272111333278844132745976022919399908525983002703377613938939123302080939966623826150226743155952034576868646685447827289597638243311158323498217686853096334747938533601745853384583460224465928323600623399095978911543109975628307595142327338953634859048484388698084301125490075093964443766964427079156824542423220632457407647677008224220462126335724602236289858510438701335074663200156288447902016715051146009803647679029718040499700433959598142307718031299074198278000674604050358794052557272040340966250906797702715246606728225710349080992517071761686421580249096297818070408178631805527093492837823188260127824533711721284515707617272184121316004136835817221275496031400391684624711503627639866239216849760151902022329462267482305371723096104225637544670331687178617913947441558330853857545782940954196995217266861075139966502266085768508466080347420242016874031630987098720613544502663891338082961710724107493495492326249130665370413985044832168596110172707325048735866099085923235909681602498473913122261067547664728348945956470540901060936785654467487138437563303258906748172134279862410607116968456293134905207951413341806494014864433422177041227458085143845369374526084090763568252009761976581423125061967374078184504136584822125842494215756512965463498649094726532468567583025952622501017273274359612344708549333424284847360312406706351296097022356589047148858005813328315702070526418915759210008600184511185198724480515467389593499752569043010985914008055705903412343634331640430473187255007193693945476339469101968322759838707874525282160810594153122630068228478562141795091631837742306262069311209012097122882400206573635759556323867504873683443674664446040461658604738201272756112969803430343654005529811282402399247484484631193070205259619632790194615275154648186457798837209317643790448128382775705915426643949473424766225571736784304868975012858610490141164120188514498439403892887247272140789631658088962969663145514695136012260701367482370486177392208068415649810351022956269549555216376275851834427156386507688892099885338645305440527734340331787210903594237556326269600383927895694850541222566648484965595886554794000870103496787538552004978407005834387595905243010058523663861548845227244530822875371472844538742583182322897736792918319852979981349070990944527659222197511983417437849140648143012014716472247632436499990740632370889623065957234750469840984390671110475921218203543735364303934177766195080891268811102612280223677162355427001486257722890285699770787188026429143577454019302094570749150921162928857802802535679672378230285410465966550129279895479437166892330393038525402580795793639635070472588479754440402625122390205986316900111595398027094998336601374471883459606534536336990530445752061037931382348236069761329251585838786622800709107392411706311107320461760922895280933247366949789865863608500830614952995838694550690695344947555552917508968946757591188302995361282022220268439425468818335663758890316423215538918383452176610217412025937640569255617046081958342958379248675642054234519512030274319554551456734404899279643312824181328573421365871848017884061327447219194379521216625696218508995441423014655770322169965041549885931384705638494958293871655494414514865237642346712739296602892384029716433340576890752028871365077727728768225074720743580436117607212346684608486601393019553277867452965018922917432444731229899071927337697726511865966096508362362026771999796419281651295367926383529204263756157860043228598829983865433310547518757371039244676187002794699888626448891809172751347112661713235057709968376391976302136887748482763139584679452732478090032540426108962572113211829047941275387396348711845566727044623277683952317374732232975201495445346528364300765489751203443190259366663226075374236644355141214300916332171716427211877495593016425015608052392815401969079056075630958219062816456071677382680537947309311935554647081834838223136939110872236468410610705761702420435686546523130693746900245482293550397244136479275058896161180845366470971707167215198476965380135523780509528468636106812079095543524236231686913561814286567643543346385946721846050509587216736323789184218130847994086680749102478020995937761111933209350097976901965951151298325880375339877782546645003506646383176228678460300523430160226984125747064751252632224966658215094392883497726497765486616940605347953548406867410335584862040736984962993952588751936668460078012003869048894610065323009907881066212563336370428854130689084697045557282977090965870655320360147523347880665233211454129199516161066901537164709089072393974090009563301443626671278003030506021508722725251550095263006314392234588035661964097805847013218941050723080163480919675211447309346595468833756546244822188127063106320225229199312659718246386593744715999358793811492468502549324804930967342654112253483526596602347155381521619751428934167388287216591710191456239167468580513903669650986961892961400598488057289228184913918222804643059661379146006440002184288009338402096809381541468247869225689036895072231277965542941279220266349340156710850602081013420175330378029916456929398932060461151897260604279678288438679964894641888865603473776787723617912469690160687386609009328345267237925472071251694128635177350110986518024647089919507933139820399962378193722698332246547962685775366186059581356134017362380416681011128681008261843733675293374973959866181185980892673702184847347581264383248174735281855126152689673435389359094396074919547076345493439916079365991513613805765855455698611843485108722748360435675131502869241508559763897836192847452954582471166685230789021491617501211016883197632030601035397644825695461212126938136676273746788082128463527209142668531862932012244596012370260637648510980894374562213451726379412731640196490776062082932348444390788652285186732749076765368752023752076002580398044839539940143643397041042620761807148839653548271787013596954023969487344549517203581384490753162423635259872804273512091704653531901718950636767838708698411812826081886727741394492913703894322439282895532120320324891811838167577046557190141786190017677169573378213508640787049821445435911119801159145625781486953259415624836940694921275220532175153290082305583411454830351690135689851080343442873060599504182564513201064713953766058980094100529091023925241598478366603248639261853144283699997444466840821068963976798911845964467101625690201538015646204829967797929701842991905816884573552141958671203398779345302814710560335393858363258083971422984552293396266090907595430656075163875887913163421172146046918664056904362568735988965141018479618930343122128108319071145629350528145920524732182622915764304597372192147090165010077224832480227440547646571605097924935786839747299055387159692831980929926799273048615331860082988871575863664562655977401287590554503259168287854599878807615545325426146429872914697938414955420256551735694863097478012110979154211516430608866257415357016613351522904324919726957331834935525842633256064165777898218078868493945387314127730467319749947393946670620360705242444718380102321923438840731800247397958593309027367380900158518867654485570522113635553321100368047297403238479777740918081035329626642118147528519913364890263082815565111291089679579241956534713211149965998537836722253834900529082830158716464692030372672756241892172507445354926866965527241340287354457495628856368661792279580819414356481896090070495527236055992719286401888790548529365414112250445394187071443454087879062341668292354952813919076056174614644594677523632160770369678973822005181227908729574246930437393270552354129069907967859083622739554591353961706728871268862539328476712120438044508282847637145091878551999541052474321585377708205775482670899186140274520105421899755821812052883803189641217924765440038840238404616559804484022507598220597904470120687435830233150099911088039036575592919478635541932541270255775194660154581748179565577966771999494297912503035151698294794979797872526921085090511160657623856204925502543577694572430113839124862713591855386283390080255480447189864137351176122673480168357432824533767720007721033079364895550271690174188505671689934893862901164592282939389250471455783347442084135252329926363250045573639210729109116005629724610861454800587505925355410474328492207601114254879017700355835574544321347537066113749654904229306538924495773222367948462986780910844701262828861615558012221336690047985522621108104041341106399755662983657978867236851405624045304507094893941017217525317976555060359599640460752170018422212881055983364643938226363639561707572688035984180664263363701783186579258870762298471407202414034692427447965628781056944110038187379690017340600818413305173568930687165639993416603161726853128110889624327545180176442497318381789849718795774658420672983311810840609075543757532163062444088064358695967087589976368463475826909695466904222529645076685801279326524536229228459368733073707413363244296714472561386847436061166934367650110966113520316287329088043801068173243743401112553396654390099849409319010598772717357533897348924902461337806324898527193541634830665239926572308154254980062913253694417345213240241881079271423791937484277410669384530605388032081415061092027013871848318784242198528149779551266768634179765399728173985795711764331545037924209117292361795664859357872484453149392933273338861150306359491685773936258061701822945059411563383102710615958843708966325628017830373780907361125088731888779443838584751904768206680683269658777570987846773210549705122466364681318595753720407251659405691095511889302378914451219161893702669605560822301838777412584272912002189080730201895804011864882608364161442419716233619271242436892158797013276394373726655045000586349642158879114168995568398071041556320937372228717753500861401499869375300382915350740225925344391815245046377227842212139340047177791552212943238713262918965909454547140424699063878899896757219040772655425145669266928997042657451887761083366334134901902566619337465984396974087388673320742220912525445538629819086958786705326558565015744577067181876607024188904151635573294527128434087007204162862422719979236949253474227441219493420124962751268008719478436949898490974189486651368712067961604473158290324530360170498340779989640692692894336913320033675722911159402587698138850028107290056152981982578260729499146569880427485002380846970586612556967199361208789183503984824323120739438485962693639655353553130822063732097289190899912396940528670923086013459589333523649016714214674624357845639827120426092032338507113625666510310457248462666287792522612782575928114724969798538136574178553300985632345495848313749898844660722372995946048620105733587285119324131690561350292038895312774185060339640526434144608656410358623379906498354350890951925654160700263445597334648653704303259124110179040811199156125707110470664229005947842154644203215958641145269034258627318482049986527460105854864285442886502826535953349631777125081536581932933850224201028856245667906453226768434702823969604490554234390634084065103162740368591040180253700518279083008163772756637442931442825178428468368444958999761514951099084779117845688465128014242190121341136649475805307425766466217518997584687030528241964451100852398427888101989800144618207223184359658588673462178125163765199753778955490533642911708385991099873289763565608920338815858436393420752769332160661581654908154872256204800147614345010570162674404577481333719351089946908482245077280566398420811448354542288044031225750846190114561305424554378935300922200212127531263380062087477810687169017260569956118044448121333077469769139219886441340242657928073008944136510123273277055844572182095125520522912014207210214288774557116215490171512154022785220016883938814082884509262268521946881702006633412894235383779558525917882571745115297948637495176417231207712290513508051959156869308313187918564734840673242438877926009971508244119014828128552379337985886144770823260407119771147981914836372186593309746613664886941995593565459409335510956363940438949962281980542582495954095663754424649993332625837693598252193341547926521586720134754529358656249970624439558478278595000731391858027322831544304576979162849844227259017229589263752905351776640037258898855509713856440130147610468193794084481345284721027528715877077470788238579935042207426819720358666512070552729531174673440159941421069126172799454128961472416484912470181471047084585695653789803697137936760216162299254389911116354139655959669259900702730711519983059709022231159317166478994800305273296915829323698054248463529192592121603254433443556967394758193430186307736205878159634555061547376320841170903435105812204901418892977240010684818908067821225784543811211538826838248179958937468777901218738512440352244327093176930571249807320356985477177256685195441144999390404935310929955332823872319599758455961981557952168959926400813188442163304045068458479975307292620186061407260943151730037789405297923653119485983919174214930850056394348920967686865144284246895215661071279882811938524870272998058681515703409685075798676221136062151386922776477485838995727144466193513078803544827401145074663861622172848945402673000785614805998874662597408106399945132956369383414970990972804313043523431784055740561108727164374244285848173485897807662990740949461504057496132762307377948450160008903262578035752799592642703240766551760691039649364764286427927492817950968128090819709554285621791252388589650894193945148069098852064937740079454114189381493794009201503577669347253898408399420653265966320881806112706258441037616287490225842410647913583428695508661666752220099082255119334149343187949565307082087229777298241046258568147930746136587122556750542129345813002750538671636682316739656725709490125909711062742301097355282462691265871249719563598779966703527819776506988850128543054139241679438053407994511084755322761349539461970673516350292431861540486862612759836141649313376437336184060561990698940917603255845456995943777527619237005138900521550367525970486840695016924983018202774321499887730023655838853588910868474192541813839",
        "denominator": "124646478802409721401290712593462569189266445064130068674265256008769355264997710101441482965618059489164918258968181599134133668983625340998708365147297708146385933456384002243413201264997380569888549432336199285198363385917610841817825274836322961062135738333435209655661459374496747550759964791739586710667533177367040929126989614263136255285603720883501908811594601479933165886056442351791765483202243184522843694040023325032631013370642935197873119759835479945283996578251895837747366469151565618657426063155971027351370858004153338941552684632725465178363330734101274795216460490325484664922393748524831579228028995084670942851852042754617864083559154483551474869180595526660226800950672301934371550512745230219858003091526658270417383836271778789508172489310580873402198997179299838318100952397273377062195289105571820202611470743083123270324141769740791085729405128633943715121991604236591293808899620402634935793071835238858409378055648822140007705324139288827310075889737883829124124348359866226352609274430301070728999856532510463249728943595054646096957054084713045909938462970163836687183189443458982114139369908985708807841056673708969039539535375921421663036193363092476333329088079943695334874198756402618379398864494734383461374791075867694966206464873450369223503354265521208236306273988670368842643612467459876552395583997289310572003571151803641383082644561620413540721635953405396059363208181625700452104892468016434311114345713260712594006427037305376404762223132140445728226156790753027150243120692371541934771504675616947465609455719713527028550487182489532898241363580843875841288806236785922283242360687008284450619194346130238423862409228929732015179277686608252612674037283467409523908471595425255318706652892856489670172846919495150445339013046178830415096014489170348280018919769964323153256690125400223540351106975338861256773028199422394362791433176562128191424334753498401145112215965189898014695960542577265870139560931428973696156335474195865248383328148929691517533160148946993719245387063107373591292660752754012316845912562938590533395989060292227497041575460177173207743536762542977742464753764037664873202451185317572194900990577347909281171430498563479622101820023899563790974721625771718857759940230194407609121281582386396325278004327402417082083989069548221164027665807755652822880688730285292783735036333714183648185852149925449954742174679151191269263400478100446493290826547444388883124749760713580351730396877195801520079262359209844153099633903789111035539507901969742109842893967675909709357062714456161160732875473196317659315670170693915716485941656140704870858532582457543152497162576764509923185634374721169039988633204226974115917953387269088431066810022900175797291782157597581170832117001804217280710998515325596950280112088351938715687212750938030927138686681067694976503401161965845854042232287191829156522278440247666923348388075656101500470154745711692717119333521388324193136291830163173199240448354475774122993677889443754247291092657760401058627360001818377274957248006901650232772314072315443570501552374312453489284572057720907433608472041242114295381478107745907029157728760487995398110310116223169003429266277753737316736299467342686560028304657968633242654821984970373544479217104060374149513529965768163432757955989199003414154963769263999922585418096669193135431544008984165760023252549640381781132556034841590719044885372927208155263204607812609275260045946068853063960983004794494654285086342500389935408269486903421157606613890856919928708390267402949838511117568033073281938499332532513862071534556866091082573909028214205531246844769783176198658708723983695437175345714052227956926668190041571122350520944170107839312513185735162038393854445049575791666793915371131771567993121151306975452531788381336051719403517491198663419371286047027750494282467532797617542863113545537483619114638597717937094179749868731473506889843534924704811512652394114469137762967443273265783744722259127686605004233636651168035514573164281715041423016910253285360632990089184473955320248493828623730340637489697665179950826933484205171940285941180991414115084533799136634167255304413422909241098456301100697926318288037451599893487999386181273929240167813180898919313487754849969563437002933252026283164815515006102709269705482905049291806890916344874659287670962124774084423238240328810777451247006119207322370332534242206802156528112598000543509071331909146172506883552527397464291456949256968456946554066885274585226886234443240307569296656977132821578789627722382138239735138858859764215782896603832332023459733520478110634281156387906481183280449133260278078751135890355927787812154112789062610505821595853162640358056126918871145559719434358594318347107345014493426396907014008391059620460136080439259094006929928643870899254853673463864411245076822289918888125618046090457186765085769677799271149786867019870742739194994914280745492128783110890535549415348600537197068807781423822343497708343788479649495914567390139973535250235099017860563982889552968375675892610577752786808865266571075083729306911208475871109370777330127070120394204345458922310585896610515605751176551359352585080378245589656403618704830733248379716153879893553424283117015812169908588124290812272750573076208365594582549974652927485275950112855697242230155750257914383550046150891590388967302746251861659197167667269004155632725917956593038189281772332401350286490964403400041453375652102456710611803440766519003411512736815146707750873667439938811724282736445379030810532035537284371766153850266097934033545925225880404388522987166786420930378217092657522286783722573668451542742754302530371866497641894058205153557242821002202613349472889033918119254098800528450684421161195554870839513941759300083413759527211231236609969682827713038653154864818487032878969364371037846665634701462661120891705108041516386509833651671954816119049222150609817670070417994107507873394803327896446452083657789231143064245231318625378708830953285295890890781580101829055723575663284450502190734426514957266209760822495015819055267280942095794653180003156915522679236916670119518608617571362778709927484176947071109412951638498246281688902366041565377563403538238953510880438762794895397099963603022562752508920616825638557255590647032222195404862040792706334731383308532878636813467521460312079050800970224314071471325908515925446273634742230021103760324712708987371890395975711403095799744150168069825065932241566817535993842466654975397282331214794081977546997428423742501595567820383745643477585753929055800800392315803338685288778285177664114016589344603336702077950604751619286582126943739450429740053927808678433406950671031199472062016460953126345255510916952077880080747397861222069378589706456888059918091842297527401728915032474238569657122318650631211912424252483040164566596871895897848921150497925994180027209245944479494188817256555624355164171314898724332442309075408533479941309807461962722430537809464855506837650053293366221404044640156574954519685755590000274352230342594992604913943181353721090668150960897551847360430148068944032800320257905577813174802033943563398877897855016217489630870813381551468359425401729474233220303562211247307689864928464087644538382894038035198445057921188329053589865967057231974107493990329682040085492229782391034366717021608033721562837483414363561994141330255547488095731658949759603098351727941277443202978684585948522542620212603387768763808500344141167175340945618443195833289194172004753958548754581368387062341696786527398250659047617868647478434284408964928199855428937134786801553366883237101967875773007469678156897900971445770706089724571177604391729603225195333106781775387040047889762701587236580217446443941506955857058455090437949028662540013503243080054253937338767225088597977333855070568042544357648468013153867949957663019011250244763661176208219416916436463124734864093682194019854872363984700993836081198199294811879879703575163710138888662382603051707935352093628766648980338809481250737893758987544776504565450606937177337721309410955206113562395654756770976151276682224486193714210289324621446886662030474522132738102328810791080143050095476434347857472723776272304334448969342526905322234428532064585926996488148555960096307273776796878576829022387211384852511557922265639049419137422756465292288697521696763129380326069631175820863194688459491215833860709461998532111696043366056458864086538612653391246139388175207104034527562179789437725930563036732397415099758023760430435462832788144151259150301824410880327472688106205401702506698346777463112069427522945490328853715165799473090933104728781372478693676597643044253993596847403185588492482449531774567770465768225964434987513954060514820030128762891147350366800835091083515400467307257028443722329671860101561988046729216981003886508458401517139051656286187058026470995475813494276394756361551811844865520002863199579731375147766733695048385662751388512042524421921379239951558408806264402106281829364649762806880152444464326623541323018629955932114149731811463180662823764065496739081845328066656197262625933192870867292133488415186027891078676705511158208987422806684997617300599138220532454543076295117783744552778731969978696482554488955551549937604695902844960830114836466458181742182522516024036927692262393462981303061821097562593726434092775320846512705370210751714661810431017436355419696587003361468387444078896116417501357712988973590216603603689069000600203739445551002291432469860292939930459093762471073245751372079243111383880418371094005964937194928256284087491214029318126506734335054440846594208644149346072879798845028494482931662661124772518937856103346280243815758638835716492364076096936002728421129835050409528375385986835768281158274028926509569007655324190361472101345915767307429440435432795216466262642968880956469514572331392466466924050772036564178017487471715551798821939787132318758210967948026777283132332660728652921919358585757772971797595609499209505131242764925026397080285114844878229389584624468403571266732058487517115578490188879146436453082742411230126098583099008099954305278105985536251122866499200115113577073735773961537635378221220449092745409550697188341625065065537451857877694695874793274796676267669373512660043201742069797647439554275252114813621272137919909822595986603418731020286410933304273884283479154347640057324072151125323074908153411889848982801107373944282989719142525743545097147393527051047064387172337274741675423483994349219558059340556416961674569884690394166906698908099969713937798428505017207634475452014126888785770250261614581416256387421529504985158413521455564819966329994800387259038609693089477472101869747224423897919333153402548450970032627556664679004514571056506716282715795350602314249520057282730583627526932424943852094016056140165073978977559342818419153820580566872939979273595091484020664956606757935090044413646553116163816855262838233983768509725283459859755587955250821262745520576405854027012422971777757816148351472830526029429527294590734022318825938478204218765098295996442707638772770580489550264308151293566787513249593319671932865282256051629144913159003233798308838141610682654152932352199087605803789502360237200013163342694723818575544245389262915208329129623211107690243744903056858246499632783948431441709065403871802441676458245596301842938609432483062918987515772165634984688402035758265703361724373061704710352453027639810880314416453167762494990777859809658864884198339141775588646059709839002802713300089001826558116749511489783589910725988353800794870069300100089294987612788532550230137828537568975594631089272322791332069066607778204159652880445817271909956522797326522457092127689093215527074739562675022893333407034018481773413982541742957574268114141820517968129472449397611685703813467653226122495250003909377385797369069058840137131954811501783694660725338440913115559782034268190247633870996950495375753442008311003942269975619347936319595590902459117972960453197586938292782569670049850228328262715457422037519414537520458356861046044852946013732688088118090327537440192224709572954621704125899154630295047577835332845639633388665227488269490127516536604187554538000156717144335760814478312561711028531328370571003379368757853129060858266208399002207569042254871158385736733770382714587881148089806080248506546329508689415053215249649933897438034982930055375131642734417213647032449804741148868095941793774138226382106495229935993325588245382641523506707492631335768231950099771251126340345557766391932554087424149830705427802029215882014669769842364435479816405606272538223896510490283425075763088618252875635205020681116409047328001804042877683529576375388945489795559300344586567850038090770951385357261693105337694455687386637189512303314521638562312310490317481864963433888059765258890370581153389281191265343592829569818108645943624578104116003874892394631074831907400294719046297366983196826071688715498088362604622389452747730941477555098205052778862127863371964447441962755738045262813928357428981820683552504523713866839007047048890929493281647319521847605825755769086033844487157928016504693424986086191866416673451447832511306681513683612609736447504075116207646150874790735859794044575034398287445691541477396716307872957960376290331135244300155036670576165302514033495507326041100347424217348977723076149446463578843473904113511363880708907204115458466257402549769715079471710588493720979657868926540244576723603939948998455075448367037306039972308216556877874634054804950884368737186024145355677629171045621488011734932262601062824637798672927063250531839191461953307729081293293538806494952858696879215679689666155451213069405305056866642879847918570182213150743506536237551221007746723395223665027488606761720693085996975250653562625898492816292554646078616766036540421383820249387255821723673920873174719545973023134048130230367918781944860311591045446500532906339076781907466350454135625672870943059427325224775878955354607920986442213401973278151083668774572695997887780663772975433374683385310430121777378828487666732924158513030713159760530781770959656317545535275035905461072843242425290495718226132891976270247778663268944426604830469050495349557699424029344227575879150138366325302590831156747139666365966786053756248817387569838936535142477632586411520834959952492300086743355826679869869177930978996915236765672930871648709511795446783370584410187816720355683840406841636076825699833463640585052269926397187378848259904291670430259605638786922071769479638718288271244720738775871092387270287516032568011702602089417564706010522999805722269435572933739150718665536452840582321500434212591688744938464567130661134779467371056972767469726564159207933731328283612031717531142660172916267389527387414225987203760863333192647500989625709497549857738528630867160614293154800627407436493955773722720613104129229951805184661586365097661998180595092598796658987797402960428595644430648951965517618964478029011658844077070867262854502516682803453831146155565052773042479325909407756424756718703238552126625860121335081818184702880268706023891791787902260838184154834234202974170542792772133182973301695616858552921775387536059300142712062704124284159373715546692912759569726215856072639940535932404826051386316617590522789814721360829066015562669832951554101132220096671430042417264320726612170560057892761152624705789591149365620035756055526194217364696442210592665621754981701741894132989117381741152273776872361210814324079059930107726806465005184326014850703512360096900036684726918478752399251150845312186995078164276893358354275516001319948653596103888255016389028646524945415513305842077689242831789081438108121378430102525314590221975532578531912031107879284424960042173277887168727151743306899612035468118049045650500392924577453405676501921081511840370694741398658288459451090918912453769993066666134948136076591208140860535248214401867884316713565466310236367034125585845721811764788019702711079817020296570676091357104363396971363081233481551620170380513218882855312998185217966937393501793082735998780680476582286770563657581933693402222363556599627394837347394302303463193230878892627347705835868122524022144891940617833655985252439276562486324874869702968699406586763720579245251330830639380529932634419492798266561240724548251721379178472009748078492120805556280165461377832951924069257581036683556225133737473646927613552908532384394898203390685741132348626639148365956585344997315152144462343193223408832520208490849597393182116476305531786869255585614901799841476118282125897399588681068031542345419543170363802704223216880588759241401685194292816581136719233756988695665838107715976478057700897344307834651215999596928611980639728710468436217439418594441059933952986785601692588438650376391533293538299329136706466903155163393367751019253161381205813646352704094049257952017509671257226395653171857898321689124400091763604977393463451642019221006844005966660198475016967887682693667531382721382403403095923685486661356907713301530734021503449371587225697364206514498449162649979547714873996148122214496305497363664815151716419075889144815260863524667655425388929248550998861353336129808302667826599033164929418036862755298754010977764037847602895735729073759454566285652937931507208939675022927996715013564742087003539584303832720756553085213729624791498205417643642568466672619793297908513828346578351034268196274637389948888592708732742596657459210827405797638026938072850377771638374769598557787881029230300399499868984530695871119013905460503903681505698822667510430678977443767673713793962567768878769522852288374609084466988797151556046561654189780658379814086015962750367843381995475601896956482592276697832316494243524442727991610156959220899350689918811164115210989316746086437934466712217907673840277060822047956606725970241728904952859409931263972004739439565675700670180781381531058651591648448925769418837710804830493460033019417149612183473836011132312897140990478738071642432677647921215772402250985953822057851704761644949374525480400758302941709804454692236388262761119963171639226189946684420993389452811892624072059794782641445103993080874439178093797398906771890364744305198326553149486234225454894698880631436356399268991491598140069617304289598156782929716470706539092543915496079227478588313125930703712435120672846932039773969052929979762912445661850819450130664964597340397837812067750456138811008550983003109189034149856288331005027000560500000",
        "display": 4.873677836217931e-07
      }
    },
    {
      "name": "first boundary q root comparison",
      "left": {
        "numerator": "3510669994035952114902702038056064279974574868967120822611472726782028627391417913299691485529258721421130165928192830271236888946107",
        "denominator": "2977382316585908175230429660250734337787137918112900983601805355853165539150003581920907286193409471789207674611344939755642836610764973056978509566214741885378849233372035746585287614236849161427079959866439329336843836085733904405619",
        "display": 1.1791129323497668e-102
      },
      "right": {
        "numerator": "1415799798845637691924877134245247185854641050323915922101942715665055375933970883314766211365480136586114994098543570614248262330993678225066636903169799079596628266411783503520535504883806605629672868571166259331765614401",
        "denominator": "752316384526264005099991383822237233803945956334136013765601092018187046051025390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 1.881920729052274e-102
      },
      "positive_margin": {
        "numerator": "1574242727730919241586965799468987271236779230286483518604648194104598119015810498522146053684634739471650753610732571002647707820976157333592433245002685576904139777439023542152747913938865749015525666441592574370493545014971378230373080227906705744198650164080289437612182439680085414638520813995297041627871391754658092710614456122533950528357460463184317337874885853481610201168746809929898953122510226660778151564343507345167659286266515447788251719219",
        "denominator": "2239933499766342806385785749628472097941673541145109747237479359240489229358248682314263773611604591986125563609567278608785909690439129614104598068176823360587633513655158540392271368631254516725981016366335856047416892038832850491807530181315670125712183582906644643352431808640268240395698740030638873577117919921875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": 7.028077967025072e-103
      }
    },
    {
      "name": "boundary E output j3",
      "left": {
        "numerator": "2459653",
        "denominator": "20888153",
        "display": 0.11775349404995263
      },
      "right": {
        "numerator": "58877",
        "denominator": "500000",
        "display": 0.117754
      },
      "positive_margin": {
        "numerator": "5284181",
        "denominator": "10444076500000",
        "display": 5.059500473785308e-07
      }
    },
    {
      "name": "boundary E rounded closure j3",
      "left": {
        "numerator": "58877",
        "denominator": "500000",
        "display": 0.117754
      },
      "right": {
        "numerator": "3",
        "denominator": "25",
        "display": 0.12
      },
      "positive_margin": {
        "numerator": "1123",
        "denominator": "500000",
        "display": 0.002246
      }
    },
    {
      "name": "boundary eta output j3",
      "left": {
        "numerator": "11792437873570110241",
        "denominator": "80178648364327720482",
        "display": 0.1470770350229137
      },
      "right": {
        "numerator": "73539",
        "denominator": "500000",
        "display": 0.147078
      },
      "positive_margin": {
        "numerator": "19342639620558012899",
        "denominator": "20044662091081930120500000",
        "display": 9.649770863018812e-07
      }
    },
    {
      "name": "boundary eta rounded closure j3",
      "left": {
        "numerator": "73539",
        "denominator": "500000",
        "display": 0.147078
      },
      "right": {
        "numerator": "31",
        "denominator": "200",
        "display": 0.155
      },
      "positive_margin": {
        "numerator": "3961",
        "denominator": "500000",
        "display": 0.007922
      }
    },
    {
      "name": "boundary q square comparison j3",
      "left": {
        "numerator": "771147",
        "denominator": "974249059",
        "display": 0.00079152963287594
      },
      "right": {
        "numerator": "19881",
        "denominator": "25000000",
        "display": 0.00079524
      },
      "positive_margin": {
        "numerator": "90370541979",
        "denominator": "24356226475000000",
        "display": 3.710367124060009e-06
      }
    },
    {
      "name": "boundary E output j4",
      "left": {
        "numerator": "1522941",
        "denominator": "99361691",
        "display": 0.015327245185470928
      },
      "right": {
        "numerator": "479",
        "denominator": "31250",
        "display": 0.015328
      },
      "positive_margin": {
        "numerator": "2343739",
        "denominator": "3105052843750",
        "display": 7.548145290723766e-07
      }
    },
    {
      "name": "boundary E rounded closure j4",
      "left": {
        "numerator": "479",
        "denominator": "31250",
        "display": 0.015328
      },
      "right": {
        "numerator": "2",
        "denominator": "125",
        "display": 0.016
      },
      "positive_margin": {
        "numerator": "21",
        "denominator": "31250",
        "display": 0.000672
      }
    },
    {
      "name": "boundary eta output j4",
      "left": {
        "numerator": "4889377516939130559007087405112329",
        "denominator": "194121374855500458078463393560224658",
        "display": 0.0251872186696528
      },
      "right": {
        "numerator": "6297",
        "denominator": "250000",
        "display": 0.025188
      },
      "positive_margin": {
        "numerator": "18959115151872384156068985326210713",
        "denominator": "24265171856937557259807924195028082250000",
        "display": 7.813303472009765e-07
      }
    },
    {
      "name": "boundary eta rounded closure j4",
      "left": {
        "numerator": "6297",
        "denominator": "250000",
        "display": 0.025188
      },
      "right": {
        "numerator": "13",
        "denominator": "500",
        "display": 0.026
      },
      "positive_margin": {
        "numerator": "203",
        "denominator": "250000",
        "display": 0.000812
      }
    },
    {
      "name": "boundary q square comparison j4",
      "left": {
        "numerator": "1784003086827",
        "denominator": "238413227092302019",
        "display": 7.482819257072179e-06
      },
      "right": {
        "numerator": "49",
        "denominator": "6250000",
        "display": 7.84e-06
      },
      "positive_margin": {
        "numerator": "532228834854048931",
        "denominator": "1490082669326887618750000",
        "display": 3.571807429278214e-07
      }
    },
    {
      "name": "boundary E output j5",
      "left": {
        "numerator": "3112739",
        "denominator": "18367982739",
        "display": 0.0001694654793741093
      },
      "right": {
        "numerator": "17",
        "denominator": "100000",
        "display": 0.00017
      },
      "positive_margin": {
        "numerator": "981806563",
        "denominator": "1836798273900000",
        "display": 5.34520625890708e-07
      }
    },
    {
      "name": "boundary E rounded closure j5",
      "left": {
        "numerator": "17",
        "denominator": "100000",
        "display": 0.00017
      },
      "right": {
        "numerator": "1",
        "denominator": "1000",
        "display": 0.001
      },
      "positive_margin": {
        "numerator": "83",
        "denominator": "100000",
        "display": 0.00083
      }
    },
    {
      "name": "boundary eta output j5",
      "left": {
        "numerator": "689222018199025743319235325507176688589603936578526044964609",
        "denominator": "1598797041023532332373210516029517743033722939562610177089929218",
        "display": 0.0004310878745170765
      },
      "right": {
        "numerator": "27",
        "denominator": "62500",
        "display": 0.000432
      },
      "positive_margin": {
        "numerator": "45571985098132008312238044299218012530136666016298485570013193",
        "denominator": "49962407531985385386662828625922429469803841861331568034060288062500",
        "display": 9.121254829234825e-07
      }
    },
    {
      "name": "boundary eta rounded closure j5",
      "left": {
        "numerator": "27",
        "denominator": "62500",
        "display": 0.000432
      },
      "right": {
        "numerator": "1",
        "denominator": "1000",
        "display": 0.001
      },
      "positive_margin": {
        "numerator": "71",
        "denominator": "125000",
        "display": 0.000568
      }
    },
    {
      "name": "u5 initialization",
      "left": {
        "numerator": "1784003086827",
        "denominator": "119209289550781250",
        "display": 1.4965302566181666e-05
      },
      "right": {
        "numerator": "3",
        "denominator": "200000",
        "display": 1.5e-05
      },
      "positive_margin": {
        "numerator": "132360205911",
        "denominator": "3814697265625000000",
        "display": 3.4697433818333187e-08
      }
    },
    {
      "name": "q at most 2x via squaring",
      "left": {
        "numerator": "30000",
        "denominator": "9991",
        "display": 3.00270243218897
      },
      "right": {
        "numerator": "4",
        "denominator": "1",
        "display": 4.0
      },
      "positive_margin": {
        "numerator": "9964",
        "denominator": "9991",
        "display": 0.99729756781103
      }
    },
    {
      "name": "E quadratic endpoint exact",
      "equal_value": {
        "numerator": "42430000",
        "denominator": "6792093",
        "display": 6.246969822115215
      }
    },
    {
      "name": "eta quadratic endpoint exact",
      "equal_value": {
        "numerator": "3645000",
        "denominator": "1495729",
        "display": 2.4369387770110764
      }
    },
    {
      "name": "E quadratic endpoint below10",
      "left": {
        "numerator": "42430000",
        "denominator": "6792093",
        "display": 6.246969822115215
      },
      "right": {
        "numerator": "10",
        "denominator": "1",
        "display": 10.0
      },
      "positive_margin": {
        "numerator": "25490930",
        "denominator": "6792093",
        "display": 3.7530301778847845
      }
    },
    {
      "name": "eta quadratic endpoint below10",
      "left": {
        "numerator": "3645000",
        "denominator": "1495729",
        "display": 2.4369387770110764
      },
      "right": {
        "numerator": "10",
        "denominator": "1",
        "display": 10.0
      },
      "positive_margin": {
        "numerator": "11312290",
        "denominator": "1495729",
        "display": 7.563061222988924
      }
    },
    {
      "name": "quadratic invariant interval",
      "left": {
        "numerator": "1",
        "denominator": "10",
        "display": 0.1
      },
      "right": {
        "numerator": "1",
        "denominator": "1",
        "display": 1.0
      },
      "positive_margin": {
        "numerator": "9",
        "denominator": "10",
        "display": 0.9
      }
    },
    {
      "name": "same-field product bound endpoint",
      "left": {
        "numerator": "113",
        "denominator": "50",
        "display": 2.26
      },
      "right": {
        "numerator": "4",
        "denominator": "1",
        "display": 4.0
      },
      "positive_margin": {
        "numerator": "87",
        "denominator": "50",
        "display": 1.74
      }
    },
    {
      "name": "gap ratio strict constant",
      "left": {
        "numerator": "5",
        "denominator": "12",
        "display": 0.4166666666666667
      },
      "right": {
        "numerator": "1",
        "denominator": "1",
        "display": 1.0
      },
      "positive_margin": {
        "numerator": "7",
        "denominator": "12",
        "display": 0.5833333333333334
      }
    },
    {
      "name": "b5",
      "equal_value": {
        "numerator": "392",
        "denominator": "1",
        "display": 392.0
      }
    },
    {
      "name": "M5",
      "equal_value": {
        "numerator": "1920",
        "denominator": "1",
        "display": 1920.0
      }
    },
    {
      "name": "minimum odd length",
      "equal_value": {
        "numerator": "1921",
        "denominator": "1",
        "display": 1921.0
      }
    }
  ],
  "success": true,
  "wall_seconds": 0.02835017116740346
}