import Mathlib
import Proof.Pieces
-- import Proof.Eqns

-- vol' e.1 =sum(vol' e.2)/4; e.3 is the coefficient of this eqn for linear_combination
def part0: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 0 0], [[], [Piece.treePiece 0 3 3], [], [Piece.treePiece 1 3 3]], 1/4) ,
  ([Piece.treePiece 0 0 3], [[], [Piece.treePiece 1 3 3], [Piece.treePiece 0 3 3], []], 21330466264694411118705366274969148868597023488809482950268001379227926734844653002742531656783041090887107469343925961194056902636554948928340001407335855138766815143504103340041316806185810931015033900383375938862019/154866390708323530670381178291540808500932175557095479800438653104944580267698405240939599604178028046983621932505732389308889591544694394643480685766119607291179630329136764331873408772421837889405020894961858799002472) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 4543266721356550064243107471444960050283001566395774737049476090769189190178861929218647835457199588650983572629663499168361114217338184992257720653768009396300288218933687996433023103186765454982462654090345294819007/88583575485161059543458033982761342462533204418658614445850909576028299913123487797817450973589832042874631745393278926684684846363565193736070952258220415370554748548266229197831589817825291272739671951918183233029413984) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 1115450993719087277353641734487976850523441625456237448932061920167766172103997034613901086263751163436461296199173501354173477583758547159469782885277843527178099582020875028325486699066395218544456617515604125407341909/3294201713354426901772345638733937422825453539318867224705080699858552403019279702481336458080371879094400368031812560086086717724145080642060138537102571696592504711638650398294362246350378019205006550711957438978281332530) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 43710584766378878470654003533016087088577949682558182883150696569548457669884315719320949780723012232093738517109299533538955466363269126230896794644251021515441146151200862874167863516622905614409329835827750718515045406667844983/264986915393665946273467536755472237441069134314982502627549707824361192929262820917871711299200425190015538143773783505979466895155936241953657453560221771828022512026402700629830294524652912442382907064281786624270113437250509900288) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 36757239554447307382641698603997641440079785000771222433787336778672856959868726839623575098246425284802629151002754514747380709945803786235473642199155828153053528977434098812231314851292600050478209058663988478455421684684381321/264986915393665946273467536755472237441069134314982502627549707824361192929262820917871711299200425190015538143773783505979466895155936241953657453560221771828022512026402700629830294524652912442382907064281786624270113437250509900288) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 52138520992433300847128804448658835438348301423483302174633511382261274371661619665077713966201626050298498423375379513349102680103917068751268332102297684785684575203236296406110463154090751976693806776659670792515332533185053/2591110121265443114931504247608944730136724673391036174445550730958875231137694660961634380581956729221741095184729789440975692615091153582392554404230687174480971591265255850014509347446174921480029965904202871980466923816662669952) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 80489827794983333227976969626602833342194284473396062981147288566130816209998260118548799631716314485025671370784317092062093256999341319521876483010893186035685929514467220840549470039538952591002400554565236549757934791177/15423274531341923303163715759577051965099551627327596276461611493802828756771992029533537979654504340605601757051963032386760075089828295133289014310896947467148640424197951488181603258608184056428749797048826618931350737003944464) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 50289827199278044046213618607355619953040689666413884353481752828654209625586396871452139682233249701119334506393908820777455221921458467402306125987795065735024692015561819547343391758458636665782027353917222496988999/310042514198063708402103118939664698618866215465305150560478183516099049695932207292361078407564412150061211108876476243396396962272478178076248332903771453796941619918931802192410564362388519454588851831713641315602948944) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 840348595160654262987252974180487162419452519693010176855013487122181586130053342986642659523191971411756198519221260061151485286106392688879965735622073006041480445692832040303611659721861769594689233939935807199503/22145893871290264885864508495690335615633301104664653611462727394007074978280871949454362743397458010718657936348319731671171211590891298434017738064555103842638687137066557299457897454456322818184917987979545808257353496) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 440163020043993437726258591582655350578867403701289068553003386948397213302274165970530906319807609504163702318569135064439331388738166795660664487442054437251472504534020245008082122895344758391314488612739845400109/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 152665602839421536445169349023080535011320182087229687698236465802932367309568926468568460469061730771692598445272547934546716114653149273707908206823069852053556472915419818424204419027255997367864018597144110924851/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
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]
def part1: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 5 2 2, Piece.treePiece 6 0 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 0], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3, Piece.trianglePiece 0]], 2962588487667255179988503084453038002462841927313395484255009555113842463889424528944370314800325338991181691900104205487047400242398903014316116761843890201835735257125987138882787103989260498330885126765556533878815/1342175386138803932476636878526687007008078854828160824937134993576186362320052845421476529902876243073858056748383014040677043126720684753576832609973036596523556796185851957542902876027655928374843514423002776258021424) ,
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]
def part2: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part3: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1], [[Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 10318027203105536856778402841519682793585381498041830262572636406550577986271437834931669902507736431249395180603081077491110051598614869290603620896366467133045384307291191797661055085618891824565219029458329968457099/5536473467822566221466127123922583903908325276166163402865681848501768744570217987363590685849364502679664484087079932917792802897722824608504434516138775960659671784266639324864474363614080704546229496994886452064338374) ,
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]
def part4: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2], [[Piece.treePiece 2 2 3, Piece.treePiece 3 1 2, Piece.treePiece 3 3 0, Piece.treePiece 6 0 0, Piece.treePiece 6 1 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 0 2, Piece.treePiece 5 1 0], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2]], 82022861403991761934216988201288030871737305015957741713327810743537905520161925818629673381451398614001894506750997255658721493164345811404371547220793202674610986002028456425828585581054075485575736790604911236240/145696670205857005828055976945331155366008559899109563233307417065836019593953104930620807522351697438938539054923156129415600076255863805486958803056283577912096625901753666443801956937212650119637618341970696106956273) ,
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  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 0 2, Piece.treePiece 5 1 0], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2]], 135760963979314937967147441050238581738405253672180728829635702402153160073171435713629607013871601871216000899123683648748892241686795579279528249153644369851608027443945118832647922919187187348358158311929720298463237/11250114086615454562019170315810690492741716961169644034623065516155594088966682950322816273645908669445078231664946423688954975488172779604481010936793992752060453065629811108124611906863811991637938337893609270594735575968) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.trianglePiece 3]], 26600762586092154677910622341506043920056397224061604730271779812741331902892269516321099662664186904262110498390711716707498767619615196118482869783583435507631685393238677015657857652519077908518424124302988885863765248/5433209849051511993911205874080936922306641209272821779397081024933500906319218921568975835329961961728169529846001214775038212892160751925276116957208975457514640633260090339881017273589702926556889974103966675965986850691)
]
def part5: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3], [[Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2]], 288515267750721304262722189101704682938319214489718083190976436871605466406559472671683605102400965305269888128239972744984896758617196004759988986046140489399050976591578966065065508331795480711391704914894481172109902967/478122466716533055464186116919122449162984426416008316586943130194148079756091265098069873509036652632078918626448106900203362734510146169424298292234389840261288375726887949909529520075893857537006317721149067485006842860808) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2]], 2014669173919380868182880766661352090108182367185128151869423064537084360440877186711119400403028311505050231442813759067991715210338844105723807964493010571517538479050992389077878783736247677456066663319380514923848293/5254093040841022587518528757352993946845982707868223259197177254880748129187816099978789818780622556396471633257671504397839150928682924938728552661916371871003168964031735713291533187647185247659410084847791950384690580888) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.trianglePiece 0], [[Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2]], 2535589426241479915822643084540425814095005757423556573749728090688232190757060274055785086892166390901219500067704193672925178607651480715321821426098037223783000326904083389311294516671742616753575625866432433083488/922745577970427703577687853987097317318054212694360567144280308083628124095036331227265114308227417113277414014513322152965467149620470768084072419356462660109945297377773220810745727269013450757704916165814408677389729) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.trianglePiece 0], [[Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0]], 33301149573481613348206403145056967000611793952880780647421116421003705733477122883274969802822685773693852201676408655706426899255294982125340015197511132644635912166617318119756338403269397061486180895307058874291328/922745577970427703577687853987097317318054212694360567144280308083628124095036331227265114308227417113277414014513322152965467149620470768084072419356462660109945297377773220810745727269013450757704916165814408677389729) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 135481986144658018969690161276488088181169098016255195216410053000486385917021379614904648393912780131370428599981116284345503310881916040735643613940645119280427605650889556415408652590633358061076640697614821067173744107833076/496612363669788527152297068176853060173189392122394180266916781515780304476572471145128784370696179890263919658927988149933314545517422914092754138085311380357260275170253414931769522262045618380995536861897193369159159125850853237) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 5 2 2], [[Piece.treePiece 2 2 3, Piece.treePiece 3 3 0, Piece.treePiece 6 0 0], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 5 1 0], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 6 1 1], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 0 0]], 776954847446348761925054353843504662016045129951113645491219876836907469356009770299082824928738820301264777524309136244687802426518987319782153037709519671126493458638583021842579848094577189223653491413574275989399171/44291787742580529771729016991380671231266602209329307222925454788014149956561743898908725486794916021437315872696639463342342423181782596868035476129110207685277374274133114598915794908912645636369835975959091616514706992) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1], [[Piece.treePiece 2 2 3, Piece.treePiece 3 3 0, Piece.treePiece 6 0 0], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 6 1 1], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 0 0]], 28458157522811480690607316017387688499866662576457260494670010086722980929131304326462258814703949490576004204460943663829919062753555486869126818186884743029397743420283979762624729597990756404787813369745599560517287953/24379273713825234629505632261558742795294744319098713224158120023317849085181439884235699689155844079193557742777629067034857811353754517863969587527550236739253885645919814956809287840166342283000657595979422427950701145536) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 6 1 1, Piece.trianglePiece 2], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 0 0, Piece.trianglePiece 1]], 303846467084775276820103844050237551742787961707454417577177642475584030068710170343674728641122220009431882992965354768297816635133532172259158072715328291185688461706726354511950901725591145363691405783305694179903/5536473467822566221466127123922583903908325276166163402865681848501768744570217987363590685849364502679664484087079932917792802897722824608504434516138775960659671784266639324864474363614080704546229496994886452064338374) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 5 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 0 0, Piece.trianglePiece 1, Piece.trianglePiece 3]], 33870496536164504742422540319122022045292274504063798804102513250121596479255344903726162098478195032842607149995279071086375827720479010183910903485161279820106901412722389103852163147658339515269160174403705266793436026958269/1986449454679154108609188272707412240692757568489576721067667126063121217906289884580515137482784719561055678635711952599733258182069691656371016552341245521429041100681013659727078089048182473523982147447588773476636636503403412948) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 5 2 2, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 5 1 0], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 2], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 0 0, Piece.trianglePiece 1]], 9477688723164548054397284303511830896038351122479223031425208459156074467095085350237036445664475807378238587653927504440003472230234944789205946386188883417026852165039331146632402518402856330644950984589669342665673/2109132749646691893891857951970508153869838200444252724901212132762578569360083042805177404133091239116062660604601879206778210627703933184192165529957628937394160679720624504710275948043459316017611236950432934119747952) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3], [[], [Piece.treePiece 1 3 3], [Piece.treePiece 0 3 3, Piece.treePiece 6 3 3], []], 776954847446348761925054353843504662016045129951113645491219876836907469356009770299082824928738820301264777524309136244687802426518987319782153037709519671126493458638583021842579848094577189223653491413574275989399171/44291787742580529771729016991380671231266602209329307222925454788014149956561743898908725486794916021437315872696639463342342423181782596868035476129110207685277374274133114598915794908912645636369835975959091616514706992) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 121582319222270518017879541977905923249067664577826881368470416425052646366696328487806835510969185805560358808800784780371212858340192391493459043887572804480661004707201399561621497488620376212284256365295955781183/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
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  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 3 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 0 2, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1]], 135760963979314937967147441050238581738405253672180728829635702402153160073171435713629607013871601871216000899123683648748892241686795579279528249153644369851608027443945118832647922919187187348358158311929720298463237/11250114086615454562019170315810690492741716961169644034623065516155594088966682950322816273645908669445078231664946423688954975488172779604481010936793992752060453065629811108124611906863811991637938337893609270594735575968) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1], [[Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 2184316755847326822188337931351143322054941095328038656496876450636377095090060812357354946564061036107851663670555702791318161006281519729979744628604825807826073880838555682148506551216097070188243701864885824824464/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
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]
def part6: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2]], 59170338631281924952315007869678167470688942018620235153066771762706780619123930603558608655878677653430828198091559650864905667643856807162088474303233255554214251203766632999839976764325625669435010777167133456863/44291787742580529771729016991380671231266602209329307222925454788014149956561743898908725486794916021437315872696639463342342423181782596868035476129110207685277374274133114598915794908912645636369835975959091616514706992)
]
def part7: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 1], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2]], 6068336110364640177034712901203082834460296436520386909463122285741399726185604378430772999850016378117302581948448516660766730287723336639275153182953352946059291389996488067623360258535606651969494790286977072482657/44291787742580529771729016991380671231266602209329307222925454788014149956561743898908725486794916021437315872696639463342342423181782596868035476129110207685277374274133114598915794908912645636369835975959091616514706992) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 2943691797480358881958821108556534279217039688846659979123166919526630048764833134757369102425093640666686495251984349585143065062016055546310436651453864531531038136711184750868877543400670885231291190074419396485603187533359951994553692771/8892759862114434312346219573705791119925184747991872602405558927708339301328438483587918878121179079987493350076765172388499107499926962058507430216179408208972930452642325504311437283910660910336351565742112461467307753709774792948701501184000) ,
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  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.trianglePiece 0], [[Piece.treePiece 1 2 3, Piece.treePiece 3 1 0, Piece.treePiece 4 2 3, Piece.treePiece 6 1 0, Piece.trianglePiece 0], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3]], 177637430470673140324785441733525504520947540294649219500556741574584640840243920235918170119281851592020860263099115924184036965646201731006953794699366194845978066771885714781881235388067570386275224745932971586286470695/1434367400149599166392558350757367347488953279248024949760829390582444239268273795294209620527109957896236755879344320700610088203530438508272894876703169520783865127180663849728588560227681572611018953163447202455020528582424) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 5 2 2, Piece.treePiece 6 3 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3]], 906782894124014393565048534167329343368024662011505131108947875709525534012210561486068794710327746379686461577435517623413722669510523911320213635945225273345116394311550621450274473072269268720312101163999583110093278422196052739/1485669347956424434742876745512004206572304546101773886280295820642794887482483490486063796347986439518209560070103105775349352772773586399670871997330037180000499445898573025412823189915220089416356385167092523171318081412903550998080) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 5 2 2, Piece.treePiece 6 3 3, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 1899577922574583116232070343118189553256583964677695267340204016342989072818774698627792246662602109687779811366282304107638815959822817348294563197093794538622513309171750883837777085519528125753480262570998200248598/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 5 3 2], [Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 5 2 2, Piece.treePiece 6 3 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3]], 14435361502411153648004260486604501149018121222506146572608567926990391674802547283434654864901075442210807522103848982387954292236936562341394659703466429601688822771380278530674318518424930656237113273522740627152841/22145893871290264885864508495690335615633301104664653611462727394007074978280871949454362743397458010718657936348319731671171211590891298434017738064555103842638687137066557299457897454456322818184917987979545808257353496) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 5 3 2], [Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 5 2 2, Piece.treePiece 6 3 3, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 14256310735559278232570804955746460181491097739786610666973013974160354113322861268292621216591008237860219750096530474275282106060180741284492566592640493886903759679296756634397887886299672657391506381942612609843771/22145893871290264885864508495690335615633301104664653611462727394007074978280871949454362743397458010718657936348319731671171211590891298434017738064555103842638687137066557299457897454456322818184917987979545808257353496) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 4 2 0], [[Piece.treePiece 3 1 3, Piece.treePiece 6 1 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0]], 5126428837749485120888561762580501929483581563497358857082988171471119095010120363664354586340712413375118406671937328478670093322771613212773221701299575167163186625126778526614286598815879717848483549412806952265/145696670205857005828055976945331155366008559899109563233307417065836019593953104930620807522351697438938539054923156129415600076255863805486958803056283577912096625901753666443801956937212650119637618341970696106956273) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 3]], 2014669173919380868182880766661352090108182367185128151869423064537084360440877186711119400403028311505050231442813759067991715210338844105723807964493010571517538479050992389077878783736247677456066663319380514923848293/5254093040841022587518528757352993946845982707868223259197177254880748129187816099978789818780622556396471633257671504397839150928682924938728552661916371871003168964031735713291533187647185247659410084847791950384690580888) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 6 1 1], [[], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3], [Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 6 3 3], []], 190062618697472306206598075668463192950541214655122078566166871818535875792978086485144465876880543217112946572890310907078734910771394019529874636952317211356333151541722503406397899911269202187396170300063898472666987997907/40225801627811637138684293231571925612236328126512876819860898038474450990549375808988904487107142730669370275583087960607515388733694954475549819420457890619768911315767694678735324936274464766951085033366047006118656890134400) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3], [Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 2], [Piece.trianglePiece 3]], 760555108395315952917814952144738271979242864006750837750144779129932867129195534671551229316199238164832848290188820613836520774748491052628559074159713249623375119107333187629744689187640072311043421512721525744768/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.trianglePiece 1, Piece.trianglePiece 3]], 33870496536164504742422540319122022045292274504063798804102513250121596479255344903726162098478195032842607149995279071086375827720479010183910903485161279820106901412722389103852163147658339515269160174403705266793436026958269/1986449454679154108609188272707412240692757568489576721067667126063121217906289884580515137482784719561055678635711952599733258182069691656371016552341245521429041100681013659727078089048182473523982147447588773476636636503403412948) ,
  ([Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3], [Piece.treePiece 0 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 2], [Piece.trianglePiece 3]], 9477688723164548054397284303511830896038351122479223031425208459156074467095085350237036445664475807378238587653927504440003472230234944789205946386188883417026852165039331146632402518402856330644950984589669342665673/2109132749646691893891857951970508153869838200444252724901212132762578569360083042805177404133091239116062660604601879206778210627703933184192165529957628937394160679720624504710275948043459316017611236950432934119747952) ,
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]
def part8: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 0 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [[Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 1 3, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2]], 154899342761327093337413703063610809604331740119093148799287970509711042818522306980825891292164808424129996976181708677642836310359669074894825387535402496793680011165070039097034484093037044489918006434583181345002667/14763929247526843257243005663793557077088867403109769074308484929338049985520581299636241828931638673812438624232213154447447474393927532289345158709703402561759124758044371532971931636304215212123278658653030538838235664) ,
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]
def part9: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 0 3, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 88925569771373353066165155812684380119872581339146417915514346225259236684270277617815916188234967384239957378236839409470969667776064491634345843942683392242863161910303940578847456853576684908945525858939930973481/790924781117509460209446731988940557701189325166594771837954549785966963510031141051941526549909214668523497726725704702541828985388974944072062073734110851522810254895234189266353480516297243506604213856412350294905482) ,
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  ([Piece.treePiece 0 0 3, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3], [Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.trianglePiece 2], [Piece.trianglePiece 3]], 108512304747271385702351272631690515835993167968369776857723387193355916447490843150946127220226825307763405256075679265196555730235118556282193395044639114605072530368848789725684113417173565666611184163013221436466793/5536473467822566221466127123922583903908325276166163402865681848501768744570217987363590685849364502679664484087079932917792802897722824608504434516138775960659671784266639324864474363614080704546229496994886452064338374) ,
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  ([Piece.treePiece 0 1 0], [[], [Piece.treePiece 2 3 3], [], [Piece.treePiece 3 3 3]], 1/4) ,
  ([Piece.treePiece 0 1 3], [[], [Piece.treePiece 3 3 3], [Piece.treePiece 2 3 3], []], 1/12) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 2 2 0, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece]], 2542947254267486711761532948847287850820575882764524913309679920807664464143988900779951927125696332356492070758132975759201853324794581748994157359524317221423728914874589907323956877220752200675724691080066481997580/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
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]
def part10: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 2 2 0, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 0], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 0]], 797066862001191028208556213754230693169191453268216432808905410869927388189947299386958257713398349204475477832954279934185445309686943659640464399164308270197794329955300753060504198307651618522292400211764389472250/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
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]
def part11: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part12: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 2 2 0, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.trianglePiece 1], [[Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0], [Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3, Piece.trianglePiece 0], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 0]], 3568982846461264989402108009154598510849176930086649269916997007505208314581437920763623830414653142594076638062097243301641207278844207525579696940445026937540269042842996850047245738741450926343449968766911336386698085/1434367400149599166392558350757367347488953279248024949760829390582444239268273795294209620527109957896236755879344320700610088203530438508272894876703169520783865127180663849728588560227681572611018953163447202455020528582424) ,
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  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 1], [[Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 3], [Piece.fullPiece]], 33511125242715535226976802590310632643640405247457591003870235092567891367262098015163864648107894937968288955935819635072749884328591686440202487575728760101190162284651239242274095872697876269344119911319426067808/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
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]
def part13: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 1], [[Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 3], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 3 3 2, Piece.treePiece 5 2 1, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2, Piece.trianglePiece 1, Piece.trianglePiece 3]], 54902651818148812218496540233408242118253546452164062804655378601066196587412313639272611031668893877527704242987970126389345900224619266014631381392658392626106964639994303912550947618767366315501377231037099013763886828737260224219/452832017257118167709628832032058882163238425651820680538234166131923881704660967900152245126866266765150273909367426640326482725141389134619681784786195332464152231109885058145828508286159083254105426198929801062617751214653002344214784) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 3 3 2, Piece.treePiece 5 2 1, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2, Piece.trianglePiece 1, Piece.trianglePiece 3]], 5805644487434467480355158801028533656275220052901666277821901130529399884778964602583207375928386912628372250508576463267810708311504639363378370236994011103431680800385509370256881946949344514930131980682341169023821638676505674455101590271/2936389306470186209936721703237652227799296003786916333314315557929293637298650387280730813555613332211870304195347859922682405296475882871719153457382440590602861635462495881523636591147300232593063287008045534776505020274967636631661235690956800) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 3 3 2, Piece.treePiece 4 2 3, Piece.treePiece 6 0 2, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 3 3 2, Piece.treePiece 5 2 1, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2, Piece.trianglePiece 3]], 858194180531641750978575337405148599710222041812185874596104910014580743249961948044024034804747206690578908984109254385382582066578038297820341968803443445604132442745133711571876783655452699949429944126630841168/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 3 1], [[Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 2], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 3], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 5 2 1, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2, Piece.trianglePiece 3]], 27210143783339168573130757605216742539960661429578935328040904528347193919183611612000227472047241586911157517644417039547518145409240302670499562501771848739489841931866352232359994200951694336491803686913509648768/11983708804810749397112829272559705419714989775251435936938705299787378235000471834120326159847109313159446935253419768220330742202863256728364576874759255326103185680230821049490204250246927931918245664491096216589477) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 3 1], [[Piece.treePiece 2 3 3, Piece.treePiece 5 3 3, Piece.trianglePiece 0], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.trianglePiece 3], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.treePiece 6 3 0, Piece.trianglePiece 1]], 948079611256179232086061537252400983580321113969472071467963795076274993148648087864056188424954499531788344208382945443760807157806514873281791983290828504243547519553408183095472368817057730567560782738532007022987432/9851424451576917351597241420036863650336217577252918610994707352901402742227155187460230910213667293243384312358134070745948407991280484260116036241093197258130941807559504462421624726838472339361393909089609906971294839165) ,
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]
def part14: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 3], [Piece.fullPiece]], 4760131715999652884558673807752624073522989552697154993639438777747921435277587447936191003635021199288982169855474211915831060970599023285916432179078239097001040520857168132786842548154990092885468367269347365326283011/9473780283465645946963511844893213046519340598879700239682581487288921338077206695008687388333396774269539563507323304159119979358461288087984009209931783370156171002635630406841778447885315361379316495068302543658724695552)
]
def part15: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece]], 9749434834940019578543721393319087998245443994355527837884691345179487841840051202573595115603621042150983572833714928908994037353797017503568092284681109842879198586300388728550242238728890313047329230024215216356217479/34286061978256623427106042867232580549308089786421772295994104430188477223517509943840963881587531183070714610788408148385386591963955137842227842854991216006279476009538471948570245811394474641182288267866237777050622707712) ,
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  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 0], [[Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.trianglePiece 0]], 858194180531641750978575337405148599710222041812185874596104910014580743249961948044024034804747206690578908984109254385382582066578038297820341968803443445604132442745133711571876783655452699949429944126630841168/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 5805644487434467480355158801028533656275220052901666277821901130529399884778964602583207375928386912628372250508576463267810708311504639363378370236994011103431680800385509370256881946949344514930131980682341169023821638676505674455101590271/2936389306470186209936721703237652227799296003786916333314315557929293637298650387280730813555613332211870304195347859922682405296475882871719153457382440590602861635462495881523636591147300232593063287008045534776505020274967636631661235690956800) ,
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  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.trianglePiece 0], [[Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.trianglePiece 0]], 9074458410494823002001947497763966367903122768170816112904682153753011566710203067607709641826341256780673478213250609039355922712348522380234422465811492954688146571237152810274495670323669210422656221391847852163848/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 12160264403858748996767463579342903766973695393938401176889802276329329514296393229205063695831789465113884014698076484232228877220548543208381961081833741299706899057496674123875132033336674347378298383836045269744844569174158786910360457643/978796435490062069978907234412550742599765334595638777771438519309764545766216795760243604518537777403956768065115953307560801765491960957239717819127480196867620545154165293841212197049100077531021095669348511592168340091655878877220411896985600) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 3 1, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.trianglePiece 2], [Piece.fullPiece]], 28433906622257805001368983272959096441769114170247708307027573817905205060430292747456537820675687120678303393849703142092321816765945633084499574788151226084315600096173833641457375563106960846720513190099604187467719172146424771877/452832017257118167709628832032058882163238425651820680538234166131923881704660967900152245126866266765150273909367426640326482725141389134619681784786195332464152231109885058145828508286159083254105426198929801062617751214653002344214784) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 3], [Piece.fullPiece]], 6894886680778607340876531728436099761664457040724653320348340574016211520156883764107076201626259422498508209698778618886969409098780062459966548237602317485086760343876524906840806186825913026738979612673593171917138158872993/3596713397094437510190891915366135338331801105025755980841461536586556456061520693139513544913552290430835103332044902175314393148071090744689215262697363147415659431788307364241783617140853911320456446339992546621155093185781760) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 2 2 0, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 3], [Piece.fullPiece]], 59170338631281924952315007869678167470688942018620235153066771762706780619123930603558608655878677653430828198091559650864905667643856807162088474303233255554214251203766632999839976764325625669435010777167133456863/177167150970322119086916067965522684925066408837317228891701819152056599826246975595634901947179664085749263490786557853369369692727130387472141904516440830741109497096532458395663179635650582545479343903836366466058827968) ,
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  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 5 2 0], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1], [Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0], [Piece.treePiece 0 0 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1]], 15527043115147430374107840146597541128231208841009355655206279947983591752205828458276726274525750587130516029499308237845184286167894670850951036677583259212296304753440145189906255940804999471381559957663297941972329043850528752126357/4830208184075927122236040875008628076407876540286087259074497772073854738183050324268290614686573512161602921699919217496815815734841484102609939037719416879617623798505440620222170755052363554710457879455251211334589346289632025004957696) ,
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  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 2 2 0, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.treePiece 0 0 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1]], 1839276904341484845287471113379837949017791334075900838938498608195923166260958734309764875235417542994235121635206063280208848139758631869153729462123643135051470871982063998519023490873666020054893034995305397738676398067193/46757274162227687632481594899759759398313414365334827750938999975625233928799769010813676083876179775600856343316583728279087110924924179680959798415065720916403572613247995735143187022831100847165933802419903106075016211415162880) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1], [Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0], [Piece.treePiece 0 0 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1]], 30499572207275133470856166381789159713526578235099291535973414202474532286406455082939393446490400383006493370782550432435246104479810036261108684744358944465126792315762780497558134405657411630224920690311166630793072/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3], [[Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [Piece.treePiece 0 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 3 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.treePiece 0 0 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0]], 28458157522811480690607316017387688499866662576457260494670010086722980929131304326462258814703949490576004204460943663829919062753555486869126818186884743029397743420283979762624729597990756404787813369745599560517287953/24379273713825234629505632261558742795294744319098713224158120023317849085181439884235699689155844079193557742777629067034857811353754517863969587527550236739253885645919814956809287840166342283000657595979422427950701145536) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1], [[Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 3 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.treePiece 0 0 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0]], 126818273442629827923491516422776564246008146949520889045057148690415372445296981864704350183495752496478746125218297656959412601700830446829156684099321262921288973038787336673972740913043678480383971054922867261489680045/268172010852077580924561954877146170748242187510085845465739320256496339936995838726592696580714284871129135170553919737383435924891299696503665462803052604131792742105117964524902166241829765113007233555773646707457712600896) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 3 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.fullPiece]], 303846467084775276820103844050237551742787961707454417577177642475584030068710170343674728641122220009431882992965354768297816635133532172259158072715328291185688461706726354511950901725591145363691405783305694179903/5536473467822566221466127123922583903908325276166163402865681848501768744570217987363590685849364502679664484087079932917792802897722824608504434516138775960659671784266639324864474363614080704546229496994886452064338374) ,
  ([Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 6 1 3, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 1 0], [Piece.fullPiece]], 5126428837749485120888561762580501929483581563497358857082988171471119095010120363664354586340712413375118406671937328478670093322771613212773221701299575167163186625126778526614286598815879717848483549412806952265/582786680823428023312223907781324621464034239596438252933229668263344078375812419722483230089406789755754156219692624517662400305023455221947835212225134311648386503607014665775207827748850600478550473367882784427825092)
]
def part16: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 1], [[Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece]], 152665602839421536445169349023080535011320182087229687698236465802932367309568926468568460469061730771692598445272547934546716114653149273707908206823069852053556472915419818424204419027255997367864018597144110924851/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
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  ([Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3], [[Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 2 2 0, Piece.treePiece 3 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 2]], 10318027203105536856778402841519682793585381498041830262572636406550577986271437834931669902507736431249395180603081077491110051598614869290603620896366467133045384307291191797661055085618891824565219029458329968457099/5536473467822566221466127123922583903908325276166163402865681848501768744570217987363590685849364502679664484087079932917792802897722824608504434516138775960659671784266639324864474363614080704546229496994886452064338374) ,
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]
def part17: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part18: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part19: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 2]], 783051213059796804909500995417429057055040023635082959731494072378267778478350193109380493713724039553274470222730355430864160207618950508662288578920090313352066165122781581700295835226188853470770754122147164284/11983708804810749397112829272559705419714989775251435936938705299787378235000471834120326159847109313159446935253419768220330742202863256728364576874759255326103185680230821049490204250246927931918245664491096216589477) ,
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  ([Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3], [[Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1]], 134044500970862140907907210361242530574561620989830364015480940370271565469048392060655458592431579751873155823743278540290999537314366745760809950302915040404760649138604956969096383490791505077376479645277704271232/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
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]
def part20: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 2]], 391986473337407176793526791990419497098308771010345974598172150879963213683122869968759407206358812800749437491730828512033599817427051040028748003393726865652828156515246232650781409421384127515795450652150816358985585/15000152115487272749358893754414253990322289281559525379497420688207458785288910600430421698194544892593437642219928564918606633984230372805974681249058657002747270754173081477499482542485082655517251117191479027459647434624) ,
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]
def part21: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.trianglePiece 1]], 5179245076765742011220749491932654984470275154987811327434840526804949042683375138767058184824285792237361942265067424483050961699445242321742690064810752515680596936681495229571559756473931359884442858124306105147798365650431773/44164485898944324378911256125912039573511522385830417104591617970726865488210470152978618549866737531669256357295630584329911149192656040325609575593370295304670418671067116771638382420775485407063817844046964437378352239541751650048) ,
  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.trianglePiece 1, Piece.trianglePiece 3]], 9713951525533997894120363415647044969660615297690884830316734751100613038675834416572836993985074636725924080685605368398478649145690522456192910873448512064647882723556150485115432028566140961754039663244680614154423932554566430667/188140709929502821854161951096385288583159085363637576865560292555296446979776602851688915022432301884911032082079386289245421495560714731787096792027757457997895983538745917447179509112503567834091864015640068503231780540447862029204480) ,
  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.trianglePiece 3]], 127660957958218779560121669780252298756264790946649355897761488097539323409772399807318405739066091637606651107245792091210008202345683742195547124927056041409926818476928515883697421758261001614325705418206010414909268387061883/4140420553026030410522930261804253710016705223671601603555464184755643639519731576841745489050006643593992783496465367280929170236811503780525897711878465184812851750412542197341098351947701756912232922879402916004220522457039217192) ,
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]
def part22: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 8975052114978188144957949980647937314244996808493200339531568986787506196640831589635818359440263165227147685939378972505560113400057352953545671790743752909157722599599638259725194391773119067180370910625750221229660715147365/7399285595634651204843770659838666315980988043699336897104354843263139767658298664373381118302280633578095305934346485332759983110811483195913646172711253663609703651697108569070304908192751481811739115232999277466530218143120695296)
]
def part23: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3], [[Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 2 1 3, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0], [Piece.treePiece 2 0 3, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2]], 5341311398148792217452939723739247169788981238719431210396545267633634246117368922806772598604320049374952065424599967391106914876730057665285418611359304118550197857392554504401187912589710574477195866114499705297268368941/13075764702682636367393201698707674192532604336896724735037096051422184559279054721596509203143640473467924137202347189637706356482023363458365000444554067905421808747490339716415220092499819572849138092828719352284827864520398) ,
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  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.trianglePiece 1, Piece.trianglePiece 3]], 6310628431122948125385184539951679254562465359385696261925657699992036005745445740221136348629064290434236828398631757589893120709284204178283061494152343703958105205865261976526732196553557280875275018455041866760062403836325331614534924111/164421392250786695371107655729025244664694732671827710161057551683149654068562195251955902062329480452448981696584045535724990498109324672411312687900326803542454014072822825348379665233256854107438931657405720287427015906041623242249483762937600) ,
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  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 0], [[Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.treePiece 1 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0]], 190863340406177248044851708246682494555722196029525194467721250399858340546364363336435494140148538176661008038730565941141636484930026671618036033438205441381326088513101064887674284345134491984635713445914845443448578115/800325844886669030571739584086483103326785278350412445061815783890481264499471956199675078858069193912276012774621854216253691588347472531753126615552860115455818964719961425379004902377960705259130962643011976892569111043299)
]
def part24: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2]], 4459403705235873298433914574460506342541332239058124298391440506117704527870106358858337192497082676210266574624909842654762203568634520770967561665116722694033626267460188245123663025253383792297821973537078993333264171633181543917553021/11421269936980398303478755403257165328729255436084982741200703119861826110354318452714627275351775318225409113574711224074932557309508748507867497856837044245220273576703109664548479280183641588936380696933445998557188469488427912344887162880) ,
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]
def part25: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3]], 4109207704543812692784769032234688806746563227679894352530861100771656764702680305332728176456912895719929364590113729444594148335212506436977042029994705271359075852139792177322101333398425428021038505960358766343516022113359989011217612747869881647/13940050155735399682625836157535048877729621087801794533461716078042284573267924124154853743348359618996029217399959490716786780689793003695758692850983785043154951567943067048175947029163588875399283437197922921248032448972245959957497177290049618739200) ,
  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 3]], 1050819381390102517431817974417709183202030307434897793629049940952756722534109743866691074391742050760128866607838311982869345990374942038823274972541357860698923796158269286188301687478649025793305722461292533951661680278485107206472599904347/1204672535987768701512501211584677837045865027194632341872539716073556364019959133243376744022815726035639099157065788686228679095990105793525806546618437165375532978651280361650722704060430864653564425439198168113437957035884158618117430027059200) ,
  ([Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 20868566212504105939951521312595671924063652644420427139605740264040097652634788889211150877088471380792330490150510241782538203140239262529138421367130314240717075389404794751927513407349572184321414499126707036035880675/56221042574582219123581365567725865349554407071042000634966710610919294344862373589014808884571680069877766281076267692135879982492076042957826364366550556955178747078632966797557115671046451527765445132150740291896001408512) ,
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]
def part26: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 12182552599744111152685961214340097119903410747323406735223628599163214822880700937762233535318768929822502090350043284711169694453526239012268534531478251647702018937748198604942672506618186308204952227437257529179557716178870351415543694219508497/1088494730008210342672227364007001848064189573128880281812299352550545842663309035941225456337568762900608580623750117713449886418691185984117640714742172191689920758914189618591166467500306480428159271014798443325797809335759363015053913449813585715200) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 2], [[Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.fullPiece]], 30562790753043372062254576400140906028182125631875265463215747429854879909373455635020531997247698277761127847197834677461262956099524507059427878641129707975608212607973912012926680543928891354857565033608731073806371333616698929774213589/8407700233271828804400062142412747967929265579919588642274346622560611703074160020846759666587296584715448258254396162985490065272658218673497934022569622306665316064316380476803540704788261224318005116701633599932727330780150713333317782937600) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3], [[Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1]], 897076550669660921162336425634747355218991605134292679950753744525442818589809221247963482542754225161377619173281653050682716216438351949828665220589667564957560651308844489956307931847750460404280091724019187568176/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
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  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 3200623295642796685519221460582906863853663769817370597083955881817354240115086801307111542832416043695034537407583826170242667471415980283957001295787492967266318535327627964196549601190992228382331361818821291050170877454056926486523721/18075485262072715270765294496876529899514337598419998093862395919599802566248884336008124342095557895584667705166513642602134421471116205346779644407835737152706876538491742628066638109494920131089464941518541208715231716594975827431200204800)
]
def part27: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0]], 1102000041655300694037955286698547913716889537767756268416684859708998614578843724562989629274390139851044593426168259171136494255223011113302590901086440818788491844744091776099914268723388525016856587223487161324509215/7500076057743636374679446877207126995161144640779762689748710344103729392644455300215210849097272446296718821109964282459303316992115186402987340624529328501373635377086540738749741271242541327758625558595739513729823717312) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 1]], 2464150585410785000756140506989393314368592240653210060305025131645019799305928512723950166422684431404222263220978685093887959464385650064861731649706483085488938080441061824499284935477214694889267307536039311599548315/6308732807584384212358611620647122186358339964138499346134210652951356480937515913501805084223132974989508848369756839098787227769640370235520611232599221788382714152448287754650415485676729341007771672788148734607363017488064) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 1, Piece.trianglePiece 3]], 74160535005954439210727094469654287309810626198334461626686408838214652464118488436868792389836194186282995342342217756342297718297659848234951027920974945072984394967957702813458242746831763571666123807761049029454847393809/7882761643076688073342085219998579171854745785191054932994696210862719922931426133920505452736804652249391306038011170453934641098165642609283003735132727624584201333484135549435694149353073311589210705148791843891900090351335968) ,
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  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 196769672069669184162136682108548379919194541119782872092346776972257492330923389457360692820413227002948595617457880371049019619660469059907502185263612009741432415813930622187880412303749426246585001330897578898235851139/123576268320580851258435796372942417629817513289060611056317609034795195998497434671501136537720242526445012814220433783437176829842622394558895558608273066405994534034026423976616860573461797024949325195620066673047922462485760)
]
def part28: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 2]], 652904944435086854164382015967751995009087930903581201760828987747853085805064036839020949792303333277095209462342688469044952082067547590479837255356857185343931474020375819818468700953556851639135067257713774613587678753918575893508145086550813/7438646847317000139824962580012351422549248171277466155530770338644882176339928444241901869371514784527460077975288589147292080617367220756925594432143770026678786117793729040499772442373781831324701164751118298940144191361828541387111505067217510400) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 0, Piece.trianglePiece 2]], 113819571299529093095567030182876736155673498313862946237058463103014598261658629148550919136233707983246294482774210909367552970945347511270874763496327836982896312171398712969028857807855599676596361447737936309172485033070277327937961115302377924980429/1188162749961412122699009862592302972282187091392426204816442542766836572746774927817183765247118246675602805308563797241881925268618644428753372486787539188422008353204167391017466625096972043308563674665268462788924485747588169089527325034845766691212288000) ,
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  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.treePiece 1 1 3, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 4 3 1, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0], [Piece.treePiece 1 0 3, Piece.treePiece 4 0 3]], 12988739645920367039374114971976388138691000977259386318517480191574795781575861561194859442596849355754708584516970477414883441456333161769487336727135092474657411357372534032353937401990245907755138150893872711714524649/33838925835331524745600968981414832820687684087927590718315047458042810566813172338766266271911315840378109326740232549993549611310881904007179103762640198671551913945437699553571667310409261266186554685632745995017236141888) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 0 3]], 2014669173919380868182880766661352090108182367185128151869423064537084360440877186711119400403028311505050231442813759067991715210338844105723807964493010571517538479050992389077878783736247677456066663319380514923848293/5254093040841022587518528757352993946845982707868223259197177254880748129187816099978789818780622556396471633257671504397839150928682924938728552661916371871003168964031735713291533187647185247659410084847791950384690580888)
]
def part29: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 134234876719722049688716015687696408448900983461180044122849236432317290371364070687141851652977089413901252580937247855822602649358442881277399675264382087849339334517756643701773673497194526400736053680852238931267671047/107099432544503404423977690189883428612508511517185862915475261163489169865364443381967651666024210189585677772324375945645553252530272741951042817460503324218528596162822900779734612497000224088289415169537391116641532800820992) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.fullPiece]], 818182904345846292996758807255968378446616548476304279351371180263943525556479746441962957143952599171447788459359981444005252448930093384549792992851360590170758039900303796003255956339784630552362946736681498703979/10866419698103023987822411748161873844613282418545643558794162049867001812638437843137951670659923923456339059692002429550076425784321503850552233914417950915029281266520180679762034547179405853113779948207933351931973701382) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 4 3 1, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3]], 282011413562437210628943341304936899813287743111240279916567856089749544236490244534411326708773266830811840794220089411652380312949419061150509643784325400507155421414637219023714272488523117523249889661719204536216833/865393391278111889386090024293130037903208997013049541124851193550430314535898688486370482588146820726544479358842032591458075037551752277267770072061076365543111774279216239086508608220293230125995256761046866968825813536) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.fullPiece], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 4 3 1, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 2]], 3879762199562940675921458277713045642808409137178722465857298437104617136845338104970645577538719035787148702302523196672145237578122558379921470759848801711028061857126928801827969460476067397707741728016283404956104255/50526828178483445050472063172763802914769816527358401278307101265540913803078435706712999404444782796104211005372390955515306556578460203135914715786302844640832912014056695503156151722055015260689687973697613566179865042944) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 4 3 1, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0, Piece.trianglePiece 2]], 35561386878568064984598391478250714622880021960975635859843896156569159159498494370079694373533762343035086033073076336348733941077532808206052205141204729084565196840700850330814351729638795147715305627608320655109895680338822971/22197856786903953614531311979515998947942964131098010691313064529789419302974895993120143354906841900734285917803039455998279949332434449587740938518133760990829110955091325707210914724578254445435217345698997832399590654429362085888) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 4 3 1, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0, Piece.trianglePiece 0], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0]], 24599451578332286981190234822581806503108921893351790205967024423444370574047793441896700724598429393786867393293997958270847711078166610275914558168352766414399923746921011439936952906412769415946256464851538195263958889/182164659818999094131854910546185653131097066464499168619625332603970418387070772002364621806942964652822067996676728728977481201848365690550657649341302529139550871151944308915530747148915559721599407051757794711787607129967848) ,
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  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3], [Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.trianglePiece 1]], 12015833574950473085195719758141309767937944077796302678264365239380990878345208906401200390333293915408273185263495213330428243497791414816565698336462082478401066213508268547123814217578960323051994856491649960361871109189484233160889/23258061256096691101186986734285242754468178635159058818904934650406040041839393578199416153070643886290743480118098417022482877445917398241978950156413662790091583500366533406615998677689111906294893822923184404157308364907219750654124032) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.trianglePiece 1, Piece.trianglePiece 3]], 389539771052996870751014983169294199156960741739603936498790138363655342440726701695020109119847780027242844354039586729203669863437217275139304696607082711213842174074143666291252154221408498272275242189229097509968268841101194187240173049341/584609394669463805763938331480978647696692382833165191683760183762309881132665583118065429554949263830929712698965495238133299548833154390795778445867828634817614272258925601238683254162691036826449534781887005466407167665925771527998164490444800) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 1 3, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0], [Piece.treePiece 2 0 3, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.trianglePiece 3]], 1553604655604388138180933736272966417835106744799659344814185746921276047280540217771585556719081309244353705154848194197331558751867651659091892169730118113910973812441588245401629108340055764711590149633279927015252879297783/2561042703637340897829566669076745930645712890721319824197810508449540046398310259838960252345821420519283240878789933492011813082711912101610005169769152369458620687103876561212815687609474256829219080457638326056221155338556800) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0], [[Piece.treePiece 1 3 3, Piece.treePiece 4 3 3], [Piece.treePiece 5 3 3], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3], []], 108644416389957883913315769197203212755612304684442266277830951389409040660216144143930228403796371233433060257877810842893945290257339287767724373050413449469092729805409331333789163862740533779013928520562038322601195301/33838925835331524745600968981414832820687684087927590718315047458042810566813172338766266271911315840378109326740232549993549611310881904007179103762640198671551913945437699553571667310409261266186554685632745995017236141888) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3], [[Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3], [Piece.treePiece 5 3 3], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3], [Piece.treePiece 1 3 3]], 1501036080772368042575460207754718555684933076615939673586700931271807201886307420149653642562791573016410056479585215362877400395209478952971410010845626132933419620355461986996376973738982070915010292469334027238171351/128177749376255775551518821899298609169271530636089358781496391886525797601565046737751008605724681213553444419470577840884657618601825393966587514252424994967999674035748861945347224660641141159797555627396765132641045992) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [[Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.trianglePiece 0], [Piece.treePiece 5 3 3, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 3 3]], 57708201427575394969053224802060167995717493597688700415878527307033594982678688744084193786908521003845529472878105617439188892642125003581002692374424146586133115468129336315036755030447891662263470194527776742431386241/91322801098100952407190615038593280074830887432294585451052734327393035017187048849245461101320663624220422545540202594295092013525242538439374606279425236164850727760249991670201537153966993842120964457851373254052766037920240) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 709081058517198582256729254528630649382254744210171915649512004784510066724091992202425254664587596986368608930795135778665296948453859554559278483035810805200914980398645373311196504481863239266076222103108010707234449063348411/1549224350575144050222890177678706694730784462638093959481112199192382750840899013224959800912430756564908373508556140863647086275312487820095801320819177553030171705918950258691077596689803808069431273320179456247952203804889063424) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3], [Piece.fullPiece], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3, Piece.trianglePiece 1], [Piece.treePiece 1 3 3, Piece.trianglePiece 2]], 154332556963750540567226274187423536348676654258296069953524453265689020896575919102140148399791363224386604061339300844885924721064941249784158051712387791040596917625260628439501614863987147123298584126026762924731533297/24467438075472364014904026635143777811780959898134394427492935623037799020826671381901452686486750275039694580490101375342274783320211501664552484780254171070854826066587124926814854538373155859322832968299269024633708116910080) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2]], 709081058517198582256729254528630649382254744210171915649512004784510066724091992202425254664587596986368608930795135778665296948453859554559278483035810805200914980398645373311196504481863239266076222103108010707234449063348411/1549224350575144050222890177678706694730784462638093959481112199192382750840899013224959800912430756564908373508556140863647086275312487820095801320819177553030171705918950258691077596689803808069431273320179456247952203804889063424) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.trianglePiece 2], [Piece.treePiece 5 3 3, Piece.trianglePiece 1], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3], [Piece.fullPiece]], 154332556963750540567226274187423536348676654258296069953524453265689020896575919102140148399791363224386604061339300844885924721064941249784158051712387791040596917625260628439501614863987147123298584126026762924731533297/24467438075472364014904026635143777811780959898134394427492935623037799020826671381901452686486750275039694580490101375342274783320211501664552484780254171070854826066587124926814854538373155859322832968299269024633708116910080) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 5 3 3], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.trianglePiece 0]], 57708201427575394969053224802060167995717493597688700415878527307033594982678688744084193786908521003845529472878105617439188892642125003581002692374424146586133115468129336315036755030447891662263470194527776742431386241/91322801098100952407190615038593280074830887432294585451052734327393035017187048849245461101320663624220422545540202594295092013525242538439374606279425236164850727760249991670201537153966993842120964457851373254052766037920240) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0], [[Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 0], [Piece.treePiece 5 3 3, Piece.trianglePiece 3], [Piece.fullPiece], []], 3878081809959090980980629018817160132463866073508566815918785001458343198185579663594411541134072555305865487956964143790989363268135790814181412252265404555700709214050269823761723076005726474422518685572864602377597771502729/2561042703637340897829566669076745930645712890721319824197810508449540046398310259838960252345821420519283240878789933492011813082711912101610005169769152369458620687103876561212815687609474256829219080457638326056221155338556800)
]
def part30: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 1618109302614469776699991208762733088015994662680348637849056943202492505584015819669204020878174578361602139771217511884873488004168972142348165577589286477200942610940725729933298851701472411390688536967886734494954878071229567127264429257/53146308606314891433085302861907149790608398439378653789432743978391807375696871192551402686813569439175428427178681385284845413530286762799616222351620784983419479296265963748971204923881003347859048616535182315127924333265979229818014953676800) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 2], [Piece.treePiece 5 3 3, Piece.trianglePiece 1], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3], [Piece.fullPiece]], 90836103696457967944377379623829761382224812073966470227155684294396532668002465350953361759603424656660137676390699424121819750242161095879634306973726862210467901315489520023534749726384040206011165829408778703067287213060570121275543/70966904858346313872852600548203689430300339938049435883325313420469711922535585533480269800395041601758935234206505426299370831181132574122961412015723740308228165039579935266341124170384726073053650382765613951146658857024593598149763072) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 3], [[Piece.treePiece 2 3 3, Piece.treePiece 4 3 0], [Piece.treePiece 5 3 3], [Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 1 3 3]], 12988739645920367039374114971976388138691000977259386318517480191574795781575861561194859442596849355754708584516970477414883441456333161769487336727135092474657411357372534032353937401990245907755138150893872711714524649/11279641945110508248533656327138277606895894695975863572771682486014270188937724112922088757303771946792703108913410849997849870436960634669059701254213399557183971315145899851190555770136420422062184895210915331672412047296) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [[Piece.treePiece 2 3 3, Piece.treePiece 4 3 0], [Piece.fullPiece], [Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.treePiece 1 3 3, Piece.trianglePiece 2]], 12636284739102096955751794762293046881625353678153609795528338160372426374513797507989828763448514925282080488763745308838660049875174848699897639573818596521021155502936944380551986608451133427236149166037948324236961846/800325844886669030571739584086483103326785278350412445061815783890481264499471956199675078858069193912276012774621854216253691588347472531753126615552860115455818964719961425379004902377960705259130962643011976892569111043299) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2]], 1740017315669343367776402964799312394529845602084794250006650996788768270499431179912735950101347763207412780798129906452498207140813114876318561695088779200942891983629859231725828555821976842589883841154817950802020354394300806714348292287/12179362388947162620082048572520388493681091309024274826745003828381455856930532981626363115728109663144369014561781150794443740600690716474912050955579763225366964005394283359139234461722729933884365307955979280550149326373453573499961760217600) ,
  ([Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 5 3 3], [Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.trianglePiece 0]], 160505166049514472236292268138017949299154248275079193066857036762201252947366388289792448359749730911823446242064749922511701257532119303708611566797169916707637169147156017175653392054916686894419621602796905723264502910753529562267453/864909152961095700325391069181232464931785392994977499828027257311974614055902448689290788192314569521437023166891784883023582005020053247123592208941633085006530761419880461058532450826563849015341364039955920029599904819987234477450237440) ,
  ([Piece.treePiece 0 2 3], [[], [Piece.treePiece 5 3 3], [Piece.treePiece 4 3 3], []], 1464223122151681006717894327979733131718048503906704353859534282704704262645878874910608842809147299183883349544349501426737885941329630690491740557494552229608138834903970067147328361342131627118461045526564759654079400473/11279641945110508248533656327138277606895894695975863572771682486014270188937724112922088757303771946792703108913410849997849870436960634669059701254213399557183971315145899851190555770136420422062184895210915331672412047296) ,
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]
def part31: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 1]], 3081917505296766488251974593708296230270317156623126227650486558956295835019781074523002898787232906515175608753987526460029991687845036534266051951873763775754991911617435171894579397663232647804089394847160387926306466285/485772426183997584351613094789828408349592177238664449652334220277254449032188725339638991485181239074192181324471276610606616538262308508135087064910140077705468989738518157108081992397108159257598418804687452564766952346580928) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 1, Piece.trianglePiece 3]], 2490781257468664806057549465155629753525719617687641865797113272199289390805914556209416099624619241428738369609002968232786425475211140376364145646318330086521545821383531443900039719542777135640197062408442649981138765965035/173420756147687137613525874839968741780804407274203208525883316638979838304491374946251119960209702349486608732836245749986562104159644137404226082172920007740852429336650982087585271285767612854962635513273420565621801987729391296) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 3]], 47260611054962216459396192831888541717090578231981560852968999507950538582403260427019747041402687329769661460685386757668591024273007167469538933393082322197849089613660952961367905715532561292545952280688354718733413/7500076057743636374679446877207126995161144640779762689748710344103729392644455300215210849097272446296718821109964282459303316992115186402987340624529328501373635377086540738749741271242541327758625558595739513729823717312) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0]], 728863072531440408017168939761613177664510544335024186770444498160500646083018381119566182320103393273392038228192611450891978286513675354144740118123752819376280649303968790620069013133645720083731262540292618641560/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 501429790040704739667251486600329344545475719121988932468264504697746994451202027176827731522606122382059118243607529269290194081676574632852563397010521878764056935641029350999273180547469611411151584845319804772912489748903/1606491488167551066359665352848251429187627672757787943732128917452337547980466650729514774990363152843785166584865639184683298787954091129265642261907549863277928942442343511696019187455003361324341227543060866749622992012314880) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 2], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.fullPiece]], 6545463234766770343974070458047747027572932387810434234810969442111548204451837971535703657151620793371582307674879851552042019591440747076398343942810884721366064319202430368026047650718277044418903573893451989631832/5433209849051511993911205874080936922306641209272821779397081024933500906319218921568975835329961961728169529846001214775038212892160751925276116957208975457514640633260090339881017273589702926556889974103966675965986850691) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 1], [[Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 1]], 2653842467942275351877348992408066858413753254515344846175379513106890295731255214832417660495242059567958147496628245034822288742324677231706957554708228166150007331562253440191543603700300703569318158350354920206523689/12790308277044951317533699585237154072105166307044059586982175676105467089241883592331297073014098546809582989571456945979704763799053576812237339815045551283592538901995797152689290917922548157159798943676662920735681517916) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 1, Piece.trianglePiece 3]], 37386961162116844393494533486185812775604149642507640695698199219289235192829611395752647953549448409822430261196332629245686455688813849235950673122864802088205252252882867378410925008306885041647922578515691679937976358155843/34913409342889364112595181287831430920916116195269545360902468431318721848878433290826918590274130631721192311641138991818969792863111955080283984092980263364562162843726342969300126127324304568872399488886255774818634400651045600) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 3]], 2653842467942275351877348992408066858413753254515344846175379513106890295731255214832417660495242059567958147496628245034822288742324677231706957554708228166150007331562253440191543603700300703569318158350354920206523689/12790308277044951317533699585237154072105166307044059586982175676105467089241883592331297073014098546809582989571456945979704763799053576812237339815045551283592538901995797152689290917922548157159798943676662920735681517916) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 1, Piece.trianglePiece 3]], 1009276354723899664972829498727765184839749552515987660731447117599818492376028638828614094022772022858403087626721027265559025381679391035104626218552295399557340779742597004866487808555256966860586505275050867083748105/21082890965468332171343012087897199506082902651640750238112516479094735379323390095880553331714380026204162355403600384550954993434528516109184886637456458858192030154487362549083918376642419322912041924556527609461000528192) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 3]], 47260611054962216459396192831888541717090578231981560852968999507950538582403260427019747041402687329769661460685386757668591024273007167469538933393082322197849089613660952961367905715532561292545952280688354718733413/1845491155940855407155375707974194634636108425388721134288560616167256248190072662454530228616454834226554828029026644305930934299240941536168144838712925320219890594755546441621491454538026901515409832331628817354779458) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 6 2 0], [[Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3], [Piece.treePiece 2 0 3, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3], [Piece.treePiece 2 1 3, Piece.treePiece 5 1 3]], 109291521930609307440726334019602752129274672366021375404000001395419526549932381446223109117350613594596423253889813739125313584420179841490534924743236650030481334735868060061729484980193579383724153662523968093211073/22145893871290264885864508495690335615633301104664653611462727394007074978280871949454362743397458010718657936348319731671171211590891298434017738064555103842638687137066557299457897454456322818184917987979545808257353496) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 2 0 3, Piece.treePiece 2 3 3, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 8437175822532079764606446893381566128042578828820717719111623369011605416622813264879936911971638721899358825696951529691239359557676174514778728409852660042237330278264392813588182263979048117689224486844859080606058907047/107099432544503404423977690189883428612508511517185862915475261163489169865364443381967651666024210189585677772324375945645553252530272741951042817460503324218528596162822900779734612497000224088289415169537391116641532800820992) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 2], [[Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.trianglePiece 1], [Piece.treePiece 2 0 3, Piece.treePiece 2 3 3, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3], [Piece.fullPiece]], 1662547661630759667369413896344127745003524826503850295641986238296333243930766844770068728916511681516381906149419482294218672976225949757405179361473964719226980337077417313478616103282442369282401507768936805366485328/5433209849051511993911205874080936922306641209272821779397081024933500906319218921568975835329961961728169529846001214775038212892160751925276116957208975457514640633260090339881017273589702926556889974103966675965986850691) ,
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  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1]], 9074458410494823002001947497763966367903122768170816112904682153753011566710203067607709641826341256780673478213250609039355922712348522380234422465811492954688146571237152810274495670323669210422656221391847852163848/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1]], 906782894124014393565048534167329343368024662011505131108947875709525534012210561486068794710327746379686461577435517623413722669510523911320213635945225273345116394311550621450274473072269268720312101163999583110093278422196052739/11885354783651395477943013964096033652578436368814191090242366565142359099859867923888510370783891516145676480560824846202794822182188691197366975978640297440003995567188584203302585519321760715330851081336740185370544651303228407984640)
]
def part32: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 8710076495380116733643071659359436539889267657933374493421758290540954472352074201451561869533272461622345741369247556224297219022326534554437059820275757130622062030681255195322285660469293451424930049383188371677782671362649816882900941/18075485262072715270765294496876529899514337598419998093862395919599802566248884336008124342095557895584667705166513642602134421471116205346779644407835737152706876538491742628066638109494920131089464941518541208715231716594975827431200204800) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3]], 32207045881293643150870170141169005425691533471613263074739570021057009979279017667364635651114284759627501014052392127682667280237574418583001752895198662979018722295491122311318987734416641530637447101948200787983321719517540897205350034025007907/548820872273047231599442368406891688099591381409519469821327404647334038317634808037592667060959040117953906196848798847117589790936732428966877671298574214297439038107994765676218386974944443913357615637713500836536710589458502360531384932679118848000) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 3]], 25968106306280488525663983592804764228747400348886057362450739869977107513271355846963854196587521552553276745796184361960236838364868603887207445712529423485639551114492585870929339708964154167086310019363139034249972577076630633731456536659/616564683773267445656004557110268184314812809194103167100118752321111524892105068195429042216401749545799538938655718618935938119994936036056515161655105635822123178049867901632259651684472489783320375224786463995066670923877718977776637415424000) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3]], 72687201708299902097670331195002509335047840269077951967510185575434840395492578442104175015107200806514933789992725281547618986999762218138102804426987292354728176178400824636834282416951899442715440903389135425164096723577501573200517/88605319912121153288065169102335930879972243129509794577756842743136287089455315372588844814193911252866018162580949228441835399368216692876370805920763417415229786953390895235620775046543726132791494811365398081937410375465567781525491200) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 3]], 4226378085455894462188470140220643675320256874988264686729821729117034354617881112397571238001423108037194221438535689933803583132165816854617609586085021345869118668554872219105391183212548960052371296771934016911331074980391296531/2742774180842629725679157068637546227518100700495582559286699976571313638429200290128117777873205734495156110898651887585260343580505082584007763687378530178462460515505057893069827427535790934307119480308478504316279534916129632611840) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0], [[Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 5 1 1], [Piece.treePiece 1 0 3, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2], [Piece.treePiece 2 0 3, Piece.treePiece 5 0 3]], 5126428837749485120888561762580501929483581563497358857082988171471119095010120363664354586340712413375118406671937328478670093322771613212773221701299575167163186625126778526614286598815879717848483549412806952265/2331146723293712093248895631125298485856136958385753011732918673053376313503249678889932920357627159023016624878770498070649601220093820887791340848900537246593546014428058663100831310995402401914201893471531137711300368) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1], [[Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 5 1 1], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2], [Piece.treePiece 2 0 3, Piece.treePiece 5 0 3]], 12988739645920367039374114971976388138691000977259386318517480191574795781575861561194859442596849355754708584516970477414883441456333161769487336727135092474657411357372534032353937401990245907755138150893872711714524649/33838925835331524745600968981414832820687684087927590718315047458042810566813172338766266271911315840378109326740232549993549611310881904007179103762640198671551913945437699553571667310409261266186554685632745995017236141888) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3], [[Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 5 1 1], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 5 0 2]], 3509738327392006587610275804614829009238917776959837471571816407316992936676926016670958849169429128721872302516735053477805497773440859358833660763174812864107316515255036684730848812283210713214891788364360053046177197822807/575333646918036000165300874743137664471434590823455888341632226262576120608278407750246404938320180832588662036903276344059079685209027992168060019560378987838559584889574947522269684069992061205362076084463651500532426038897512) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [[Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 5 0 2]], 10820732217255223060672731918208225110891902760716733530769475494115359688422035622634057699480977662176930715182424259402625573969358035043435806680660154807102195385483672167755584214727960250018928514053449295632224309689943708545791837/8513949474460785800078068337252757076672262462294309763932143314164750107112789729285206196268096543726645696799091007442263385361916149151372860806769200680533037182726948288544928812823987888744766552268316087791374063071749339387400774800) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 23942577267589089854207466103641472047950540078418317774176442733374859104608629673610891791081107303770472350084305316651224070066169928485002642678842741086179668849866137678851268673443327103245088067517231373762469054476983697914485744747/164421392250786695371107655729025244664694732671827710161057551683149654068562195251955902062329480452448981696584045535724990498109324672411312687900326803542454014072822825348379665233256854107438931657405720287427015906041623242249483762937600) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 5 1 1, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2], [Piece.fullPiece]], 832162916265946858252133388879484539482892110856513131556088178842599689237505709143579368567054733067415188581587310875778825170126487729358995758407821178243343598226476821168125636231871283795540930273503472383924679189188710325924687/5448927663654902912049963735841764529070247975868358248916571721065440068552185426742531965611581787985053245951418244763048566631626335456878630916332288435541143796945246904668754440207352248796650593451722296186479400365919577207936495872) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0], [[Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 5 0 3]], 391423712476014553624543380492536571457266658315124422967636681759375294485129572844399463577176298369166692864236104503806792139832189455392814769449015047675897719424292930349814265885961937120249268436370275869435843844524543120479291/254385044988557558919232667406244842626995703822052205831772722738816062957618367261556114174210167506305006813791701436183406472064721543271644767335774436766626694535258959134862485537224661475100401188222329420470560241172716022779481600) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 66604994314200533766768034481637101495900329377550396968318979437315256449210524409985398368746753966697633843611999029889983167502126851303738821359176972301549322597420972686950609144140293639324331255443592182865705906984508625736500250969/146152348667365951440984582870244661924173095708291297920940045940577470283166395779516357388737315957732428174741373809533324887208288597698944611466957158704403568064731400309670813540672759206612383695471751366601791916481442881999541122611200) ,
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  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 4 3 1, Piece.treePiece 5 1 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0, Piece.trianglePiece 2]], 3524989811584958230785779263542364838366386374013032269365472233197768254369732074189837760807461605793855684400392904479610635242539574064502490096533669830612281069493990530131700779514058787722169322387744097111052686577833/13340058165206702893348144218459133983138800559554092963529485895306141408037798072788547689246900180729739133295095826922043238781511087492632775551763077518527109948973152468275790098905200988843279654867186197355523229825337792) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 4 3 1, Piece.treePiece 5 1 3, Piece.trianglePiece 0], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0]], 36257853003491370450023230514215249767886084195566190913535135987721127470820953817917681162202740076649124808870441487765058725739353370991365317080867809126529316607263943198759757619567442915342228174672475152074193721/1457317278551992753054839284369485225048776531715993348957002660831763347096566176018916974455543717222576543973413829831819849614786925524405261194730420233116406969215554471324245977191324477772795256414062357694300857039742784) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 0 3]], 37490328421056251118984020265528101436340515284110119977813625320931686854364536058889559000401368366944752845811193845330517687972927100584050368341977664903606054551950795007993846034784742096965683037182502915506913353767/7649959467464528887426977870705959186607750822656133065391090083106369276097460241569117976144586442113262698023169710403253803752162338710788772675750237444180614011630207198552472321214301720592101083538385079760109485772928) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 2430286711160263937422332311590120533069190126504140188217862775981564989378284027184002480568901595729390641010099655006207320395633645678717527384002697488585872059737097770092398311441717227035756098063975746317039620941/123576268320580851258435796372942417629817513289060611056317609034795195998497434671501136537720242526445012814220433783437176829842622394558895558608273066405994534034026423976616860573461797024949325195620066673047922462485760) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.trianglePiece 0], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 0 3]], 40386013452387263253103708526754862048447756135466495366266197219607176026261545893275660889744331654685509887265666249693429158811467564052567417872952717751544906567832837729623599283095557723046084533354351835703214121969/1676075067825484880778512217982163567176513671938036534160870751603102124606223992041204353629464280444557094815961998358646474530570623103147909142519078775823704638156987278280638539011436031956295209723585291921610703755600)
]
def part33: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 3352048382071741517626898775302385443797364369702494615127113088350586879707446986573971762236353099956045044916017993228775741596987837659567715643900351866039220126804571147847881156655979971330208392213243771211268897755074343/11555505130414937754281282179460740782924681035590848072534160735920401638251156991145006636393320463668467321585651346091878515659973614792373294425637256406778536078035322579581581853143820395742970393194930859259682090201348550400) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 2, Piece.trianglePiece 1], [[Piece.treePiece 2 0 3, Piece.treePiece 5 0 3], [Piece.fullPiece], [Piece.treePiece 2 1 3, Piece.treePiece 4 3 1, Piece.treePiece 5 1 3, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 2]], 288515267750721304262722189101704682938319214489718083190976436871605466406559472671683605102400965305269888128239972744984896758617196004759988986046140489399050976591578966065065508331795480711391704914894481172109902967/478122466716533055464186116919122449162984426416008316586943130194148079756091265098069873509036652632078918626448106900203362734510146169424298292234389840261288375726887949909529520075893857537006317721149067485006842860808) ,
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  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 3], [[Piece.treePiece 1 0 3, Piece.treePiece 4 0 3], [Piece.treePiece 2 1 3, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0], [Piece.treePiece 2 0 3, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3], [Piece.treePiece 1 1 3, Piece.treePiece 4 1 3]], 1868517675549592260640429414851621320951056235619161740737156688565221616866103774723828787407506343484045624260492900297982480992055323074009265129274779482596403145849868103882799292943071280525236808362793073818323943607/11279641945110508248533656327138277606895894695975863572771682486014270188937724112922088757303771946792703108913410849997849870436960634669059701254213399557183971315145899851190555770136420422062184895210915331672412047296) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 0 3], [Piece.treePiece 2 1 3, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0], [Piece.treePiece 2 0 3, Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3], [Piece.treePiece 1 1 3, Piece.treePiece 4 1 3]], 109291521930609307440726334019602752129274672366021375404000001395419526549932381446223109117350613594596423253889813739125313584420179841490534924743236650030481334735868060061729484980193579383724153662523968093211073/22145893871290264885864508495690335615633301104664653611462727394007074978280871949454362743397458010718657936348319731671171211590891298434017738064555103842638687137066557299457897454456322818184917987979545808257353496) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3]], 5341311398148792217452939723739247169788981238719431210396545267633634246117368922806772598604320049374952065424599967391106914876730057665285418611359304118550197857392554504401187912589710574477195866114499705297268368941/13075764702682636367393201698707674192532604336896724735037096051422184559279054721596509203143640473467924137202347189637706356482023363458365000444554067905421808747490339716415220092499819572849138092828719352284827864520398) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3]], 1374925820683875735545031902396297729931281288820529869520515850383277041180472160334985201187189828530511119473147344351681964185536639599381933790340034219740937572821156913777443131869791869009738416060659575947675463829769196890934167/6811159579568628640062454669802205661337809969835447811145714651331800085690231783428164957014477234981316557439272805953810708289532919321098288645415360544426429746181558630835943050259190310995813241814652870233099250457399471509920619840) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 6310628431122948125385184539951679254562465359385696261925657699992036005745445740221136348629064290434236828398631757589893120709284204178283061494152343703958105205865261976526732196553557280875275018455041866760062403836325331614534924111/164421392250786695371107655729025244664694732671827710161057551683149654068562195251955902062329480452448981696584045535724990498109324672411312687900326803542454014072822825348379665233256854107438931657405720287427015906041623242249483762937600) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 2], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.fullPiece]], 1234059916629782244280767367423805271230813781236179854195629733264815268674331780013987544547587028487284266402838239297993307539211999153099872701245344436094154313524436056526237859421710389680287043030748068316547868163451549726747253/681115957956862864006245466980220566133780996983544781114571465133180008569023178342816495701447723498131655743927280595381070828953291932109828864541536054442642974618155863083594305025919031099581324181465287023309925045739947150992061984) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3], [Piece.treePiece 2 1 3, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0], [Piece.treePiece 2 0 3, Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3]], 83390165220792173431494412209308943856253730250797662378959937856109258407905217080268151490364999834326361366879201328094935719081730877031571318496143196768073255184622942129799785701198839255677462006492223604670533513/867664765008500634502588948241405969761222668921220274828590960462636168379824931763237596715674765137900239147185449999834605418227741128389207788785646119783382408857376911630042751548955417081706530400839640897877849792) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [[Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0], [Piece.treePiece 2 1 3, Piece.treePiece 5 1 3, Piece.treePiece 5 3 0, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3]], 1553604655604388138180933736272966417835106744799659344814185746921276047280540217771585556719081309244353705154848194197331558751867651659091892169730118113910973812441588245401629108340055764711590149633279927015252879297783/2561042703637340897829566669076745930645712890721319824197810508449540046398310259838960252345821420519283240878789933492011813082711912101610005169769152369458620687103876561212815687609474256829219080457638326056221155338556800) ,
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  ([Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.trianglePiece 1, Piece.trianglePiece 3]], 33978274260896624269873429901948379535414021999753113505417530571277263891651814387971279598924413953508776708542412111732584788485265685976035901996313485703333546142550665613187769538295032113209224620281984445753534486536281/6876883658447905052480869041542554575331962280886425601389880145562778545991206557284090025357025730490537879565678892327978898594249324485510481715283991268777395711643067554559115752351756960535472626598807955646094654673690800) ,
  ([Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 2], [[Piece.treePiece 1 3 3, Piece.trianglePiece 2], [Piece.treePiece 5 3 3, Piece.trianglePiece 1], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0], [Piece.fullPiece]], 42311408647483463302192776650687459253591621152364806460420043798558661718290046213503068367929225676524795977632622423581048760056898511867819010992076467492185150093275075956444575281502465431638121016972380976261535769810627742804458579/2883030509870319001084636897270774883105951309983258332760090857706582046853008162297635960641048565071456743889639282943411940016733510823745307363138776950021769204732934870195108169421879496717804546799853066765333016066624114924834124800)
]
def part34: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 5 3 3], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.trianglePiece 3], [Piece.trianglePiece 3]], 462275636399206579354857668398619436174365717025592171428833139744092132171366112572052586318015333506684212627233450175355556194555388492647832103502990675253900156967616649209828676621849756694311911210753465053215692821/4566140054905047620359530751929664003741544371614729272552636716369651750859352442462273055066033181211021127277010129714754600676262126921968730313971261808242536388012499583510076857698349692106048222892568662702638301896012) ,
  ([Piece.treePiece 0 2 3, Piece.trianglePiece 1], [[], [Piece.fullPiece], [Piece.treePiece 4 3 3, Piece.trianglePiece 0], [Piece.trianglePiece 3]], 6854345817663754089329575332979565474173468795273733733803699912875185009306571010422698907607834709020076216434661533869895245528815359495851936321275971301414939531626687000794051565863182465051144363987492652651417488132471/2561042703637340897829566669076745930645712890721319824197810508449540046398310259838960252345821420519283240878789933492011813082711912101610005169769152369458620687103876561212815687609474256829219080457638326056221155338556800) ,
  ([Piece.treePiece 0 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 4 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.trianglePiece 1, Piece.trianglePiece 3]], 1706901553365450765586623948627051852572144390410274962980815268335278377692342905041361824742857817425529282634840942878429603921751075682000453711951986616319910347142825112550532104356126519457715769386641833500571576136924865722617869741/2149299245108322815308596806915362675355486701592519087072647734420256915928917584992887608657901705260771002569726085434313601282474832319102126639219958216241228942128402945730453140304011164803123289639290461273555763477668277676463840038400) ,
  ([Piece.treePiece 0 2 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 5 3 3], [Piece.treePiece 4 3 3, Piece.trianglePiece 2], [Piece.trianglePiece 3]], 75417133222187539638182508752523204761499087202341565878368004158855639819618195589109827556786281532027047840571292709201778307860664687441794143432146676684159389139034029234021737363077616085470099654069425653128374725243069776131809907/864909152961095700325391069181232464931785392994977499828027257311974614055902448689290788192314569521437023166891784883023582005020053247123592208941633085006530761419880461058532450826563849015341364039955920029599904819987234477450237440) ,
  ([Piece.treePiece 0 3 0], [[], [Piece.treePiece 6 3 3], [], []], 1/4) ,
  ([Piece.treePiece 0 3 3], [[], [], [Piece.treePiece 6 3 3], []], 15566412454430203491230993556597111988366486062138266742009053297798443443405912791997915566544957471396385307679042704952379102182930046066277120232942215622122961839117432921035306011956382790307185042211222524126252843906822832216812974881/32434093236041088762202165094296217434941952237311656243551022149199048027096341825848404557211796357053888368758441933113384325188251996767134707835311240687744903553245517289694966905996144338075301151498347001109996430749521292904383904000) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 1 2 0], [[Piece.treePiece 0 1 3, Piece.treePiece 5 2 0], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0], [Piece.treePiece 0 0 3, Piece.treePiece 4 2 0, Piece.treePiece 6 3 3], [Piece.treePiece 1 1 3, Piece.treePiece 5 1 0]], 5766443892337946659268661738620542532854048177196139868347992513397782450838673586921553708270310227883289451225229453261483926614372434458505603767579701732926613917398670982332315324295452143577545932732604110426465690321559681694363/4528320172571181677096288320320588821632384256518206805382341661319238817046609679001522451268662667651502739093674266403264827251413891346196817847861953324641522311098850581458285082861590832541054261989298010626177512146530023442147840) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 3432776722126567003914301349620594398840888167248743498384419640058322972999847792176096139218988826762315635936437017541530328266312153191281367875213773782416529770980534846287507134621810799797719776506523364672/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 1090976738052781837896227289305539627143114093881477553083554606610351355889708708632777469220111938169137768051473302455645388384063693148536466194787762354353253974987083661178689858748155559605466174067824159102703831781065/8961949248974091797668680220355527510858669315306496977392779620683211340951799949873907984956724336783534163412262699742270931248509748442696748294109232001759419373187320773465580848371648824485352646925114536805672126530387916) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 29260643893728410294709961162895751021684881623539084224429810234787216137346165160946283834951692850760253007006718579304802069584677329242054779277238358503709876471642656031557399404009377971515278236431112259135013478753325/370158588752206159275929178229849247162389239055862310635078675851267890162527808708804911511708104174534442169247112777282241802155879083198936343461526739211567370180750835716358478206596417354289995129171838854352417688094667136) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3]], 8788984781212415416258781156137619810640579464995390452212206253445183502624598205974583860644899950062192498618760608496887173098778755557523658153388200318090660364855892629284784102789951338360023820477817064224891/14763929247526843257243005663793557077088867403109769074308484929338049985520581299636241828931638673812438624232213154447447474393927532289345158709703402561759124758044371532971931636304215212123278658653030538838235664) ,
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]
def part35: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 1], [[Piece.treePiece 0 1 3, Piece.treePiece 3 1 3, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1, Piece.trianglePiece 1, Piece.trianglePiece 3]], 304885164220297697936025411817203378747107355162739118381936285949940872608872653650549144927770687733901151009213780392221782672255824006953272471327637412842864161819618821478070490665906063579738662706527892143443536131/882687630861291794703112831235302983070125094921861507545125778819965685703553104796436689555144589474607234387288812738836977356018731389706396847201950474328532385957331599832977575524727121606780894254429047664628017589184) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1, Piece.trianglePiece 3]], 1397848477508354650460864531942886292837322822197413687095544659635752135671376015027661123077281539199114189422081882298594070826819266102506044829890910734280625117794655593243527455131224816689529531684298589354019241021/1434367400149599166392558350757367347488953279248024949760829390582444239268273795294209620527109957896236755879344320700610088203530438508272894876703169520783865127180663849728588560227681572611018953163447202455020528582424) ,
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]
def part36: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part37: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.trianglePiece 1], [[Piece.treePiece 1 2 3, Piece.treePiece 4 2 3], [Piece.fullPiece], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.treePiece 6 3 0, Piece.trianglePiece 1], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 1]], 5126428837749485120888561762580501929483581563497358857082988171471119095010120363664354586340712413375118406671937328478670093322771613212773221701299575167163186625126778526614286598815879717848483549412806952265/145696670205857005828055976945331155366008559899109563233307417065836019593953104930620807522351697438938539054923156129415600076255863805486958803056283577912096625901753666443801956937212650119637618341970696106956273) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.treePiece 6 3 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3]], 37490328421056251118984020265528101436340515284110119977813625320931686854364536058889559000401368366944752845811193845330517687972927100584050368341977664903606054551950795007993846034784742096965683037182502915506913353767/122399351479432462198831645931295346985724013162498129046257441329701908417559363865105887618313383073812203168370715366452060860034597419372620362812003799106889824186083315176839557139428827529473617336614161276161751772366848) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.trianglePiece 2], [[Piece.treePiece 1 2 3, Piece.treePiece 4 2 3, Piece.trianglePiece 2], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3, Piece.trianglePiece 2], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.treePiece 6 3 0], [Piece.fullPiece]], 108512304747271385702351272631690515835993167968369776857723387193355916447490843150946127220226825307763405256075679265196555730235118556282193395044639114605072530368848789725684113417173565666611184163013221436466793/22145893871290264885864508495690335615633301104664653611462727394007074978280871949454362743397458010718657936348319731671171211590891298434017738064555103842638687137066557299457897454456322818184917987979545808257353496) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.treePiece 6 3 0, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 27330312985108803637639764448838633815592142389546870841224650107161785617172776251971198818363889329251388111883712108864045700619210302880913437410051677277506187071621235977847367863831942644367388774915635955906603664863120819502707/217359368283416720500621839375388263438354444312873926658352399743323463218237264592073077660895808047272131476496364787356711708067866784617447256697373759582793070932744827909997683977356359961970604575486304510056520583033441125223096320) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 4 2 0, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 4 0 0], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 3]], 193143434336209242487374791995086898178283111134827424720223615301285197906976942854117861102040877784942912834410457349944816699937893425247802396498330765215897517414826161609831796277327970521979720228128292889398005260579113521001/94340003595232951606172673340012267117341338677462641778798784610817475355137701645865051068097138909406307064451547216734683901071122736379100371830457360930031714814559387113714272559616475677938630458110375221378698169719375488378080) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 4 3 3], [Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 2], [Piece.trianglePiece 3]], 20505715350997940483554247050322007717934326253989435428331952685884476380040481454657418345362849653500473626687749313914680373291086452851092886805198300668652746500507114106457146395263518871393934197651227809060/145696670205857005828055976945331155366008559899109563233307417065836019593953104930620807522351697438938539054923156129415600076255863805486958803056283577912096625901753666443801956937212650119637618341970696106956273) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3], [], [Piece.treePiece 6 3 3], []], 776954847446348761925054353843504662016045129951113645491219876836907469356009770299082824928738820301264777524309136244687802426518987319782153037709519671126493458638583021842579848094577189223653491413574275989399171/88583575485161059543458033982761342462533204418658614445850909576028299913123487797817450973589832042874631745393278926684684846363565193736070952258220415370554748548266229197831589817825291272739671951918183233029413984) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 33870496536164504742422540319122022045292274504063798804102513250121596479255344903726162098478195032842607149995279071086375827720479010183910903485161279820106901412722389103852163147658339515269160174403705266793436026958269/7945797818716616434436753090829648962771030273958306884270668504252484871625159538322060549931138878244222714542847810398933032728278766625484066209364982085716164402724054638908312356192729894095928589790355093906546546013613651792) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 1], [[Piece.treePiece 0 3 3], [Piece.fullPiece], [Piece.treePiece 6 3 3, Piece.trianglePiece 0], [Piece.trianglePiece 3]], 9477688723164548054397284303511830896038351122479223031425208459156074467095085350237036445664475807378238587653927504440003472230234944789205946386188883417026852165039331146632402518402856330644950984589669342665673/8436530998586767575567431807882032615479352801777010899604848531050314277440332171220709616532364956464250642418407516827112842510815732736768662119830515749576642718882498018841103792173837264070444947801731736478991808)
]
def part38: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 0 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 6 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.trianglePiece 1, Piece.trianglePiece 3]], 33870496536164504742422540319122022045292274504063798804102513250121596479255344903726162098478195032842607149995279071086375827720479010183910903485161279820106901412722389103852163147658339515269160174403705266793436026958269/7945797818716616434436753090829648962771030273958306884270668504252484871625159538322060549931138878244222714542847810398933032728278766625484066209364982085716164402724054638908312356192729894095928589790355093906546546013613651792) ,
  ([Piece.treePiece 0 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 2], [[Piece.treePiece 0 3 3, Piece.trianglePiece 3], [Piece.trianglePiece 3], [Piece.treePiece 6 3 3], [Piece.fullPiece]], 9477688723164548054397284303511830896038351122479223031425208459156074467095085350237036445664475807378238587653927504440003472230234944789205946386188883417026852165039331146632402518402856330644950984589669342665673/8436530998586767575567431807882032615479352801777010899604848531050314277440332171220709616532364956464250642418407516827112842510815732736768662119830515749576642718882498018841103792173837264070444947801731736478991808) ,
  ([Piece.treePiece 0 3 3, Piece.trianglePiece 1], [[], [Piece.fullPiece], [Piece.treePiece 6 3 3, Piece.trianglePiece 0], [Piece.trianglePiece 3]], 518550169021409529077304680072768425258233100363521382878342585525152403867153392847735660832792424146538975025956400382647295314355259180501348157165027072580516738064782365299476008067638485566330826062579170301569582073453/301693512208587278540132199236789442091772460948846576148956735288558382429120318567416783653303570480020277066873159704556365415502712158566623645653434179648266834868257710090514937022058485752133137750245352545889926676008000) ,
  ([Piece.treePiece 0 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 6 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.trianglePiece 1, Piece.trianglePiece 3]], 33870496536164504742422540319122022045292274504063798804102513250121596479255344903726162098478195032842607149995279071086375827720479010183910903485161279820106901412722389103852163147658339515269160174403705266793436026958269/23837393456149849303310259272488946888313090821874920652812005512757454614875478614966181649793416634732668143628543431196799098184836299876452198628094946257148493208172163916724937068578189682287785769371065281719639638040840955376) ,
  ([Piece.treePiece 0 3 3, Piece.trianglePiece 2], [[Piece.trianglePiece 3], [Piece.trianglePiece 3], [Piece.treePiece 6 3 3], [Piece.fullPiece]], 27846728435666757400115486918059111197166539802300793707554803199133393681150427183486969279255020625158592989942886399610571579160897373545233133963855132303221308959326732668745979448860370930485506871938939807310035/8053052316832823594859821271160122042048473128968964949622809961457118173920317072528859179417257458443148340490298084244062258760324108521460995659838219579141340777115111745257417256165935570249061086538016657548128544) ,
  ([Piece.treePiece 0 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [], [Piece.treePiece 6 3 3, Piece.trianglePiece 2], [Piece.trianglePiece 3]], 518550169021409529077304680072768425258233100363521382878342585525152403867153392847735660832792424146538975025956400382647295314355259180501348157165027072580516738064782365299476008067638485566330826062579170301569582073453/75423378052146819635033049809197360522943115237211644037239183822139595607280079641854195913325892620005069266718289926139091353875678039641655911413358544912066708717064427522628734255514621438033284437561338136472481669002000) ,
  ([Piece.treePiece 1 0 0], [[Piece.treePiece 1 2 3], [Piece.treePiece 0 1 3], [Piece.treePiece 0 2 3], [Piece.treePiece 1 1 3]], 1/4) ,
  ([Piece.treePiece 1 0 3], [[Piece.treePiece 0 2 3], [Piece.treePiece 1 1 3], [Piece.treePiece 0 1 3], [Piece.treePiece 1 2 3]], 1/12) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1], [Piece.fullPiece], [Piece.fullPiece]], 799533974991497908177710399784966421970869499238453418345998942457389687562709009078768241628890810294666265919592064595765054228701376556049082550310881211188058563910314227327257623626220144838364404200527760437964580715373/1363753829731640889280713184576326315784141252322265809402387499289069322923326596148732219113055243455024976680067025408140040735310288574027994120439416860061770867886399875608342954832573774709006402570580507260521306166275584) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.fullPiece], [Piece.fullPiece]], 108774594630759715780239709773657994867499152427595567063928572462244096409178317396237298468019415274610394813378041838027263293353877492390527666764049835104387447446439196566354275387119410684247938446112554941781763754597323/30684461168961920008816046652967342105143178177250980711553718734004059765774848413346474930043742977738061975301508071683150916544481492915629867709886879351389844527443997201187716483732909930952644057838061413361729388741200640) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 47375665013643516856620881514969615671450322100815862085548236107896658823775847977086779608773039442329099800317664565060385592948470788994631926322605915734078657831654482655689613426869650510006989658005925494645292823198223529258433/361941652932477411025735206441248197037194714523819875601430732671677588004186148149407202387908372760664373317508454284064764140090065973840871410956103514813318528839183052749775751836805543311364177015496528123291183892238912715154874880) ,
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]
def part39: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [Piece.fullPiece]], 251470373319990698807074005790703182609684779718649480406776441261487297411542775208418354933873287484335315239246161767711057365218368618602670322533923900271061302490326495662918842681022789994393769798791436979011/1845491155940855407155375707974194634636108425388721134288560616167256248190072662454530228616454834226554828029026644305930934299240941536168144838712925320219890594755546441621491454538026901515409832331628817354779458) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 35831831494915537187734370177802553833199839053981755867945538170804771124657630940527656874995361369265195586467122381215398101612169103101401137107316894766584279982749567456659292505028274288380004493032067987305883262881750759/5684236898646476693435339531897489730598251886427597737739809738521076300083214438238265280524359158152315358237421174982416687025484107269432233184822109510865883055285885904310794949115217299063232441737921944939466606866375934136320) ,
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]
def part40: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 2 2 0, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.trianglePiece 2], [Piece.fullPiece]], 24367600056300822256317969463242670520555463783391413768489972655555172337463748463993906347695950227379774080960305746862508693195206061095134551328035126976083462382516985973229374739822875229214271753722472586721014/11204767732498050686300495369843324567433515439860092601037689455301198649725441164902504959457047207804082884461947483286009243959677145041020879377899903729906478611015817681273340973980877616343559696299174962511160995) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 2 2 0, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 2], [Piece.fullPiece]], 81769859840440211885437505823726949237423751900976465780831971127244726128704971359141278184229662821026501190180475029538745274800129003139720014770069003952265573006734117428821982154848937493102229119224381500292342/78433374127486354804103467588903271972034608079020648207263826187108390548078088154317534716199330454628580191233632383002064707717740015287146155645299326109345350277110723768913386817866143314404917874094224737578126965) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 32375643035475344179467777711616551586994418523347971812386141305330294725383862317932818290478056700221381333244231324487344763549208505266203219228532610701277517300067669390104084316269600452635606928645184211372302992/5080051208863163714306977492265676022356709530670088363736270758312823347408469691666992406033514434215838510406011135814660729054170303050133169354990392052776188992098184467788751150806372236330692125787208842028197705396085) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 4070127606983423080113798611823108951561240465853446012686617125409731465411113068586281114988602145307404537834803447741730524911900284866461114294576177549777822265673998967796061537124371371422002916049415492958830415639/210079656144987447139340853834002109970689772591403038795739935359151833197445638941551932114124412294956521784174737431843200610732458070750122449634064212890190707857844920760248662974885054942413852832554113344181468186225792) ,
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]
def part41: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part42: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 1404284382380903718983438652662544398904891214381762843336536913408028512777111239333050097442929999367522314185499834473257624614133050786619559757736998059789626163702354905224704984629788546122849606117559466765569396174861654455009/192104470226656326331340734820007562935298520753707093144654609923058294637612315154700413420601242108915649846991886029705754354713260889277731752714248013029223383736441800022087626100297883839141003600974810051174213445656041070071070720) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.fullPiece], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3, Piece.trianglePiece 1]], 40884929920220105942718752911863474618711875950488232890415985563622363064352485679570639092114831410513250595090237514769372637400064501569860007385034501976132786503367058714410991077424468746551114559612190750146171/156866748254972709608206935177806543944069216158041296414527652374216781096156176308635069432398660909257160382467264766004129415435480030574292311290598652218690700554221447537826773635732286628809835748188449475156253930) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 4070127606983423080113798611823108951561240465853446012686617125409731465411113068586281114988602145307404537834803447741730524911900284866461114294576177549777822265673998967796061537124371371422002916049415492958830415639/840318624579949788557363415336008439882759090365612155182959741436607332789782555766207728456497649179826087136698949727372802442929832283000489798536256851560762831431379683040994651899540219769655411330216453376725872744903168) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 3]], 155843648777201601655044755625600889182570132721193317158642699201815940538009535713332630270782484864883659217879160979529275262770130591378817127342056201095475509847239801906147564863011242773173140322112289601491808977/30480307253178982285841864953594056134140257184020530182417624549876940084450818150001954436201086605295031062436066814887964374325021818300799016129942352316657133952589106806732506904838233417984152754723253052169186232376510) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 449953243139411569456007741126300753395183156090608957876677896095604965828000017820024242843222094916268305779186973046121881116703523871870855222055969519210619471156271403074213836471219863171824730002804210440850359604265/43696568478157389004982897597472438873903472699011832069513906554703581305068692899842801879737877757350956531108345385823385727032351278716025469523885356281159667234431743518131721898776091428022081389171255575589745382734964736) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [Piece.fullPiece]], 175821880167045365703436103985371981043220569176883122957422585731376078154550817461476951102131277260762138507912730656214400940594941810243646021998144749151760076505369428493068484388794036338577062685716237339080/145696670205857005828055976945331155366008559899109563233307417065836019593953104930620807522351697438938539054923156129415600076255863805486958803056283577912096625901753666443801956937212650119637618341970696106956273) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3]], 127660957958218779560121669780252298756264790946649355897761488097539323409772399807318405739066091637606651107245792091210008202345683742195547124927056041409926818476928515883697421758261001614325705418206010414909268387061883/4140420553026030410522930261804253710016705223671601603555464184755643639519731576841745489050006643593992783496465367280929170236811503780525897711878465184812851750412542197341098351947701756912232922879402916004220522457039217192)
]
def part43: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 3 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [Piece.fullPiece]], 271787727303445499252293647542754400684928592408350366641455645785924638784240196477000055063001550871050427850901599589520053554103068632390599203022795286220926198154408310060490814428352290671452416825708703812864/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
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]
def part44: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part45: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 2718336461833828663461485359342924666055885801626869439556185231836916696206853913091886314199756966177700209021338988166322713720556573024174537101282534335286542046812752639672159110579977583495329344633931968202403616986135/107261863786150648426547659600694952302737790862778283195392116297810581808459762750846877767597234732393503128588651997962467794942896779790600872253056043748806453859194844440535695389411461846981759952203203304386211943709250136) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 9330418420003173116956742711578352281564723011840100001286382478003676712722845446792510455523734215422564635078615724441265745855494528534813807264289310674374462975280310340615680113218784198754468554490589356061328622945951546397/28711855698276805570818277521914024832396851858148490845742561690597936538488509293146692240830427793167092917460610366814593379350314610014348041484698041790680511569029275959842594941837660107200077504005753460518101213092092076404480) ,
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]
def part46: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part47: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.fullPiece]], 489797281850735194912230478666168223074246072779739884797915222630592510907140334198063656935859801694858832111538402716814545077581533906211560031049438479278291638064190342932882808975612644709740364763516468898076527/5625057043307727281009585157905345246370858480584822017311532758077797044483341475161408136822954334722539115832473211844477487744086389802240505468396996376030226532814905554062305953431905995818969168946804635297367787984)
]
def part48: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 6 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0], [Piece.fullPiece], [Piece.fullPiece]], 31307612357885198940247515839148464820452166569799389811779867172263957207961052387083603263405450370537434168296121455428845853181557880078647797342243276687288975765166861472650249874824972303924084867221854793485/48565556735285668609351992315110385122002853299703187744435805688612006531317701643540269174117232479646179684974385376471866692085287935162319601018761192637365541967251222147933985645737550039879206113990232035652091) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.fullPiece], [Piece.fullPiece]], 28513819340301270743386247166248997821668799862231989309632302156901952952749102835559642805618800555353410650999886758572075545200392968641917250597019221534946709440047050376681611453460441120259632122704275508032/48565556735285668609351992315110385122002853299703187744435805688612006531317701643540269174117232479646179684974385376471866692085287935162319601018761192637365541967251222147933985645737550039879206113990232035652091) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1], [Piece.fullPiece], [Piece.fullPiece]], 3500175657112054503092196243338388421270207942678877805528456103727980540157752668457553199154849105263901699114878824536393158030033236529740771843367168372376830608809932143811799224012116279788939523458579023990116/141180073429475438647386241660025889549662294542237166773074887136795102986540558677771562489158794818331444344220538289403716473891932027516863080161538786996821630498799302784044096272159057965928852173369604527640628537) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1], [Piece.fullPiece], [Piece.fullPiece]], 229008624765383408126415492866031075827150854872815255148996150492205213125741002141529633835820663332496685222982987297937606619325733545603674198716564552897137634328726870925507739275909575135938560601605837293863854/235300122382459064412310402766709815916103824237061944621791478561325171644234264462952604148597991363885740573700897149006194123153220045861438466935897978328036050831332171306740160453598429943214753622282674212734380895) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 761196986961110728222143674112438091375965059907196690492696394736519530245766257025135455303557280598550165019281028995742512652433177035636399312932522515182770932574244568884473291394647648463598608687140699285128572723/17967339012400242189548888814750180458019520024264733581214599734664301523465745435790625772918535262068649889435997280355010578549486545524681525297650228734029468435210420854494951438641484962180132150152654430752362410664048) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.fullPiece]], 1136879555012308098078626827094563228934064257885755004803563146077341701377561089509876288763403850188933505683834341914777836580135691078444504286075943647014259627340068574604039906483632450472161438373971018152233412448/9144092175953694685752559486078216840242077155206159054725287364963082025335245445000586330860325981588509318730820044466389312297506545490239704838982705694997140185776732042019752071451470025395245826416975915650755869712953) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0], [Piece.fullPiece], [Piece.treePiece 1 2 3, Piece.treePiece 3 1 0, Piece.treePiece 3 3 2, Piece.treePiece 4 2 3, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2, Piece.trianglePiece 2]], 377041377316092563968873057660208833090386827579562344334948947187062389973766595635718732663726891124494014378785124377490754619257196957702429565393086186217875537231771737011780695367539222263327716375951898306393907/35859738651086761416436105381646575945614222813728240360361021332745956158581301904153976872246333883856186863432016725508543984368550734989283222361030851897192694146695022907147200453128400723345928452035879550020719648398) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 2 2 0, Piece.treePiece 3 3 1, Piece.treePiece 6 0 1, Piece.trianglePiece 2], [Piece.fullPiece]], 271842735700383095669108112193523697424812902743987638116603174859163967405310011772428863559920547204174055855777271117833307484247070822084594964245834912831268970830963289748976990845511675606739176469113933494395053437864/156741538423182884660418507542200966282281859679467149067431856513842853370845079034522257755632100547339859849797366952708403119367844164532965069431513506302171681780813687626259369057529888469409539958908366594696334017007335) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.trianglePiece 0], [Piece.fullPiece]], 47777325894359458840101959328921091524209608904457198334833128373353738597044720355551196960040605089666373479497532929939789637950219728207857701861452870121340863865647912190478976229067207862016829881023288282631072/41523551008669246660995953429419379279312439571246225521492613863763265584276634905226930143870233770097483630653099496883446021732921184563783258871040819704947538381999794936483557727105605284096721227461648390482537805) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [Piece.fullPiece]], 73785689098806056808193278492314258277328709837241595218479463695051899046234893170590006062373423586023423527855214778735736436221562548711293741815289762946414711814634584969558853538142894591208555416875447785220816/705900367147377193236931208300129447748311472711185833865374435683975514932702793388857812445793974091657221721102691447018582369459660137584315400807693934984108152493996513920220481360795289829644260866848022638203142685) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 2 2 0, Piece.treePiece 3 3 1, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1, Piece.trianglePiece 2], [Piece.fullPiece]], 14038953309568026350441103218459316036955671107839349886287265629267971746707704066683835396677716514887489210066940213911221991093763437435334643052699251456429266061020146738923395249132842852859567153457440212184708791291228/18338759995512397505268965382437513055026977582497656440889527212119613844388874247039104157408955764038763602426291933466883164966037767250356913123487080237354086768355201452272346179730996950920916175192278891579471079989858195) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 64070475107623155250632760108549495512328385865731495295392646523186939785626685850612973482234352200428115799036500241059641868979889996088165363554411024207087340546150099505886576357432740020393771873069529023764512103375935101753389637415359/2165880046589595293116102385826913620327590588331690115597751339587407100022052482713462413287559442970886062367203919135734983809563953399477434196138014770388144155090782283727247444909914241151933722549228855670973473987263178066139137142468079200)
]
def part49: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 23412145097374911934858322516211846243726799861210109355188369485619230332021955338128212808442774927466080334971983480732140830813334323378497069047777006599087953847618915658222813509427853943584718119582889955878384986438372059095925145601161842247761/891122062471059092024257396944227229211640318544319653612331907075127429560081195862887823935338685006702103981422847931411443951463983321565029365090654391316506264903125543263099968822729032481422755998951347091693364310691126817145493776134325018409216000) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 2 2 2, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [Piece.fullPiece]], 83324059878083223644816796470185930125149387763748895703946144049814229256905056566823476226696465694564462896913397538472559031400239547252275662213391740798477341727401704560983647789410774541533107766421443680364937205868344672723773354402755909/4505030496906358209681492962519980330281388423729915440443322786341806768045869164044001819638123641379443009723784151802328766323893023070913063127967070722407339842588827150152674685412621621596022142902396019795624825893507410377569405256333604736000) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 0], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 2, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 240562761532650022869903830345596294153971900460447587768896593599161026460313911858029532880537838833580441108614987889059546454325940498104038766136404098709620794186678347650973283643461084164555750186584372909329336725841691580169456114575838973/4004471552805651741939104855573315849139011932204369280394064698970494904929661479150223839678332125670616008643363690490958903399016020507478278335970729531028746526745624133469044164811219219196464127024352017596110956349784364780061693561185426432000) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 28070268358444443375465659883260662605934148723006452748171265362791696937945531052707612286092375139869668331076361715090518735817299244067080175804924074070131168411153583068822859720834708763308593892873063287379526302010730200327149602549634286697/290149633690210530573628782073822459653769741487771966988142257085918576983339420712376987850334126172308377364728644015111581262177935147436720997994515064327718767571225248111713461562142135118086367439625998239053598473159504051166623940133276359270400) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 2 2 2, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.trianglePiece 0], [Piece.fullPiece]], 69073226812995539973329477614373738323924490101647598865576872074004505319254111058775417961518272168662393314317010712521433489630502626013635214432019100876914445945346715248565379781751077946973048471875488973926735484319807073889507534889940899/500558944100706467742388106946664481142376491525546160049258087371311863116207684893777979959791515708827001080420461311369862924877002563434784791996341191378593315843203016683630520601402402399558015878044002199513869543723045597507711695148178304000)
]
def part50: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1], [Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1, Piece.trianglePiece 2], [Piece.fullPiece]], 26181852939067081375896281832190988110291729551241736939243877768446192817807351886142814628606483173486329230699519406208168078365762988305593375771243538885464257276809721472104190602873108177675614295573807958527328/21390920216587187673846400251519074174191256748823813147435588960120470149475842223904782195327090123989612779427354286273290374832110913260130769721445270757094186439212015573340014586690766358474068511116606746612216445) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 26181852939067081375896281832190988110291729551241736939243877768446192817807351886142814628606483173486329230699519406208168078365762988305593375771243538885464257276809721472104190602873108177675614295573807958527328/1385468511508135558447357497890638915188193508364569553746255661358042731111400825000088838009140300240683230110730309767634744287500991740945409824088288741666233361481323036669659404765374246272006943396511502371326646926205) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 36157192122079728664865061098593827171244545578326917990898175620531770190402272812263917041950138239911495075469251225764559344171063479820888256769690211786018325208688461360956820420443299471362751008143100078916369785721/6827588824712092032028577749605068574047417609220598760861547899172434578916983265600437793709043399586086957985678966534904019848804887299378979613107086918931198005379959924708081546683764285628450217058008683685897716052338240) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1, Piece.trianglePiece 2], [Piece.fullPiece]], 9443404654569645586204370074614756854819701141834625448136454390524230406466138882732678551387579177876897345880595485917417309567126611702891461998851509370466521856021123687964418111134883797050845951505785560159056479961/30480307253178982285841864953594056134140257184020530182417624549876940084450818150001954436201086605295031062436066814887964374325021818300799016129942352316657133952589106806732506904838233417984152754723253052169186232376510) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 0], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 822142086988901483520161149911093395575772108453800986171270930689067677767531216310934136847306902162285441903662838177734900670578037746332206446786552383108110988009538121171193417043308779965561464630779776926528243447/28687348002991983327851167015147346949779065584960498995216587811648884785365475905884192410542199157924735117586886414012201764070608770165457897534063390415677302543613276994571771204553631452220379063268944049100410571648480) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 5342024045085431358425114083971444660561548652540982382918292970023026956302113540828174829052869235302169224857881353170666087000232427715394916312862234479210644521766160145982217887351702269951071046618684553129740074799/66937145340314627764986056368677142882817819698241164322172038227180731165852777113729782291265131368491048607702734966028470782831420463719401760912814577636580372601764312987334132810625140055180884480960869447900958000513120) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 0 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 6 0 1, Piece.trianglePiece 2], [Piece.fullPiece]], 822142086988901483520161149911093395575772108453800986171270930689067677767531216310934136847306902162285441903662838177734900670578037746332206446786552383108110988009538121171193417043308779965561464630779776926528243447/1792959250186998957990697938446709184361191599060031187201036738228055299085342244117762025658887447370295944849180400875762610254413048135341118595878961900979831408975829812160735700284601965763773691454309003068775660728030) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 2 2 2, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 0 3], [Piece.treePiece 1 2 3, Piece.treePiece 3 1 0, Piece.treePiece 3 3 2, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2]], 2535589426241479915822643084540425814095005757423556573749728090688232190757060274055785086892166390901219500067704193672925178607651480715321821426098037223783000326904083389311294516671742616753575625866432433083488/922745577970427703577687853987097317318054212694360567144280308083628124095036331227265114308227417113277414014513322152965467149620470768084072419356462660109945297377773220810745727269013450757704916165814408677389729) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 6 2 0], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0], [Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1], [Piece.treePiece 1 2 3, Piece.treePiece 3 1 0, Piece.treePiece 6 1 0]], 108512304747271385702351272631690515835993167968369776857723387193355916447490843150946127220226825307763405256075679265196555730235118556282193395044639114605072530368848789725684113417173565666611184163013221436466793/5536473467822566221466127123922583903908325276166163402865681848501768744570217987363590685849364502679664484087079932917792802897722824608504434516138775960659671784266639324864474363614080704546229496994886452064338374) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 1 0, Piece.treePiece 5 0 1, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 3 1 3, Piece.treePiece 5 2 0, Piece.treePiece 6 1 3]], 760555108395315952917814952144738271979242864006750837750144779129932867129195534671551229316199238164832848290188820613836520774748491052628559074159713249623375119107333187629744689187640072311043421512721525744768/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
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]
def part51: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part52: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 5 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1]], 596826063579937553506140919757344074111236688051785791346788400118154726817530921556080313678965218972860066679084988855126483357306096431651299639638884251573448991029059710473687082580304899380799269551044855865463765/34286061978256623427106042867232580549308089786421772295994104430188477223517509943840963881587531183070714610788408148385386591963955137842227842854991216006279476009538471948570245811394474641182288267866237777050622707712)
]
def part53: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 517098471166702818261174791971663987986199993888660903244128579670978260250339278990132036886741083230965615863721011880848650203407416883104211191863554514260452706944729745469670030328266293394847661709552092506237556564121809/5549464196725988403632827994878999736985741032774502672828266132447354825743723998280035838726710475183571479450759863999569987333108612396935234629533440247707277738772831426802728681144563611358804336424749458099897663607340521472) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1]], 7835067320794381019742285095130841704745812330304088282574468644797518216705989428432814104486196854993110716372498381859598997087890280700255690358300571142953608848743878226541972416234735587951525962853677465031815/170456274039628099424532883572889249890026014563176424767016144184175668014646711368527519297665282870379973207044642783165984477093526963704257741466575647758491713115603198607948665255512302903605126331721352584768720848) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 581131889760176696921188119356336980338365225360925797295718507787075721565102479849982814822072105848976394090827006225431669605342802573010587345602105134057581990819402523420002270623152867097604906000105602847063026311581/21677594518460892201690734354996092722600550909275401065735414579872479788061421868281389995026212793685826091604530718748320263019955517175528260271615000967606553667081372760948158910720951606870329439159177570702725248466173912) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 2], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3], [Piece.fullPiece]], 9663335629061901963749570615644679664190557806483176707078529928019685487474229461662549672245821299624401032239132098407403762605433921822987182940025423864662502276239458135291313472459665470153989441317801221959013/1577183201896096053089652905161780546589584991034624836533552663237839120234378978375451271055783243747377212092439209774696806942410092558880152808149805447095678538112071938662603871419182335251942918197037183651840754372016) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [Piece.fullPiece]], 18446422274701514202048319623078564569332177459310398804619865923762974761558723292647501515593355896505855881963803694683934109055390637177823435453822440736603677953658646242389713384535723647802138854218861946305204/705900367147377193236931208300129447748311472711185833865374435683975514932702793388857812445793974091657221721102691447018582369459660137584315400807693934984108152493996513920220481360795289829644260866848022638203142685) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [Piece.fullPiece]], 3345452133435700199141368596063923169736352002340611558757006756841713138554525017172959628134701826152859851369000695198541377962781933975317173360273376066085376516893634189150571372010782996661280225593537189084439/13841183669556415553665317809806459759770813190415408507164204621254421861425544968408976714623411256699161210217699832294482007244307061521261086290346939901649179460666598312161185909035201761365573742487216130160845935) ,
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]
def part54: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 2], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1], [Piece.fullPiece]], 3879762199562940675921458277713045642808409137178722465857298437104617136845338104970645577538719035787148702302523196672145237578122558379921470759848801711028061857126928801827969460476067397707741728016283404956104255/12631707044620861262618015793190950728692454131839600319576775316385228450769608926678249851111195699026052751343097738878826639144615050783978678946575711160208228003514173875789037930513753815172421993424403391544966260736) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1]], 327245658158958176013532199443092836349954935104319458746026232261611878293008652624018996429604906742438380391749382126315995112826704916687012688933527406877876082345213362167043520774826800209206578380952348639358169/2114932864708220296600060561338427051292980255495474419894690466127675660425823271172891641994457240023631832921264534374596850706930119000448693985165012416971994621589856222098229206900578829136659667852046624688577258868) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1]], 1456050565266507053982766941423148514196971883663000841469608639843040498112770995747948629006382820595642651180550394894061452921948606020378230946689515054341649991275044632727965229065109629838090858126025176904677317973/556634216216996281339066605949520945218016837682557473225464285424109927723806773938258048617573568757153051706149806289036751320534811662868569028750782391861947293014857092085037940747989295799594450028808370310416859659704320) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 76533175244902070860785436606906182312868945493149865671771916013613599755191269697629436883924219689750553389250383977401958434687307295782755479077597342508476160601523183151534752515937799247856931087873221316172790109735099/387306087643786012555722544419676673682696115659523489870278049798095687710224753306239950228107689141227093377139035215911771568828121955023950330204794388257542926479737564672769399172450952017357818330044864061988050951222265856) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [Piece.fullPiece]], 3509738327392006587610275804614829009238917776959837471571816407316992936676926016670958849169429128721872302516735053477805497773440859358833660763174812864107316515255036684730848812283210713214891788364360053046177197822807/18338759995512397505268965382437513055026977582497656440889527212119613844388874247039104157408955764038763602426291933466883164966037767250356913123487080237354086768355201452272346179730996950920916175192278891579471079989858195) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 1, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.fullPiece]], 35103817585444878969694867766294099052264626942788779735301618405915576775329276011974660320947008035842578434880162475356590550788400985449203521597235806501769940471513309247384240448450689151756741382625152506962647607360001/13664031006361722820758027720907427237015028573143263792643773409906433413661573168841983847414324899404604226532262439861578574580490642474596714386591609401119911190591071885362487858450041584286616446485389290719871651121095995520) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1], [Piece.fullPiece], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.trianglePiece 3]], 12283195412145959560110641981765758283548851203288691898047966692344889037471094093074763215700496666328253449940977744315307948981933588823228063207951332727512856904319251391974920954606337946602093490767985732112864/8304710201733849332199190685883875855862487914249245104298522772752653116855326981045386028774046754019496726130619899376689204346584236912756651774208163940989507676399958987296711545421121056819344245492329678096507561) ,
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]
def part55: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.fullPiece]], 958428978450636140193347813660118850555065442497779386806085413997218984250429304675375366432857536940435630199510404567821563549680528730160232982884138736491116022933301506568555883275612672516717760248232851911304781473975516651421208687141/8809167919410558629810165109712956683397888011360748999942946673787880911895951161842192440666839996635610912586043579768047215889427648615157460372147321771808584906387487644570909773441900697779189861024136604329515060824902909894983707072870400) ,
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]
def part56: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 2 2 0, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1]], 658468294676825731249426176847848428812701175445114478957738683185701791247990403526008116579927349197101349936930240432928604104148015093136883050128318818034418580617495104610688491268552403519193401375910483752202286042921856140689/6306629240341322814872643212779820056794268490588377602912698751233148227490955355026078663902293736093811627258585931438713618786604554926942859856866074578172620135353295028551799120610361399070197446124678583549165972645740251398074648) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 6 0 3]], 10820732217255223060672731918208225110891902760716733530769475494115359688422035622634057699480977662176930715182424259402625573969358035043435806680660154807102195385483672167755584214727960250018928514053449295632224309689943708545791837/2128487368615196450019517084313189269168065615573577440983035828541187526778197432321301549067024135931661424199772751860565846340479037287843215201692300170133259295681737072136232203205996972186191638067079021947843515767937334846850193700) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [Piece.fullPiece]], 51950360517334569927181050131353327748916681419191184541251449235673198288592685907713474603896527501420969338694392551356091191715506265006954938603146146850299815883239973483377463540640626635617203296036145623328/56494627222679247157817623713495754121513523226185340845568182127569068822145081503710109039279229619180249837623264621610130641813498210290861576695293632251629303921088156376168105751164088821900300989743739306778963) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 0, Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 1, Piece.treePiece 6 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 5 3 1], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 3 3 1, Piece.treePiece 6 1 3, Piece.treePiece 6 3 1, Piece.trianglePiece 2], [Piece.fullPiece]], 858194180531641750978575337405148599710222041812185874596104910014580743249961948044024034804747206690578908984109254385382582066578038297820341968803443445604132442745133711571876783655452699949429944126630841168/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
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]
def part57: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.trianglePiece 0], [Piece.fullPiece]], 348206489308850621436389743567050678697638704179836427434913927826452941728557193701170731343340627257981861853359512815931129313035863101950737713130095179137429117601525184261228202989562115370313970620965462841683/97131113470571337218703984630220770244005706599406375488871611377224013062635403287080538348234464959292359369948770752943733384170575870324639202037522385274731083934502444295867971291475100079758412227980464071304182) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1], [Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3]], 183920975884425845388301701553531803400700121553158700253728089109940678129009029177738949240333869744045046616669099081174592296776392971960815553180172586465337066991519456186360297466183354574542433688880469467927/141960858149296569781182746767245741125854494260670856483735432012865865245390204804194632970496525709734986771463588023533148792249303195089857295285609640016914661135042033970883958041386684731954602487048370565752266) ,
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]
def part58: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part59: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 2274593160089039839501571039754820702451696015220656519133512387820276043540382005732542468829660748656517559106879919430055834294056215614402288708720888183935914519458991112434606921460398512599045868171826091609748326522774208757/47035177482375705463540487774096322145789771340909394216390073138824111744944150712922228755608075471227758020519846572311355373890178682946774198006939364499473995884686479361794877278125891958522966003910017125807945135111965507301120) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3]], 10212307249313922171205227876790695147270726710466892203660486326539814021234449689121949716810595705732702610828267326049575764931964031405215573423011629748287614493540356468765720259933597057111320722708860371818181947789327/172517523042751267105122094241843904584029384319650066814811007698151818313322149035072728710416943483083032645686056970038715426533812657521912404661602716033868822933855924889212431331154239871343038453308454833509188435709967383) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 5 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1]], 1715846314572222257171548137354431430620757864226420729886248286199950767880484067537168066504449340887189750416382411942301652662196171882226740737742378733981731319561567795701179150059685151647220719865369067096085/216348347819527972346522506073282509475802249253262385281212798387607578633974672121592620647036705181636119839710508147864518759387938069316942518015269091385777943569804059771627152055073307531498814190261716742206453384) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 1 2 0, Piece.treePiece 2 2 2, Piece.treePiece 6 0 3, Piece.treePiece 6 1 1]], 12051455819015365197146029172131578137858097449155298017507094874527387338512831408890035495557685269091263672474773623205490711189616827704732428015235992160451517851483543005148815957460803129599217831575530453277020315/1875019014435909093669861719301781748790286160194940672437177586025932348161113825053802712274318111574179705277491070614825829248028796600746835156132332125343408844271635184687435317810635331939656389648934878432455929328)
]
def part60: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 2 3 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 530675513500803026839717424600204047888304081537430225941806247605329026910032973873944018867963964765541437808780527109951322415080266100298954297579320813403396457672552183346499839325834306432932699051972919599217308956325/43355189036921784403381468709992185445201101818550802131470829159744959576122843736562779990052425587371652183209061437496640526039911034351056520543230001935213107334162745521896317821441903213740658878318355141405450496932347824) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 1 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1]], 154332556963750540567226274187423536348676654258296069953524453265689020896575919102140148399791363224386604061339300844885924721064941249784158051712387791040596917625260628439501614863987147123298584126026762924731533297/6116859518868091003726006658785944452945239974533598606873233905759449755206667845475363171621687568759923645122525343835568695830052875416138121195063542767713706516646781231703713634593288964830708242074817256158427029227520)
]
def part61: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0, Piece.trianglePiece 0], [Piece.fullPiece]], 67960683925095773917277028048380924356203225685996909529150793714790991851327502943107215889980136801043513963944317779458326871061767705521148741061458728207817242707740822437244247711377918901684794117278483373598763359466/156741538423182884660418507542200966282281859679467149067431856513842853370845079034522257755632100547339859849797366952708403119367844164532965069431513506302171681780813687626259369057529888469409539958908366594696334017007335) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 8136848350702574453933294845483958744665027414934642952501914718278271321581110057360949892151139984940774751423782161781211785939810427230205594033395162674440137645993307797918543172254952927533777288922711622423579689970628038081184122953683899/450503049690635820968149296251998033028138842372991544044332278634180676804586916404400181963812364137944300972378415180232876632389302307091306312796707072240733984258882715015267468541262162159602214290239601979562482589350741037756940525633360473600) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 1462618037574285933925373123217983929404367206537217896846200588509436266842022098823861250260670448815938047371003096484611441416698334206252341608619566658211858700665376478102346010280433312984348498187369446705337585278354211661/22736947594585906773741358127589958922393007545710390950959238954084305200332857752953061122097436632609261432949684699929666748101936429077728932739288438043463532221143543617243179796460869196252929766951687779757866427465503736545280) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.fullPiece]], 539710106449836486659526729643493042287400031729701008219155769901640181288229765268740271179412990881234963036896532089523253392999637592476764520292264946605103600744310749389958322510028203307985823656554227584392967397298951/116004834666254626396639582283622239399964324212808117096730810990226046940473764045678883276007329758210517515049411734335034429091512393253719044588206316548283327658895630700220305083984026511494539627304529488560542997272978247680) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1], [Piece.fullPiece], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 4 2 3, Piece.treePiece 6 0 2, Piece.trianglePiece 2]], 11945579666574364421343015409865797604902266570101445740390281503897312641411394385776918296571617388198357233914704283126450692620982154280220612207869723289472970831173800503022544306647046559413252173724497102458272/4613727889852138517888439269935486586590271063471802835721401540418140620475181656136325571541137085566387070072566610764827335748102353840420362096782313300549726486888866104053728636345067253788524580829072043386948645) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 2 2 0, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.trianglePiece 1]], 3795897353757143861016653461615285724175102882480001662571832310041846599520215021524167085294702385183367441800174065832767629811441739533532331830759777055224147642310104949368764925509870072740137547418463839821637791096995218250845636163039/11745557225880744839746886812950608911197184015147665333257262231717174549194601549122923254222453328847481216781391439690729621185903531486876613829529762362411446541849983526094546364589200930372253148032182139106020081099870546526644942763827200) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 20087269658350117515756648594299969160862709215138313740782017680676903347033498143156307125289530795942283185352225190906315362586006588899357819123549548107279499547115522795862397523326144569491239990069384467970773582438187100472835068813071195483/172798538388803391899216094036111543380190094734209744737702522217399152522800309455669541193589041110471612174020331187010169468967225774978675463465319835430774920477627601951347676715673653767970284273599252877970402232051798878639808760157906732288000) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 4 2 3, Piece.treePiece 6 0 2, Piece.trianglePiece 2]], 155560885007627372751732721502058878837696720629856153343759721023494418323414497294951862939952159307768152531332619711738908157384946517404594992754682784269605454613773747498445889574090387526020419758814604127972670418314423729256540709708097/234911144517614896794937736259012178223943680302953306665145244634343490983892030982458465084449066576949624335627828793814592423718070629737532276590595247248228930836999670521890927291784018607445062960643642782120401621997410930532898855276544000) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 1832696533728325521827695087488525043425290942852545693684056061545226244555932309036380497646543812166200241627900525358075099699717728787671791609661951707546584844832946889343461606359539450346945874196176908855604057538651872396786217337087109983/4100014751686882259595834163980896728744006202294645451018151787659495462725860036516133453925988123234126240411752791387290229614645001086987850838524642659751456343512666778875278537989290845705671599175859682720009543815366458811028581555896946688000)
]
def part62: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.fullPiece]], 1050819381390102517431817974417709183202030307434897793629049940952756722534109743866691074391742050760128866607838311982869345990374942038823274972541357860698923796158269286188301687478649025793305722461292533951661680278485107206472599904347/4517522009954132630671879543442541888921993851979871282022023935275836365074846749662662790085558972633646621838996707573357546609962896725721774549819139370158248669942301356190210140226615742450866595396993130425392338884565594817940362601472000) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.fullPiece], [Piece.fullPiece]], 147706201604826207996965701587144498581181407076534185294903243598746400388149144158987250026008851026519586320101832630353972023974914444234941274487552268463901098246855845938276178423016669077702302295299083463125/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.fullPiece], [Piece.fullPiece]], 138277761996269390791469766927642328723377017397591993584663339938622764729153239357378624473038317066342011893900824911968110285343704909204646417516431738709744229005258965157512906261146873101449676888418169925831/212941287223944854671774120150868611688781741391006284725603148019298797868085307206291949455744788564602480157195382035299723188373954792634785942928414460025371991702563050956325937062080027097931903730572555848628399) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 5 1 0], [Piece.fullPiece], [Piece.fullPiece]], 2208406214440218485020219154684200450418312386236983221675015586134321939434159358187145978398395513708508210142234115898905316133705301883308294564288534891904908293919298731731625346352547208095342295718600369213406/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 5 1 0, Piece.treePiece 5 3 1], [Piece.fullPiece], [Piece.fullPiece]], 2697250636422579093831347757652298583739407782015277603322756105151849428922631659525059071341409982330803697978404890877017964120440892866279202870844945225399506324330579503093411689761163701213135558948354130488872/922745577970427703577687853987097317318054212694360567144280308083628124095036331227265114308227417113277414014513322152965467149620470768084072419356462660109945297377773220810745727269013450757704916165814408677389729) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 5 1 0], [Piece.fullPiece], [Piece.fullPiece]], 26559612889976952638901252175401793416031731859339006463396631834636602642611060964172530836159789244266364798493478338034963430686136781747367186280602865428592962858025860018023394389608505852890296942781216616733514/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 3 1, Piece.treePiece 6 0 1], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 6 0 2]], 357219335139678543229811731241853328327768496776542932732524325519592419609139604961561420951331118133255715166137908748790761517500673150089833539658464977545546534655482418379039348310514499573255773165973555418959688002469/7990745096083833335629178815876912006547702650325776226967114253646890564003866774308977846365558067119286972734767727000820551183458722113445278049449708164424438679021874271142634500972111961185584390061995159729617028318021) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 6 2 2], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 3 3 2, Piece.treePiece 6 0 2, Piece.treePiece 6 3 2]], 54959983067729786798674524120007694268378657339322851642583842621173505011617667094302446207379571931088886755176382767370389895144465180269897981393696971911716976278191260859904694794968504540243969514722287728665037385/1875019014435909093669861719301781748790286160194940672437177586025932348161113825053802712274318111574179705277491070614825829248028796600746835156132332125343408844271635184687435317810635331939656389648934878432455929328) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1], [Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3], [Piece.treePiece 0 1 3, Piece.treePiece 1 2 2, Piece.treePiece 2 2 0, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1]], 145846936738638891859581591675126671602764418459245762040331104326995815269841145740659285652878193975411128785392505015095640476286674609989272962708102192388447162162733262634600227755073237890013761188556370703167225/72116115939842657448840835357760836491934083084420795093737599462535859544658224040530873549012235060545373279903502715954839586462646023105647506005089697128592647856601353257209050685024435843832938063420572247402151128) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 6310628431122948125385184539951679254562465359385696261925657699992036005745445740221136348629064290434236828398631757589893120709284204178283061494152343703958105205865261976526732196553557280875275018455041866760062403836325331614534924111/41105348062696673842776913932256311166173683167956927540264387920787413517140548812988975515582370113112245424146011383931247624527331168102828171975081700885613503518205706337094916308314213526859732914351430071856753976510405810562370940734400)
]
def part63: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 3 3 1, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1], [Piece.fullPiece]], 1374925820683875735545031902396297729931281288820529869520515850383277041180472160334985201187189828530511119473147344351681964185536639599381933790340034219740937572821156913777443131869791869009738416060659575947675463829769196890934167/1702789894892157160015613667450551415334452492458861952786428662832950021422557945857041239253619308745329139359818201488452677072383229830274572161353840136106607436545389657708985762564797577748953310453663217558274812614349867877480154960) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 6 0 2]], 1963558674124351364370630859292650368476475789715304744775293772631918784892325965773734230620154481179636016955534757207283893880598037470097547960023657469175721790755961408580767190047085759589026492402360821137801703154019284828580257/236498596512799605557724120479243252129785068397064160109226203171243058530910825813477949896336015103517936022196972428951760704497670809760357244632477796681473255075748563570692467022888552465132404229675446883093723974215259427427799300) ,
  ([Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 0 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 18332619960050343195944010562910126083145289001626586852394785170979015324845619109706408902281534614073701576260540089276073387303866636841477227110126758258460705652798463676907930025623141626480517398245988186048338568695039297530387427/22388533803211695992797883405368361201619653141588740490340080566877676207592891510342579256853142763133031276767980056607433346692446169990647152491874564752512801480504197351358886878166782966699200933742608971599539202892377892463165000400) ,
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  ([Piece.treePiece 1 0 3, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 1618109302614469776699991208762733088015994662680348637849056943202492505584015819669204020878174578361602139771217511884873488004168972142348165577589286477200942610940725729933298851701472411390688536967886734494954878071229567127264429257/13286577151578722858271325715476787447652099609844663447358185994597951843924217798137850671703392359793857106794670346321211353382571690699904055587905196245854869824066490937242801230970250836964762154133795578781981083316494807454503738419200)
]
def part64: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 0 3, Piece.treePiece 4 0 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0], [Piece.treePiece 1 1 3, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [Piece.treePiece 0 1 3, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1], [Piece.fullPiece]], 3878081809959090980980629018817160132463866073508566815918785001458343198185579663594411541134072555305865487956964143790989363268135790814181412252265404555700709214050269823761723076005726474422518685572864602377597771502729/640260675909335224457391667269186482661428222680329956049452627112385011599577564959740063086455355129820810219697483373002953270677978025402501292442288092364655171775969140303203921902368564207304770114409581514055288834639200) ,
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]
def part65: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part66: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part67: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part68: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part69: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part70: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part71: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 1 3, Piece.trianglePiece 1], [[Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 6 1 0, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.trianglePiece 2], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2]], 10893292763666888403365940945065824885641012801227283040752687223512358107634609908509847773410978695939977367174304455960561826748685202880851391761006837133108224239744128018467348659505833289540189054453835903651217022457597272268545/43245457648054785016269553459061623246589269649748874991401362865598730702795122434464539409615728476071851158344589244151179100251002662356179610447081654250326538070994023052926622541328192450767068201997796001479995240999361723872511872) ,
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  ([Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 1 0, Piece.treePiece 2 3 1, Piece.treePiece 4 0 2, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 1], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3]], 751561173660555422500198751852881113035460644618706212190568530875168599645577087863333178040209715895185462766706123262672234503054091778146664210080224687887726944154579141300639230409296173019489369946146230971413348628008899/37756176052725028246144776179444623210563702383697955684778024936829324796577836488298100974194226625802513101263205503282788663819899666486291507033075727399579871758436585243068564777072834570137579503175527563143946604185656047872) ,
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]
def part72: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part73: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.treePiece 5 0 1, Piece.treePiece 5 3 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 1]], 840338592073084544488816690825815380462891923406406694364303212569772538871491776285550704972781078055021825087507181321639217882825667196657561149560959848524942181265328747948491079038044088104218867283983135254121472262670323/177632403082702396669854360371796554081195371450862429304369054328783634377600451194945790016386223692259854944919411718200521469546378352169757287025690922214558845477683934509712342159850540595726013804310060779358331464574247941760) ,
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]
def part74: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 2 3 1, Piece.treePiece 4 1 3, Piece.treePiece 5 0 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 1 1, Piece.trianglePiece 0], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 2, Piece.trianglePiece 1]], 20681841688790029860001337406364686751106185020347717649856681614244462035746360484080636423606500627411368871435120744205719799100245181935702628696394561827204265448549427839408746000400716282960037984523995012502738746272577500088528206271897/117455572258807448397468868129506089111971840151476653332572622317171745491946015491229232542224533288474812167813914396907296211859035314868766138295297623624114465418499835260945463645892009303722531480321821391060200810998705465266449427638272000) ,
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  ([Piece.treePiece 1 1 3, Piece.treePiece 2 0 1, Piece.treePiece 4 0 2, Piece.treePiece 5 1 0], [[Piece.treePiece 2 2 3, Piece.treePiece 3 1 2, Piece.treePiece 6 0 0], [Piece.treePiece 0 0 3, Piece.treePiece 3 1 1, Piece.treePiece 4 2 0], [Piece.treePiece 1 0 3, Piece.treePiece 2 1 1, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2], [Piece.treePiece 3 2 2, Piece.treePiece 3 2 3]], 4486580867826118426297221991573972267077316350984518635832151058542823075366336741501975392505906799632141731084051751141056202871665330977052473305167650560685992751475771679419742787328615305059051461093951177976342/251657884901025737339369414723753813814014785280280154675712811295534942935009908516526849356789295576348385640321815132626945586260128391295656114369944361848166899284847242039294289255185486570283158954313020548379017) ,
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]
def part75: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part76: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part77: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 1 3, Piece.treePiece 2 3 1, Piece.treePiece 5 1 0], [[Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 3 1 1, Piece.treePiece 3 3 3], [Piece.treePiece 2 2 3, Piece.treePiece 3 1 2, Piece.treePiece 4 2 1, Piece.treePiece 6 0 0], [Piece.treePiece 2 1 3, Piece.treePiece 2 3 0, Piece.treePiece 4 1 2], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3]], 82022861403991761934216988201288030871737305015957741713327810743537905520161925818629673381451398614001894506750997255658721493164345811404371547220793202674610986002028456425828585581054075485575736790604911236240/145696670205857005828055976945331155366008559899109563233307417065836019593953104930620807522351697438938539054923156129415600076255863805486958803056283577912096625901753666443801956937212650119637618341970696106956273) ,
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]
def part78: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 1 3, Piece.treePiece 4 1 3, Piece.treePiece 4 3 2, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 1 3, Piece.treePiece 4 0 1, Piece.treePiece 4 3 1, Piece.trianglePiece 2], [Piece.treePiece 3 2 1, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 0]], 290426729179130633102107610534535916641110453632603269465666753181297655031911713438102529614460755312978254655229123185098847970734116333145044463295901185125273039071926560021369816152495586392075868505461904089380125429631767289886779/504530339227305825189811457022385604543541479247070208233015900098651858199276428402086293112183498887504930180686874515097089502928364394155428788549285966253809610828263602284143929648828911925615795689974286683933277811659220111845971840) ,
  ([Piece.treePiece 1 1 3, Piece.treePiece 4 1 3, Piece.treePiece 5 3 1], [[Piece.treePiece 2 2 3, Piece.treePiece 6 3 0, Piece.trianglePiece 1], [Piece.fullPiece], [Piece.treePiece 2 1 3, Piece.treePiece 4 0 1, Piece.treePiece 5 3 0], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 2]], 205053325103108501197235925484999742577481904626961965958192440860542774566529696454154392683306070142913279195595245367209723455931601706931867017694786938127687180531360759047665404570570696137189693979748665051890895/528733216177055074150015140334606762823245063873868604973672616531918915106455817793222910498614310005907958230316133593649212676732529750112173496291253104242998655397464055524557301725144707284164916963011656172144314717) ,
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  ([Piece.treePiece 1 1 3, Piece.treePiece 5 1 0, Piece.trianglePiece 2], [[Piece.treePiece 2 2 3, Piece.treePiece 3 1 2, Piece.trianglePiece 1], [Piece.treePiece 3 1 3, Piece.treePiece 4 2 2, Piece.trianglePiece 1], [Piece.treePiece 2 1 3, Piece.treePiece 4 1 2], [Piece.fullPiece]], 360511080255572640518244861393595360792820593183318519149924931045707600592108854001864420546025446758571891897640720703597405924524057150206559482947210455005483628939390744790267881190523587266736332461537084826944/145696670205857005828055976945331155366008559899109563233307417065836019593953104930620807522351697438938539054923156129415600076255863805486958803056283577912096625901753666443801956937212650119637618341970696106956273) ,
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]
def part79: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 2 3, Piece.treePiece 2 2 1, Piece.treePiece 3 3 2, Piece.treePiece 4 2 3, Piece.treePiece 6 0 2, Piece.treePiece 6 3 2, Piece.trianglePiece 2], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 1 0, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [Piece.fullPiece]], 30093810122833148992251178713938664077602764602897854098399563936503444360200224264219640130531144348975589134590043822622771483347388849504130420338966603712589088595578040635080737762762804009743719280623900140001124824819942515799/90947790378343627094965432510359835689572030182841563803836955816337220801331431011812244488389746530437045731798738799718666992407745716310915730957153752173854128884574174468972719185843476785011719067806751119031465709862014946181120) ,
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]
def part80: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 2 3, Piece.treePiece 3 3 2, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2], [[Piece.treePiece 0 0 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2], [Piece.treePiece 1 1 3, Piece.treePiece 1 3 2, Piece.treePiece 4 3 2, Piece.treePiece 5 1 0], [Piece.treePiece 1 0 3, Piece.treePiece 2 3 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 1 2 2, Piece.treePiece 4 2 2, Piece.treePiece 5 2 0]], 435746451208706235275527749819342664006104432897275502852053994575045123075860230911470139838960555136885064567114672920686957932435587123085723844610463889208870863135776174762214360899349776017121101700088590942525/777048907764570697749631877041766161952045652795251003910972891017792104501083226296644306785875719674338874959590166023549867073364606962597113616300179082197848671476019554366943770331800800638067297823843712570433456) ,
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  ([Piece.treePiece 1 2 3, Piece.treePiece 6 1 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 5 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3]], 33870496536164504742422540319122022045292274504063798804102513250121596479255344903726162098478195032842607149995279071086375827720479010183910903485161279820106901412722389103852163147658339515269160174403705266793436026958269/23837393456149849303310259272488946888313090821874920652812005512757454614875478614966181649793416634732668143628543431196799098184836299876452198628094946257148493208172163916724937068578189682287785769371065281719639638040840955376) ,
  ([Piece.treePiece 1 2 3, Piece.treePiece 6 1 0, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 1 1 3, Piece.treePiece 5 1 0], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3], [Piece.treePiece 0 1 3, Piece.treePiece 5 2 0, Piece.trianglePiece 3]], 456891171962161561835032636974247927683708884538143158182550118811375973230571392212376011215623918307568297416952859964676535608784559651037298863842747523048409811014245886443707111532362468069123182275187396141780420787/274266829280533889581938362942535856447065873589860523771778850262325802208291198697651621503003245890927524606248327004142150377729738325969657859684940163316606213516597918264104488201871350683757397954768502314445387887280) ,
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  ([Piece.treePiece 1 3 3], [[Piece.treePiece 0 2 3, Piece.treePiece 6 2 0], [Piece.treePiece 1 3 3], [Piece.treePiece 1 2 3, Piece.treePiece 6 1 0], [Piece.treePiece 0 3 3]], 119692498645788038362970388717242993230349643346469241404682110235146086803262920677544647643004877342218845085797812546912422773693048684023505781673708127496942258172278945771737655205311541805222760931901838128839544805/222624512074549504905269532772466005399261079525839412620493733276597437939560344333988593894153393686698087675922582565747036916518959894784073051070001307049683644377879602326129390200060929382806280826531223651429185144) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2], [Piece.fullPiece], [Piece.fullPiece]], 12964706372415302282799473961159387220198700444326544334313939525988218995045220288976348579698707527659348157954920696131017579473211895450618716483369891985746962879342256189410756102628100294315959849688084250876579/1406264260826931820252396289476336311592714620146205504327883189519449261120835368790352034205738583680634778958118302961119371936021597450560126367099249094007556633203726388515576488357976498954742292236701158824341946996) ,
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]
def part81: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 596826063579937553506140919757344074111236688051785791346788400118154726817530921556080313678965218972860066679084988855126483357306096431651299639638884251573448991029059710473687082580304899380799269551044855865463765/8571515494564155856776510716808145137327022446605443073998526107547119305879377485960240970396882795767678652697102037096346647990988784460556960713747804001569869002384617987142561452848618660295572066966559444262655676928) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 62502714557862750769307059043383249072717714190503274846360671717755144627787428051360235749662439421719560997419479411576899189293151303075005538515140828698061336712262024385207446404364160224768930887112746228162515936301/40804883799455797085535499962345586301365742888047813770796074503289373718703852928529675284755224082232143231255587235290955789214033914683347313452451766527259395138035525197078887361357085377638267179593746015440423997112797952) ,
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]
def part82: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [Piece.fullPiece], [Piece.fullPiece]], 39208247648436719441003266200197686684583251103559758813337351222246160382753787830478573438103353411522315099926001152744255470496458903979922903191601458990257089451904249708826883183530324185203065257725927068381/24671302821525119653550812096076075641977449476249219374173389289814899317909392434918456740451554099660259279966987771247708279579326271062458357317530685859781695319363620851150464708034675420258636705907037874111262228) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 31344280559064396634043350543579925451445255325868780493947600466152023302091036189871495676499112282089922570117902461839307867453404493586016052093359599574620978913960174830220441450021649605549258145598171468257688247/30360776636499849021975818424364275521849511077416528103270888767328403064511795333727436967823827442137011332779454788162913533641394281758442941556883754856591811858657384819255124524819259953599901175292965785297934521661308) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 62502714557862750769307059043383249072717714190503274846360671717755144627787428051360235749662439421719560997419479411576899189293151303075005538515140828698061336712262024385207446404364160224768930887112746228162515936301/40804883799455797085535499962345586301365742888047813770796074503289373718703852928529675284755224082232143231255587235290955789214033914683347313452451766527259395138035525197078887361357085377638267179593746015440423997112797952) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 596826063579937553506140919757344074111236688051785791346788400118154726817530921556080313678965218972860066679084988855126483357306096431651299639638884251573448991029059710473687082580304899380799269551044855865463765/8571515494564155856776510716808145137327022446605443073998526107547119305879377485960240970396882795767678652697102037096346647990988784460556960713747804001569869002384617987142561452848618660295572066966559444262655676928) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 0], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 49198903156664573962380469645163613006217843786703580411934048846888741148095586883793401449196858787573734786587995916541695422156333220551829116336705532828799847493842022879873905812825538831892512929703076390527917778/22770582477374886766481863818273206641387133308062396077453166575496302298383846500295577725867870581602758499584591091122185150231045711318832206167662816142443858893993038614441343393614444965199925881469724338973450891245981) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 3325705466992048928988590082672451061470024098878584624385474197271227496036771413892645391483971053270969990536152117013321183047757253375160806586452564046627554474687500321877207899027325629877298031402457771585481861308169/1849821398908662801210942664959666578995247010924834224276088710815784941914574666093345279575570158394523826483586621333189995777702870798978411543177813415902425912924277142267576227048187870452934778808249819366632554535780173824) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 5085704852194390231552228416243946400537051508923857213337356402936017917315242469880031044986685893845233930469745238379912947116432310747428741555366191701495698608248021499151245048443440897546698929118594762047403053/60000608461949090997435575017657015961289157126238101517989682752829835141155642401721686792778179570373750568879714259674426535936921491223898724996234628010989083016692325909997930169940330622069004468765916109838589738496) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2], [Piece.fullPiece], [Piece.fullPiece]], 327245658158958176013532199443092836349954935104319458746026232261611878293008652624018996429604906742438380391749382126315995112826704916687012688933527406877876082345213362167043520774826800209206578380952348639358169/528733216177055074150015140334606762823245063873868604973672616531918915106455817793222910498614310005907958230316133593649212676732529750112173496291253104242998655397464055524557301725144707284164916963011656172144314717) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 1456050565266507053982766941423148514196971883663000841469608639843040498112770995747948629006382820595642651180550394894061452921948606020378230946689515054341649991275044632727965229065109629838090858126025176904677317973/139158554054249070334766651487380236304504209420639368306366071356027481930951693484564512154393392189288262926537451572259187830133702915717142257187695597965486823253714273021259485186997323949898612507202092577604214914926080) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 240422981173460527295155684141463848542188076736190872063390601106150093931739340057050779749222203191512482990271272638806939002443152573941530167885478700049004427185832297821239830630776212159419846229863231731559709053476519/1694464133441563804931286131836085447361795506010415268182466467866668633732233295714799782247971139992868533524983279069614000613623033553229782694645975448626750303348851845443366121379472915075940455193946280271197722911597413120) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 1456050565266507053982766941423148514196971883663000841469608639843040498112770995747948629006382820595642651180550394894061452921948606020378230946689515054341649991275044632727965229065109629838090858126025176904677317973/139158554054249070334766651487380236304504209420639368306366071356027481930951693484564512154393392189288262926537451572259187830133702915717142257187695597965486823253714273021259485186997323949898612507202092577604214914926080) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 2 1 1, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 0], [[Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.fullPiece]], 57708201427575394969053224802060167995717493597688700415878527307033594982678688744084193786908521003845529472878105617439188892642125003581002692374424146586133115468129336315036755030447891662263470194527776742431386241/5707675068631309525449413439912080004676930464518411590690795895462064688574190553077841318832541476513776409096262662143443250845327658652460912892464077260303170485015624479387596072122937115132560278615710828378297877370015) ,
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]
def part83: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part84: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part85: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part86: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part87: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3], [Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1], [Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3]], 2002064270130510855784377455937494116796783173195738981318206046670210708701886562919992914798716163232054473169424688304504046970580367831401845694351182216157592066828184461727876813628699048844345179006590722704817129/256355498752511551103037643798597218338543061272178717562992783773051595203130093475502017211449362427106888838941155681769315237203650787933175028504849989935999348071497723890694449321282282319595111254793530265282091984) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 0 0 3, Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 2 2 0, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1]], 11092671629109380675101786207343665368890465751235184583907541513426370455948827553825754558040676084330403010311529192708331829906804193866760219405524664252406139206740911894082422177739310048467195618391802587692306165/1208533065547554455200034606479101172167417288854556811368394552072957520243327583527366652568261280013503904526436876785483914689674353714542110848665721381126854069479917841198988118228902188078091238772598071250615576496) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 2 2 0, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1, Piece.treePiece 6 3 1]], 1456050565266507053982766941423148514196971883663000841469608639843040498112770995747948629006382820595642651180550394894061452921948606020378230946689515054341649991275044632727965229065109629838090858126025176904677317973/6679610594603955376068799271394251342616202052190689678705571425089319132685681287259096583410882825085836620473797675468441015846417739954422828345009388702343367516178285105020455288975871549595133400345700443725002315916451840) ,
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  ([Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.trianglePiece 0], [[Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [Piece.treePiece 1 3 3, Piece.treePiece 2 3 2, Piece.treePiece 4 3 3, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 3 3 3, Piece.treePiece 6 0 3, Piece.treePiece 6 3 3]], 57708201427575394969053224802060167995717493597688700415878527307033594982678688744084193786908521003845529472878105617439188892642125003581002692374424146586133115468129336315036755030447891662263470194527776742431386241/273968403294302857221571845115779840224492662296883756353158202982179105051561146547736383303961990872661267636620607782885276040575727615318123818838275708494552183280749975010604611461900981526362893373554119762158298113760720) ,
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  ([Piece.treePiece 1 3 3, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2], [Piece.treePiece 1 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 1 2 3, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 5 2 0]], 8586909137203373250408282396439132679584738446382748603687882925398627197734049203041470668532970405989481029956327633827295988390817630287556774016663716101728439360618578993823828937367360120614396075250156759752061343/42298657294164405932001211226768541025859605109909488397893809322553513208516465423457832839889144800472636658425290687491937014138602380008973879703300248339439892431797124441964584138011576582733193357040932493771545177360) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 1 3, Piece.treePiece 0 3 1, Piece.treePiece 5 2 0]], 20687711608710276662723227709498465035629903650234964873185876979793852257309582449174544953922484017718759588670306919515762224849761557713135904738375978868460347549181175733083649025852898662443558140265516959197747363978699812189589/22523675858361867195973725759927928774265244609244205724688209825832672241039126267950280942508191914620755811637806897995405781380730553310510213774521694922045071911976053673399282573608433568107848021873852084104164188020500897850266600) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 596800740186446913767516689767240085915558191788442659366487561016672258865482398636431192449640289293264446614911578197551151462204070868677490876485098698652438388726132756318867856865111379618137668347927725793415130725802120843122847481/2507515785959709951193362941401256454581401151857938934918089023490299735250403849158368876767551989470899502998013766340032534829553971038952481079089951252281433765816470103352195330354679692270310504579172204819148390723946323955874480044800) ,
  ([Piece.treePiece 1 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 1, Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.treePiece 1 2 3, Piece.treePiece 6 1 0, Piece.treePiece 6 3 2], [Piece.fullPiece]], 20687711608710276662723227709498465035629903650234964873185876979793852257309582449174544953922484017718759588670306919515762224849761557713135904738375978868460347549181175733083649025852898662443558140265516959197747363978699812189589/22523675858361867195973725759927928774265244609244205724688209825832672241039126267950280942508191914620755811637806897995405781380730553310510213774521694922045071911976053673399282573608433568107848021873852084104164188020500897850266600) ,
  ([Piece.treePiece 1 3 3, Piece.trianglePiece 0], [[Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0], [Piece.treePiece 1 3 3, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 3 3]], 3926862724865801580588460370630058170058695666264743368531824187408428849031860712651733974864912513048621915433579457824977178332297898527514548027351360830893262414004770976461037504340499815503372990916192743406405826942320145788790127/3603788137337898751355796121588468603882439137479072915950113572133227558566260202872044950801310706339320929862049103679264925020916888529681634203923471187527211505916168587743885211777349370897255683499816333456666270083280143656042656000) ,
  ([Piece.treePiece 1 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 11154074282447690296317008074151997930047815485730052257943847192256475404615458289845387183479489447767051114214516271056120710271213879411067310737170195350738171406677489097951659128386055174932447502174376343756796027583335204890695044251/10746496225541614076542984034576813376777433507962595435363238672101284579644587924964438043289508526303855012848630427171568006412374161595510633196099791081206144710642014728652265701520055824015616448196452306367778817388341388382319200192000)
]
def part88: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 1 3 3, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 2], [Piece.treePiece 1 3 3, Piece.trianglePiece 2], [Piece.treePiece 1 2 3, Piece.treePiece 6 1 0], [Piece.fullPiece]], 102824398485374785208463204835675559834384972849209129871445796741729087085479315046265424510567275435979558985856868668485865788618246867178732822793536703739408692666772274266945473133233950079858810119237225662558789202992126244580213/19306007878595886167977479222795367520798781093637890621161322707856576206604965372528812236435593069674933552832405912567490669754911902837580183235304309933181490210265188862913670777378657344092441161606158929232140732589000769585942800) ,
  ([Piece.treePiece 2 0 0], [[Piece.treePiece 1 0 3], [], [Piece.treePiece 0 0 3], []], 1/4) ,
  ([Piece.treePiece 2 0 3], [[Piece.treePiece 0 0 3], [], [], [Piece.treePiece 1 0 3]], 1/12) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 5 0 2]], 646588036090938668219700283764796403157395968697915901677456972013805941313149024638852308322112610953986903002075091380828116413464296238469388016396434963667258544449308951292996409352570641649929053114379855631353381/1406264260826931820252396289476336311592714620146205504327883189519449261120835368790352034205738583680634778958118302961119371936021597450560126367099249094007556633203726388515576488357976498954742292236701158824341946996) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1, Piece.treePiece 4 3 0], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2]], 3767634094029373074487889223329522280884843668535249078600103711513511777739983177160344897929131130723825082716927521563336953913953797567970268640862229167574402794960381888088046093734582769982862577738859233588026082901/7748601305293414143640415821456399521500802570012873917059019882324257516609810205390523972233268428721732822045835371637159322359717548716068148411587595795805516294809090202320130425185078265392081832787389245798416512308384) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2]], 4900917957500468610811556879048860228870213305929268412883194342369652284557949410464326502610720310516151772204154090720604561147757136604265261607189470917980153524170317492963768383263076921466176025474212733494292268715/170469228716455111160089148072040789473017656540283226175298437411133665365415824518591527389131905431878122085008378176017505091913786071753499265054927107507721358485799984451042869354071721838625800321322563407565163270784448) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3, Piece.trianglePiece 1], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0]], 5179245076765742011220749491932654984470275154987811327434840526804949042683375138767058184824285792237361942265067424483050961699445242321742690064810752515680596936681495229571559756473931359884442858124306105147798365650431773/353315887191554595031290049007296316588092179086643336836732943765814923905683761223828948398933900253354050858365044674639289193541248322604876604746962362437363349368536934173107059366203883256510542752375715499026817916334013200384) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2]], 187321010712859964587842725865654151126754864264242833585160111545638891909628381598521554106480240396600650621757582622320851303746042782353049993471396878884121831922111587461719358594164679286766961428382917277565191548083447491/47035177482375705463540487774096322145789771340909394216390073138824111744944150712922228755608075471227758020519846572311355373890178682946774198006939364499473995884686479361794877278125891958522966003910017125807945135111965507301120) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.treePiece 5 3 2, Piece.trianglePiece 2]], 127660957958218779560121669780252298756264790946649355897761488097539323409772399807318405739066091637606651107245792091210008202345683742195547124927056041409926818476928515883697421758261001614325705418206010414909268387061883/33123364424208243284183442094434029680133641789372812828443713478045149116157852614733963912400053148751942267971722938247433361894492030244207181695027721478502814003300337578728786815581614055297863383035223328033764179656313737536) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1, Piece.treePiece 4 3 0, Piece.trianglePiece 1], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0]], 10212307249313922171205227876790695147270726710466892203660486326539814021234449689121949716810595705732702610828267326049575764931964031405215573423011629748287614493540356468765720259933597057111320722708860371818181947789327/5520560737368040547363907015739004946688940298228802138073952246340858186026308769122327318733342191458657044661953823041238893649082005040701196949171286913083802333883389596454797802596935675882977230505870554672294029942718956256) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1, Piece.treePiece 4 3 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 0, Piece.trianglePiece 2]], 135815740560639540817911249660472198221888337310626297169780096534248917018382056675665712655966434668279978312576557630807145699694738031433695854601579271518678675854055325343647372227467908835390099480779408053960469957014459367/14698492963242407957356402429405100670559303544034185692621897855882534920295047097788196486127523584758674381412452053847298554340680838420866936877168551406085623713964524800560899149414341237038426876221880351814982854722489221031600) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 4 1 1, Piece.treePiece 4 3 0, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 0, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 2 3 2, Piece.treePiece 4 0 3, Piece.treePiece 4 3 3, Piece.treePiece 5 0 2, Piece.trianglePiece 2]], 10212307249313922171205227876790695147270726710466892203660486326539814021234449689121949716810595705732702610828267326049575764931964031405215573423011629748287614493540356468765720259933597057111320722708860371818181947789327/5520560737368040547363907015739004946688940298228802138073952246340858186026308769122327318733342191458657044661953823041238893649082005040701196949171286913083802333883389596454797802596935675882977230505870554672294029942718956256) ,
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]
def part89: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 4 0 0, Piece.treePiece 5 0 3, Piece.treePiece 5 3 3], [[Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2]], 607692934169550553640207688100475103485575923414908835154355284951168060137420340687349457282244440018863765985930709536595633270267064344518316145430656582371376923413452709023901803451182290727382811566611388359806/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 4 0 0, Piece.treePiece 5 0 3, Piece.trianglePiece 0], [[Piece.treePiece 0 0 3, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 5 0 2, Piece.treePiece 5 1 1]], 132191048010490684676574981577634519830831457140528860541129979795264890191833837948531457455224582362826117377312809772245380990759886255226361001303347722772627077653304592009011345492057162008017055153319510152501/75326169630238996210423498284661005495351364301580454460757576170092091762860108671613478719038972825573666450164352828813507522417997613721148768927058176335505738561450875168224141001552118429200401319658319075705284) ,
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  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 4 1 1, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 0 3, Piece.treePiece 4 1 0, Piece.treePiece 5 3 2]], 47534694274707247057363434509046141998702679000421927359384048695620804195574720916971951832262452385302053018136801288364782548421780690789284942134982078101460944944208324226859043074227504519440213844545095359048/395462390558754730104723365994470278850594662583297385918977274892983481755015570525970763274954607334261748863362852351270914492694487472036031036867055425761405127447617094633176740258148621753302106928206175147452741) ,
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  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.trianglePiece 1], [[Piece.treePiece 0 0 3, Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 0]], 240562761532650022869903830345596294153971900460447587768896593599161026460313911858029532880537838833580441108614987889059546454325940498104038766136404098709620794186678347650973283643461084164555750186584372909329336725841691580169456114575838973/250279472050353233871194053473332240571188245762773080024629043685655931558103842446888989979895757854413500540210230655684931462438501281717392395998170595689296657921601508341815260300701201199779007939022001099756934771861522798753855847574089152000)
]
def part90: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 0, Piece.trianglePiece 2]], 148199362300132448934780889877349940575406429955756737021904055341559625717257378188277508979921001956780519438304955039866344402228724235383476468229924352357667545650812166032846865783164753620297686765999766871649530735191080623398566218166904075457/505171237228491548766585825932101603861474103483174406809711965462090379569207027133156362775135308960715478447518621276310342376113369229912148166151164620927724639967758244480215401826943895964525371881491693362637961627375922231941889895767757946944000) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 4 3 0, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 3 2 2, Piece.treePiece 3 2 3, Piece.treePiece 6 2 0, Piece.treePiece 6 2 2, Piece.trianglePiece 1], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.treePiece 5 1 1, Piece.trianglePiece 2]], 14814591022936984995956147812395476008746825875253914952279409222039238572689308594383088540943779581409316298094473549041077171123745490410274763648458002277988188797115487703739110756422729060940702456247314129327715409662477876226184419758331299/62569868012588308467798513368333060142797061440693270006157260921413982889525960611722247494973939463603375135052557663921232865609625320429348098999542648922324164480400377085453815075175300299944751984755500274939233692965380699688463961893522288000) ,
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  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3], [[Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2]], 418909647025073302014340509315055809764667672819867791027902044295139085084917630178285034057703730775781267691192310499330689253852207812889494012339896622167428116428955543553667049645969730842809828729180927336437248/21390920216587187673846400251519074174191256748823813147435588960120470149475842223904782195327090123989612779427354286273290374832110913260130769721445270757094186439212015573340014586690766358474068511116606746612216445) ,
  ([Piece.treePiece 2 0 3, Piece.treePiece 2 1 2, Piece.treePiece 5 0 3, Piece.treePiece 5 1 2, Piece.treePiece 5 3 3, Piece.trianglePiece 1], [[Piece.treePiece 0 0 3, Piece.treePiece 0 1 1, Piece.treePiece 4 2 0, Piece.treePiece 5 2 2, Piece.treePiece 6 1 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 3 2 2, Piece.treePiece 6 2 0, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 1 0 3, Piece.treePiece 2 0 2, Piece.treePiece 4 1 0, Piece.treePiece 5 1 1, Piece.treePiece 5 3 2, Piece.trianglePiece 0]], 418909647025073302014340509315055809764667672819867791027902044295139085084917630178285034057703730775781267691192310499330689253852207812889494012339896622167428116428955543553667049645969730842809828729180927336437248/1385468511508135558447357497890638915188193508364569553746255661358042731111400825000088838009140300240683230110730309767634744287500991740945409824088288741666233361481323036669659404765374246272006943396511502371326646926205) ,
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]
def part91: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part92: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part93: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part94: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 2 1 3, Piece.treePiece 5 0 0, Piece.trianglePiece 1], [[Piece.treePiece 2 0 3, Piece.treePiece 5 1 2], [Piece.fullPiece], [Piece.treePiece 6 1 3, Piece.trianglePiece 1], [Piece.fullPiece]], 387376722093794325737491574050256248035650972141653677551651051580628365320134664031264708781254397879541429228116784582653843161280816813808935498753923041948647657212032397522201054374143992738047758420295448914495/7568658192512052250808102698458761317714730384369327960171813873549923095789771684707574416745542724100703327528475643086524679286018898986335522236690055995433590955935255399678023736998059746474681472310166031530196) ,
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  ([Piece.treePiece 2 1 3, Piece.treePiece 5 1 3], [[Piece.treePiece 2 0 3, Piece.treePiece 4 1 1], [Piece.treePiece 3 2 3, Piece.trianglePiece 1], [Piece.treePiece 4 2 3, Piece.trianglePiece 2], [Piece.fullPiece]], 6853519627037558178827109918555277510358395816246556419007304847263586215130604013717607657049045878589357490192719711239940116782644878841664577941533147459325212032475367656414723377914113800247624147773817058402703709/40671785859773467242308856948815904832557312605682200382590201271686070392804293676401762346047254615839073710024317968742247128979425365393244115099327161864846050415189542732658253978857285175704993612539358167088024209) ,
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]
def part95: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 2 3 3, Piece.treePiece 5 3 3], [[Piece.treePiece 0 1 3, Piece.treePiece 2 2 0, Piece.treePiece 5 2 0, Piece.treePiece 6 0 1], [Piece.treePiece 0 3 3, Piece.treePiece 3 3 3, Piece.treePiece 6 3 3], [Piece.treePiece 0 2 2, Piece.treePiece 0 2 3, Piece.treePiece 3 2 3, Piece.treePiece 6 2 3], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3]], 14516885722814986109884156742860362124065747298996345051085669088341901814936615978296861962839945216725088029254571894995026273633108672982993966758533092829373988786059276400596166994155293498482340910119814255448901919437/39044914425382528552616502670863268639255020101454912367286593220818627577092121929345691852205364431205510761623345249992557243820248350777514350495354075390252208398581961023351923819702993768676793868037783840404503240640)
]
def part96: List (List Piece × List (List Piece) × ℚ) :=[
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]
def part97: List (List Piece × List (List Piece) × ℚ) :=[
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  ([Piece.treePiece 3 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 5 0 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 1 3, Piece.treePiece 4 1 3, Piece.trianglePiece 1, Piece.trianglePiece 3]], 166096351202976708208038570795061886770018364978462415067395202029927867696632205451141776088613797270082791218872023450829825454358777919478598942521690853061022692652510510255172233413567021238208279282754133806134310572592083/14161158248057521757697649729731299979074364014204470677125196980294609850797986508756135583815343705476062894100062924132204063308791194598496684345143696576934480487788385514193115016107623033998738226954572131445688836031064400) ,
  ([Piece.treePiece 3 2 3, Piece.trianglePiece 2], [[Piece.treePiece 1 0 3, Piece.treePiece 4 0 3, Piece.trianglePiece 2], [Piece.treePiece 2 1 3, Piece.treePiece 5 1 3, Piece.trianglePiece 2], [Piece.treePiece 2 0 3, Piece.treePiece 5 0 3], [Piece.fullPiece]], 213571877801762674693841701518546498879422855480865703955884874822257169004240630200825514993467646045018354372938878205712329750198637880212330159397666118338021364871916125368788863644030059652640486427953220305699439094593/5028225203476454642335536653946490701529541015814109602482612254809306373818671976123613060888392841333671284447885995075939423591711869309443727427557236327471113914470961834841915617034308095868885629170755875764832111266800) ,
  ([Piece.treePiece 3 3 0], [[Piece.treePiece 1 3 3, Piece.treePiece 4 3 3], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3], [Piece.treePiece 1 2 3, Piece.treePiece 4 2 3], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3]], 1/4) ,
  ([Piece.treePiece 3 3 3], [[Piece.treePiece 1 2 3, Piece.treePiece 4 2 3], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3]], 1/6) ,
  ([Piece.treePiece 3 3 3, Piece.treePiece 4 2 0, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 0 3, Piece.treePiece 2 3 3, Piece.treePiece 4 0 0, Piece.treePiece 5 3 3], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 1 3 3, Piece.treePiece 4 1 0, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 33942972676555447560320257541377021522155201704672715669526639631953584283124643843727482953223642977090575073910585028821752559837317177030586939534840057576358938422538701890007706862564174201340200578222880137895282702/896479625093499478995348969223354592180595799530015593600518369114027649542671122058881012829443723685147972424590200437881305127206524067670559297939480950489915704487914906080367850142300982881886845727154501534387830364015) ,
  ([Piece.treePiece 3 3 3, Piece.treePiece 6 1 1, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 3 3, Piece.treePiece 4 3 0, Piece.treePiece 5 3 3], [Piece.treePiece 2 2 3, Piece.treePiece 3 3 0, Piece.treePiece 5 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 14295753407009828674671484701923327727793970890578016060676414076340501608734832697634066958393520095153852811384899902983071283571990937312894133159408331612111575981947764624574291345541129724097048712029913009890506/2768236733911283110733063561961291951954162638083081701432840924250884372285108993681795342924682251339832242043539966458896401448861412304252217258069387980329835892133319662432237181807040352273114748497443226032169187) ,
  ([Piece.treePiece 3 3 3, Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3]], 2227267627816275929635672336251253255259747319821645870060982920449921756891603731569297710239028825900811487624199872480682485571009518048746404664339130645183238818673915649568699504479415750683416890803990213299540058705077/13408600542603879046228097743857308537412109375504292273286966012824816996849791936329634829035714243556456758527695986869171796244564984825183273140152630206589637105255898226245108312091488255650361677788682335372885630044800) ,
  ([Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0, Piece.trianglePiece 1], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3]], 27330312985108803637639764448838633815592142389546870841224650107161785617172776251971198818363889329251388111883712108864045700619210302880913437410051677277506187071621235977847367863831942644367388774915635955906603664863120819502707/217359368283416720500621839375388263438354444312873926658352399743323463218237264592073077660895808047272131476496364787356711708067866784617447256697373759582793070932744827909997683977356359961970604575486304510056520583033441125223096320) ,
  ([Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 37490328421056251118984020265528101436340515284110119977813625320931686854364536058889559000401368366944752845811193845330517687972927100584050368341977664903606054551950795007993846034784742096965683037182502915506913353767/122399351479432462198831645931295346985724013162498129046257441329701908417559363865105887618313383073812203168370715366452060860034597419372620362812003799106889824186083315176839557139428827529473617336614161276161751772366848) ,
  ([Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 1], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0], [Piece.fullPiece], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 1]], 108512304747271385702351272631690515835993167968369776857723387193355916447490843150946127220226825307763405256075679265196555730235118556282193395044639114605072530368848789725684113417173565666611184163013221436466793/22145893871290264885864508495690335615633301104664653611462727394007074978280871949454362743397458010718657936348319731671171211590891298434017738064555103842638687137066557299457897454456322818184917987979545808257353496) ,
  ([Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 2], [[Piece.treePiece 0 3 3, Piece.treePiece 1 2 0, Piece.treePiece 4 2 0, Piece.trianglePiece 3], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3, Piece.trianglePiece 2], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3], [Piece.fullPiece]], 5126428837749485120888561762580501929483581563497358857082988171471119095010120363664354586340712413375118406671937328478670093322771613212773221701299575167163186625126778526614286598815879717848483549412806952265/145696670205857005828055976945331155366008559899109563233307417065836019593953104930620807522351697438938539054923156129415600076255863805486958803056283577912096625901753666443801956937212650119637618341970696106956273)
]
def part98: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 46452347584061011103279010339783216727882795034490212230701075370463274399355929262398547204057245874638806924296460271507759947968300017181617042055661226002622814609874355245424222030396309533696564343168743572302063679029748187697/3657032241123506300905542758183394970024134267327443412382266635428418184572267053504157037164274312660208147864869183447013791440673443445343684916504706904616614020673410524093103236714387912409492640411304672421706046554839510149120) ,
  ([Piece.treePiece 3 3 3, Piece.trianglePiece 0], [[Piece.treePiece 1 2 3, Piece.treePiece 4 2 3, Piece.trianglePiece 0], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3]], 701318875569023860511506589030242205150341153575017357238692483604634702995413860428752590169026880153805528075836412005315630150292632348867199162298199752479434445490650165849119263150126735635604960644574727214909418678797399491908481/16719951406416670807740141490414481802950341870221071281411723057178727939864404968621005973915062157482471652038181906719747054466758983432111327438259519967907159302518832916153667998258181535536200351960484962312040044848726240401776640) ,
  ([Piece.treePiece 3 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 1 2 3, Piece.treePiece 4 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 516817558586239184327853444828217880206572397429265848399998966419162105759694509636554356077430667922808049123445394317909412733870399655295476510214134220795459817229612313686252066599033032299531938247005335678019316197467561788958349/65874096501818435819780359800313028309723758056192714059177846829046936659237114641610437089086711552640007807772890858461247180387569591752445117992238147162848032281604389748153917823775606081369497450512833161885838494560735054453254144) ,
  ([Piece.treePiece 3 3 3, Piece.trianglePiece 1], [[Piece.treePiece 1 2 3, Piece.treePiece 4 2 3], [Piece.fullPiece], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.trianglePiece 1], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 1]], 892442104094695384004296083074391089212042318416097672956310948780736950204634435194350604695144025900751546008828212330580011949301456822447290386055794796852181221985734817076530114958380754536966099552315258526275749/44291787742580529771729016991380671231266602209329307222925454788014149956561743898908725486794916021437315872696639463342342423181782596868035476129110207685277374274133114598915794908912645636369835975959091616514706992) ,
  ([Piece.treePiece 3 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3]], 516817558586239184327853444828217880206572397429265848399998966419162105759694509636554356077430667922808049123445394317909412733870399655295476510214134220795459817229612313686252066599033032299531938247005335678019316197467561788958349/65874096501818435819780359800313028309723758056192714059177846829046936659237114641610437089086711552640007807772890858461247180387569591752445117992238147162848032281604389748153917823775606081369497450512833161885838494560735054453254144) ,
  ([Piece.treePiece 3 3 3, Piece.trianglePiece 2], [[Piece.treePiece 1 2 3, Piece.treePiece 4 2 3, Piece.trianglePiece 2], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3, Piece.trianglePiece 2], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3], [Piece.fullPiece]], 892442104094695384004296083074391089212042318416097672956310948780736950204634435194350604695144025900751546008828212330580011949301456822447290386055794796852181221985734817076530114958380754536966099552315258526275749/44291787742580529771729016991380671231266602209329307222925454788014149956561743898908725486794916021437315872696639463342342423181782596868035476129110207685277374274133114598915794908912645636369835975959091616514706992) ,
  ([Piece.treePiece 3 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 2 3 3, Piece.treePiece 5 3 3], [Piece.treePiece 2 2 3, Piece.treePiece 5 2 3, Piece.trianglePiece 3], [Piece.treePiece 1 3 3, Piece.treePiece 4 3 3, Piece.trianglePiece 3]], 701318875569023860511506589030242205150341153575017357238692483604634702995413860428752590169026880153805528075836412005315630150292632348867199162298199752479434445490650165849119263150126735635604960644574727214909418678797399491908481/16719951406416670807740141490414481802950341870221071281411723057178727939864404968621005973915062157482471652038181906719747054466758983432111327438259519967907159302518832916153667998258181535536200351960484962312040044848726240401776640) ,
  ([Piece.treePiece 4 0 0], [[], [Piece.treePiece 6 0 3], [], [Piece.treePiece 5 0 3]], 1/4) ,
  ([Piece.treePiece 4 0 3], [[], [Piece.treePiece 5 0 3], [Piece.treePiece 6 0 3], []], 1/12) ,
  ([Piece.treePiece 4 1 0], [[Piece.trianglePiece 3], [Piece.treePiece 4 0 3], [Piece.trianglePiece 3], [Piece.fullPiece]], 1/4) ,
  ([Piece.treePiece 4 1 3], [[Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 4 0 3], [Piece.trianglePiece 3]], 1/12) ,
  ([Piece.treePiece 4 2 0], [[Piece.treePiece 3 1 3, Piece.treePiece 6 1 3], [Piece.treePiece 2 0 3, Piece.treePiece 4 0 0], [Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0]], 1/4) ,
  ([Piece.treePiece 4 2 3], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0], [Piece.treePiece 2 0 3, Piece.treePiece 4 0 0], [Piece.treePiece 3 1 3, Piece.treePiece 6 1 3]], 1/12) ,
  ([Piece.treePiece 4 2 3, Piece.trianglePiece 2], [[Piece.fullPiece], [Piece.treePiece 1 0 3, Piece.treePiece 4 1 0, Piece.trianglePiece 3], [Piece.treePiece 2 0 3, Piece.treePiece 4 0 0], [Piece.fullPiece]], 47564411967509489422633613438799594437639609437300678485365183634999131467661608846136078136745291116644678588806907347317575026537338105864891405708232045343961090178239367664532432734098950928537796994235020298073864352864168006149/1036703336211351116551348058681453484805948776675413645920865764954038190715798919185330231517550977026442934774192826557523998912869480619550553536598432537692656206753399858392464533622159073383940994045168958476688990876037093278880) ,
  ([Piece.treePiece 4 3 0], [[Piece.treePiece 3 3 3, Piece.treePiece 6 3 3], [Piece.treePiece 0 0 3, Piece.treePiece 4 2 0], [Piece.treePiece 3 2 3, Piece.treePiece 6 2 3], [Piece.treePiece 4 3 3]], 1/4) ,
  ([Piece.treePiece 4 3 3], [[Piece.treePiece 3 2 3, Piece.treePiece 6 2 3], [Piece.treePiece 4 3 3], [Piece.treePiece 0 0 3, Piece.treePiece 4 2 0], [Piece.treePiece 3 3 3, Piece.treePiece 6 3 3]], 12330337318704961232006014698587033742197937890567741979802823268578025082836088716803779858115222801276528785674515886137045841868953622259898260646369491819543842780565207791078936361464162450913180598447728910836614768985/33838925835331524745600968981414832820687684087927590718315047458042810566813172338766266271911315840378109326740232549993549611310881904007179103762640198671551913945437699553571667310409261266186554685632745995017236141888) ,
  ([Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1], [Piece.treePiece 4 3 3, Piece.treePiece 5 3 2], [Piece.treePiece 0 0 3, Piece.treePiece 4 2 0, Piece.treePiece 6 3 3], [Piece.treePiece 0 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 3 1]], 12988739645920367039374114971976388138691000977259386318517480191574795781575861561194859442596849355754708584516970477414883441456333161769487336727135092474657411357372534032353937401990245907755138150893872711714524649/33838925835331524745600968981414832820687684087927590718315047458042810566813172338766266271911315840378109326740232549993549611310881904007179103762640198671551913945437699553571667310409261266186554685632745995017236141888) ,
  ([Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 2], [Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 0 1 3, Piece.treePiece 3 3 1, Piece.treePiece 5 2 0, Piece.treePiece 6 3 1]], 12636284739102096955751794762293046881625353678153609795528338160372426374513797507989828763448514925282080488763745308838660049875174848699897639573818596521021155502936944380551986608451133427236149166037948324236961846/2400977534660007091715218752259449309980355835051237335185447351671443793498415868599025236574207581736828038323865562648761074765042417595259379846658580346367456894159884276137014707133882115777392887929035930677707333129897) ,
  ([Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 1740017315669343367776402964799312394529845602084794250006650996788768270499431179912735950101347763207412780798129906452498207140813114876318561695088779200942891983629859231725828555821976842589883841154817950802020354394300806714348292287/36538087166841487860246145717561165481043273927072824480235011485144367570791598944879089347184328989433107043685343452383331221802072149424736152866739289676100892016182850077417703385168189801653095923867937841650447979120360720499885280652800) ,
  ([Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [[Piece.treePiece 0 2 3, Piece.treePiece 3 2 1, Piece.treePiece 6 2 0, Piece.treePiece 6 2 1, Piece.trianglePiece 0], [Piece.treePiece 4 3 3, Piece.treePiece 5 3 2, Piece.trianglePiece 2], [Piece.treePiece 0 0 3, Piece.treePiece 4 2 0, Piece.treePiece 6 3 3], [Piece.fullPiece]], 160505166049514472236292268138017949299154248275079193066857036762201252947366388289792448359749730911823446242064749922511701257532119303708611566797169916707637169147156017175653392054916686894419621602796905723264502910753529562267453/2594727458883287100976173207543697394795356178984932499484081771935923842167707346067872364576943708564311069500675354649070746015060159741370776626824899255019592284259641383175597352479691547046024092119867760088799714459961703432350712320) ,
  ([Piece.treePiece 4 3 3, Piece.trianglePiece 0], [[Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 0], [Piece.treePiece 4 3 3, Piece.trianglePiece 0], [Piece.fullPiece], [Piece.treePiece 3 3 3, Piece.treePiece 6 3 3]], 2284781939221251363109858444326521824724489598424577911267899970958395003102190336807566302535944903006692072144887177956631748509605119831950645440425323767138313177208895666931350521954394155017048121329164217550472496044157/2561042703637340897829566669076745930645712890721319824197810508449540046398310259838960252345821420519283240878789933492011813082711912101610005169769152369458620687103876561212815687609474256829219080457638326056221155338556800) ,
  ([Piece.treePiece 4 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 4 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.fullPiece], [Piece.fullPiece]], 1706901553365450765586623948627051852572144390410274962980815268335278377692342905041361824742857817425529282634840942878429603921751075682000453711951986616319910347142825112550532104356126519457715769386641833500571576136924865722617869741/6447897735324968445925790420746088026066460104777557261217943203260770747786752754978662825973705115782313007709178256302940803847424496957306379917659874648723686826385208837191359420912033494409369868917871383820667290433004833029391520115200) ,
  ([Piece.treePiece 4 3 3, Piece.trianglePiece 2], [[Piece.treePiece 3 2 3, Piece.treePiece 6 2 3, Piece.trianglePiece 2], [Piece.treePiece 4 3 3, Piece.trianglePiece 2], [Piece.treePiece 0 0 3, Piece.treePiece 4 2 0], [Piece.fullPiece]], 75417133222187539638182508752523204761499087202341565878368004158855639819618195589109827556786281532027047840571292709201778307860664687441794143432146676684159389139034029234021737363077616085470099654069425653128374725243069776131809907/2594727458883287100976173207543697394795356178984932499484081771935923842167707346067872364576943708564311069500675354649070746015060159741370776626824899255019592284259641383175597352479691547046024092119867760088799714459961703432350712320) ,
  ([Piece.treePiece 4 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 4 3 3], [Piece.treePiece 0 0 3, Piece.treePiece 4 2 0, Piece.trianglePiece 0], [Piece.treePiece 3 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 3]], 41964661733427798614280685886476768459106764500740356600667836717361611041452721691492720281796614532177768966506066813063685742263039705270288065892745238651500682703366294868572523981047410051468323372012661365894489/851765148895779418687096480603474446755126965564025138902412592077195191472341228825167797822979154258409920628781528141198892753495819170539143771713657840101487966810252203825303748248320108391727614922290223394513596) ,
  ([Piece.treePiece 5 0 0], [[Piece.treePiece 5 1 3], [Piece.treePiece 6 2 3], [Piece.treePiece 6 1 3], [Piece.treePiece 5 2 3]], 1/4) ,
  ([Piece.treePiece 5 0 3], [[Piece.treePiece 6 1 3], [Piece.treePiece 5 2 3], [Piece.treePiece 6 2 3], [Piece.treePiece 5 1 3]], 1/12) ,
  ([Piece.treePiece 5 1 0], [[Piece.treePiece 3 1 3], [Piece.treePiece 4 2 3], [Piece.treePiece 4 1 3], [Piece.treePiece 3 2 3]], 1/4) ,
  ([Piece.treePiece 5 1 3], [[Piece.treePiece 4 1 3], [Piece.treePiece 3 2 3], [Piece.treePiece 4 2 3], [Piece.treePiece 3 1 3]], 1/12) ,
  ([Piece.treePiece 5 2 0], [[Piece.treePiece 1 1 3, Piece.treePiece 5 1 0], [Piece.treePiece 2 2 3, Piece.treePiece 6 0 0], [Piece.treePiece 2 1 3, Piece.treePiece 5 0 0], [Piece.treePiece 1 2 3, Piece.treePiece 6 1 0]], 1/4) ,
  ([Piece.treePiece 5 2 3], [[Piece.treePiece 2 1 3, Piece.treePiece 5 0 0], [Piece.treePiece 1 2 3, Piece.treePiece 6 1 0], [Piece.treePiece 2 2 3, Piece.treePiece 6 0 0], [Piece.treePiece 1 1 3, Piece.treePiece 5 1 0]], 84126954879592256175393137036168824469957662658565070768153976647516057404815226547660633750724237358649487593698449650925499200767232414957265703264593259741678378765112279962080344235283057027123649522692638954715772894519912627530291/646902881795883096728041188617226974518912036645458115054620237331319831006658525571646064466951809664500391299096323771894975321630555906599545406837421903520217473014121511636897868980227261791579180284185430089453930306647146206021120) ,
  ([Piece.treePiece 5 2 3, Piece.treePiece 6 3 0], [[Piece.treePiece 2 1 3, Piece.treePiece 5 0 0], [Piece.treePiece 1 2 3, Piece.treePiece 6 1 0], [Piece.treePiece 0 3 3, Piece.treePiece 2 2 2, Piece.treePiece 6 0 3], [Piece.treePiece 1 1 3, Piece.treePiece 5 1 0]], 5766443892337946659268661738620542532854048177196139868347992513397782450838673586921553708270310227883289451225229453261483926614372434458505603767579701732926613917398670982332315324295452143577545932732604110426465690321559681694363/4528320172571181677096288320320588821632384256518206805382341661319238817046609679001522451268662667651502739093674266403264827251413891346196817847861953324641522311098850581458285082861590832541054261989298010626177512146530023442147840) ,
  ([Piece.treePiece 5 3 0], [[Piece.treePiece 5 3 3], [Piece.treePiece 0 2 3, Piece.treePiece 6 2 0], [Piece.treePiece 0 1 3, Piece.treePiece 5 2 0], [Piece.treePiece 6 3 3]], 1/4) ,
  ([Piece.treePiece 5 3 3], [[Piece.treePiece 0 1 3, Piece.treePiece 5 2 0], [Piece.treePiece 6 3 3], [Piece.treePiece 0 2 3, Piece.treePiece 6 2 0], [Piece.treePiece 5 3 3]], 119692498645788038362970388717242993230349643346469241404682110235146086803262920677544647643004877342218845085797812546912422773693048684023505781673708127496942258172278945771737655205311541805222760931901838128839544805/222624512074549504905269532772466005399261079525839412620493733276597437939560344333988593894153393686698087675922582565747036916518959894784073051070001307049683644377879602326129390200060929382806280826531223651429185144) ,
  ([Piece.treePiece 5 3 3, Piece.trianglePiece 1], [[Piece.treePiece 0 1 3, Piece.treePiece 5 2 0], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 2], [Piece.treePiece 5 3 3, Piece.trianglePiece 1]], 102824398485374785208463204835675559834384972849209129871445796741729087085479315046265424510567275435979558985856868668485865788618246867178732822793536703739408692666772274266945473133233950079858810119237225662558789202992126244580213/19306007878595886167977479222795367520798781093637890621161322707856576206604965372528812236435593069674933552832405912567490669754911902837580183235304309933181490210265188862913670777378657344092441161606158929232140732589000769585942800) ,
  ([Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0, Piece.trianglePiece 2], [Piece.treePiece 5 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3]], 11154074282447690296317008074151997930047815485730052257943847192256475404615458289845387183479489447767051114214516271056120710271213879411067310737170195350738171406677489097951659128386055174932447502174376343756796027583335204890695044251/10746496225541614076542984034576813376777433507962595435363238672101284579644587924964438043289508526303855012848630427171568006412374161595510633196099791081206144710642014728652265701520055824015616448196452306367778817388341388382319200192000) ,
  ([Piece.treePiece 5 3 3, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.treePiece 6 3 3], [Piece.treePiece 0 2 3, Piece.treePiece 6 2 0, Piece.trianglePiece 0], [Piece.treePiece 5 3 3, Piece.trianglePiece 3]], 3926862724865801580588460370630058170058695666264743368531824187408428849031860712651733974864912513048621915433579457824977178332297898527514548027351360830893262414004770976461037504340499815503372990916192743406405826942320145788790127/3603788137337898751355796121588468603882439137479072915950113572133227558566260202872044950801310706339320929862049103679264925020916888529681634203923471187527211505916168587743885211777349370897255683499816333456666270083280143656042656000) ,
  ([Piece.treePiece 6 0 0], [[Piece.treePiece 5 3 3], [], [Piece.treePiece 6 3 3], []], 1/4) ,
  ([Piece.treePiece 6 0 3], [[Piece.treePiece 6 3 3], [], [], [Piece.treePiece 5 3 3]], 21330466264694411118705366274969148868597023488809482950268001379227926734844653002742531656783041090887107469343925961194056902636554948928340001407335855138766815143504103340041316806185810931015033900383375938862019/154866390708323530670381178291540808500932175557095479800438653104944580267698405240939599604178028046983621932505732389308889591544694394643480685766119607291179630329136764331873408772421837889405020894961858799002472)
]
def part99: List (List Piece × List (List Piece) × ℚ) :=[
  ([Piece.treePiece 6 0 3, Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3, Piece.treePiece 6 3 3], [], [], [Piece.treePiece 5 3 3]], 776954847446348761925054353843504662016045129951113645491219876836907469356009770299082824928738820301264777524309136244687802426518987319782153037709519671126493458638583021842579848094577189223653491413574275989399171/44291787742580529771729016991380671231266602209329307222925454788014149956561743898908725486794916021437315872696639463342342423181782596868035476129110207685277374274133114598915794908912645636369835975959091616514706992) ,
  ([Piece.treePiece 6 0 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0], [[Piece.treePiece 0 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 1], [Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 5 3 3]], 9477688723164548054397284303511830896038351122479223031425208459156074467095085350237036445664475807378238587653927504440003472230234944789205946386188883417026852165039331146632402518402856330644950984589669342665673/2109132749646691893891857951970508153869838200444252724901212132762578569360083042805177404133091239116062660604601879206778210627703933184192165529957628937394160679720624504710275948043459316017611236950432934119747952) ,
  ([Piece.treePiece 6 0 3, Piece.treePiece 6 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 3 3, Piece.treePiece 6 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 33870496536164504742422540319122022045292274504063798804102513250121596479255344903726162098478195032842607149995279071086375827720479010183910903485161279820106901412722389103852163147658339515269160174403705266793436026958269/1986449454679154108609188272707412240692757568489576721067667126063121217906289884580515137482784719561055678635711952599733258182069691656371016552341245521429041100681013659727078089048182473523982147447588773476636636503403412948) ,
  ([Piece.treePiece 6 0 3, Piece.trianglePiece 0], [[Piece.treePiece 6 3 3, Piece.trianglePiece 1], [Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 5 3 3]], 27846728435666757400115486918059111197166539802300793707554803199133393681150427183486969279255020625158592989942886399610571579160897373545233133963855132303221308959326732668745979448860370930485506871938939807310035/2013263079208205898714955317790030510512118282242241237405702490364279543480079268132214794854314364610787085122574521061015564690081027130365248914959554894785335194278777936314354314041483892562265271634504164387032136) ,
  ([Piece.treePiece 6 1 0], [[Piece.treePiece 3 3 3], [], [Piece.treePiece 4 3 3], []], 1/4) ,
  ([Piece.treePiece 6 1 3], [[Piece.treePiece 4 3 3], [], [], [Piece.treePiece 3 3 3]], 1/12) ,
  ([Piece.treePiece 6 1 3, Piece.trianglePiece 1], [[Piece.treePiece 4 3 3], [Piece.fullPiece], [Piece.trianglePiece 3], [Piece.treePiece 3 3 3, Piece.trianglePiece 2]], 892442104094695384004296083074391089212042318416097672956310948780736950204634435194350604695144025900751546008828212330580011949301456822447290386055794796852181221985734817076530114958380754536966099552315258526275749/11072946935645132442932254247845167807816650552332326805731363697003537489140435974727181371698729005359328968174159865835585605795445649217008869032277551921319343568533278649728948727228161409092458993989772904128676748) ,
  ([Piece.treePiece 6 1 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.treePiece 3 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2]], 29709039300735784146387013511753434775653328902373159220879328796334163122752080399124874975023951902979385798991929426946932641378254609215647487367526524143177798506343915289619557920524895574387128151753935775032979900537487/305607608412177555170644349647294190875808856690704110933487250163557110447121520704694636535813033778623950559340300399958962797241491024057079469590960849450621707797079024573396629084335765157535714991936734381021021000523601992) ,
  ([Piece.treePiece 6 2 0], [[Piece.treePiece 1 3 3], [], [Piece.treePiece 2 3 3], []], 1/4) ,
  ([Piece.treePiece 6 2 3], [[Piece.treePiece 2 3 3], [], [], [Piece.treePiece 1 3 3]], 1464223122151681006717894327979733131718048503906704353859534282704704262645878874910608842809147299183883349544349501426737885941329630690491740557494552229608138834903970067147328361342131627118461045526564759654079400473/11279641945110508248533656327138277606895894695975863572771682486014270188937724112922088757303771946792703108913410849997849870436960634669059701254213399557183971315145899851190555770136420422062184895210915331672412047296) ,
  ([Piece.treePiece 6 2 3, Piece.trianglePiece 0], [[Piece.treePiece 2 3 3, Piece.trianglePiece 1], [Piece.trianglePiece 3], [Piece.fullPiece], [Piece.treePiece 1 3 3]], 75417133222187539638182508752523204761499087202341565878368004158855639819618195589109827556786281532027047840571292709201778307860664687441794143432146676684159389139034029234021737363077616085470099654069425653128374725243069776131809907/864909152961095700325391069181232464931785392994977499828027257311974614055902448689290788192314569521437023166891784883023582005020053247123592208941633085006530761419880461058532450826563849015341364039955920029599904819987234477450237440) ,
  ([Piece.treePiece 6 2 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 2 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 1706901553365450765586623948627051852572144390410274962980815268335278377692342905041361824742857817425529282634840942878429603921751075682000453711951986616319910347142825112550532104356126519457715769386641833500571576136924865722617869741/2149299245108322815308596806915362675355486701592519087072647734420256915928917584992887608657901705260771002569726085434313601282474832319102126639219958216241228942128402945730453140304011164803123289639290461273555763477668277676463840038400) ,
  ([Piece.treePiece 6 2 3, Piece.trianglePiece 2], [[Piece.treePiece 2 3 3, Piece.trianglePiece 3], [Piece.trianglePiece 3], [], [Piece.fullPiece]], 6854345817663754089329575332979565474173468795273733733803699912875185009306571010422698907607834709020076216434661533869895245528815359495851936321275971301414939531626687000794051565863182465051144363987492652651417488132471/2561042703637340897829566669076745930645712890721319824197810508449540046398310259838960252345821420519283240878789933492011813082711912101610005169769152369458620687103876561212815687609474256829219080457638326056221155338556800) ,
  ([Piece.treePiece 6 3 0], [[], [], [Piece.treePiece 0 3 3], []], 1/4) ,
  ([Piece.treePiece 6 3 3], [[Piece.treePiece 0 3 3], [], [], []], 15566412454430203491230993556597111988366486062138266742009053297798443443405912791997915566544957471396385307679042704952379102182930046066277120232942215622122961839117432921035306011956382790307185042211222524126252843906822832216812974881/32434093236041088762202165094296217434941952237311656243551022149199048027096341825848404557211796357053888368758441933113384325188251996767134707835311240687744903553245517289694966905996144338075301151498347001109996430749521292904383904000) ,
  ([Piece.treePiece 6 3 3, Piece.trianglePiece 0], [[Piece.treePiece 0 3 3, Piece.trianglePiece 1], [Piece.trianglePiece 3], [Piece.fullPiece], []], 518550169021409529077304680072768425258233100363521382878342585525152403867153392847735660832792424146538975025956400382647295314355259180501348157165027072580516738064782365299476008067638485566330826062579170301569582073453/75423378052146819635033049809197360522943115237211644037239183822139595607280079641854195913325892620005069266718289926139091353875678039641655911413358544912066708717064427522628734255514621438033284437561338136472481669002000) ,
  ([Piece.treePiece 6 3 3, Piece.trianglePiece 0, Piece.trianglePiece 2], [[Piece.treePiece 0 3 3, Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.fullPiece], [Piece.fullPiece]], 33870496536164504742422540319122022045292274504063798804102513250121596479255344903726162098478195032842607149995279071086375827720479010183910903485161279820106901412722389103852163147658339515269160174403705266793436026958269/23837393456149849303310259272488946888313090821874920652812005512757454614875478614966181649793416634732668143628543431196799098184836299876452198628094946257148493208172163916724937068578189682287785769371065281719639638040840955376) ,
  ([Piece.treePiece 6 3 3, Piece.trianglePiece 1], [[Piece.treePiece 0 3 3], [Piece.fullPiece], [Piece.trianglePiece 3], [Piece.trianglePiece 3]], 27846728435666757400115486918059111197166539802300793707554803199133393681150427183486969279255020625158592989942886399610571579160897373545233133963855132303221308959326732668745979448860370930485506871938939807310035/8053052316832823594859821271160122042048473128968964949622809961457118173920317072528859179417257458443148340490298084244062258760324108521460995659838219579141340777115111745257417256165935570249061086538016657548128544) ,
  ([Piece.treePiece 6 3 3, Piece.trianglePiece 2], [[Piece.treePiece 0 3 3, Piece.trianglePiece 3], [Piece.trianglePiece 3], [], [Piece.fullPiece]], 518550169021409529077304680072768425258233100363521382878342585525152403867153392847735660832792424146538975025956400382647295314355259180501348157165027072580516738064782365299476008067638485566330826062579170301569582073453/301693512208587278540132199236789442091772460948846576148956735288558382429120318567416783653303570480020277066873159704556365415502712158566623645653434179648266834868257710090514937022058485752133137750245352545889926676008000) ,
  ([Piece.trianglePiece 1, Piece.trianglePiece 3], [[Piece.fullPiece], [Piece.fullPiece], [Piece.trianglePiece 1, Piece.trianglePiece 3], [Piece.trianglePiece 1, Piece.trianglePiece 3]], 80504674265826347111651862483415320908583452272036818608522156888999635265380830379849033086464776689787093789632985956253869978327740373167235516166877627734519040063411385226597600730380847420670339628939365594719981667691988657188901412821338070215697/1156731176858745734689241834309247997061038599294256986336397942383842333134065768096209538717039860896777165929823925087535806424989481093943093133732161707049101479575672869104185777177140975198149807838181674580433885777171392138607923681814372234995200) ,
  ([Piece.trianglePiece 3], [[Piece.fullPiece], [], [Piece.trianglePiece 3], [Piece.trianglePiece 3]], 29332679257146131398062953450883525535157283845871073115672606405383620728763777923030613643787096114507483071185866490586047128035121946578138664316906427305776714550707579568580170257683676385393594297165598056541578846440200218214184870481/12973637294416435504880866037718486973976780894924662497420408859679619210838536730339361822884718542821555347503376773245353730075300798706853883134124496275097961421298206915877986762398457735230120460599338800443998572299808517161753561600)
]
@[irreducible]
def allparts: List (List Piece × List (List Piece) × ℚ) := part0++part1++part2++part3++part4++part5++part6++part7++part8++part9++part10++part11++part12++part13++part14++part15++part16++part17++part18++part19++part20++part21++part22++part23++part24++part25++part26++part27++part28++part29++part30++part31++part32++part33++part34++part35++part36++part37++part38++part39++part40++part41++part42++part43++part44++part45++part46++part47++part48++part49++part50++part51++part52++part53++part54++part55++part56++part57++part58++part59++part60++part61++part62++part63++part64++part65++part66++part67++part68++part69++part70++part71++part72++part73++part74++part75++part76++part77++part78++part79++part80++part81++part82++part83++part84++part85++part86++part87++part88++part89++part90++part91++part92++part93++part94++part95++part96++part97++part98++part99
-- def qFull:  ℚ := 12823413011547414368862997525616691741041579688920794331363953564934456759066858494476606822552437442098640979/877512406035620068631903180662851572553488753575243048137500508983979170248733422547196905684808937723408093
-- def qEmpty:  ℚ := 11746934357449947552830291532943152290456105411186011016486060686616960007897677336844906536622212814156785625/877512406035620068631903180662851572553488753575243048137500508983979170248733422547196905684808937723408093
--