{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "On a vu en cours à quoi servaient les croissances comparées, et dans quels cas utiliser ces fameuses échelles de croissance.\n", "\n", "> Je suppose, pour fixer les idées que je m'intéresse ici à $x \\to +\\infty$, c'est-à-dire par rapport au diagramme fait en cours, $a=+\\infty$\n", "\n", "\n", "\n", "Je rappelle simplement, afin de clarifier les choses, que :\n", "\n", "1. L'on dit croissances *comparées* parce que l'on *compare* les croissances de deux fonctions, qui mettons tendent toutes deux vers $+\\infty$.\n", "2. Quand on parle de la *croissance* d'une fonction $f$ dans ce contexte, on ne parle pas de la monotonie de la fonction (si elle est croissante ou décroissante), mais, on veut dire :\n", " > comment grossit le nombre $f(x)$ quand la variable $x$ grossit ($x\\to +\\infty$) ?\n", "\n", "**La question se résume donc, quand on étudie les croissances comparées de $f$ et $g$, en : ** lequel des deux nombres $f(x)$ et $g(x)$ grossit le plus vite avec $x$ ?\n", "\n", "\n", "**Réponse : ** Rien de mieux que de regarder le phénomène avec les yeux pour rendre ça plus concret !" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Préparatifs\n", "\n", "je charge quelques modules (pas de panique) : " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from __future__ import division\n", "from IPython.display import HTML\n", "from IPython.display import display, Math\n", "from ipywidgets import StaticInteract, RangeWidget\n", "from math import floor, log10, sqrt\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Je construis une fonction\n", "\n", "Voici les 4 fonctions que je vais considérer pour tester mes croissances comparées :\n", "\n", "**Fonction ** | **Expression**\n", "---------|------------------\n", "$f_1(x)=$| $\\sqrt{x}$\n", "$f_2(x)=$| $\\log_{10}({x})$\n", "$f_3(x)=$| ${x}^3$\n", "$f_4(x)=$| $2^{x}$\n", "\n", "\n", "Je rappelle que qualitativement, $\\ln$ et $\\log_{10}$, c'est la même chose (puisqu'ils ne diffèrent l'un de l'autre que d'une constante multiplicative).\n", "\n", "\n", "La fonction Python suivante, que j'appelle de façon très originale : `croissances_comp(x)`, calcule les valeurs (arrondies à l'entier inférieur) de $f_1(x)$, $f_2(x)$, $f_3(x)$, $f_4(x)$ (en fait toutes les valeurs de ces fonctions aux entiers de $1$ jusqu'a $x$, pour des raisons que vous n'avez pas besoin de comprendre). " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [], "source": [ "def croissances_comp(x):\n", " f1 = \"racine(x)\"\n", " f2 = \"log(x)\"\n", " f3 = \"x^3 \"\n", " f4 = \"2^x \"\n", " for i in range(1,x):\n", " f1 = str(floor(log10(i)))\n", " f2 = str(floor(sqrt(i)))\n", " f3 = str(i**3)\n", " f4 = str(2**(i))\n", " return f1, f2, f3, f4\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Plus sympa comme ça : jouez avec les croissances comparées\n", "\n", "Le code ci-dessus construit l'animation : faites glisser le bouton et vous verrez, lorsque $x$ augmente (je me suis contenté de le faire aller de $1$ à $1000$), comment les valeurs des fonctions $f_1$, $f_2$, $f_3$, $f_4$ augmentent. C'est assez éloquent :" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", "
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('0.0', '2.0', '125', '32')

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('0.0', '2.0', '512', '256')

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('0.0', '3.0', '729', '512')

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('1.0', '3.0', '1000', '1024')

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('1.0', '3.0', '1331', '2048')

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('1.0', '3.0', '1728', '4096')

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('1.0', '3.0', '2197', '8192')

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('1.0', '3.0', '2744', '16384')

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('1.0', '3.0', '3375', '32768')

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('1.0', '4.0', '4096', '65536')

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('1.0', '4.0', '4913', '131072')

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('1.0', '4.0', '5832', '262144')

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('1.0', '4.0', '6859', '524288')

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('1.0', '4.0', '8000', '1048576')

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('1.0', '4.0', '9261', '2097152')

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('1.0', '4.0', '10648', '4194304')

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('1.0', '4.0', '12167', '8388608')

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('1.0', '4.0', '13824', '16777216')

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('1.0', '5.0', '15625', '33554432')

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('1.0', '5.0', '17576', '67108864')

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('1.0', '5.0', '24389', '536870912')

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('1.0', '5.0', '27000', '1073741824')

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('1.0', '5.0', '29791', '2147483648')

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('1.0', '5.0', '32768', '4294967296')

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('1.0', '5.0', '42875', '34359738368')

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('2.0', '10.0', '1520875', '41538374868278621028243970633760768')

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('2.0', '10.0', '1560896', '83076749736557242056487941267521536')

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('2.0', '10.0', '1601613', '166153499473114484112975882535043072')

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('2.0', '10.0', '1685159', '664613997892457936451903530140172288')

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('2.0', '10.0', '1728000', '1329227995784915872903807060280344576')

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('2.0', '11.0', '1815848', '5316911983139663491615228241121378304')

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('2.0', '11.0', '1860867', '10633823966279326983230456482242756608')

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('2.0', '11.0', '1906624', '21267647932558653966460912964485513216')

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('2.0', '11.0', '1953125', '42535295865117307932921825928971026432')

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('2.0', '11.0', '2000376', '85070591730234615865843651857942052864')

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('2.0', '11.0', '2048383', '170141183460469231731687303715884105728')

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('2.0', '11.0', '2097152', '340282366920938463463374607431768211456')

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('2.0', '11.0', '2248091', '2722258935367507707706996859454145691648')

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('2.0', '11.0', '2299968', '5444517870735015415413993718908291383296')

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('2.0', '11.0', '2352637', '10889035741470030830827987437816582766592')

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('2.0', '11.0', '2406104', '21778071482940061661655974875633165533184')

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('2.0', '11.0', '2460375', '43556142965880123323311949751266331066368')

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('2.0', '11.0', '2515456', '87112285931760246646623899502532662132736')

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('2.0', '11.0', '2571353', '174224571863520493293247799005065324265472')

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('2.0', '11.0', '2628072', '348449143727040986586495598010130648530944')

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('2.0', '11.0', '2685619', '696898287454081973172991196020261297061888')

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('2.0', '11.0', '2744000', '1393796574908163946345982392040522594123776')

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('2.0', '11.0', '2803221', '2787593149816327892691964784081045188247552')

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('2.0', '11.0', '2863288', '5575186299632655785383929568162090376495104')

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('2.0', '11.0', '2924207', '11150372599265311570767859136324180752990208')

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('2.0', '12.0', '2985984', '22300745198530623141535718272648361505980416')

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('2.0', '12.0', '3048625', '44601490397061246283071436545296723011960832')

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('2.0', '12.0', '3112136', '89202980794122492566142873090593446023921664')

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('2.0', '12.0', '3176523', '178405961588244985132285746181186892047843328')

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('2.0', '12.0', '3241792', '356811923176489970264571492362373784095686656')

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('2.0', '12.0', '3307949', '713623846352979940529142984724747568191373312')

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('2.0', '12.0', '3375000', '1427247692705959881058285969449495136382746624')

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('2.0', '12.0', '3442951', '2854495385411919762116571938898990272765493248')

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('2.0', '12.0', '3511808', '5708990770823839524233143877797980545530986496')

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('2.0', '12.0', '3581577', '11417981541647679048466287755595961091061972992')

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('2.0', '12.0', '3652264', '22835963083295358096932575511191922182123945984')

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('2.0', '12.0', '3723875', '45671926166590716193865151022383844364247891968')

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('2.0', '12.0', '3796416', '91343852333181432387730302044767688728495783936')

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('2.0', '12.0', '3869893', '182687704666362864775460604089535377456991567872')

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('2.0', '12.0', '3944312', '365375409332725729550921208179070754913983135744')

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('2.0', '12.0', '4019679', '730750818665451459101842416358141509827966271488')

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('2.0', '12.0', '4096000', '1461501637330902918203684832716283019655932542976')

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('2.0', '12.0', '4173281', '2923003274661805836407369665432566039311865085952')

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('2.0', '12.0', '4251528', '5846006549323611672814739330865132078623730171904')

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('2.0', '12.0', '4330747', '11692013098647223345629478661730264157247460343808')

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('2.0', '12.0', '4410944', '23384026197294446691258957323460528314494920687616')

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('2.0', '12.0', '4492125', '46768052394588893382517914646921056628989841375232')

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('2.0', '12.0', '4574296', '93536104789177786765035829293842113257979682750464')

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('2.0', '12.0', '4657463', '187072209578355573530071658587684226515959365500928')

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('2.0', '12.0', '4741632', '374144419156711147060143317175368453031918731001856')

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('2.0', '13.0', '4826809', '748288838313422294120286634350736906063837462003712')

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('2.0', '13.0', '4913000', '1496577676626844588240573268701473812127674924007424')

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('2.0', '13.0', '5000211', '2993155353253689176481146537402947624255349848014848')

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('2.0', '13.0', '5088448', '5986310706507378352962293074805895248510699696029696')

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('2.0', '13.0', '5177717', '11972621413014756705924586149611790497021399392059392')

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('2.0', '13.0', '5268024', '23945242826029513411849172299223580994042798784118784')

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('2.0', '13.0', '5359375', '47890485652059026823698344598447161988085597568237568')

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('2.0', '13.0', '5451776', '95780971304118053647396689196894323976171195136475136')

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('2.0', '13.0', '5545233', '191561942608236107294793378393788647952342390272950272')

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('2.0', '13.0', '5639752', '383123885216472214589586756787577295904684780545900544')

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('2.0', '13.0', '5735339', '766247770432944429179173513575154591809369561091801088')

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('2.0', '13.0', '5832000', '1532495540865888858358347027150309183618739122183602176')

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('2.0', '13.0', '5929741', '3064991081731777716716694054300618367237478244367204352')

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('2.0', '13.0', '6028568', '6129982163463555433433388108601236734474956488734408704')

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('2.0', '13.0', '6128487', '12259964326927110866866776217202473468949912977468817408')

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('2.0', '13.0', '6229504', '24519928653854221733733552434404946937899825954937634816')

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('2.0', '13.0', '6331625', '49039857307708443467467104868809893875799651909875269632')

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('2.0', '13.0', '6434856', '98079714615416886934934209737619787751599303819750539264')

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('2.0', '13.0', '6539203', '196159429230833773869868419475239575503198607639501078528')

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('2.0', '13.0', '6644672', '392318858461667547739736838950479151006397215279002157056')

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('2.0', '13.0', '6751269', '784637716923335095479473677900958302012794430558004314112')

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('2.0', '13.0', '6859000', '1569275433846670190958947355801916604025588861116008628224')

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('2.0', '13.0', '6967871', '3138550867693340381917894711603833208051177722232017256448')

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('2.0', '13.0', '7077888', '6277101735386680763835789423207666416102355444464034512896')

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('2.0', '13.0', '7189057', '12554203470773361527671578846415332832204710888928069025792')

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('2.0', '13.0', '7301384', '25108406941546723055343157692830665664409421777856138051584')

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('2.0', '13.0', '7414875', '50216813883093446110686315385661331328818843555712276103168')

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('2.0', '14.0', '7529536', '100433627766186892221372630771322662657637687111424552206336')

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('2.0', '14.0', '7645373', '200867255532373784442745261542645325315275374222849104412672')

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('2.0', '14.0', '7762392', '401734511064747568885490523085290650630550748445698208825344')

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('2.0', '14.0', '7880599', '803469022129495137770981046170581301261101496891396417650688')

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('2.0', '14.0', '8000000', '1606938044258990275541962092341162602522202993782792835301376')

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('2.0', '14.0', '8120601', '3213876088517980551083924184682325205044405987565585670602752')

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('2.0', '14.0', '8242408', '6427752177035961102167848369364650410088811975131171341205504')

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('2.0', '14.0', '8365427', '12855504354071922204335696738729300820177623950262342682411008')

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('2.0', '14.0', '8489664', '25711008708143844408671393477458601640355247900524685364822016')

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('2.0', '14.0', '8615125', '51422017416287688817342786954917203280710495801049370729644032')

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('2.0', '14.0', '8741816', '102844034832575377634685573909834406561420991602098741459288064')

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('2.0', '14.0', '8869743', '205688069665150755269371147819668813122841983204197482918576128')

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('2.0', '14.0', '8998912', '411376139330301510538742295639337626245683966408394965837152256')

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('2.0', '14.0', '9129329', '822752278660603021077484591278675252491367932816789931674304512')

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('2.0', '14.0', '9261000', '1645504557321206042154969182557350504982735865633579863348609024')

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('2.0', '14.0', '9393931', '3291009114642412084309938365114701009965471731267159726697218048')

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('2.0', '14.0', '9528128', '6582018229284824168619876730229402019930943462534319453394436096')

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('2.0', '14.0', '9663597', '13164036458569648337239753460458804039861886925068638906788872192')

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('2.0', '14.0', '9800344', '26328072917139296674479506920917608079723773850137277813577744384')

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('2.0', '14.0', '9938375', '52656145834278593348959013841835216159447547700274555627155488768')

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('2.0', '14.0', '10077696', '105312291668557186697918027683670432318895095400549111254310977536')

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('2.0', '14.0', '10218313', '210624583337114373395836055367340864637790190801098222508621955072')

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('2.0', '14.0', '10360232', '421249166674228746791672110734681729275580381602196445017243910144')

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('2.0', '14.0', '10503459', '842498333348457493583344221469363458551160763204392890034487820288')

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('2.0', '14.0', '10648000', '1684996666696914987166688442938726917102321526408785780068975640576')

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('2.0', '14.0', '10793861', '3369993333393829974333376885877453834204643052817571560137951281152')

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('2.0', '14.0', '10941048', '6739986666787659948666753771754907668409286105635143120275902562304')

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('2.0', '14.0', '11089567', '13479973333575319897333507543509815336818572211270286240551805124608')

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('2.0', '14.0', '11239424', '26959946667150639794667015087019630673637144422540572481103610249216')

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('2.0', '15.0', '11390625', '53919893334301279589334030174039261347274288845081144962207220498432')

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('2.0', '15.0', '11543176', '107839786668602559178668060348078522694548577690162289924414440996864')

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('2.0', '15.0', '11697083', '215679573337205118357336120696157045389097155380324579848828881993728')

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('2.0', '15.0', '11852352', '431359146674410236714672241392314090778194310760649159697657763987456')

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('2.0', '15.0', '12008989', '862718293348820473429344482784628181556388621521298319395315527974912')

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('2.0', '15.0', '12167000', '1725436586697640946858688965569256363112777243042596638790631055949824')

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('2.0', '15.0', '12326391', '3450873173395281893717377931138512726225554486085193277581262111899648')

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('2.0', '15.0', '12487168', '6901746346790563787434755862277025452451108972170386555162524223799296')

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('2.0', '15.0', '12649337', '13803492693581127574869511724554050904902217944340773110325048447598592')

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('2.0', '15.0', '12812904', '27606985387162255149739023449108101809804435888681546220650096895197184')

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('2.0', '15.0', '12977875', '55213970774324510299478046898216203619608871777363092441300193790394368')

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('2.0', '15.0', '13144256', '110427941548649020598956093796432407239217743554726184882600387580788736')

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('2.0', '15.0', '13312053', '220855883097298041197912187592864814478435487109452369765200775161577472')

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('2.0', '15.0', '13481272', '441711766194596082395824375185729628956870974218904739530401550323154944')

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('2.0', '15.0', '13651919', '883423532389192164791648750371459257913741948437809479060803100646309888')

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('2.0', '15.0', '13824000', '1766847064778384329583297500742918515827483896875618958121606201292619776')

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('2.0', '15.0', '13997521', '3533694129556768659166595001485837031654967793751237916243212402585239552')

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('2.0', '15.0', '14172488', '7067388259113537318333190002971674063309935587502475832486424805170479104')

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('2.0', '15.0', '14348907', '14134776518227074636666380005943348126619871175004951664972849610340958208')

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('2.0', '15.0', '14526784', '28269553036454149273332760011886696253239742350009903329945699220681916416')

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('2.0', '15.0', '14706125', '56539106072908298546665520023773392506479484700019806659891398441363832832')

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('2.0', '15.0', '14886936', '113078212145816597093331040047546785012958969400039613319782796882727665664')

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('2.0', '15.0', '15069223', '226156424291633194186662080095093570025917938800079226639565593765455331328')

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('2.0', '15.0', '15252992', '452312848583266388373324160190187140051835877600158453279131187530910662656')

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('2.0', '15.0', '15438249', '904625697166532776746648320380374280103671755200316906558262375061821325312')

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('2.0', '15.0', '15625000', '1809251394333065553493296640760748560207343510400633813116524750123642650624')

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('2.0', '15.0', '15813251', '3618502788666131106986593281521497120414687020801267626233049500247285301248')

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('2.0', '15.0', '16003008', '7237005577332262213973186563042994240829374041602535252466099000494570602496')

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('2.0', '15.0', '16194277', '14474011154664524427946373126085988481658748083205070504932198000989141204992')

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('2.0', '15.0', '16387064', '28948022309329048855892746252171976963317496166410141009864396001978282409984')

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\n", "

('2.0', '15.0', '16581375', '57896044618658097711785492504343953926634992332820282019728792003956564819968')

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\n", " \n", "
\n", "

('2.0', '16.0', '16777216', '115792089237316195423570985008687907853269984665640564039457584007913129639936')

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('2.0', '16.0', '16974593', '231584178474632390847141970017375815706539969331281128078915168015826259279872')

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\n", "

('2.0', '16.0', '17173512', '463168356949264781694283940034751631413079938662562256157830336031652518559744')

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\n", " \n", "
\n", "

('2.0', '16.0', '17373979', '926336713898529563388567880069503262826159877325124512315660672063305037119488')

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\n", " \n", "
\n", "

('2.0', '16.0', '17576000', '1852673427797059126777135760139006525652319754650249024631321344126610074238976')

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\n", "

('2.0', '16.0', '17779581', '3705346855594118253554271520278013051304639509300498049262642688253220148477952')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '17984728', '7410693711188236507108543040556026102609279018600996098525285376506440296955904')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '18191447', '14821387422376473014217086081112052205218558037201992197050570753012880593911808')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '18399744', '29642774844752946028434172162224104410437116074403984394101141506025761187823616')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '18609625', '59285549689505892056868344324448208820874232148807968788202283012051522375647232')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '18821096', '118571099379011784113736688648896417641748464297615937576404566024103044751294464')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '19034163', '237142198758023568227473377297792835283496928595231875152809132048206089502588928')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '19248832', '474284397516047136454946754595585670566993857190463750305618264096412179005177856')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '19465109', '948568795032094272909893509191171341133987714380927500611236528192824358010355712')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '19683000', '1897137590064188545819787018382342682267975428761855001222473056385648716020711424')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '19902511', '3794275180128377091639574036764685364535950857523710002444946112771297432041422848')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '20123648', '7588550360256754183279148073529370729071901715047420004889892225542594864082845696')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '20346417', '15177100720513508366558296147058741458143803430094840009779784451085189728165691392')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '20570824', '30354201441027016733116592294117482916287606860189680019559568902170379456331382784')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '20796875', '60708402882054033466233184588234965832575213720379360039119137804340758912662765568')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '21024576', '121416805764108066932466369176469931665150427440758720078238275608681517825325531136')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '21253933', '242833611528216133864932738352939863330300854881517440156476551217363035650651062272')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '21484952', '485667223056432267729865476705879726660601709763034880312953102434726071301302124544')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '21717639', '971334446112864535459730953411759453321203419526069760625906204869452142602604249088')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '21952000', '1942668892225729070919461906823518906642406839052139521251812409738904285205208498176')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '22188041', '3885337784451458141838923813647037813284813678104279042503624819477808570410416996352')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '22425768', '7770675568902916283677847627294075626569627356208558085007249638955617140820833992704')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '22665187', '15541351137805832567355695254588151253139254712417116170014499277911234281641667985408')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '22906304', '31082702275611665134711390509176302506278509424834232340028998555822468563283335970816')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '23149125', '62165404551223330269422781018352605012557018849668464680057997111644937126566671941632')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '23393656', '124330809102446660538845562036705210025114037699336929360115994223289874253133343883264')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '23639903', '248661618204893321077691124073410420050228075398673858720231988446579748506266687766528')

\n", "
\n", " \n", "
\n", "

('2.0', '16.0', '23887872', '497323236409786642155382248146820840100456150797347717440463976893159497012533375533056')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '24137569', '994646472819573284310764496293641680200912301594695434880927953786318994025066751066112')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '24389000', '1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '24642171', '3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '24897088', '7957171782556586274486115970349133441607298412757563479047423630290551952200534008528896')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '25153757', '15914343565113172548972231940698266883214596825515126958094847260581103904401068017057792')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '25412184', '31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '25672375', '63657374260452690195888927762793067532858387302060507832379389042324415617604272068231168')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '25934336', '127314748520905380391777855525586135065716774604121015664758778084648831235208544136462336')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '26198073', '254629497041810760783555711051172270131433549208242031329517556169297662470417088272924672')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '26463592', '509258994083621521567111422102344540262867098416484062659035112338595324940834176545849344')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '26730899', '1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '27000000', '2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '27270901', '4074071952668972172536891376818756322102936787331872501272280898708762599526673412366794752')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '27543608', '8148143905337944345073782753637512644205873574663745002544561797417525199053346824733589504')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '27818127', '16296287810675888690147565507275025288411747149327490005089123594835050398106693649467179008')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '28094464', '32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '28372625', '65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '28652616', '130370302485407109521180524058200202307293977194619920040712988758680403184853549195737432064')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '28934443', '260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '29218112', '521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '29503629', '1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899456512')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '29791000', '2085924839766513752338888384931203236916703635113918720651407820138886450957656787131798913024')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '30080231', '4171849679533027504677776769862406473833407270227837441302815640277772901915313574263597826048')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '30371328', '8343699359066055009355553539724812947666814540455674882605631280555545803830627148527195652096')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '30664297', '16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '30959144', '33374797436264220037422214158899251790667258161822699530422525122222183215322508594108782608384')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '31255875', '66749594872528440074844428317798503581334516323645399060845050244444366430645017188217565216768')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '31554496', '133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '31855013', '266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '32157432', '533996758980227520598755426542388028650676130589163192486760401955554931445160137505740521734144')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '32461759', '1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '32768000', '2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '33076161', '4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924173873152')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '33386248', '8543948143683640329580086824678208458410818089426611079788166431288878903122562200091848347746304')

\n", "
\n", " \n", "
\n", "

('2.0', '17.0', '33698267', '17087896287367280659160173649356416916821636178853222159576332862577757806245124400183696695492608')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '34012224', '34175792574734561318320347298712833833643272357706444319152665725155515612490248800367393390985216')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '34328125', '68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '34645976', '136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '34965783', '273406340597876490546562778389702670669146178861651554553221325801244124899921990402939147127881728')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '35287552', '546812681195752981093125556779405341338292357723303109106442651602488249799843980805878294255763456')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '35611289', '1093625362391505962186251113558810682676584715446606218212885303204976499599687961611756588511526912')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '35937000', '2187250724783011924372502227117621365353169430893212436425770606409952999199375923223513177023053824')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '36264691', '4374501449566023848745004454235242730706338861786424872851541212819905998398751846447026354046107648')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '36594368', '8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '36926037', '17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '37259704', '34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '37595375', '69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '37933056', '139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '38272753', '279968092772225526319680285071055534765205687154331191862498637620473983897520118172609686658950889472')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '38614472', '559936185544451052639360570142111069530411374308662383724997275240947967795040236345219373317901778944')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '38958219', '1119872371088902105278721140284222139060822748617324767449994550481895935590080472690438746635803557888')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '39304000', '2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '39651821', '4479489484355608421114884561136888556243290994469299069799978201927583742360321890761754986543214231552')

\n", "
\n", " \n", "
\n", "

('2.0', '18.0', '40001688', '8958978968711216842229769122273777112486581988938598139599956403855167484720643781523509973086428463104')

\n", "
\n", " \n", "
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('2.0', '18.0', '40353607', '17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946172856926208')

\n", "
\n", " \n", "
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('2.0', '18.0', '40707584', '35835915874844867368919076489095108449946327955754392558399825615420669938882575126094039892345713852416')

\n", "
\n", " \n", "
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('2.0', '18.0', '41063625', '71671831749689734737838152978190216899892655911508785116799651230841339877765150252188079784691427704832')

\n", "
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('2.0', '18.0', '41421736', '143343663499379469475676305956380433799785311823017570233599302461682679755530300504376159569382855409664')

\n", "
\n", " \n", "
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('2.0', '18.0', '41781923', '286687326998758938951352611912760867599570623646035140467198604923365359511060601008752319138765710819328')

\n", "
\n", " \n", "
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('2.0', '18.0', '42144192', '573374653997517877902705223825521735199141247292070280934397209846730719022121202017504638277531421638656')

\n", "
\n", " \n", "
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('2.0', '18.0', '42508549', '1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555062843277312')

\n", "
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('2.0', '18.0', '42875000', '2293498615990071511610820895302086940796564989168281123737588839386922876088484808070018553110125686554624')

\n", "
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('2.0', '18.0', '43243551', '4586997231980143023221641790604173881593129978336562247475177678773845752176969616140037106220251373109248')

\n", "
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('2.0', '18.0', '43614208', '9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496')

\n", "
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('2.0', '18.0', '43986977', '18347988927920572092886567162416695526372519913346248989900710715095383008707878464560148424881005492436992')

\n", "
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('2.0', '18.0', '44361864', '36695977855841144185773134324833391052745039826692497979801421430190766017415756929120296849762010984873984')

\n", "
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('2.0', '18.0', '44738875', '73391955711682288371546268649666782105490079653384995959602842860381532034831513858240593699524021969747968')

\n", "
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('2.0', '18.0', '45118016', '146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936')

\n", "
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('2.0', '18.0', '45499293', '293567822846729153486185074598667128421960318613539983838411371441526128139326055432962374798096087878991872')

\n", "
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('2.0', '18.0', '45882712', '587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744')

\n", "
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('2.0', '18.0', '46268279', '1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488')

\n", "
\n", " \n", "
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('2.0', '18.0', '46656000', '2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384768703031934976')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '47045881', '4697085165547666455778961193578674054751365097816639741414581943064418050229216886927397996769537406063869952')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '47437928', '9394170331095332911557922387157348109502730195633279482829163886128836100458433773854795993539074812127739904')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '47832147', '18788340662190665823115844774314696219005460391266558965658327772257672200916867547709591987078149624255479808')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '48228544', '37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156299248510959616')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '48627125', '75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '49027896', '150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '49430863', '300613450595050653169853516389035139504087366260264943450533244356122755214669880763353471793250393988087676928')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '49836032', '601226901190101306339707032778070279008174732520529886901066488712245510429339761526706943586500787976175353856')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '50243409', '1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '50653000', '2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003151904701415424')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '51064811', '4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006303809402830848')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '51478848', '9619630419041620901435312524449124464130795720328478190417063819395928166869436184427311097384012607618805661696')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '51895117', '19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '52313624', '38478521676166483605741250097796497856523182881313912761668255277583712667477744737709244389536050430475222646784')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '52734375', '76957043352332967211482500195592995713046365762627825523336510555167425334955489475418488779072100860950445293568')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '53157376', '153914086704665934422965000391185991426092731525255651046673021110334850669910978950836977558144201721900890587136')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '53582633', '307828173409331868845930000782371982852185463050511302093346042220669701339821957901673955116288403443801781174272')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '54010152', '615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576806887603562348544')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '54439939', '1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '54872000', '2462625387274654950767440006258975862817483704404090416746768337765357610718575663213391640930307227550414249394176')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '55306341', '4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498788352')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '55742968', '9850501549098619803069760025035903451269934817616361666987073351061430442874302652853566563721228910201656997576704')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '56181887', '19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '56623104', '39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '57066625', '78804012392788958424558080200287227610159478540930893335896586808491443542994421222828532509769831281613255980613632')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '57512456', '157608024785577916849116160400574455220318957081861786671793173616982887085988842445657065019539662563226511961227264')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '57960603', '315216049571155833698232320801148910440637914163723573343586347233965774171977684891314130039079325126453023922454528')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '58411072', '630432099142311667396464641602297820881275828327447146687172694467931548343955369782628260078158650252906047844909056')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '58863869', '1260864198284623334792929283204595641762551656654894293374345388935863096687910739565256520156317300505812095689818112')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '59319000', '2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '59776471', '5043456793138493339171717132818382567050206626619577173497381555743452386751642958261026080625269202023248382759272448')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '60236288', '10086913586276986678343434265636765134100413253239154346994763111486904773503285916522052161250538404046496765518544896')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '60698457', '20173827172553973356686868531273530268200826506478308693989526222973809547006571833044104322501076808092993531037089792')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '61162984', '40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153616185987062074179584')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '61629875', '80695308690215893426747474125094121072803306025913234775958104891895238188026287332176417290004307232371974124148359168')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '62099136', '161390617380431786853494948250188242145606612051826469551916209783790476376052574664352834580008614464743948248296718336')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '62570773', '322781234760863573706989896500376484291213224103652939103832419567580952752105149328705669160017228929487896496593436672')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '63044792', '645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344')

\n", "
\n", " \n", "
\n", "

('2.0', '19.0', '63521199', '1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '64000000', '2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '64481201', '5164499756173817179311838344006023748659411585658447025661318713081295244033682389259290706560275662871806343945494986752')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '64964808', '10328999512347634358623676688012047497318823171316894051322637426162590488067364778518581413120551325743612687890989973504')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '65450827', '20657999024695268717247353376024094994637646342633788102645274852325180976134729557037162826241102651487225375781979947008')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '65939264', '41315998049390537434494706752048189989275292685267576205290549704650361952269459114074325652482205302974450751563959894016')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '66430125', '82631996098781074868989413504096379978550585370535152410581099409300723904538918228148651304964410605948901503127919788032')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '66923416', '165263992197562149737978827008192759957101170741070304821162198818601447809077836456297302609928821211897803006255839576064')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '67419143', '330527984395124299475957654016385519914202341482140609642324397637202895618155672912594605219857642423795606012511679152128')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '67917312', '661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '68417929', '1322111937580497197903830616065542079656809365928562438569297590548811582472622691650378420879430569695182424050046716608512')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '68921000', '2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '69426531', '5288447750321988791615322464262168318627237463714249754277190362195246329890490766601513683517722278780729696200186866434048')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '69934528', '10576895500643977583230644928524336637254474927428499508554380724390492659780981533203027367035444557561459392400373732868096')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '70444997', '21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '70957944', '42307582002575910332922579714097346549017899709713998034217522897561970639123926132812109468141778230245837569601494931472384')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '71473375', '84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460491675139202989862944768')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '71991296', '169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '72511713', '338460656020607282663380637712778772392143197677711984273740183180495765112991409062496875745134225841966700556811959451779072')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '73034632', '676921312041214565326761275425557544784286395355423968547480366360991530225982818124993751490268451683933401113623918903558144')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '73560059', '1353842624082429130653522550851115089568572790710847937094960732721983060451965636249987502980536903367866802227247837807116288')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '74088000', '2707685248164858261307045101702230179137145581421695874189921465443966120903931272499975005961073806735733604454495675614232576')

\n", "
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\n", "

('2.0', '20.0', '74618461', '5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '75151448', '10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '75686967', '21661481985318866090456360813617841433097164651373566993519371723551728967231450179999800047688590453885868835635965404913860608')

\n", "
\n", " \n", "
\n", "

('2.0', '20.0', '76225024', '43322963970637732180912721627235682866194329302747133987038743447103457934462900359999600095377180907771737671271930809827721216')

\n", "
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\n", "

('2.0', '20.0', '76765625', '86645927941275464361825443254471365732388658605494267974077486894206915868925800719999200190754361815543475342543861619655442432')

\n", "
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\n", "

('2.0', '20.0', '77308776', '173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631086950685087723239310884864')

\n", "
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('2.0', '20.0', '77854483', '346583711765101857447301773017885462929554634421977071896309947576827663475703202879996800763017447262173901370175446478621769728')

\n", "
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('2.0', '20.0', '78402752', '693167423530203714894603546035770925859109268843954143792619895153655326951406405759993601526034894524347802740350892957243539456')

\n", "
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\n", "

('2.0', '20.0', '78953589', '1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912')

\n", "
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\n", "

('2.0', '20.0', '79507000', '2772669694120814859578414184143083703436437075375816575170479580614621307805625623039974406104139578097391210961403571828974157824')

\n", "
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\n", "

('2.0', '20.0', '80062991', '5545339388241629719156828368286167406872874150751633150340959161229242615611251246079948812208279156194782421922807143657948315648')

\n", "
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\n", "

('2.0', '20.0', '80621568', '11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296')

\n", "
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\n", "

('2.0', '20.0', '81182737', '22181357552966518876627313473144669627491496603006532601363836644916970462445004984319795248833116624779129687691228574631793262592')

\n", "
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\n", "

('2.0', '20.0', '81746504', '44362715105933037753254626946289339254982993206013065202727673289833940924890009968639590497666233249558259375382457149263586525184')

\n", "
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('2.0', '20.0', '82312875', '88725430211866075506509253892578678509965986412026130405455346579667881849780019937279180995332466499116518750764914298527173050368')

\n", "
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('2.0', '20.0', '82881856', '177450860423732151013018507785157357019931972824052260810910693159335763699560039874558361990664932998233037501529828597054346100736')

\n", "
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('2.0', '20.0', '83453453', '354901720847464302026037015570314714039863945648104521621821386318671527399120079749116723981329865996466075003059657194108692201472')

\n", "
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('2.0', '20.0', '84027672', '709803441694928604052074031140629428079727891296209043243642772637343054798240159498233447962659731992932150006119314388217384402944')

\n", "
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('2.0', '20.0', '84604519', '1419606883389857208104148062281258856159455782592418086487285545274686109596480318996466895925319463985864300012238628776434768805888')

\n", "
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('2.0', '20.0', '85184000', '2839213766779714416208296124562517712318911565184836172974571090549372219192960637992933791850638927971728600024477257552869537611776')

\n", "
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\n", "

('2.0', '21.0', '85766121', '5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552')

\n", "
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('2.0', '21.0', '86350888', '11356855067118857664833184498250070849275646260739344691898284362197488876771842551971735167402555711886914400097909030211478150447104')

\n", "
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('2.0', '21.0', '86938307', '22713710134237715329666368996500141698551292521478689383796568724394977753543685103943470334805111423773828800195818060422956300894208')

\n", "
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('2.0', '21.0', '87528384', '45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657600391636120845912601788416')

\n", "
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('2.0', '21.0', '88121125', '90854840536950861318665475986000566794205170085914757535186274897579911014174740415773881339220445695095315200783272241691825203576832')

\n", "
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('2.0', '21.0', '88716536', '181709681073901722637330951972001133588410340171829515070372549795159822028349480831547762678440891390190630401566544483383650407153664')

\n", "
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('2.0', '21.0', '89314623', '363419362147803445274661903944002267176820680343659030140745099590319644056698961663095525356881782780381260803133088966767300814307328')

\n", "
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('2.0', '21.0', '89915392', '726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656')

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('2.0', '21.0', '90518849', '1453677448591213781098647615776009068707282721374636120562980398361278576226795846652382101427527131121525043212532355867069203257229312')

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('2.0', '21.0', '91125000', '2907354897182427562197295231552018137414565442749272241125960796722557152453591693304764202855054262243050086425064711734138406514458624')

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('2.0', '21.0', '91733851', '5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248')

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('2.0', '21.0', '92345408', '11629419588729710248789180926208072549658261770997088964503843186890228609814366773219056811420217048972200345700258846936553626057834496')

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('2.0', '21.0', '92959677', '23258839177459420497578361852416145099316523541994177929007686373780457219628733546438113622840434097944400691400517693873107252115668992')

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('2.0', '21.0', '93576664', '46517678354918840995156723704832290198633047083988355858015372747560914439257467092876227245680868195888801382801035387746214504231337984')

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('2.0', '21.0', '94196375', '93035356709837681990313447409664580397266094167976711716030745495121828878514934185752454491361736391777602765602070775492429008462675968')

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('2.0', '21.0', '94818816', '186070713419675363980626894819329160794532188335953423432061490990243657757029868371504908982723472783555205531204141550984858016925351936')

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('2.0', '21.0', '95443993', '372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872')

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('2.0', '21.0', '96071912', '744282853678701455922507579277316643178128753343813693728245963960974631028119473486019635930893891134220822124816566203939432067701407744')

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('2.0', '21.0', '96702579', '1488565707357402911845015158554633286356257506687627387456491927921949262056238946972039271861787782268441644249633132407878864135402815488')

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('2.0', '21.0', '97336000', '2977131414714805823690030317109266572712515013375254774912983855843898524112477893944078543723575564536883288499266264815757728270805630976')

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('2.0', '21.0', '97972181', '5954262829429611647380060634218533145425030026750509549825967711687797048224955787888157087447151129073766576998532529631515456541611261952')

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('2.0', '21.0', '98611128', '11908525658859223294760121268437066290850060053501019099651935423375594096449911575776314174894302258147533153997065059263030913083222523904')

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('2.0', '21.0', '99252847', '23817051317718446589520242536874132581700120107002038199303870846751188192899823151552628349788604516295066307994130118526061826166445047808')

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('2.0', '21.0', '99897344', '47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616')

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('2.0', '21.0', '100544625', '95268205270873786358080970147496530326800480428008152797215483387004752771599292606210513399154418065180265231976520474104247304665780191232')

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('2.0', '21.0', '101194696', '190536410541747572716161940294993060653600960856016305594430966774009505543198585212421026798308836130360530463953040948208494609331560382464')

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('2.0', '21.0', '101847563', '381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928')

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('2.0', '21.0', '102503232', '762145642166990290864647761179972242614403843424065222377723867096038022172794340849684107193235344521442121855812163792833978437326241529856')

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('2.0', '21.0', '103161709', '1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711624327585667956874652483059712')

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('2.0', '21.0', '103823000', '3048582568667961163458591044719888970457615373696260889510895468384152088691177363398736428772941378085768487423248655171335913749304966119424')

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('2.0', '21.0', '104487111', '6097165137335922326917182089439777940915230747392521779021790936768304177382354726797472857545882756171536974846497310342671827498609932238848')

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('2.0', '21.0', '105154048', '12194330274671844653834364178879555881830461494785043558043581873536608354764709453594945715091765512343073949692994620685343654997219864477696')

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('2.0', '21.0', '105823817', '24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899385989241370687309994439728955392')

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('2.0', '21.0', '106496424', '48777321098687378615337456715518223527321845979140174232174327494146433419058837814379782860367062049372295798771978482741374619988879457910784')

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('2.0', '21.0', '107171875', '97554642197374757230674913431036447054643691958280348464348654988292866838117675628759565720734124098744591597543956965482749239977758915821568')

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('2.0', '21.0', '107850176', '195109284394749514461349826862072894109287383916560696928697309976585733676235351257519131441468248197489183195087913930965498479955517831643136')

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('2.0', '21.0', '108531333', '390218568789499028922699653724145788218574767833121393857394619953171467352470702515038262882936496394978366390175827861930996959911035663286272')

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('2.0', '21.0', '109215352', '780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544')

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('2.0', '21.0', '109902239', '1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088')

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('2.0', '21.0', '110592000', '3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176')

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('2.0', '21.0', '111284641', '6243497100631984462763194459586332611497196285329942301718313919250743477639531240240612206126983942319653862242813245790895951358576570612580352')

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('2.0', '21.0', '111980168', '12486994201263968925526388919172665222994392570659884603436627838501486955279062480481224412253967884639307724485626491581791902717153141225160704')

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('2.0', '21.0', '112678587', '24973988402527937851052777838345330445988785141319769206873255677002973910558124960962448824507935769278615448971252983163583805434306282450321408')

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('2.0', '22.0', '113379904', '49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816')

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('2.0', '22.0', '114084125', '99895953610111751404211111353381321783955140565279076827493022708011895642232499843849795298031743077114461795885011932654335221737225129801285632')

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('2.0', '22.0', '114791256', '199791907220223502808422222706762643567910281130558153654986045416023791284464999687699590596063486154228923591770023865308670443474450259602571264')

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('2.0', '22.0', '115501303', '399583814440447005616844445413525287135820562261116307309972090832047582568929999375399181192126972308457847183540047730617340886948900519205142528')

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('2.0', '22.0', '116214272', '799167628880894011233688890827050574271641124522232614619944181664095165137859998750798362384253944616915694367080095461234681773897801038410285056')

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('2.0', '22.0', '116930169', '1598335257761788022467377781654101148543282249044465229239888363328190330275719997501596724768507889233831388734160190922469363547795602076820570112')

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('2.0', '22.0', '117649000', '3196670515523576044934755563308202297086564498088930458479776726656380660551439995003193449537015778467662777468320381844938727095591204153641140224')

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('2.0', '22.0', '118370771', '6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448')

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('2.0', '22.0', '119095488', '12786682062094304179739022253232809188346257992355721833919106906625522642205759980012773798148063113870651109873281527379754908382364816614564560896')

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('2.0', '22.0', '119823157', '25573364124188608359478044506465618376692515984711443667838213813251045284411519960025547596296126227741302219746563054759509816764729633229129121792')

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('2.0', '22.0', '120553784', '51146728248377216718956089012931236753385031969422887335676427626502090568823039920051095192592252455482604439493126109519019633529459266458258243584')

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('2.0', '22.0', '121287375', '102293456496754433437912178025862473506770063938845774671352855253004181137646079840102190385184504910965208878986252219038039267058918532916516487168')

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('2.0', '22.0', '122023936', '204586912993508866875824356051724947013540127877691549342705710506008362275292159680204380770369009821930417757972504438076078534117837065833032974336')

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('2.0', '22.0', '122763473', '409173825987017733751648712103449894027080255755383098685411421012016724550584319360408761540738019643860835515945008876152157068235674131666065948672')

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('2.0', '22.0', '123505992', '818347651974035467503297424206899788054160511510766197370822842024033449101168638720817523081476039287721671031890017752304314136471348263332131897344')

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('2.0', '22.0', '124251499', '1636695303948070935006594848413799576108321023021532394741645684048066898202337277441635046162952078575443342063780035504608628272942696526664263794688')

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('2.0', '22.0', '125000000', '3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376')

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('2.0', '22.0', '125751501', '6546781215792283740026379393655198304433284092086129578966582736192267592809349109766540184651808314301773368255120142018434513091770786106657055178752')

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('2.0', '22.0', '126506008', '13093562431584567480052758787310396608866568184172259157933165472384535185618698219533080369303616628603546736510240284036869026183541572213314110357504')

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('2.0', '22.0', '127263527', '26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008')

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('2.0', '22.0', '128024064', '52374249726338269920211035149241586435466272736689036631732661889538140742474792878132321477214466514414186946040961136147476104734166288853256441430016')

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('2.0', '22.0', '128787625', '104748499452676539840422070298483172870932545473378073263465323779076281484949585756264642954428933028828373892081922272294952209468332577706512882860032')

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('2.0', '22.0', '129554216', '209496998905353079680844140596966345741865090946756146526930647558152562969899171512529285908857866057656747784163844544589904418936665155413025765720064')

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('2.0', '22.0', '130323843', '418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689089179808837873330310826051531440128')

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('2.0', '22.0', '131096512', '837987995621412318723376562387865382967460363787024586107722590232610251879596686050117143635431464230626991136655378178359617675746660621652103062880256')

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('2.0', '22.0', '131872229', '1675975991242824637446753124775730765934920727574049172215445180465220503759193372100234287270862928461253982273310756356719235351493321243304206125760512')

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('2.0', '22.0', '132651000', '3351951982485649274893506249551461531869841455148098344430890360930441007518386744200468574541725856922507964546621512713438470702986642486608412251521024')

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('2.0', '22.0', '133432831', '6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048')

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('2.0', '22.0', '134217728', '13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096')

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('2.0', '22.0', '135005697', '26815615859885194199148049996411692254958731641184786755447122887443528060147093953603748596333806855380063716372972101707507765623893139892867298012168192')

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('2.0', '22.0', '135796744', '53631231719770388398296099992823384509917463282369573510894245774887056120294187907207497192667613710760127432745944203415015531247786279785734596024336384')

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('2.0', '22.0', '136590875', '107262463439540776796592199985646769019834926564739147021788491549774112240588375814414994385335227421520254865491888406830031062495572559571469192048672768')

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('2.0', '22.0', '137388096', '214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536')

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('2.0', '22.0', '138188413', '429049853758163107186368799942587076079339706258956588087153966199096448962353503257659977541340909686081019461967553627320124249982290238285876768194691072')

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('2.0', '22.0', '138991832', '858099707516326214372737599885174152158679412517913176174307932398192897924707006515319955082681819372162038923935107254640248499964580476571753536389382144')

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('2.0', '22.0', '139798359', '1716199415032652428745475199770348304317358825035826352348615864796385795849414013030639910165363638744324077847870214509280496999929160953143507072778764288')

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('2.0', '22.0', '140608000', '3432398830065304857490950399540696608634717650071652704697231729592771591698828026061279820330727277488648155695740429018560993999858321906287014145557528576')

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('2.0', '22.0', '141420761', '6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057152')

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('2.0', '22.0', '142236648', '13729595320261219429963801598162786434538870600286610818788926918371086366795312104245119281322909109954592622782961716074243975999433287625148056582230114304')

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('2.0', '22.0', '143055667', '27459190640522438859927603196325572869077741200573221637577853836742172733590624208490238562645818219909185245565923432148487951998866575250296113164460228608')

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('2.0', '22.0', '143877824', '54918381281044877719855206392651145738155482401146443275155707673484345467181248416980477125291636439818370491131846864296975903997733150500592226328920457216')

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('2.0', '22.0', '144703125', '109836762562089755439710412785302291476310964802292886550311415346968690934362496833960954250583272879636740982263693728593951807995466301001184452657840914432')

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('2.0', '22.0', '145531576', '219673525124179510879420825570604582952621929604585773100622830693937381868724993667921908501166545759273481964527387457187903615990932602002368905315681828864')

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('2.0', '22.0', '146363183', '439347050248359021758841651141209165905243859209171546201245661387874763737449987335843817002333091518546963929054774914375807231981865204004737810631363657728')

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('2.0', '22.0', '147197952', '878694100496718043517683302282418331810487718418343092402491322775749527474899974671687634004666183037093927858109549828751614463963730408009475621262727315456')

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('2.0', '23.0', '148035889', '1757388200993436087035366604564836663620975436836686184804982645551499054949799949343375268009332366074187855716219099657503228927927460816018951242525454630912')

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('2.0', '23.0', '148877000', '3514776401986872174070733209129673327241950873673372369609965291102998109899599898686750536018664732148375711432438199315006457855854921632037902485050909261824')

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('2.0', '23.0', '149721291', '7029552803973744348141466418259346654483901747346744739219930582205996219799199797373501072037329464296751422864876398630012915711709843264075804970101818523648')

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('2.0', '23.0', '150568768', '14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296')

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('2.0', '23.0', '151419437', '28118211215894977392565865673037386617935606989386978956879722328823984879196799189494004288149317857187005691459505594520051662846839373056303219880407274094592')

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('2.0', '23.0', '152273304', '56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184')

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('2.0', '23.0', '153130375', '112472844863579909570263462692149546471742427957547915827518889315295939516787196757976017152597271428748022765838022378080206651387357492225212879521629096378368')

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('2.0', '23.0', '153990656', '224945689727159819140526925384299092943484855915095831655037778630591879033574393515952034305194542857496045531676044756160413302774714984450425759043258192756736')

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('2.0', '23.0', '154854153', '449891379454319638281053850768598185886969711830191663310075557261183758067148787031904068610389085714992091063352089512320826605549429968900851518086516385513472')

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('2.0', '23.0', '155720872', '899782758908639276562107701537196371773939423660383326620151114522367516134297574063808137220778171429984182126704179024641653211098859937801703036173032771026944')

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('2.0', '23.0', '156590819', '1799565517817278553124215403074392743547878847320766653240302229044735032268595148127616274441556342859968364253408358049283306422197719875603406072346065542053888')

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('2.0', '23.0', '157464000', '3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776')

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('2.0', '23.0', '158340421', '7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552')

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('2.0', '23.0', '159220088', '14396524142538228424993723224595141948383030778566133225922417832357880258148761185020930195532450742879746914027266864394266451377581759004827248578768524336431104')

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('2.0', '23.0', '160103007', '28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208')

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('2.0', '23.0', '160989184', '57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416')

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('2.0', '23.0', '161878625', '115172193140305827399949785796761135587064246228529065807379342658863042065190089480167441564259605943037975312218134915154131611020654072038617988630148194691448832')

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('2.0', '23.0', '162771336', '230344386280611654799899571593522271174128492457058131614758685317726084130380178960334883128519211886075950624436269830308263222041308144077235977260296389382897664')

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('2.0', '23.0', '163667323', '460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328')

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('2.0', '23.0', '164566592', '921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185557531590656')

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('2.0', '23.0', '165469149', '1842755090244893238399196572748178169393027939656465052918069482541808673043041431682679065028153695088607604995490158642466105776330465152617887818082371115063181312')

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('2.0', '23.0', '166375000', '3685510180489786476798393145496356338786055879312930105836138965083617346086082863365358130056307390177215209990980317284932211552660930305235775636164742230126362624')

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('2.0', '23.0', '167284151', '7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248')

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('2.0', '23.0', '168196608', '14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496')

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('2.0', '23.0', '169112377', '29484081443918291814387145163970850710288447034503440846689111720668938768688662906922865040450459121417721679927842538279457692421287442441886205089317937841010900992')

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('2.0', '23.0', '170031464', '58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984')

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('2.0', '23.0', '170953875', '117936325775673167257548580655883402841153788138013763386756446882675755074754651627691460161801836485670886719711370153117830769685149769767544820357271751364043603968')

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('2.0', '23.0', '171879616', '235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936')

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('2.0', '23.0', '172808693', '471745303102692669030194322623533611364615152552055053547025787530703020299018606510765840647207345942683546878845480612471323078740599079070179281429087005456174415872')

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('2.0', '23.0', '173741112', '943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744')

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('2.0', '23.0', '174676879', '1886981212410770676120777290494134445458460610208220214188103150122812081196074426043063362588829383770734187515381922449885292314962396316280717125716348021824697663488')

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('2.0', '23.0', '175616000', '3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976')

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('2.0', '23.0', '176558481', '7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952')

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('2.0', '23.0', '177504328', '15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904')

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('2.0', '23.0', '178453547', '30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808')

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('2.0', '23.0', '179406144', '60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616')

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('2.0', '23.0', '180362125', '120766797594289323271729746591624604509341479053326093708038601607859973196548763266756055205685080561326988000984443036792658708157593364241965896045846273396780650463232')

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('2.0', '23.0', '181321496', '241533595188578646543459493183249209018682958106652187416077203215719946393097526533512110411370161122653976001968886073585317416315186728483931792091692546793561300926464')

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('2.0', '23.0', '182284263', '483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928')

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('2.0', '23.0', '183250432', '966134380754314586173837972732996836074731832426608749664308812862879785572390106134048441645480644490615904007875544294341269665260746913935727168366770187174245203705856')

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('2.0', '23.0', '184220009', '1932268761508629172347675945465993672149463664853217499328617625725759571144780212268096883290961288981231808015751088588682539330521493827871454336733540374348490407411712')

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('2.0', '23.0', '185193000', '3864537523017258344695351890931987344298927329706434998657235251451519142289560424536193766581922577962463616031502177177365078661042987655742908673467080748696980814823424')

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('2.0', '23.0', '186169411', '7729075046034516689390703781863974688597854659412869997314470502903038284579120849072387533163845155924927232063004354354730157322085975311485817346934161497393961629646848')

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('2.0', '23.0', '187149248', '15458150092069033378781407563727949377195709318825739994628941005806076569158241698144775066327690311849854464126008708709460314644171950622971634693868322994787923259293696')

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('2.0', '23.0', '188132517', '30916300184138066757562815127455898754391418637651479989257882011612153138316483396289550132655380623699708928252017417418920629288343901245943269387736645989575846518587392')

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('2.0', '23.0', '189119224', '61832600368276133515125630254911797508782837275302959978515764023224306276632966792579100265310761247399417856504034834837841258576687802491886538775473291979151693037174784')

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('2.0', '23.0', '190109375', '123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568')

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('2.0', '24.0', '191102976', '247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136')

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('2.0', '24.0', '192100033', '494660802946209068121005042039294380070262698202423679828126112185794450213063734340632802122486089979195342852032278678702730068613502419935092310203786335833213544297398272')

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('2.0', '24.0', '193100552', '989321605892418136242010084078588760140525396404847359656252224371588900426127468681265604244972179958390685704064557357405460137227004839870184620407572671666427088594796544')

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('2.0', '24.0', '194104539', '1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088')

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('2.0', '24.0', '195112000', '3957286423569672544968040336314355040562101585619389438625008897486355601704509874725062416979888719833562742816258229429621840548908019359480738481630290686665708354379186176')

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('2.0', '24.0', '196122941', '7914572847139345089936080672628710081124203171238778877250017794972711203409019749450124833959777439667125485632516458859243681097816038718961476963260581373331416708758372352')

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('2.0', '24.0', '197137368', '15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662833417516744704')

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('2.0', '24.0', '198155287', '31658291388557380359744322690514840324496812684955115509000071179890844813636078997800499335839109758668501942530065835436974724391264154875845907853042325493325666835033489408')

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('2.0', '24.0', '199176704', '63316582777114760719488645381029680648993625369910231018000142359781689627272157995600998671678219517337003885060131670873949448782528309751691815706084650986651333670066978816')

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('2.0', '24.0', '200201625', '126633165554229521438977290762059361297987250739820462036000284719563379254544315991201997343356439034674007770120263341747898897565056619503383631412169301973302667340133957632')

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('2.0', '24.0', '201230056', '253266331108459042877954581524118722595974501479640924072000569439126758509088631982403994686712878069348015540240526683495797795130113239006767262824338603946605334680267915264')

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('2.0', '24.0', '202262003', '506532662216918085755909163048237445191949002959281848144001138878253517018177263964807989373425756138696031080481053366991595590260226478013534525648677207893210669360535830528')

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('2.0', '24.0', '203297472', '1013065324433836171511818326096474890383898005918563696288002277756507034036354527929615978746851512277392062160962106733983191180520452956027069051297354415786421338721071661056')

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('2.0', '24.0', '204336469', '2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112')

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('2.0', '24.0', '205379000', '4052261297735344686047273304385899561535592023674254785152009111026028136145418111718463914987406049109568248643848426935932764722081811824108276205189417663145685354884286644224')

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('2.0', '24.0', '206425071', '8104522595470689372094546608771799123071184047348509570304018222052056272290836223436927829974812098219136497287696853871865529444163623648216552410378835326291370709768573288448')

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('2.0', '24.0', '207474688', '16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896')

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('2.0', '24.0', '208527857', '32418090381882757488378186435087196492284736189394038281216072888208225089163344893747711319899248392876545989150787415487462117776654494592866209641515341305165482839074293153792')

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('2.0', '24.0', '209584584', '64836180763765514976756372870174392984569472378788076562432145776416450178326689787495422639798496785753091978301574830974924235553308989185732419283030682610330965678148586307584')

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('2.0', '24.0', '210644875', '129672361527531029953512745740348785969138944757576153124864291552832900356653379574990845279596993571506183956603149661949848471106617978371464838566061365220661931356297172615168')

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('2.0', '24.0', '211708736', '259344723055062059907025491480697571938277889515152306249728583105665800713306759149981690559193987143012367913206299323899696942213235956742929677132122730441323862712594345230336')

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('2.0', '24.0', '212776173', '518689446110124119814050982961395143876555779030304612499457166211331601426613518299963381118387974286024735826412598647799393884426471913485859354264245460882647725425188690460672')

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('2.0', '24.0', '213847192', '1037378892220248239628101965922790287753111558060609224998914332422663202853227036599926762236775948572049471652825197295598787768852943826971718708528490921765295450850377380921344')

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('2.0', '24.0', '214921799', '2074757784440496479256203931845580575506223116121218449997828664845326405706454073199853524473551897144098943305650394591197575537705887653943437417056981843530590901700754761842688')

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('2.0', '24.0', '216000000', '4149515568880992958512407863691161151012446232242436899995657329690652811412908146399707048947103794288197886611300789182395151075411775307886874834113963687061181803401509523685376')

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('2.0', '24.0', '217081801', '8299031137761985917024815727382322302024892464484873799991314659381305622825816292799414097894207588576395773222601578364790302150823550615773749668227927374122363606803019047370752')

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('2.0', '24.0', '218167208', '16598062275523971834049631454764644604049784928969747599982629318762611245651632585598828195788415177152791546445203156729580604301647101231547499336455854748244727213606038094741504')

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('2.0', '24.0', '219256227', '33196124551047943668099262909529289208099569857939495199965258637525222491303265171197656391576830354305583092890406313459161208603294202463094998672911709496489454427212076189483008')

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('2.0', '24.0', '220348864', '66392249102095887336198525819058578416199139715878990399930517275050444982606530342395312783153660708611166185780812626918322417206588404926189997345823418992978908854424152378966016')

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('2.0', '24.0', '221445125', '132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032')

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('2.0', '24.0', '222545016', '265568996408383549344794103276234313664796558863515961599722069100201779930426121369581251132614642834444664743123250507673289668826353619704759989383293675971915635417696609515864064')

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('2.0', '24.0', '223648543', '531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728128')

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('2.0', '24.0', '224755712', '1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957533174703887662541670786438063456256')

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('2.0', '24.0', '225866529', '2124551971267068394758352826209874509318372470908127692797776552801614239443408970956650009060917142675557317944986004061386317350610828957638079915066349407775325083341572876126912512')

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('2.0', '24.0', '226981000', '4249103942534136789516705652419749018636744941816255385595553105603228478886817941913300018121834285351114635889972008122772634701221657915276159830132698815550650166683145752253825024')

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('2.0', '24.0', '228099131', '8498207885068273579033411304839498037273489883632510771191106211206456957773635883826600036243668570702229271779944016245545269402443315830552319660265397631101300333366291504507650048')

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('2.0', '24.0', '229220928', '16996415770136547158066822609678996074546979767265021542382212422412913915547271767653200072487337141404458543559888032491090538804886631661104639320530795262202600666732583009015300096')

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('2.0', '24.0', '230346397', '33992831540273094316133645219357992149093959534530043084764424844825827831094543535306400144974674282808917087119776064982181077609773263322209278641061590524405201333465166018030600192')

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('2.0', '24.0', '231475544', '67985663080546188632267290438715984298187919069060086169528849689651655662189087070612800289949348565617834174239552129964362155219546526644418557282123181048810402666930332036061200384')

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('2.0', '24.0', '232608375', '135971326161092377264534580877431968596375838138120172339057699379303311324378174141225600579898697131235668348479104259928724310439093053288837114564246362097620805333860664072122400768')

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('2.0', '24.0', '233744896', '271942652322184754529069161754863937192751676276240344678115398758606622648756348282451201159797394262471336696958208519857448620878186106577674229128492724195241610667721328144244801536')

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('2.0', '24.0', '234885113', '543885304644369509058138323509727874385503352552480689356230797517213245297512696564902402319594788524942673393916417039714897241756372213155348458256985448390483221335442656288489603072')

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('2.0', '24.0', '236029032', '1087770609288739018116276647019455748771006705104961378712461595034426490595025393129804804639189577049885346787832834079429794483512744426310696916513970896780966442670885312576979206144')

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('2.0', '24.0', '237176659', '2175541218577478036232553294038911497542013410209922757424923190068852981190050786259609609278379154099770693575665668158859588967025488852621393833027941793561932885341770625153958412288')

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('2.0', '24.0', '238328000', '4351082437154956072465106588077822995084026820419845514849846380137705962380101572519219218556758308199541387151331336317719177934050977705242787666055883587123865770683541250307916824576')

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('2.0', '24.0', '239483061', '8702164874309912144930213176155645990168053640839691029699692760275411924760203145038438437113516616399082774302662672635438355868101955410485575332111767174247731541367082500615833649152')

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('2.0', '24.0', '240641848', '17404329748619824289860426352311291980336107281679382059399385520550823849520406290076876874227033232798165548605325345270876711736203910820971150664223534348495463082734165001231667298304')

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('2.0', '24.0', '241804367', '34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608')

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('2.0', '24.0', '242970624', '69617318994479297159441705409245167921344429126717528237597542082203295398081625160307507496908132931192662194421301381083506846944815643283884602656894137393981852330936660004926669193216')

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('2.0', '25.0', '244140625', '139234637988958594318883410818490335842688858253435056475195084164406590796163250320615014993816265862385324388842602762167013693889631286567769205313788274787963704661873320009853338386432')

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('2.0', '25.0', '245314376', '278469275977917188637766821636980671685377716506870112950390168328813181592326500641230029987632531724770648777685205524334027387779262573135538410627576549575927409323746640019706676772864')

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('2.0', '25.0', '246491883', '556938551955834377275533643273961343370755433013740225900780336657626363184653001282460059975265063449541297555370411048668054775558525146271076821255153099151854818647493280039413353545728')

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('2.0', '25.0', '247673152', '1113877103911668754551067286547922686741510866027480451801560673315252726369306002564920119950530126899082595110740822097336109551117050292542153642510306198303709637294986560078826707091456')

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('2.0', '25.0', '248858189', '2227754207823337509102134573095845373483021732054960903603121346630505452738612005129840239901060253798165190221481644194672219102234100585084307285020612396607419274589973120157653414182912')

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('2.0', '25.0', '250047000', '4455508415646675018204269146191690746966043464109921807206242693261010905477224010259680479802120507596330380442963288389344438204468201170168614570041224793214838549179946240315306828365824')

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('2.0', '25.0', '251239591', '8911016831293350036408538292383381493932086928219843614412485386522021810954448020519360959604241015192660760885926576778688876408936402340337229140082449586429677098359892480630613656731648')

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('2.0', '25.0', '252435968', '17822033662586700072817076584766762987864173856439687228824970773044043621908896041038721919208482030385321521771853153557377752817872804680674458280164899172859354196719784961261227313463296')

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('2.0', '25.0', '253636137', '35644067325173400145634153169533525975728347712879374457649941546088087243817792082077443838416964060770643043543706307114755505635745609361348916560329798345718708393439569922522454626926592')

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('2.0', '25.0', '254840104', '71288134650346800291268306339067051951456695425758748915299883092176174487635584164154887676833928121541286087087412614229511011271491218722697833120659596691437416786879139845044909253853184')

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('2.0', '25.0', '256047875', '142576269300693600582536612678134103902913390851517497830599766184352348975271168328309775353667856243082572174174825228459022022542982437445395666241319193382874833573758279690089818507706368')

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('2.0', '25.0', '257259456', '285152538601387201165073225356268207805826781703034995661199532368704697950542336656619550707335712486165144348349650456918044045085964874890791332482638386765749667147516559380179637015412736')

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('2.0', '25.0', '258474853', '570305077202774402330146450712536415611653563406069991322399064737409395901084673313239101414671424972330288696699300913836088090171929749781582664965276773531499334295033118760359274030825472')

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('2.0', '25.0', '259694072', '1140610154405548804660292901425072831223307126812139982644798129474818791802169346626478202829342849944660577393398601827672176180343859499563165329930553547062998668590066237520718548061650944')

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('2.0', '25.0', '260917119', '2281220308811097609320585802850145662446614253624279965289596258949637583604338693252956405658685699889321154786797203655344352360687718999126330659861107094125997337180132475041437096123301888')

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('2.0', '25.0', '262144000', '4562440617622195218641171605700291324893228507248559930579192517899275167208677386505912811317371399778642309573594407310688704721375437998252661319722214188251994674360264950082874192246603776')

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('2.0', '25.0', '263374721', '9124881235244390437282343211400582649786457014497119861158385035798550334417354773011825622634742799557284619147188814621377409442750875996505322639444428376503989348720529900165748384493207552')

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('2.0', '25.0', '264609288', '18249762470488780874564686422801165299572914028994239722316770071597100668834709546023651245269485599114569238294377629242754818885501751993010645278888856753007978697441059800331496768986415104')

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('2.0', '25.0', '265847707', '36499524940977561749129372845602330599145828057988479444633540143194201337669419092047302490538971198229138476588755258485509637771003503986021290557777713506015957394882119600662993537972830208')

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('2.0', '25.0', '267089984', '72999049881955123498258745691204661198291656115976958889267080286388402675338838184094604981077942396458276953177510516971019275542007007972042581115555427012031914789764239201325987075945660416')

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('2.0', '25.0', '268336125', '145998099763910246996517491382409322396583312231953917778534160572776805350677676368189209962155884792916553906355021033942038551084014015944085162231110854024063829579528478402651974151891320832')

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('2.0', '25.0', '269586136', '291996199527820493993034982764818644793166624463907835557068321145553610701355352736378419924311769585833107812710042067884077102168028031888170324462221708048127659159056956805303948303782641664')

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('2.0', '25.0', '270840023', '583992399055640987986069965529637289586333248927815671114136642291107221402710705472756839848623539171666215625420084135768154204336056063776340648924443416096255318318113913610607896607565283328')

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('2.0', '25.0', '272097792', '1167984798111281975972139931059274579172666497855631342228273284582214442805421410945513679697247078343332431250840168271536308408672112127552681297848886832192510636636227827221215793215130566656')

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('2.0', '25.0', '273359449', '2335969596222563951944279862118549158345332995711262684456546569164428885610842821891027359394494156686664862501680336543072616817344224255105362595697773664385021273272455654442431586430261133312')

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('2.0', '25.0', '274625000', '4671939192445127903888559724237098316690665991422525368913093138328857771221685643782054718788988313373329725003360673086145233634688448510210725191395547328770042546544911308884863172860522266624')

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('2.0', '25.0', '275894451', '9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248')

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('2.0', '25.0', '277167808', '18687756769780511615554238896948393266762663965690101475652372553315431084886742575128218875155953253493318900013442692344580934538753794040842900765582189315080170186179645235539452691442089066496')

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('2.0', '25.0', '278445077', '37375513539561023231108477793896786533525327931380202951304745106630862169773485150256437750311906506986637800026885384689161869077507588081685801531164378630160340372359290471078905382884178132992')

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('2.0', '25.0', '279726264', '74751027079122046462216955587793573067050655862760405902609490213261724339546970300512875500623813013973275600053770769378323738155015176163371603062328757260320680744718580942157810765768356265984')

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('2.0', '25.0', '281011375', '149502054158244092924433911175587146134101311725520811805218980426523448679093940601025751001247626027946551200107541538756647476310030352326743206124657514520641361489437161884315621531536712531968')

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('2.0', '25.0', '282300416', '299004108316488185848867822351174292268202623451041623610437960853046897358187881202051502002495252055893102400215083077513294952620060704653486412249315029041282722978874323768631243063073425063936')

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('2.0', '25.0', '283593393', '598008216632976371697735644702348584536405246902083247220875921706093794716375762404103004004990504111786204800430166155026589905240121409306972824498630058082565445957748647537262486126146850127872')

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('2.0', '25.0', '284890312', '1196016433265952743395471289404697169072810493804166494441751843412187589432751524808206008009981008223572409600860332310053179810480242818613945648997260116165130891915497295074524972252293700255744')

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('2.0', '25.0', '286191179', '2392032866531905486790942578809394338145620987608332988883503686824375178865503049616412016019962016447144819201720664620106359620960485637227891297994520232330261783830994590149049944504587400511488')

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('2.0', '25.0', '287496000', '4784065733063810973581885157618788676291241975216665977767007373648750357731006099232824032039924032894289638403441329240212719241920971274455782595989040464660523567661989180298099889009174801022976')

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('2.0', '25.0', '288804781', '9568131466127621947163770315237577352582483950433331955534014747297500715462012198465648064079848065788579276806882658480425438483841942548911565191978080929321047135323978360596199778018349602045952')

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('2.0', '25.0', '290117528', '19136262932255243894327540630475154705164967900866663911068029494595001430924024396931296128159696131577158553613765316960850876967683885097823130383956161858642094270647956721192399556036699204091904')

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('2.0', '25.0', '292754944', '76545051729020975577310162521900618820659871603466655644272117978380005723696097587725184512638784526308634214455061267843403507870735540391292521535824647434568377082591826884769598224146796816367616')

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('2.0', '25.0', '294079625', '153090103458041951154620325043801237641319743206933311288544235956760011447392195175450369025277569052617268428910122535686807015741471080782585043071649294869136754165183653769539196448293593632735232')

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('2.0', '25.0', '295408296', '306180206916083902309240650087602475282639486413866622577088471913520022894784390350900738050555138105234536857820245071373614031482942161565170086143298589738273508330367307539078392896587187265470464')

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('2.0', '25.0', '296740963', '612360413832167804618481300175204950565278972827733245154176943827040045789568780701801476101110276210469073715640490142747228062965884323130340172286597179476547016660734615078156785793174374530940928')

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('2.0', '25.0', '298077632', '1224720827664335609236962600350409901130557945655466490308353887654080091579137561403602952202220552420938147431280980285494456125931768646260680344573194358953094033321469230156313571586348749061881856')

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('2.0', '25.0', '299418309', '2449441655328671218473925200700819802261115891310932980616707775308160183158275122807205904404441104841876294862561960570988912251863537292521360689146388717906188066642938460312627143172697498123763712')

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('2.0', '25.0', '300763000', '4898883310657342436947850401401639604522231782621865961233415550616320366316550245614411808808882209683752589725123921141977824503727074585042721378292777435812376133285876920625254286345394996247527424')

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('2.0', '25.0', '302111711', '9797766621314684873895700802803279209044463565243731922466831101232640732633100491228823617617764419367505179450247842283955649007454149170085442756585554871624752266571753841250508572690789992495054848')

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('2.0', '25.0', '303464448', '19595533242629369747791401605606558418088927130487463844933662202465281465266200982457647235235528838735010358900495684567911298014908298340170885513171109743249504533143507682501017145381579984990109696')

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('2.0', '25.0', '304821217', '39191066485258739495582803211213116836177854260974927689867324404930562930532401964915294470471057677470020717800991369135822596029816596680341771026342219486499009066287015365002034290763159969980219392')

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('2.0', '25.0', '306182024', '78382132970517478991165606422426233672355708521949855379734648809861125861064803929830588940942115354940041435601982738271645192059633193360683542052684438972998018132574030730004068581526319939960438784')

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('2.0', '25.0', '307546875', '156764265941034957982331212844852467344711417043899710759469297619722251722129607859661177881884230709880082871203965476543290384119266386721367084105368877945996036265148061460008137163052639879920877568')

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('2.0', '26.0', '308915776', '313528531882069915964662425689704934689422834087799421518938595239444503444259215719322355763768461419760165742407930953086580768238532773442734168210737755891992072530296122920016274326105279759841755136')

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('2.0', '26.0', '310288733', '627057063764139831929324851379409869378845668175598843037877190478889006888518431438644711527536922839520331484815861906173161536477065546885468336421475511783984145060592245840032548652210559519683510272')

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('2.0', '26.0', '311665752', '1254114127528279663858649702758819738757691336351197686075754380957778013777036862877289423055073845679040662969631723812346323072954131093770936672842951023567968290121184491680065097304421119039367020544')

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('2.0', '26.0', '313046839', '2508228255056559327717299405517639477515382672702395372151508761915556027554073725754578846110147691358081325939263447624692646145908262187541873345685902047135936580242368983360130194608842238078734041088')

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('2.0', '26.0', '314432000', '5016456510113118655434598811035278955030765345404790744303017523831112055108147451509157692220295382716162651878526895249385292291816524375083746691371804094271873160484737966720260389217684476157468082176')

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('2.0', '26.0', '315821241', '10032913020226237310869197622070557910061530690809581488606035047662224110216294903018315384440590765432325303757053790498770584583633048750167493382743608188543746320969475933440520778435368952314936164352')

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('2.0', '26.0', '317214568', '20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704')

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('2.0', '26.0', '318611987', '40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408')

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('2.0', '26.0', '320013504', '80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816')

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('2.0', '26.0', '321419125', '160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632')

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('2.0', '26.0', '322828856', '321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264')

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('2.0', '26.0', '324242703', '642106433294479187895628647812515706243937964211813215270786243050382343053842873793172184604197808987668819440451442591921317413352515120010719576495590924066799764542046459740193329819863612948155914518528')

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('2.0', '26.0', '325660672', '1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919480386659639727225896311829037056')

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('2.0', '26.0', '327082769', '2568425733177916751582514591250062824975751856847252861083144972201529372215371495172688738416791235950675277761805770367685269653410060480042878305982363696267199058168185838960773319279454451792623658074112')

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('2.0', '26.0', '328509000', '5136851466355833503165029182500125649951503713694505722166289944403058744430742990345377476833582471901350555523611540735370539306820120960085756611964727392534398116336371677921546638558908903585247316148224')

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('2.0', '26.0', '329939371', '10273702932711667006330058365000251299903007427389011444332579888806117488861485980690754953667164943802701111047223081470741078613640241920171513223929454785068796232672743355843093277117817807170494632296448')

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('2.0', '26.0', '331373888', '20547405865423334012660116730000502599806014854778022888665159777612234977722971961381509907334329887605402222094446162941482157227280483840343026447858909570137592465345486711686186554235635614340989264592896')

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('2.0', '26.0', '332812557', '41094811730846668025320233460001005199612029709556045777330319555224469955445943922763019814668659775210804444188892325882964314454560967680686052895717819140275184930690973423372373108471271228681978529185792')

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('2.0', '26.0', '334255384', '82189623461693336050640466920002010399224059419112091554660639110448939910891887845526039629337319550421608888377784651765928628909121935361372105791435638280550369861381946846744746216942542457363957058371584')

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('2.0', '26.0', '335702375', '164379246923386672101280933840004020798448118838224183109321278220897879821783775691052079258674639100843217776755569303531857257818243870722744211582871276561100739722763893693489492433885084914727914116743168')

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('2.0', '26.0', '337153536', '328758493846773344202561867680008041596896237676448366218642556441795759643567551382104158517349278201686435553511138607063714515636487741445488423165742553122201479445527787386978984867770169829455828233486336')

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('2.0', '26.0', '338608873', '657516987693546688405123735360016083193792475352896732437285112883591519287135102764208317034698556403372871107022277214127429031272975482890976846331485106244402958891055574773957969735540339658911656466972672')

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('2.0', '26.0', '340068392', '1315033975387093376810247470720032166387584950705793464874570225767183038574270205528416634069397112806745742214044554428254858062545950965781953692662970212488805917782111149547915939471080679317823312933945344')

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('2.0', '26.0', '341532099', '2630067950774186753620494941440064332775169901411586929749140451534366077148540411056833268138794225613491484428089108856509716125091901931563907385325940424977611835564222299095831878942161358635646625867890688')

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('2.0', '26.0', '343000000', '5260135901548373507240989882880128665550339802823173859498280903068732154297080822113666536277588451226982968856178217713019432250183803863127814770651880849955223671128444598191663757884322717271293251735781376')

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('2.0', '26.0', '344472101', '10520271803096747014481979765760257331100679605646347718996561806137464308594161644227333072555176902453965937712356435426038864500367607726255629541303761699910447342256889196383327515768645434542586503471562752')

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('2.0', '26.0', '345948408', '21040543606193494028963959531520514662201359211292695437993123612274928617188323288454666145110353804907931875424712870852077729000735215452511259082607523399820894684513778392766655031537290869085173006943125504')

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('2.0', '26.0', '347428927', '42081087212386988057927919063041029324402718422585390875986247224549857234376646576909332290220707609815863750849425741704155458001470430905022518165215046799641789369027556785533310063074581738170346013886251008')

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('2.0', '26.0', '348913664', '84162174424773976115855838126082058648805436845170781751972494449099714468753293153818664580441415219631727501698851483408310916002940861810045036330430093599283578738055113571066620126149163476340692027772502016')

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('2.0', '26.0', '350402625', '168324348849547952231711676252164117297610873690341563503944988898199428937506586307637329160882830439263455003397702966816621832005881723620090072660860187198567157476110227142133240252298326952681384055545004032')

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('2.0', '26.0', '351895816', '336648697699095904463423352504328234595221747380683127007889977796398857875013172615274658321765660878526910006795405933633243664011763447240180145321720374397134314952220454284266480504596653905362768111090008064')

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('2.0', '26.0', '353393243', '673297395398191808926846705008656469190443494761366254015779955592797715750026345230549316643531321757053820013590811867266487328023526894480360290643440748794268629904440908568532961009193307810725536222180016128')

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('2.0', '26.0', '354894912', '1346594790796383617853693410017312938380886989522732508031559911185595431500052690461098633287062643514107640027181623734532974656047053788960720581286881497588537259808881817137065922018386615621451072444360032256')

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('2.0', '26.0', '356400829', '2693189581592767235707386820034625876761773979045465016063119822371190863000105380922197266574125287028215280054363247469065949312094107577921441162573762995177074519617763634274131844036773231242902144888720064512')

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('2.0', '26.0', '357911000', '5386379163185534471414773640069251753523547958090930032126239644742381726000210761844394533148250574056430560108726494938131898624188215155842882325147525990354149039235527268548263688073546462485804289777440129024')

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('2.0', '26.0', '359425431', '10772758326371068942829547280138503507047095916181860064252479289484763452000421523688789066296501148112861120217452989876263797248376430311685764650295051980708298078471054537096527376147092924971608579554880258048')

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('2.0', '26.0', '360944128', '21545516652742137885659094560277007014094191832363720128504958578969526904000843047377578132593002296225722240434905979752527594496752860623371529300590103961416596156942109074193054752294185849943217159109760516096')

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('2.0', '26.0', '362467097', '43091033305484275771318189120554014028188383664727440257009917157939053808001686094755156265186004592451444480869811959505055188993505721246743058601180207922833192313884218148386109504588371699886434318219521032192')

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('2.0', '26.0', '363994344', '86182066610968551542636378241108028056376767329454880514019834315878107616003372189510312530372009184902888961739623919010110377987011442493486117202360415845666384627768436296772219009176743399772868636439042064384')

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('2.0', '26.0', '365525875', '172364133221937103085272756482216056112753534658909761028039668631756215232006744379020625060744018369805777923479247838020220755974022884986972234404720831691332769255536872593544438018353486799545737272878084128768')

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('2.0', '26.0', '367061696', '344728266443874206170545512964432112225507069317819522056079337263512430464013488758041250121488036739611555846958495676040441511948045769973944468809441663382665538511073745187088876036706973599091474545756168257536')

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('2.0', '26.0', '368601813', '689456532887748412341091025928864224451014138635639044112158674527024860928026977516082500242976073479223111693916991352080883023896091539947888937618883326765331077022147490374177752073413947198182949091512336515072')

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('2.0', '26.0', '370146232', '1378913065775496824682182051857728448902028277271278088224317349054049721856053955032165000485952146958446223387833982704161766047792183079895777875237766653530662154044294980748355504146827894396365898183024673030144')

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('2.0', '26.0', '371694959', '2757826131550993649364364103715456897804056554542556176448634698108099443712107910064330000971904293916892446775667965408323532095584366159791555750475533307061324308088589961496711008293655788792731796366049346060288')

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('2.0', '26.0', '373248000', '5515652263101987298728728207430913795608113109085112352897269396216198887424215820128660001943808587833784893551335930816647064191168732319583111500951066614122648616177179922993422016587311577585463592732098692120576')

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('2.0', '26.0', '374805361', '11031304526203974597457456414861827591216226218170224705794538792432397774848431640257320003887617175667569787102671861633294128382337464639166223001902133228245297232354359845986844033174623155170927185464197384241152')

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('2.0', '26.0', '376367048', '22062609052407949194914912829723655182432452436340449411589077584864795549696863280514640007775234351335139574205343723266588256764674929278332446003804266456490594464708719691973688066349246310341854370928394768482304')

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('2.0', '26.0', '377933067', '44125218104815898389829825659447310364864904872680898823178155169729591099393726561029280015550468702670279148410687446533176513529349858556664892007608532912981188929417439383947376132698492620683708741856789536964608')

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('2.0', '26.0', '379503424', '88250436209631796779659651318894620729729809745361797646356310339459182198787453122058560031100937405340558296821374893066353027058699717113329784015217065825962377858834878767894752265396985241367417483713579073929216')

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('2.0', '26.0', '384240583', '706003489677054374237277210551156965837838477962894381170850482715673457590299624976468480248807499242724466374570999144530824216469597736906638272121736526607699022870679030143158018123175881930939339869708632591433728')

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('2.0', '26.0', '385828352', '1412006979354108748474554421102313931675676955925788762341700965431346915180599249952936960497614998485448932749141998289061648432939195473813276544243473053215398045741358060286316036246351763861878679739417265182867456')

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('2.0', '27.0', '387420489', '2824013958708217496949108842204627863351353911851577524683401930862693830361198499905873920995229996970897865498283996578123296865878390947626553088486946106430796091482716120572632072492703527723757359478834530365734912')

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('2.0', '27.0', '389017000', '5648027917416434993898217684409255726702707823703155049366803861725387660722396999811747841990459993941795730996567993156246593731756781895253106176973892212861592182965432241145264144985407055447514718957669060731469824')

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('2.0', '27.0', '390617891', '11296055834832869987796435368818511453405415647406310098733607723450775321444793999623495683980919987883591461993135986312493187463513563790506212353947784425723184365930864482290528289970814110895029437915338121462939648')

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('2.0', '27.0', '392223168', '22592111669665739975592870737637022906810831294812620197467215446901550642889587999246991367961839975767182923986271972624986374927027127581012424707895568851446368731861728964581056579941628221790058875830676242925879296')

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('2.0', '27.0', '393832837', '45184223339331479951185741475274045813621662589625240394934430893803101285779175998493982735923679951534365847972543945249972749854054255162024849415791137702892737463723457929162113159883256443580117751661352485851758592')

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('2.0', '27.0', '395446904', '90368446678662959902371482950548091627243325179250480789868861787606202571558351996987965471847359903068731695945087890499945499708108510324049698831582275405785474927446915858324226319766512887160235503322704971703517184')

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('2.0', '27.0', '397065375', '180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368')

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('2.0', '27.0', '398688256', '361473786714651839609485931802192366508973300717001923159475447150424810286233407987951861887389439612274926783780351561999781998832434041296198795326329101623141899709787663433296905279066051548640942013290819886814068736')

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('2.0', '27.0', '400315553', '722947573429303679218971863604384733017946601434003846318950894300849620572466815975903723774778879224549853567560703123999563997664868082592397590652658203246283799419575326866593810558132103097281884026581639773628137472')

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('2.0', '27.0', '401947272', '1445895146858607358437943727208769466035893202868007692637901788601699241144933631951807447549557758449099707135121406247999127995329736165184795181305316406492567598839150653733187621116264206194563768053163279547256274944')

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('2.0', '27.0', '403583419', '2891790293717214716875887454417538932071786405736015385275803577203398482289867263903614895099115516898199414270242812495998255990659472330369590362610632812985135197678301307466375242232528412389127536106326559094512549888')

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('2.0', '27.0', '405224000', '5783580587434429433751774908835077864143572811472030770551607154406796964579734527807229790198231033796398828540485624991996511981318944660739180725221265625970270395356602614932750484465056824778255072212653118189025099776')

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('2.0', '27.0', '406869021', '11567161174868858867503549817670155728287145622944061541103214308813593929159469055614459580396462067592797657080971249983993023962637889321478361450442531251940540790713205229865500968930113649556510144425306236378050199552')

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('2.0', '27.0', '408518488', '23134322349737717735007099635340311456574291245888123082206428617627187858318938111228919160792924135185595314161942499967986047925275778642956722900885062503881081581426410459731001937860227299113020288850612472756100399104')

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('2.0', '27.0', '410172407', '46268644699475435470014199270680622913148582491776246164412857235254375716637876222457838321585848270371190628323884999935972095850551557285913445801770125007762163162852820919462003875720454598226040577701224945512200798208')

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('2.0', '27.0', '411830784', '92537289398950870940028398541361245826297164983552492328825714470508751433275752444915676643171696540742381256647769999871944191701103114571826891603540250015524326325705641838924007751440909196452081155402449891024401596416')

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('2.0', '27.0', '413493625', '185074578797901741880056797082722491652594329967104984657651428941017502866551504889831353286343393081484762513295539999743888383402206229143653783207080500031048652651411283677848015502881818392904162310804899782048803192832')

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('2.0', '27.0', '415160936', '370149157595803483760113594165444983305188659934209969315302857882035005733103009779662706572686786162969525026591079999487776766804412458287307566414161000062097305302822567355696031005763636785808324621609799564097606385664')

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('2.0', '27.0', '416832723', '740298315191606967520227188330889966610377319868419938630605715764070011466206019559325413145373572325939050053182159998975553533608824916574615132828322000124194610605645134711392062011527273571616649243219599128195212771328')

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('2.0', '27.0', '418508992', '1480596630383213935040454376661779933220754639736839877261211431528140022932412039118650826290747144651878100106364319997951107067217649833149230265656644000248389221211290269422784124023054547143233298486439198256390425542656')

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('2.0', '27.0', '420189749', '2961193260766427870080908753323559866441509279473679754522422863056280045864824078237301652581494289303756200212728639995902214134435299666298460531313288000496778442422580538845568248046109094286466596972878396512780851085312')

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('2.0', '27.0', '421875000', '5922386521532855740161817506647119732883018558947359509044845726112560091729648156474603305162988578607512400425457279991804428268870599332596921062626576000993556884845161077691136496092218188572933193945756793025561702170624')

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('2.0', '27.0', '423564751', '11844773043065711480323635013294239465766037117894719018089691452225120183459296312949206610325977157215024800850914559983608856537741198665193842125253152001987113769690322155382272992184436377145866387891513586051123404341248')

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('2.0', '27.0', '425259008', '23689546086131422960647270026588478931532074235789438036179382904450240366918592625898413220651954314430049601701829119967217713075482397330387684250506304003974227539380644310764545984368872754291732775783027172102246808682496')

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('2.0', '27.0', '426957777', '47379092172262845921294540053176957863064148471578876072358765808900480733837185251796826441303908628860099203403658239934435426150964794660775368501012608007948455078761288621529091968737745508583465551566054344204493617364992')

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('2.0', '27.0', '428661064', '94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479868870852301929589321550737002025216015896910157522577243058183937475491017166931103132108688408987234729984')

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('2.0', '27.0', '430368875', '189516368689051383685178160212707831452256593886315504289435063235601922935348741007187305765215634515440396813614632959737741704603859178643101474004050432031793820315045154486116367874950982034333862206264217376817974469459968')

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('2.0', '27.0', '432081216', '379032737378102767370356320425415662904513187772631008578870126471203845870697482014374611530431269030880793627229265919475483409207718357286202948008100864063587640630090308972232735749901964068667724412528434753635948938919936')

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('2.0', '27.0', '433798093', '758065474756205534740712640850831325809026375545262017157740252942407691741394964028749223060862538061761587254458531838950966818415436714572405896016201728127175281260180617944465471499803928137335448825056869507271897877839872')

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('2.0', '27.0', '435519512', '1516130949512411069481425281701662651618052751090524034315480505884815383482789928057498446121725076123523174508917063677901933636830873429144811792032403456254350562520361235888930942999607856274670897650113739014543795755679744')

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('2.0', '27.0', '437245479', '3032261899024822138962850563403325303236105502181048068630961011769630766965579856114996892243450152247046349017834127355803867273661746858289623584064806912508701125040722471777861885999215712549341795300227478029087591511359488')

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('2.0', '27.0', '438976000', '6064523798049644277925701126806650606472211004362096137261922023539261533931159712229993784486900304494092698035668254711607734547323493716579247168129613825017402250081444943555723771998431425098683590600454956058175183022718976')

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('2.0', '27.0', '440711081', '12129047596099288555851402253613301212944422008724192274523844047078523067862319424459987568973800608988185396071336509423215469094646987433158494336259227650034804500162889887111447543996862850197367181200909912116350366045437952')

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('2.0', '27.0', '442450728', '24258095192198577111702804507226602425888844017448384549047688094157046135724638848919975137947601217976370792142673018846430938189293974866316988672518455300069609000325779774222895087993725700394734362401819824232700732090875904')

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('2.0', '27.0', '444194947', '48516190384397154223405609014453204851777688034896769098095376188314092271449277697839950275895202435952741584285346037692861876378587949732633977345036910600139218000651559548445790175987451400789468724803639648465401464181751808')

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('2.0', '27.0', '445943744', '97032380768794308446811218028906409703555376069793538196190752376628184542898555395679900551790404871905483168570692075385723752757175899465267954690073821200278436001303119096891580351974902801578937449607279296930802928363503616')

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('2.0', '27.0', '447697125', '194064761537588616893622436057812819407110752139587076392381504753256369085797110791359801103580809743810966337141384150771447505514351798930535909380147642400556872002606238193783160703949805603157874899214558593861605856727007232')

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('2.0', '27.0', '449455096', '388129523075177233787244872115625638814221504279174152784763009506512738171594221582719602207161619487621932674282768301542895011028703597861071818760295284801113744005212476387566321407899611206315749798429117187723211713454014464')

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('2.0', '27.0', '451217663', '776259046150354467574489744231251277628443008558348305569526019013025476343188443165439204414323238975243865348565536603085790022057407195722143637520590569602227488010424952775132642815799222412631499596858234375446423426908028928')

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('2.0', '27.0', '452984832', '1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856')

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('2.0', '27.0', '454756609', '3105036184601417870297958976925005110513772034233393222278104076052101905372753772661756817657292955900975461394262146412343160088229628782888574550082362278408909952041699811100530571263196889650525998387432937501785693707632115712')

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('2.0', '27.0', '456533000', '6210072369202835740595917953850010221027544068466786444556208152104203810745507545323513635314585911801950922788524292824686320176459257565777149100164724556817819904083399622201061142526393779301051996774865875003571387415264231424')

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('2.0', '27.0', '458314011', '12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649372640352918515131554298200329449113635639808166799244402122285052787558602103993549731750007142774830528462848')

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('2.0', '27.0', '460099648', '24840289476811342962383671815400040884110176273867145778224832608416815242982030181294054541258343647207803691154097171298745280705837030263108596400658898227271279616333598488804244570105575117204207987099463500014285549661056925696')

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('2.0', '27.0', '461889917', '49680578953622685924767343630800081768220352547734291556449665216833630485964060362588109082516687294415607382308194342597490561411674060526217192801317796454542559232667196977608489140211150234408415974198927000028571099322113851392')

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('2.0', '27.0', '463684824', '99361157907245371849534687261600163536440705095468583112899330433667260971928120725176218165033374588831214764616388685194981122823348121052434385602635592909085118465334393955216978280422300468816831948397854000057142198644227702784')

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('2.0', '27.0', '465484375', '198722315814490743699069374523200327072881410190937166225798660867334521943856241450352436330066749177662429529232777370389962245646696242104868771205271185818170236930668787910433956560844600937633663896795708000114284397288455405568')

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('2.0', '27.0', '467288576', '397444631628981487398138749046400654145762820381874332451597321734669043887712482900704872660133498355324859058465554740779924491293392484209737542410542371636340473861337575820867913121689201875267327793591416000228568794576910811136')

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('2.0', '27.0', '469097433', '794889263257962974796277498092801308291525640763748664903194643469338087775424965801409745320266996710649718116931109481559848982586784968419475084821084743272680947722675151641735826243378403750534655587182832000457137589153821622272')

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('2.0', '27.0', '470910952', '1589778526515925949592554996185602616583051281527497329806389286938676175550849931602819490640533993421299436233862218963119697965173569936838950169642169486545361895445350303283471652486756807501069311174365664000914275178307643244544')

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('2.0', '27.0', '472729139', '3179557053031851899185109992371205233166102563054994659612778573877352351101699863205638981281067986842598872467724437926239395930347139873677900339284338973090723790890700606566943304973513615002138622348731328001828550356615286489088')

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('2.0', '27.0', '474552000', '6359114106063703798370219984742410466332205126109989319225557147754704702203399726411277962562135973685197744935448875852478791860694279747355800678568677946181447581781401213133886609947027230004277244697462656003657100713230572978176')

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('2.0', '27.0', '476379541', '12718228212127407596740439969484820932664410252219978638451114295509409404406799452822555925124271947370395489870897751704957583721388559494711601357137355892362895163562802426267773219894054460008554489394925312007314201426461145956352')

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('2.0', '27.0', '478211768', '25436456424254815193480879938969641865328820504439957276902228591018818808813598905645111850248543894740790979741795503409915167442777118989423202714274711784725790327125604852535546439788108920017108978789850624014628402852922291912704')

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('2.0', '27.0', '480048687', '50872912848509630386961759877939283730657641008879914553804457182037637617627197811290223700497087789481581959483591006819830334885554237978846405428549423569451580654251209705071092879576217840034217957579701248029256805705844583825408')

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('2.0', '31.0', '976191488', '41855804968213567224547853478906320725054875457247406540771499545716837934567817284890561672488119458109166910841919797858872862722356017328064756151166307827869405370407152286801072676024887272960758524035337792904616958075776435777990406039363527010043736240963055342423554029893064011082834640896')

\n", "
\n", " \n", "
\n", "

('2.0', '31.0', '979146657', '83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792')

\n", "
\n", " \n", "
\n", "

('2.0', '31.0', '982107784', '167423219872854268898191413915625282900219501828989626163085998182867351738271269139562246689952477832436667643367679191435491450889424069312259024604665231311477621481628609147204290704099549091843034096141351171618467832303105743111961624157454108040174944963852221369694216119572256044331338563584')

\n", "
\n", " \n", "
\n", "

('2.0', '31.0', '985074875', '334846439745708537796382827831250565800439003657979252326171996365734703476542538279124493379904955664873335286735358382870982901778848138624518049209330462622955242963257218294408581408199098183686068192282702343236935664606211486223923248314908216080349889927704442739388432239144512088662677127168')

\n", "
\n", " \n", "
\n", "

('2.0', '31.0', '988047936', '669692879491417075592765655662501131600878007315958504652343992731469406953085076558248986759809911329746670573470716765741965803557696277249036098418660925245910485926514436588817162816398196367372136384565404686473871329212422972447846496629816432160699779855408885478776864478289024177325354254336')

\n", "
\n", " \n", "
\n", "

('2.0', '31.0', '991026973', '1339385758982834151185531311325002263201756014631917009304687985462938813906170153116497973519619822659493341146941433531483931607115392554498072196837321850491820971853028873177634325632796392734744272769130809372947742658424845944895692993259632864321399559710817770957553728956578048354650708508672')

\n", "
\n", " \n", "
\n", "

('2.0', '31.0', '994011992', '2678771517965668302371062622650004526403512029263834018609375970925877627812340306232995947039239645318986682293882867062967863214230785108996144393674643700983641943706057746355268651265592785469488545538261618745895485316849691889791385986519265728642799119421635541915107457913156096709301417017344')

\n", "
\n", " \n", "
\n", "

('2.0', '31.0', '997002999', '5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688')

\n", "
\n", " \n", " x: \n", "
\n", " " ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "StaticInteract(croissances_comp, x=RangeWidget(1, 1000))\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Concluson : ** y'a pas photo !" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bonus : l'échelle en zéro\n", "\n", "Certains sont perturbés avec l'échelle en $0^+$. Je comprends, elle est bien moins intuitive que l'échelle en $+\\infty$. Alors,je me suis livré au même jeu (puisque maintenant j'ai ma maginifique fonction `croissances_comp`), mais cette fois avec les quatre candidats suivants :\n", "\n", "**Fonction** | **Expression**\n", "---------|------------------------------------\n", "$f_1(x)=$| $\\log_{10}^{2} (x)$\n", "$f_2(x)=$| $\\log_{10}^{4}(x)$\n", "$f_3(x)=$| $\\dfrac{1}{x^{0.7}}$\n", "$f_4(x)=$| $\\dfrac{1}{x^2}$\n", "\n", "Je rappelle aussi que dans les croissances comparées, c'est la taille du nombre qui nous intéresse, le signe n'intervient pas (on peut donc travailler avec les valeurs absolues des fonctions)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def croissances_comp(x):\n", " f1 = \"f1(x)\"\n", " f2 = \"f2(x)\"\n", " f3 = \"f3(x) \"\n", " f4 = \"f4(x) \"\n", " for i in range(x):\n", " k = 1/(1+i*x)\n", " f1 = str(floor(log10(k)**2))\n", " f2 = str(floor((-log10(k))**4))\n", " f3 = str(floor(1/k**(0.7)))\n", " f4 = str(floor(1/k**2))\n", " return f1, f2, f3, f4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Faites glisser le bouton, cette fois, $x$ part de la valeur $1$ pour décroître vers $0$ (on a bien $x\\to 0^+$)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", "
\n", " \n", "
\n", "

('f1(x)', 'f2(x)', 'f3(x) ', 'f4(x) ')

\n", "
\n", " \n", "
\n", "

('0.0', '0.0', '1.0', '1.0')

\n", "
\n", " \n", "
\n", "

('0.0', '0.0', '2.0', '9.0')

\n", "
\n", " \n", "
\n", "

('0.0', '0.0', '3.0', '49.0')

\n", "
\n", " \n", "
\n", "

('1.0', '1.0', '6.0', '168.0')

\n", "
\n", " \n", "
\n", "

('1.0', '3.0', '8.0', '441.0')

\n", "
\n", " \n", "
\n", "

('2.0', '4.0', '11.0', '961.0')

\n", "
\n", " \n", "
\n", "

('2.0', '7.0', '13.0', '1849.0')

\n", "
\n", " \n", "
\n", "

('3.0', '9.0', '16.0', '3249.0')

\n", "
\n", " \n", "
\n", "

('3.0', '12.0', '20.0', '5329.0')

\n", "
\n", " \n", "
\n", "

('3.0', '14.0', '23.0', '8280.0')

\n", "
\n", " \n", "
\n", "

('4.0', '17.0', '27.0', '12321.0')

\n", "
\n", " \n", "
\n", "

('4.0', '20.0', '30.0', '17689.0')

\n", "
\n", " \n", "
\n", "

('4.0', '23.0', '34.0', '24648.0')

\n", "
\n", " \n", "
\n", "

('5.0', '26.0', '38.0', '33489.0')

\n", "
\n", " \n", "
\n", "

('5.0', '29.0', '42.0', '44520.0')

\n", "
\n", " \n", "
\n", "

('5.0', '32.0', '46.0', '58081.0')

\n", "
\n", " \n", "
\n", "

('5.0', '35.0', '50.0', '74529.0')

\n", "
\n", " \n", "
\n", "

('6.0', '38.0', '55.0', '94249.0')

\n", "
\n", " \n", "
\n", "

('6.0', '41.0', '59.0', '117649.0')

\n", "
\n", " \n", "
\n", "

('6.0', '44.0', '64.0', '145161.0')

\n", "
\n", " \n", "
\n", "

('6.0', '47.0', '68.0', '177241.0')

\n", "
\n", " \n", "
\n", "

('7.0', '50.0', '73.0', '214368.0')

\n", "
\n", " \n", "
\n", "

('7.0', '53.0', '78.0', '257048.0')

\n", "
\n", " \n", "
\n", "

('7.0', '56.0', '83.0', '305809.0')

\n", "
\n", " \n", "
\n", "

('7.0', '59.0', '88.0', '361201.0')

\n", "
\n", " \n", "
\n", "

('7.0', '62.0', '93.0', '423801.0')

\n", "
\n", " \n", "
\n", "

('8.0', '65.0', '98.0', '494209.0')

\n", "
\n", " \n", "
\n", "

('8.0', '68.0', '103.0', '573049.0')

\n", "
\n", " \n", "
\n", "

('8.0', '71.0', '108.0', '660969.0')

\n", "
\n", " \n", "
\n", "

('8.0', '74.0', '114.0', '758640.0')

\n", "
\n", " \n", "
\n", "

('8.0', '77.0', '119.0', '866761.0')

\n", "
\n", " \n", "
\n", "

('8.0', '80.0', '125.0', '986048.0')

\n", "
\n", " \n", "
\n", "

('9.0', '83.0', '130.0', '1117249.0')

\n", "
\n", " \n", "
\n", "

('9.0', '86.0', '136.0', '1261129.0')

\n", "
\n", " \n", "
\n", "

('9.0', '89.0', '142.0', '1418481.0')

\n", "
\n", " \n", "
\n", "

('9.0', '92.0', '148.0', '1590121.0')

\n", "
\n", " \n", "
\n", "

('9.0', '95.0', '153.0', '1776888.0')

\n", "
\n", " \n", "
\n", "

('9.0', '98.0', '159.0', '1979649.0')

\n", "
\n", " \n", "
\n", "

('10.0', '101.0', '165.0', '2199289.0')

\n", "
\n", " \n", "
\n", "

('10.0', '103.0', '171.0', '2436721.0')

\n", "
\n", " \n", "
\n", "

('10.0', '106.0', '178.0', '2692881.0')

\n", "
\n", " \n", "
\n", "

('10.0', '109.0', '184.0', '2968729.0')

\n", "
\n", " \n", "
\n", "

('10.0', '112.0', '190.0', '3265249.0')

\n", "
\n", " \n", "
\n", "

('10.0', '115.0', '196.0', '3583448.0')

\n", "
\n", " \n", "
\n", "

('10.0', '118.0', '203.0', '3924361.0')

\n", "
\n", " \n", "
\n", "

('10.0', '120.0', '209.0', '4289041.0')

\n", "
\n", " \n", "
\n", "

('11.0', '123.0', '216.0', '4678569.0')

\n", "
\n", " \n", "
\n", "

('11.0', '126.0', '222.0', '5094049.0')

\n", "
\n", " \n", "
\n", "

('11.0', '129.0', '229.0', '5536609.0')

\n", "
\n", " \n", "
\n", "

('11.0', '131.0', '235.0', '6007401.0')

\n", "
\n", " \n", "
\n", "

('11.0', '134.0', '242.0', '6507601.0')

\n", "
\n", " \n", "
\n", "

('11.0', '137.0', '249.0', '7038408.0')

\n", "
\n", " \n", "
\n", "

('11.0', '140.0', '256.0', '7601049.0')

\n", "
\n", " \n", "
\n", "

('11.0', '142.0', '262.0', '8196769.0')

\n", "
\n", " \n", "
\n", "

('12.0', '145.0', '269.0', '8826841.0')

\n", "
\n", " \n", "
\n", "

('12.0', '148.0', '276.0', '9492561.0')

\n", "
\n", " \n", "
\n", "

('12.0', '150.0', '283.0', '10195249.0')

\n", "
\n", " \n", "
\n", "

('12.0', '153.0', '290.0', '10936248.0')

\n", "
\n", " \n", "
\n", "

('12.0', '156.0', '297.0', '11716929.0')

\n", "
\n", " \n", "
\n", "

('12.0', '158.0', '305.0', '12538680.0')

\n", "
\n", " \n", "
\n", "

('12.0', '161.0', '312.0', '13402921.0')

\n", "
\n", " \n", "
\n", "

('12.0', '163.0', '319.0', '14311089.0')

\n", "
\n", " \n", "
\n", "

('12.0', '166.0', '326.0', '15264649.0')

\n", "
\n", " \n", "
\n", "

('13.0', '169.0', '334.0', '16265089.0')

\n", "
\n", " \n", "
\n", "

('13.0', '171.0', '341.0', '17313921.0')

\n", "
\n", " \n", "
\n", "

('13.0', '174.0', '348.0', '18412681.0')

\n", "
\n", " \n", "
\n", "

('13.0', '176.0', '356.0', '19562929.0')

\n", "
\n", " \n", "
\n", "

('13.0', '179.0', '363.0', '20766248.0')

\n", "
\n", " \n", "
\n", "

('13.0', '181.0', '371.0', '22024249.0')

\n", "
\n", " \n", "
\n", "

('13.0', '184.0', '379.0', '23338561.0')

\n", "
\n", " \n", "
\n", "

('13.0', '186.0', '386.0', '24710841.0')

\n", "
\n", " \n", "
\n", "

('13.0', '189.0', '394.0', '26142769.0')

\n", "
\n", " \n", "
\n", "

('13.0', '191.0', '402.0', '27636049.0')

\n", "
\n", " \n", "
\n", "

('13.0', '194.0', '410.0', '29192409.0')

\n", "
\n", " \n", "
\n", "

('14.0', '196.0', '417.0', '30813601.0')

\n", "
\n", " \n", "
\n", "

('14.0', '199.0', '425.0', '32501400.0')

\n", "
\n", " \n", "
\n", "

('14.0', '201.0', '433.0', '34257609.0')

\n", "
\n", " \n", "
\n", "

('14.0', '203.0', '441.0', '36084048.0')

\n", "
\n", " \n", "
\n", "

('14.0', '206.0', '449.0', '37982569.0')

\n", "
\n", " \n", "
\n", "

('14.0', '208.0', '457.0', '39955041.0')

\n", "
\n", " \n", "
\n", "

('14.0', '211.0', '465.0', '42003361.0')

\n", "
\n", " \n", "
\n", "

('14.0', '213.0', '473.0', '44129448.0')

\n", "
\n", " \n", "
\n", "

('14.0', '215.0', '482.0', '46335249.0')

\n", "
\n", " \n", "
\n", "

('14.0', '218.0', '490.0', '48622728.0')

\n", "
\n", " \n", "
\n", "

('14.0', '220.0', '498.0', '50993880.0')

\n", "
\n", " \n", "
\n", "

('14.0', '222.0', '506.0', '53450720.0')

\n", "
\n", " \n", "
\n", "

('15.0', '225.0', '515.0', '55995289.0')

\n", "
\n", " \n", "
\n", "

('15.0', '227.0', '523.0', '58629648.0')

\n", "
\n", " \n", "
\n", "

('15.0', '229.0', '531.0', '61355889.0')

\n", "
\n", " \n", "
\n", "

('15.0', '232.0', '540.0', '64176121.0')

\n", "
\n", " \n", "
\n", "

('15.0', '234.0', '548.0', '67092481.0')

\n", "
\n", " \n", "
\n", "

('15.0', '236.0', '557.0', '70107129.0')

\n", "
\n", " \n", "
\n", "

('15.0', '239.0', '565.0', '73222249.0')

\n", "
\n", " \n", "
\n", "

('15.0', '241.0', '574.0', '76440049.0')

\n", "
\n", " \n", "
\n", "

('15.0', '243.0', '582.0', '79762761.0')

\n", "
\n", " \n", "
\n", "

('15.0', '245.0', '591.0', '83192641.0')

\n", "
\n", " \n", "
\n", "

('15.0', '248.0', '600.0', '86731969.0')

\n", "
\n", " \n", "
\n", "

('15.0', '250.0', '609.0', '90383049.0')

\n", "
\n", " \n", "
\n", "

('15.0', '252.0', '617.0', '94148209.0')

\n", "
\n", " \n", "
\n", "

('15.0', '254.0', '626.0', '98029801.0')

\n", "
\n", " \n", "
\n", "

('16.0', '257.0', '635.0', '102030200.0')

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\n", " \n", "
\n", "

('16.0', '259.0', '644.0', '106151808.0')

\n", "
\n", " \n", "
\n", "

('16.0', '261.0', '653.0', '110397049.0')

\n", "
\n", " \n", "
\n", "

('16.0', '263.0', '662.0', '114768369.0')

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\n", " \n", "
\n", "

('16.0', '265.0', '671.0', '119268241.0')

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\n", " \n", "
\n", "

('16.0', '268.0', '680.0', '123899160.0')

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\n", " \n", "
\n", "

('16.0', '270.0', '689.0', '128663649.0')

\n", "
\n", " \n", "
\n", "

('16.0', '272.0', '698.0', '133564249.0')

\n", "
\n", " \n", "
\n", "

('16.0', '274.0', '707.0', '138603529.0')

\n", "
\n", " \n", "
\n", "

('16.0', '276.0', '716.0', '143784081.0')

\n", "
\n", " \n", "
\n", "

('16.0', '278.0', '725.0', '149108521.0')

\n", "
\n", " \n", "
\n", "

('16.0', '281.0', '734.0', '154579489.0')

\n", "
\n", " \n", "
\n", "

('16.0', '283.0', '744.0', '160199649.0')

\n", "
\n", " \n", "
\n", "

('16.0', '285.0', '753.0', '165971689.0')

\n", "
\n", " \n", "
\n", "

('16.0', '287.0', '762.0', '171898321.0')

\n", "
\n", " \n", "
\n", "

('17.0', '289.0', '772.0', '177982281.0')

\n", "
\n", " \n", "
\n", "

('17.0', '291.0', '781.0', '184226329.0')

\n", "
\n", " \n", "
\n", "

('17.0', '293.0', '790.0', '190633249.0')

\n", "
\n", " \n", "
\n", "

('17.0', '295.0', '800.0', '197205849.0')

\n", "
\n", " \n", "
\n", "

('17.0', '297.0', '809.0', '203946960.0')

\n", "
\n", " \n", "
\n", "

('17.0', '300.0', '819.0', '210859441.0')

\n", "
\n", " \n", "
\n", "

('17.0', '302.0', '828.0', '217946169.0')

\n", "
\n", " \n", "
\n", "

('17.0', '304.0', '838.0', '225210048.0')

\n", "
\n", " \n", "
\n", "

('17.0', '306.0', '847.0', '232654009.0')

\n", "
\n", " \n", "
\n", "

('17.0', '308.0', '857.0', '240281000.0')

\n", "
\n", " \n", "
\n", "

('17.0', '310.0', '867.0', '248094001.0')

\n", "
\n", " \n", "
\n", "

('17.0', '312.0', '876.0', '256096009.0')

\n", "
\n", " \n", "
\n", "

('17.0', '314.0', '886.0', '264290049.0')

\n", "
\n", " \n", "
\n", "

('17.0', '316.0', '896.0', '272679169.0')

\n", "
\n", " \n", "
\n", "

('17.0', '318.0', '906.0', '281266441.0')

\n", "
\n", " \n", "
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('17.0', '320.0', '915.0', '290054961.0')

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('29.0', '887.0', '6610.0', '82231871121.0')

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('29.0', '888.0', '6628.0', '82847835888.0')

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('29.0', '890.0', '6662.0', '84090140289.0')

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('29.0', '891.0', '6680.0', '84716505721.0')

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('29.0', '892.0', '6697.0', '85346363881.0')

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('29.0', '893.0', '6714.0', '85979727729.0')

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('29.0', '894.0', '6732.0', '86616610249.0')

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('29.0', '895.0', '6749.0', '87257024449.0')

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('29.0', '896.0', '6767.0', '87900983361.0')

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('29.0', '897.0', '6784.0', '88548500040.0')

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('29.0', '898.0', '6801.0', '89199587569.0')

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('29.0', '899.0', '6819.0', '89854259049.0')

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('30.0', '900.0', '6836.0', '90512527609.0')

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('30.0', '901.0', '6854.0', '91174406401.0')

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('30.0', '902.0', '6871.0', '91839908601.0')

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('30.0', '903.0', '6889.0', '92509047409.0')

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('30.0', '904.0', '6906.0', '93181836049.0')

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('30.0', '908.0', '6959.0', '95222233561.0')

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('30.0', '910.0', '6994.0', '96600991249.0')

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('30.0', '911.0', '7011.0', '97295957928.0')

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('30.0', '912.0', '7029.0', '97994667681.0')

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('30.0', '914.0', '7064.0', '99403370089.0')

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('30.0', '915.0', '7082.0', '1.00113389648e+11')

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('30.0', '916.0', '7099.0', '1.00827206089e+11')

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('30.0', '917.0', '7117.0', '1.01544832921e+11')

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('30.0', '918.0', '7135.0', '1.02266283681e+11')

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('30.0', '919.0', '7152.0', '1.02991571929e+11')

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('30.0', '920.0', '7170.0', '1.03720711249e+11')

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('30.0', '921.0', '7188.0', '1.04453715248e+11')

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('30.0', '922.0', '7205.0', '1.05190597561e+11')

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('30.0', '923.0', '7223.0', '1.05931371841e+11')

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('30.0', '924.0', '7241.0', '1.06676051768e+11')

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('30.0', '925.0', '7259.0', '1.07424651049e+11')

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('30.0', '926.0', '7276.0', '1.08177183408e+11')

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('30.0', '927.0', '7294.0', '1.08933662601e+11')

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('30.0', '928.0', '7312.0', '1.09694102401e+11')

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('30.0', '929.0', '7330.0', '1.10458516609e+11')

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('30.0', '930.0', '7348.0', '1.11226919048e+11')

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('30.0', '931.0', '7365.0', '1.11999323568e+11')

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('30.0', '932.0', '7383.0', '1.12775744041e+11')

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('30.0', '933.0', '7401.0', '1.1355619436e+11')

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('30.0', '934.0', '7419.0', '1.14340688448e+11')

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('30.0', '935.0', '7437.0', '1.15129240249e+11')

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('30.0', '936.0', '7455.0', '1.15921863729e+11')

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('30.0', '937.0', '7473.0', '1.16718572881e+11')

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('30.0', '938.0', '7490.0', '1.17519381721e+11')

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('30.0', '939.0', '7508.0', '1.18324304289e+11')

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('30.0', '940.0', '7526.0', '1.19133354648e+11')

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('30.0', '941.0', '7544.0', '1.19946546889e+11')

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('30.0', '942.0', '7562.0', '1.20763895121e+11')

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('30.0', '943.0', '7580.0', '1.21585413481e+11')

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('30.0', '944.0', '7598.0', '1.22411116129e+11')

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('30.0', '945.0', '7616.0', '1.23241017249e+11')

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('30.0', '946.0', '7634.0', '1.24075131048e+11')

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('30.0', '947.0', '7652.0', '1.2491347176e+11')

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('30.0', '948.0', '7670.0', '1.25756053641e+11')

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('30.0', '949.0', '7688.0', '1.26602890969e+11')

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('30.0', '950.0', '7706.0', '1.27453998048e+11')

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('30.0', '951.0', '7724.0', '1.28309389209e+11')

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('30.0', '952.0', '7742.0', '1.29169078801e+11')

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('30.0', '953.0', '7761.0', '1.30033081201e+11')

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('30.0', '954.0', '7779.0', '1.30901410809e+11')

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('30.0', '955.0', '7797.0', '1.31774082048e+11')

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('30.0', '956.0', '7815.0', '1.32651109369e+11')

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('30.0', '957.0', '7833.0', '1.3353250724e+11')

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('30.0', '958.0', '7851.0', '1.34418290161e+11')

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('30.0', '959.0', '7869.0', '1.35308472649e+11')

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('30.0', '960.0', '7887.0', '1.36203069249e+11')

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('31.0', '961.0', '7906.0', '1.37102094529e+11')

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('31.0', '962.0', '7924.0', '1.3800556308e+11')

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('31.0', '963.0', '7942.0', '1.38913489521e+11')

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('31.0', '964.0', '7960.0', '1.39825888489e+11')

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('31.0', '965.0', '7979.0', '1.40742774649e+11')

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('31.0', '966.0', '7997.0', '1.41664162689e+11')

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('31.0', '967.0', '8015.0', '1.4259006732e+11')

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('31.0', '968.0', '8033.0', '1.4352050328e+11')

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('31.0', '969.0', '8052.0', '1.44455485329e+11')

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('31.0', '970.0', '8070.0', '1.45395028249e+11')

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('31.0', '971.0', '8088.0', '1.46339146849e+11')

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('31.0', '972.0', '8106.0', '1.47287855961e+11')

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('31.0', '973.0', '8125.0', '1.48241170441e+11')

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('31.0', '974.0', '8143.0', '1.49199105168e+11')

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('31.0', '975.0', '8161.0', '1.50161675049e+11')

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('31.0', '976.0', '8180.0', '1.51128895009e+11')

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('31.0', '977.0', '8198.0', '1.52100780001e+11')

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('31.0', '978.0', '8217.0', '1.53077345e+11')

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('31.0', '979.0', '8235.0', '1.54058605009e+11')

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('31.0', '980.0', '8253.0', '1.55044575049e+11')

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('31.0', '981.0', '8272.0', '1.56035270169e+11')

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('31.0', '982.0', '8290.0', '1.57030705441e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '983.0', '8309.0', '1.58030895961e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '983.0', '8327.0', '1.59035856849e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '984.0', '8346.0', '1.60045603249e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '985.0', '8364.0', '1.61060150329e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '986.0', '8383.0', '1.6207951328e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '987.0', '8401.0', '1.63103707321e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '988.0', '8420.0', '1.64132747688e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '989.0', '8438.0', '1.65166649649e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '990.0', '8457.0', '1.66205428489e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '991.0', '8475.0', '1.6724909952e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '992.0', '8494.0', '1.68297678081e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '993.0', '8512.0', '1.69351179529e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '994.0', '8531.0', '1.70409619249e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '995.0', '8550.0', '1.71473012649e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '996.0', '8568.0', '1.72541375161e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '997.0', '8587.0', '1.73614722241e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '998.0', '8605.0', '1.74693069369e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '999.0', '8624.0', '1.75776432049e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1000.0', '8643.0', '1.76864825808e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1001.0', '8661.0', '1.779582662e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1002.0', '8680.0', '1.79056768801e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1003.0', '8699.0', '1.80160349209e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1004.0', '8717.0', '1.81269023048e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1005.0', '8736.0', '1.82382805969e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1005.0', '8755.0', '1.83501713641e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1006.0', '8774.0', '1.84625761761e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1007.0', '8792.0', '1.85754966048e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1008.0', '8811.0', '1.86889342248e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1009.0', '8830.0', '1.88028906129e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1010.0', '8849.0', '1.89173673481e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1011.0', '8867.0', '1.90323660121e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1012.0', '8886.0', '1.91478881889e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1013.0', '8905.0', '1.92639354649e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1014.0', '8924.0', '1.93805094288e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1015.0', '8943.0', '1.94976116721e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1016.0', '8962.0', '1.9615243788e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1017.0', '8980.0', '1.97334073729e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1018.0', '8999.0', '1.98521040249e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1019.0', '9018.0', '1.99713353449e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1020.0', '9037.0', '2.0091102936e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1021.0', '9056.0', '2.02114084041e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1022.0', '9075.0', '2.03322533569e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1022.0', '9094.0', '2.04536394048e+11')

\n", "
\n", " \n", "
\n", "

('31.0', '1023.0', '9113.0', '2.05755681609e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1024.0', '9132.0', '2.06980412401e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1025.0', '9151.0', '2.08210602601e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1026.0', '9170.0', '2.09446268409e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1027.0', '9189.0', '2.10687426049e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1028.0', '9208.0', '2.11934091768e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1029.0', '9227.0', '2.13186281841e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1030.0', '9246.0', '2.14444012561e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1031.0', '9265.0', '2.15707300249e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1032.0', '9284.0', '2.16976161249e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1033.0', '9303.0', '2.18250611929e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1034.0', '9322.0', '2.19530668681e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1035.0', '9341.0', '2.20816347921e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1035.0', '9360.0', '2.22107666088e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1036.0', '9379.0', '2.23404639649e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1037.0', '9398.0', '2.24707285089e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1038.0', '9417.0', '2.26015618921e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1039.0', '9436.0', '2.2732965768e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1040.0', '9456.0', '2.28649417928e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1041.0', '9475.0', '2.29974916249e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1042.0', '9494.0', '2.31306169248e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1043.0', '9513.0', '2.32643193561e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1044.0', '9532.0', '2.33986005841e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1045.0', '9551.0', '2.35334622768e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1046.0', '9571.0', '2.36689061049e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1046.0', '9590.0', '2.38049337409e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1047.0', '9609.0', '2.394154686e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1048.0', '9628.0', '2.407874714e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1049.0', '9648.0', '2.42165362608e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1050.0', '9667.0', '2.43549159049e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1051.0', '9686.0', '2.44938877569e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1052.0', '9705.0', '2.46334535041e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1053.0', '9725.0', '2.4773614836e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1054.0', '9744.0', '2.49143734448e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1055.0', '9763.0', '2.50557310248e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1056.0', '9783.0', '2.51976892729e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1057.0', '9802.0', '2.5340249888e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1057.0', '9821.0', '2.54834145721e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1058.0', '9841.0', '2.56271850289e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1059.0', '9860.0', '2.57715629649e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1060.0', '9879.0', '2.59165500888e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1061.0', '9899.0', '2.60621481121e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1062.0', '9918.0', '2.6208358748e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1063.0', '9938.0', '2.63551837128e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1064.0', '9957.0', '2.65026247248e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1065.0', '9976.0', '2.66506835048e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1066.0', '9996.0', '2.6799361776e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1066.0', '10015.0', '2.69486612641e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1067.0', '10035.0', '2.70985836969e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1068.0', '10054.0', '2.72491308049e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1069.0', '10074.0', '2.74003043209e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1070.0', '10093.0', '2.75521059801e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1071.0', '10113.0', '2.77045375201e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1072.0', '10132.0', '2.78576006809e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1073.0', '10152.0', '2.80112972049e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1074.0', '10171.0', '2.81656288369e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1075.0', '10191.0', '2.83205973241e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1075.0', '10211.0', '2.84762044161e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1076.0', '10230.0', '2.86324518649e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1077.0', '10250.0', '2.87893414249e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1078.0', '10269.0', '2.89468748529e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1079.0', '10289.0', '2.91050539081e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1080.0', '10308.0', '2.92638803521e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1081.0', '10328.0', '2.94233559488e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1082.0', '10348.0', '2.95834824649e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1083.0', '10367.0', '2.97442616689e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1083.0', '10387.0', '2.99056953321e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1084.0', '10407.0', '3.00677852281e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1085.0', '10426.0', '3.02305331329e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1086.0', '10446.0', '3.03939408249e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1087.0', '10466.0', '3.05580100849e+11')

\n", "
\n", " \n", "
\n", "

('32.0', '1088.0', '10486.0', '3.07227426961e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1089.0', '10505.0', '3.08881404441e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1090.0', '10525.0', '3.10542051169e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1091.0', '10545.0', '3.12209385048e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1091.0', '10564.0', '3.13883424009e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1092.0', '10584.0', '3.15564186001e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1093.0', '10604.0', '3.17251689001e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1094.0', '10624.0', '3.18945951009e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1095.0', '10644.0', '3.20646990049e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1096.0', '10663.0', '3.22354824169e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1097.0', '10683.0', '3.2406947144e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1098.0', '10703.0', '3.25790949961e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1098.0', '10723.0', '3.27519277849e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1099.0', '10743.0', '3.29254473249e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1100.0', '10763.0', '3.30996554328e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1101.0', '10782.0', '3.32745539281e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1102.0', '10802.0', '3.34501446321e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1103.0', '10822.0', '3.36264293688e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1104.0', '10842.0', '3.38034099648e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1105.0', '10862.0', '3.39810882489e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1105.0', '10882.0', '3.41594660521e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1106.0', '10902.0', '3.43385452081e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1107.0', '10922.0', '3.45183275529e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1108.0', '10942.0', '3.46988149248e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1109.0', '10962.0', '3.48800091649e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1110.0', '10982.0', '3.5061912116e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1111.0', '11002.0', '3.52445256241e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1112.0', '11022.0', '3.54278515369e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1112.0', '11042.0', '3.56118917049e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1113.0', '11062.0', '3.57966479809e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1114.0', '11082.0', '3.59821222201e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1115.0', '11102.0', '3.61683162801e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1116.0', '11122.0', '3.63552320209e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1117.0', '11142.0', '3.65428713049e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1118.0', '11162.0', '3.67312359969e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1118.0', '11182.0', '3.69203279641e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1119.0', '11202.0', '3.71101490761e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1120.0', '11222.0', '3.73007012048e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1121.0', '11242.0', '3.74919862249e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1122.0', '11263.0', '3.76840060128e+11')

\n", "
\n", " \n", "
\n", "

('33.0', '1123.0', '11283.0', '3.78767624481e+11')

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('33.0', '1124.0', '11303.0', '3.80702574121e+11')

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('33.0', '1124.0', '11323.0', '3.82644927889e+11')

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('33.0', '1125.0', '11343.0', '3.84594704649e+11')

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('33.0', '1126.0', '11363.0', '3.86551923289e+11')

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\n", "

('33.0', '1127.0', '11383.0', '3.88516602721e+11')

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\n", "

('33.0', '1128.0', '11404.0', '3.90488761881e+11')

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\n", "

('33.0', '1129.0', '11424.0', '3.92468419729e+11')

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('33.0', '1130.0', '11444.0', '3.94455595249e+11')

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\n", "

('33.0', '1130.0', '11464.0', '3.96450307449e+11')

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\n", "

('33.0', '1131.0', '11485.0', '3.98452575361e+11')

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\n", "

('33.0', '1132.0', '11505.0', '4.0046241804e+11')

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\n", "

('33.0', '1133.0', '11525.0', '4.02479854569e+11')

\n", "
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\n", "

('33.0', '1134.0', '11545.0', '4.04504904049e+11')

\n", "
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\n", "

('33.0', '1135.0', '11566.0', '4.06537585609e+11')

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\n", "

('33.0', '1136.0', '11586.0', '4.08577918401e+11')

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\n", "

('33.0', '1136.0', '11606.0', '4.10625921601e+11')

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\n", "

('33.0', '1137.0', '11626.0', '4.12681614409e+11')

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\n", "

('33.0', '1138.0', '11647.0', '4.14745016048e+11')

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\n", "

('33.0', '1139.0', '11667.0', '4.16816145769e+11')

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\n", "

('33.0', '1140.0', '11687.0', '4.18895022841e+11')

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\n", "

('33.0', '1141.0', '11708.0', '4.20981666561e+11')

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('33.0', '1141.0', '11728.0', '4.23076096249e+11')

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('33.0', '1142.0', '11748.0', '4.25178331249e+11')

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('33.0', '1143.0', '11769.0', '4.27288390929e+11')

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('33.0', '1144.0', '11789.0', '4.29406294681e+11')

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('33.0', '1145.0', '11810.0', '4.31532061921e+11')

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('33.0', '1146.0', '11830.0', '4.33665712089e+11')

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\n", "

('33.0', '1147.0', '11850.0', '4.35807264649e+11')

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\n", "

('33.0', '1147.0', '11871.0', '4.37956739089e+11')

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\n", "

('33.0', '1148.0', '11891.0', '4.40114154921e+11')

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\n", "

('33.0', '1149.0', '11912.0', '4.42279531681e+11')

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\n", "

('33.0', '1150.0', '11932.0', '4.44452888929e+11')

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\n", "

('33.0', '1151.0', '11953.0', '4.46634246249e+11')

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\n", "

('33.0', '1152.0', '11973.0', '4.48823623249e+11')

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\n", "

('33.0', '1152.0', '11994.0', '4.51021039561e+11')

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\n", "

('33.0', '1153.0', '12014.0', '4.53226514841e+11')

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\n", "

('33.0', '1154.0', '12035.0', '4.55440068768e+11')

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\n", "

('33.0', '1155.0', '12055.0', '4.57661721048e+11')

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\n", " \n", "
\n", "

('34.0', '1156.0', '12076.0', '4.59891491409e+11')

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\n", " \n", "
\n", "

('34.0', '1157.0', '12096.0', '4.62129399601e+11')

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\n", " \n", "
\n", "

('34.0', '1157.0', '12117.0', '4.64375465401e+11')

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\n", "

('34.0', '1158.0', '12137.0', '4.66629708608e+11')

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\n", "

('34.0', '1159.0', '12158.0', '4.68892149049e+11')

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\n", "

('34.0', '1160.0', '12178.0', '4.71162806569e+11')

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\n", "

('34.0', '1161.0', '12199.0', '4.73441701041e+11')

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\n", " \n", "
\n", "

('34.0', '1162.0', '12220.0', '4.75728852361e+11')

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\n", " \n", "
\n", "

('34.0', '1162.0', '12240.0', '4.78024280449e+11')

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\n", " \n", "
\n", "

('34.0', '1163.0', '12261.0', '4.80328005249e+11')

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\n", "

('34.0', '1164.0', '12281.0', '4.82640046729e+11')

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\n", "

('34.0', '1165.0', '12302.0', '4.8496042488e+11')

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\n", "

('34.0', '1166.0', '12323.0', '4.8728915972e+11')

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\n", "

('34.0', '1167.0', '12343.0', '4.89626271288e+11')

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\n", "

('34.0', '1167.0', '12364.0', '4.91971779649e+11')

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\n", "

('34.0', '1168.0', '12385.0', '4.94325704888e+11')

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\n", "

('34.0', '1169.0', '12405.0', '4.96688067121e+11')

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\n", "

('34.0', '1170.0', '12426.0', '4.99058886481e+11')

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\n", "

('34.0', '1171.0', '12447.0', '5.01438183129e+11')

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\n", "

('34.0', '1172.0', '12468.0', '5.03825977248e+11')

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\n", "

('34.0', '1172.0', '12488.0', '5.06222289049e+11')

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\n", "

('34.0', '1173.0', '12509.0', '5.0862713876e+11')

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\n", "

('34.0', '1174.0', '12530.0', '5.11040546641e+11')

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\n", "

('34.0', '1175.0', '12550.0', '5.13462532969e+11')

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\n", "

('34.0', '1176.0', '12571.0', '5.15893118049e+11')

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\n", "

('34.0', '1177.0', '12592.0', '5.18332322209e+11')

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\n", "

('34.0', '1177.0', '12613.0', '5.20780165801e+11')

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\n", "

('34.0', '1178.0', '12634.0', '5.23236669201e+11')

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\n", "

('34.0', '1179.0', '12654.0', '5.25701852809e+11')

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\n", "

('34.0', '1180.0', '12675.0', '5.28175737048e+11')

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\n", "

('34.0', '1181.0', '12696.0', '5.30658342369e+11')

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\n", "

('34.0', '1181.0', '12717.0', '5.33149689241e+11')

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\n", "

('34.0', '1182.0', '12738.0', '5.35649798161e+11')

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\n", "

('34.0', '1183.0', '12759.0', '5.38158689649e+11')

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\n", "

('34.0', '1184.0', '12779.0', '5.40676384249e+11')

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\n", "

('34.0', '1185.0', '12800.0', '5.43202902529e+11')

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\n", "

('34.0', '1186.0', '12821.0', '5.45738265081e+11')

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\n", "

('34.0', '1186.0', '12842.0', '5.48282492521e+11')

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\n", "

('34.0', '1187.0', '12863.0', '5.50835605489e+11')

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\n", "

('34.0', '1188.0', '12884.0', '5.53397624648e+11')

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\n", "

('34.0', '1189.0', '12905.0', '5.55968570689e+11')

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\n", "

('34.0', '1190.0', '12926.0', '5.58548464321e+11')

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\n", "

('34.0', '1190.0', '12947.0', '5.61137326281e+11')

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\n", "

('34.0', '1191.0', '12968.0', '5.63735177329e+11')

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\n", "

('34.0', '1192.0', '12989.0', '5.66342038249e+11')

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\n", "

('34.0', '1193.0', '13010.0', '5.68957929849e+11')

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('34.0', '1194.0', '13030.0', '5.71582872961e+11')

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\n", "

('34.0', '1195.0', '13051.0', '5.74216888441e+11')

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\n", "

('34.0', '1195.0', '13072.0', '5.76859997169e+11')

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\n", "

('34.0', '1196.0', '13093.0', '5.79512220049e+11')

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('34.0', '1197.0', '13115.0', '5.82173578009e+11')

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\n", "

('34.0', '1198.0', '13136.0', '5.84844092001e+11')

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('34.0', '1199.0', '13157.0', '5.87523783001e+11')

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('34.0', '1199.0', '13178.0', '5.90212672009e+11')

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\n", "

('34.0', '1200.0', '13199.0', '5.92910780049e+11')

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\n", "

('34.0', '1201.0', '13220.0', '5.95618128169e+11')

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('34.0', '1202.0', '13241.0', '5.98334737441e+11')

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\n", "

('34.0', '1203.0', '13262.0', '6.0106062896e+11')

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('34.0', '1203.0', '13283.0', '6.03795823848e+11')

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\n", "

('34.0', '1204.0', '13304.0', '6.06540343248e+11')

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\n", "

('34.0', '1205.0', '13325.0', '6.09294208329e+11')

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\n", "

('34.0', '1206.0', '13346.0', '6.12057440281e+11')

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\n", "

('34.0', '1207.0', '13367.0', '6.14830060321e+11')

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\n", "

('34.0', '1207.0', '13389.0', '6.17612089689e+11')

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\n", "

('34.0', '1208.0', '13410.0', '6.20403549649e+11')

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\n", "

('34.0', '1209.0', '13431.0', '6.23204461489e+11')

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\n", "

('34.0', '1210.0', '13452.0', '6.26014846521e+11')

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\n", "

('34.0', '1211.0', '13473.0', '6.28834726081e+11')

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\n", "

('34.0', '1211.0', '13494.0', '6.31664121528e+11')

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\n", "

('34.0', '1212.0', '13516.0', '6.34503054249e+11')

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\n", "

('34.0', '1213.0', '13537.0', '6.37351545649e+11')

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\n", "

('34.0', '1214.0', '13558.0', '6.40209617161e+11')

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\n", "

('34.0', '1215.0', '13579.0', '6.43077290241e+11')

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\n", "

('34.0', '1215.0', '13600.0', '6.45954586369e+11')

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\n", "

('34.0', '1216.0', '13622.0', '6.48841527049e+11')

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\n", "

('34.0', '1217.0', '13643.0', '6.51738133809e+11')

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\n", "

('34.0', '1218.0', '13664.0', '6.54644428201e+11')

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\n", "

('34.0', '1219.0', '13686.0', '6.57560431801e+11')

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\n", "

('34.0', '1219.0', '13707.0', '6.60486166209e+11')

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('34.0', '1220.0', '13728.0', '6.63421653049e+11')

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('34.0', '1221.0', '13749.0', '6.66366913969e+11')

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('34.0', '1222.0', '13771.0', '6.69321970641e+11')

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\n", "

('34.0', '1223.0', '13792.0', '6.72286844761e+11')

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('34.0', '1223.0', '13813.0', '6.75261558049e+11')

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\n", "

('34.0', '1224.0', '13835.0', '6.78246132249e+11')

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\n", "

('35.0', '1225.0', '13856.0', '6.81240589129e+11')

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\n", "

('35.0', '1226.0', '13877.0', '6.8424495048e+11')

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\n", "

('35.0', '1227.0', '13899.0', '6.87259238121e+11')

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\n", "

('35.0', '1227.0', '13920.0', '6.90283473889e+11')

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\n", "

('35.0', '1228.0', '13942.0', '6.93317679649e+11')

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\n", "

('35.0', '1229.0', '13963.0', '6.96361877289e+11')

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\n", "

('35.0', '1230.0', '13984.0', '6.9941608872e+11')

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\n", " \n", "
\n", "

('35.0', '1231.0', '14006.0', '7.02480335881e+11')

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\n", " \n", "
\n", "

('35.0', '1231.0', '14027.0', '7.05554640728e+11')

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\n", " \n", "
\n", "

('35.0', '1232.0', '14049.0', '7.08639025248e+11')

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\n", "

('35.0', '1233.0', '14070.0', '7.11733511449e+11')

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\n", "

('35.0', '1234.0', '14092.0', '7.1483812136e+11')

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\n", "

('35.0', '1234.0', '14113.0', '7.17952877041e+11')

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\n", "

('35.0', '1235.0', '14134.0', '7.21077800569e+11')

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\n", "

('35.0', '1236.0', '14156.0', '7.24212914049e+11')

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\n", "

('35.0', '1237.0', '14177.0', '7.27358239609e+11')

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\n", "

('35.0', '1238.0', '14199.0', '7.30513799401e+11')

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\n", "

('35.0', '1238.0', '14220.0', '7.336796156e+11')

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\n", "

('35.0', '1239.0', '14242.0', '7.36855710409e+11')

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\n", "

('35.0', '1240.0', '14263.0', '7.40042106048e+11')

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\n", "

('35.0', '1241.0', '14285.0', '7.43238824768e+11')

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\n", " \n", "
\n", "

('35.0', '1242.0', '14307.0', '7.4644588884e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1242.0', '14328.0', '7.49663320561e+11')

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\n", "

('35.0', '1243.0', '14350.0', '7.52891142249e+11')

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\n", " \n", "
\n", "

('35.0', '1244.0', '14371.0', '7.56129376249e+11')

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\n", " \n", "
\n", "

('35.0', '1245.0', '14393.0', '7.59378044929e+11')

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\n", "

('35.0', '1245.0', '14414.0', '7.6263717068e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1246.0', '14436.0', '7.65906775921e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1247.0', '14458.0', '7.69186883089e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1248.0', '14479.0', '7.72477514649e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1249.0', '14501.0', '7.75778693088e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1249.0', '14522.0', '7.79090440921e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1250.0', '14544.0', '7.82412780681e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1251.0', '14566.0', '7.85745734928e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1252.0', '14587.0', '7.89089326248e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1252.0', '14609.0', '7.92443577248e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1253.0', '14631.0', '7.95808510561e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1254.0', '14652.0', '7.99184148841e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1255.0', '14674.0', '8.02570514769e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1256.0', '14696.0', '8.05967631049e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1256.0', '14718.0', '8.09375520408e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1257.0', '14739.0', '8.127942056e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1258.0', '14761.0', '8.16223709401e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1259.0', '14783.0', '8.19664054609e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1259.0', '14805.0', '8.23115264048e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1260.0', '14826.0', '8.26577360568e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1261.0', '14848.0', '8.30050367041e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1262.0', '14870.0', '8.3353430636e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1262.0', '14892.0', '8.37029201448e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1263.0', '14914.0', '8.40535075249e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1264.0', '14935.0', '8.44051950729e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1265.0', '14957.0', '8.47579850881e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1266.0', '14979.0', '8.51118798721e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1266.0', '15001.0', '8.54668817288e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1267.0', '15023.0', '8.58229929649e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1268.0', '15045.0', '8.61802158889e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1269.0', '15066.0', '8.6538552812e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1269.0', '15088.0', '8.68980060481e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1270.0', '15110.0', '8.72585779129e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1271.0', '15132.0', '8.76202707248e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1272.0', '15154.0', '8.79830868049e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1272.0', '15176.0', '8.83470284761e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1273.0', '15198.0', '8.87120980641e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1274.0', '15220.0', '8.90782978969e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1275.0', '15242.0', '8.94456303049e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1275.0', '15264.0', '8.98140976209e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1276.0', '15286.0', '9.01837021801e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1277.0', '15307.0', '9.05544463201e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1278.0', '15329.0', '9.09263323809e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1279.0', '15351.0', '9.12993627049e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1279.0', '15373.0', '9.16735396369e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1280.0', '15395.0', '9.20488655241e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1281.0', '15417.0', '9.24253427161e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1282.0', '15439.0', '9.28029735648e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1282.0', '15462.0', '9.31817604248e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1283.0', '15484.0', '9.35617056529e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1284.0', '15506.0', '9.39428116081e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1285.0', '15528.0', '9.43250806521e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1285.0', '15550.0', '9.47085151489e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1286.0', '15572.0', '9.50931174649e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1287.0', '15594.0', '9.54788899689e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1288.0', '15616.0', '9.58658350321e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1288.0', '15638.0', '9.62539550281e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1289.0', '15660.0', '9.66432523328e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1290.0', '15682.0', '9.70337293248e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1291.0', '15704.0', '9.74253883849e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1291.0', '15727.0', '9.78182318961e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1292.0', '15749.0', '9.82122622441e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1293.0', '15771.0', '9.86074818168e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1294.0', '15793.0', '9.90038930048e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1294.0', '15815.0', '9.94014982008e+11')

\n", "
\n", " \n", "
\n", "

('35.0', '1295.0', '15837.0', '9.98002998001e+11')

\n", "
\n", " \n", " x: \n", "
\n", " " ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "StaticInteract(croissances_comp, x=RangeWidget(0,1000))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "C'est moins spectaculaire que pour $x\\to +\\infty$, mais maintenant, êtes-vous convaincus ? Et surtout : voyez-vous mieux ce qui siginifie *croître plus vite que* ?" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }