#For each case of size in 1000, 10000, we give all the choose_vectors to draw planar graphs. The order is as follows
BINARY TREES
#ch_1_or_u
#ch_1_or_v
#ch_u_or_v
#ch_dxu_or_dxv
#choose_vector_dxu                dxu = D*(1+v)^2+x*D*dxv*(1+v)+x*D*(1+v)*dxv
#choose_vector_dxv                dxv = D*dxu*(1+u)+(1+u)*D*dxu
#ch_dyu_or_dyv
#choose_vector_dyv                dyv = (1+u)^2+D*dyu*(1+u)+D*(1+u)*dyu
#choose_vector_dyu                dyu = x*(1+v)^2+x*D*dyv*(1+v)+x*D*(1+v)*dyv

3-CONNECTED NETWORKS
#ch_K_in_dyK
#ch_dxK_in_dxyK
#ch_b_or_dxb
#ch_3b_or_dyb

NETWORKS
#choose_vector_non_trivial_D       nontrivialD  = S+P+H
#choose_vector_D                   D = y+S+P+H
#choose_vector_P                   P = y*(exp(S+H)-1)+(exp(S+H)-S-H-1)
#ch_y_or_P_or_H
#ch_S_or_H
#poisson_S_plus_H
#poisson_at_least1_S_plus_H
#poisson_at_least2_S_plus_H
#choose_vector_dD                  dD = dS+dP+dH
#choose_vector_dS                  dS = (dP+dH)*x*D+(y+P+H)*D+(y+P+H)*x*dD
#choose_vector_dP                  dP = y*(dS+dH)*exp(S+H)+(dS+dH)*(exp(S+H)-1)
#choose_vector_dH                  dH = dxK+dD*dyK
#ch_dP_or_dH
#ch_dS_or_dH
#choose_vector_ddD                 ddD = ddS+ddP+ddH
#choose_vector_ddS                 ddS =(ddP+ddH)*x*D+2*(dP+dH)*D+2*(dP+dH)*x*dD+2*(y+P+H)*dD+(y+P+H)*x*ddD
#choose_vector_ddP                 ddP = y*(ddS+ddH)*exp(S+H)+y*(dS+dH)^2*exp(S+H)+(ddS+ddH)*(exp(S+H)-1)+(dS+dH)^2*exp(S+H)
#choose_vector_ddH                 ddH = dxxK+2*dD*dxyK+ddD*dyK+dD^2*dyyK
#ch_ddP_or_ddH
#ch_ddS_or_ddH

2-CONNECTED PLANAR GRAPHS
#ch_xy_in_dB:
#ch_y_in_ddB;
#ch_nontrivialD_or_dD;
#ch_dD_or_ddD;

CONNECTED PLANAR GRAPHS
#poisson_dB;
#ch_dC_or_ddC;
#ch_2ddC_or_dddC;
#choose_vector_dddC;               dddC = (2ddC+z0*dddC)*ddB*dC+(dC+z0*ddC)^2*dddB*dC+(dC+z0*ddC)*ddB*ddC

PLANAR GRAPHS
#poisson_C
#choose_vector_ddG;                ddG = ddC*G+dC*dG
#choose_vector_dddG;               dddG = dddC*G+2*ddC*dG+dC*ddG


case1000

0.6617244467515780200511702962325881919461

0.2858251517783132686093476090623008806938

0.1698436191398492749386028612247707092676

0.2321895767742127528955015279566147411533

0.03364843240680449808471298087340416706550 0.5168242162034022490423564904367020835326

0.5

0.2285947884014483960930573391284945286581

0.02007003083676521369847607696835456844309 0.5100350154183826068492380384841772842214

0.01385650199231473983487769712576176063940 0.5069282509961573699174388485628808803199

0.1024186339843654088037543604405321750267

0.01078061073976556641541284415055264091231

0.04397710280058422475312116307218613644848

0.05298452306100625068693168769815943010836

0.4660980406256318969676434530337222753358 0.9775045672000547793842549895471948329106

0.9139901861623577263938392347438175635566 0.9540791918666581513318925044172412095482 0.9980651720126795196882953091624282504390

0.9776957743366559526051044383289644084969

0.9521613895390013713258541952830207443762 0.9979843673019496028613979774671459196261

0.9539587939187408325415350815314737108849

0.9550625627761989300667508518887029560007 0.9989748398562405061169344619461292715323 0.9999843486326860775747606019203818686690 0.9999998205088520230686378064525883028181 0.9999999983519954010736528261644137986101 0.9999999999873851008017380187182014682638 0.9999999999999172092428080840487939578917 0.9999999999999995244812781665377625046808 0.9999999999999999975719557422571511442908 0.9999999999999999999888409143658784692551 0.9999999999999999999999533729088851652295 0.9999999999999999999999998213994295992454 0.9999999999999999999999999993684850860353 0.9999999999999999999999999999979264506281 0.9999999999999999999999999999999936453174 0.9999999999999999999999999999999999817418 

0.9771869468511542351667769269730548848458 0.9996517076121636795576030873024366339053 0.9999960057546877225110161493963831273949 0.9999999633266892653708534060126332175058 0.9999999997192786242918963748379480626388 0.9999999999981576439978186849703973926415 0.9999999999999894182055940296433099759852 0.9999999999999999459683415934356493439503 0.9999999999999999997516750770956041104947 0.9999999999999999999989623998608861749471 0.9999999999999999999999960255728534034220 0.9999999999999999999999999859467973035605 0.9999999999999999999999999999538569731625 0.9999999999999999999999999999998585882295 0.9999999999999999999999999999999995936984 0.9999999999999999999999999999999999988990 

0.9847327586726837381152302634675725976245 0.9998249140399482399243806940728880628418 0.9999983924417965736144000075308611956707 0.9999999876947038225654232192216403065546 0.9999999999192411471555033948805625695205 0.9999999999995361517664063415100891406535 0.9999999999999976315463759265338353084767 0.9999999999999999891147878679728590320361

0.9999999999999999999545172611336188979887 0.9999999999999999999998257827603931363986 0.9999999999999999999999993839841337874887 0.9999999999999999999999999979773410189676 0.9999999999999999999999999999938012782260 0.9999999999999999999999999999999821900026 0.9999999999999999999999999999999999517913 0.9999999999999999999999999999999999998301 0.9999999999999999999999999999999999999528 0.9999999999999999999999999999999999999531 0.9999999999999999999999999999999999999531 0.9999999999999999999999999999999999999531 0.9999999999999999999999999999999999999531

0.3891055567196265438398451709330015846671 0.9115742753315270788064697449886501066669

0.06556816973018705495140465484758324724139 0.8969713872958465274108053558476907144077

0.9569950930811788631969196173719087817784

0.7662545200247689769194826778415390779602

0.8552520396262805172195396984512919435887

0.8148273670963818568676877073503991475468

0.08882042811854977377343780748625244283478 0.6136896022043691612101041376142432527372

0.4284354825511204143503399326029708114272 0.4730383738098058161537781886946944915541 0.4785656245010309247398601307298842777281 0.5486510642484957321773936617866153505577

0.9478297131471680966695135700662347375105 0.9526183374568819273400782737421180406789 0.9952113756902861693294352963241166968314

0.5526547183924505484939228217008572314645 0.8951794326844550528405811516844186037941 0.9486833341396894432953166957482416281936

0.5760326397595181453061300662911849659944

0.1869388877214057136460781659937407661589

0.9779745059482966525571810508094799486627

0.9508157664451582952074940263488870201543

0.4097048313203836995890742553961161981762

0.07204630151125108008895823121416621322632

0.9617210129144002475253593048102995371189 0.9992578281915543947169032672223063410464 0.9999903756155112240413610101473937699578 0.9999999062718261617055708771135471919081 0.9999999992692965194890507764252732742789 0.9999999999952510986625110415478058079732 0.9999999999999735394001943915322610787696 0.9999999999999998709726339975262239147338 0.9999999999999999994406820787513188839696 0.9999999999999999999978177096886178511100 0.9999999999999999999999922589583108413144 0.9999999999999999999999999748280099094058 0.9999999999999999999999999999244404843201 0.9999999999999999999999999999997893853612 0.9999999999999999999999999999999994520572 0.9999999999999999999999999999999999986630 

0.9598542591280796711508998135832082929056

0.8349372342998613159880465101455208406446

0.2432150018911660512475627559812376703130 0.8942187008662588773362240626653251222120

0.9632712156224423142868547681962895808695 0.9993170852451002676091479876196683611671 0.9999915083441098629872875850409111116863 0.9999999207090814804479288370961515211482 0.9999999994073250455266363937405810517440 0.9999999999963069607073928339247270320330 0.9999999999999802711555809884026418973631 0.9999999999999999077657591181518543611929 0.9999999999999999996166676203912745899798 0.9999999999999999999985660490533321821826 0.9999999999999999999999951233104462914553 0.9999999999999999999999999847964023659072 0.9999999999999999999999999999562457294235 0.9999999999999999999999999999998830711207 0.9999999999999999999999999999999997083448 0.9999999999999999999999999999999999993179 

0.5228362965650393318737704603985549434846

0.7258318572428006381384938434087156909740 0.8659765283663035476955287795977248835963


case10000

0.6555410421528204868268866226466062451797

0.2819959453606310344033925095368809490853

0.1710692050781203161735415238933961027360

0.2305097115910830985084671172699999783268

0.01070828643549451802688641337274819561550 0.5053541432177472590134432066863740978076

0.5

0.2293834507206473691014551584061148930687

0.006340323787193681923428935497088356992176 0.5031701618935968409617144677485441784967

0.004395833657000865282203577263455120009365 0.5021979168285004326411017886317275600045

0.09887227621809492172304264670026514061165

0.003466846030940132430227668562158782282799

0.01422380197405583875806444106805263802667

0.01737561898560579587889689732716192405696

0.4660450662320354787903273100640185592406 0.9774590972165085034485311855558614455188

0.9139368590062744342410859200525609975617 0.9540461612508322732477649298989160368402 0.9980600591056185102722396536364380662360

0.9776814277807337582047753429048138191305

0.9521259671995741157203691395948569482917 0.9979789981308103669345925654562132853290

0.9538650223032189450975073317278092068268

0.9550334481575270053951502366549727789542 0.9989735007680102013291621746569884681723 0.9999843178378923281955614210534971206075 0.9999998200367301044262799250014866620138 0.9999999983465667452746364296562155442393 0.9999999999873351640312566417971884601512 0.9999999999999168264468284829202084153866 0.9999999999999995219661072079021334691215 0.9999999999999999975574954949455628470009 0.9999999999999999999887670165802121631832 0.9999999999999999999999530330257194233578 0.9999999999999999999999998199782949930608 0.9999999999999999999999999993630381505608 0.9999999999999999999999999999979071794990 0.9999999999999999999999999999999935820064 0.9999999999999999999999999999999999815474 

0.9771719380310539506835922490163142274384 0.9996512482842222455070277752132408328031 0.9999959978414505514727594363181515406030 0.9999999632297077054589908737677468542814 0.9999999997183498522832957585512522730404 0.9999999999981503239682933437721104538053 0.9999999999999893691227544698529755475621 0.9999999999999999456817477664058216948548 0.9999999999999999997501924661882176435655 0.9999999999999999999989555131012688823577 0.9999999999999999999999959965419265948626 0.9999999999999999999999999858347633220674 0.9999999999999999999999999999534582836531 0.9999999999999999999999999999998572718322 0.9999999999999999999999999999999995896387 0.9999999999999999999999999999999999988817 

0.9847226752646731123351474179133651081545 0.9998246825089710713085960972083725510078 0.9999983892503733097821182943648635319675 0.9999999876621086757235673281267270162434 0.9999999999189735846072764943619199108758 0.9999999999995343066240142607744805857090 0.9999999999999976205491159308429811929007 0.9999999999999999890569977358741268058598 0.9999999999999999999542454852211293235191 0.9999999999999999999998246255823708902305 0.9999999999999999999999993794814164598366 0.9999999999999999999999999979612059746853 0.9999999999999999999999999999937476876956 0.9999999999999999999999999999999820236046 0.9999999999999999999999999999999999507940 0.9999999999999999999999999999999999993123 

0.3863227063309027336506058624601703661740 0.9088059822521392309530307441326839766969

0.06637631584521710489998629353555705945149 0.8961766896243411025736650083886381432380

0.9569684295031372171205429600262804987799

0.7645864681449901009421614081667122271607

0.8513974385419680154225908152525064030393

0.8090244526538951837665827083281588238568

0.08184238593247331757456964793851919317540 0.6050878717128776913491864915553720587440

0.4687726682350615367469967761262876115640 0.4840732318240778872377177335545771773423 0.4859876141413456679739559772200619883494 0.5099201741546085451412551360397417305752

0.9540491337469277059706423164397971723497 0.9555744169570150147394317043489263698206 0.9984747167899126912312106120908708025272

0.5533484221924193919260021788667853152309 0.8938234908771469242303775876220312157613 0.9481857255727188690803208734275131746908

0.5698863438733317955290547438303024329290

0.1716656759222132629226192230232961943669

0.9779613764891599617765672896377688574596

0.9506620864108942651158377626844727753263

0.4075315156808300986428709834840174147792

0.02383502205703488950551945928507080127172

0.9617029016575161644090151194677722784252 0.9992571211227633357086440505803855253763 0.9999903618134242627695599818139397187029 0.9999999060922136444235986553618247720552 0.9999999992675434880228427269489253365908 0.9999999999952374108887295211514190567229 0.9999999999999734503377339534336327049414 0.9999999999999998704759161357295207708913 0.9999999999999999994382580770105886255184 0.9999999999999999999978071948269541795638 0.9999999999999999999999922179079747449904 0.9999999999999999999999999746823174098327 0.9999999999999999999999999999239664943865 0.9999999999999999999999999999997879619226 0.9999999999999999999999999999999994480885 0.9999999999999999999999999999999999986534 

0.9598289352871135523909375929792625527445

0.7051839276326086024069249978055580129852

0.1362580553709650205671587958348816463879 0.9499457730822961285528195238226739139358

0.9632546611819397845416978125708145085422 0.9993164656312055664193023893263942562695 0.9999914967483877003086890305724743297400 0.9999999205644099078376895278482274638362 0.9999999994059713223176198158992703544048 0.9999999999962968270424259729729011135994 0.9999999999999802079403148857670610568700 0.9999999999999999074277482869242929166565 0.9999999999999999996150862000367702727941 0.9999999999999999999985594723005564181651 0.9999999999999999999999950986944041751288 0.9999999999999999999999999847126432165110 0.9999999999999999999999999999559844785590 0.9999999999999999999999999999998823189423 0.9999999999999999999999999999999997063343 0.9999999999999999999999999999999999993133 

0.5228832048293774359172171012578365967854

0.8483959782128407402217490283458052417165 0.9258937769867637784959677934748608918619

case100000

0.6535793265240730851820582371764876629700

0.2807827160119671781679974008176573333904

0.1714490129497411608587807645644161886098

0.2299775079997770591355841837819139372363

0.003393056421354731450818558839906082700900 0.5016965282106773657254092794199530413504

0.5

0.2296223972370316669935962953322340493731

0.002004355829011561535324703639436691837281 0.5010021779145057807676623518197183459187

0.001391489632699480275545958682846410710287 0.5006957448163497401377729793414232053550

0.09773039547922473606195654583045925893144

0.001102184871781217753066212096027822223543

0.004530741754294998700666018471876276189113

0.005559799874925148777261420065534921068622

0.4660396008409005442428143841077304367589 0.9774543872428041135879252717493429891486

0.9139314911518395025831665268558747761105 0.9540428246604077374676942795907363388890 0.9980595327289200856620646855395951941813

0.9776799836347847105459137532705742672125

0.9521223898730108726191699359333356990056 0.9979784454814195522206612175265703803470

0.9538553109473722189868682827817141867564

0.9550305174213091237806156784129587530746 0.9989733659235202398556491887350098357537 0.9999843147357645473382653210459938912881 0.9999998199891533401348931731529483237826 0.9999999983460194881995301317782490267351 0.9999999999873301281224751084410775780399 0.9999999999999167878294241907967064434340 0.9999999999999995217122780473940047367466 0.9999999999999999975560356457289202443042 0.9999999999999999999887595534337159370547 0.9999999999999999999999529986874470121915 0.9999999999999999999999998198346659616700 0.9999999999999999999999999993624874475374 0.9999999999999999999999999999979052304151 0.9999999999999999999999999999999935756010 0.9999999999999999999999999999999999815280 

0.9771704271961928613097782247167748952199 0.9996512020299987787528633373315012653942 0.9999959970442989894532309339490315401736 0.9999999632199345654863986532736874146056 0.9999999997182562228650457147952740699387 0.9999999999981495857678549339322007522107 0.9999999999999893641711105823087771682945 0.9999999999999999456528246684970655641582 0.9999999999999999997500427863137026141468 0.9999999999999999999989548175816623754098 0.9999999999999999999999959936089163787144 0.9999999999999999999999999858234403443067 0.9999999999999999999999999999534179744880 0.9999999999999999999999999999998571386984 0.9999999999999999999999999999999995892359 0.9999999999999999999999999999999999988879 

0.9847216602343494360659915407879854913025 0.9998246591937829427976969234527827466689 0.9999983889288796336990523238864320185690 0.9999999876588239492606836524283140384408 0.9999999999189466115705640984777442529562 0.9999999999995341205470281939076650883142 0.9999999999999976194396715807222154804617 0.9999999999999999890511655283968496105466 0.9999999999999999999542180474720347658359 0.9999999999999999999998245087142868846100 0.9999999999999999999999993790265031446008 0.9999999999999999999999999979595752441792 0.9999999999999999999999999999937422699705 0.9999999999999999999999999999999820072921 0.9999999999999999999999999999999999512103 0.9999999999999999999999999999999999997771 

0.3854316290713562024044147692509962650716 0.9079163703607016405141069300445168885348

0.06662988921631177182408203921907688783107 0.8959313909831144289521372881039584015283

0.9569657455759197512915832634279373880551

0.7640713979003601148150534628253032224263

0.8501653615851473907500918343523153654541

0.8071608645806740940010627401936225125361

0.07963498437696750391225853284975211073552 0.6023610482925990792132956375423509904383

0.48295029918216550488541968424345132713740.4879216271784850428759775390468872296207 0.4885454765124624401064965488809684429530 0.4963101478278249096496532567546572046310

0.9560405511094318624365648908236725950423 0.9565239511008971210228585528866872554664 0.9995166000085347414137063379369853395756

0.5535958540088289148604002943074177138900 0.8933983286885962713825410472567936149060 0.9480337257586672521908512413440982332280

0.5679551645732395113378442548935271577828

0.1668538303815742183917982921832319575239

0.9779600589575766874456214436600029461009

0.9506192495864292071191439819687282156718

0.4068317716066115111159564465900935744464

0.007648834492449841599000189606219592871462

0.9617010903023023507838315707464936033735 0.9992570503881616029717343924290760165189 0.9999903604323081114198903694969726560272 0.9999999060742358157780943127372670302099 0.9999999992673679765411216226895880343050 0.9999999999952360401211766949156903449289 0.9999999999999734414161728784374432348359 0.9999999999999998704261457392412525986531 0.9999999999999999994380151312073850534767 0.9999999999999999999978061406945118670396 0.9999999999999999999999922137915188426914 0.9999999999999999999999999746677037474339 0.9999999999999999999999999999239189382993 0.9999999999999999999999999999997878190688 0.9999999999999999999999999999999994476898 0.9999999999999999999999999999999999986521 

0.9598252415593451566038643806078615052753

0.4730447679412827366680896911927335858688

0.07623941465330829775244856965773683408937 0.9812129048856527659087783605315397087935

0.9632530057363897304305010759097933604241 0.9993164036541123230033184190018027684799 0.9999914955882287064196882153619675971403 0.9999999205499317749136258718004322747212 0.9999999994058358130895046645198466138144 0.9999999999962958123949708681204373586801 0.9999999999999802016091995769219714129457 0.9999999999999999073938873877299676781331 0.9999999999999999996149277381570376785760 0.9999999999999999999985588131287898277404 0.9999999999999999999999950962265760967823 0.9999999999999999999999999847042440049629 0.9999999999999999999999999999559582741975 0.9999999999999999999999999999998822434769 0.9999999999999999999999999999999997061323 0.9999999999999999999999999999999999993126 

0.5228954065377459247131744719562191709161

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