0123_0213_0321_1032_1302<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 54, 152, 431, 1227, 3491, 9927, 28227, 80268, 228259, 649099, 1845833, 5248968, 14926420, 42446064, 120703307, 343242380, 976073769, 2775647942, 7893072987, 22445426241, 63827758836, 181506145369, 516146601544, 1467759197594, 4173847228038, 11869113619966, 33752039887173, 95980225063235, 272937684180980, 776149247378772, 2207125249172951, 6276372594560358, 17848036925185620, 50754224240746017, 144329109642579919, 410426761552127125, 1167125100510358355, 3318938061177834273, 9438019839619685410, 26838770971653254643, 76321054575986502377, 217033163617771248089, 617174308867042033080, 1755050339663028177404, 4990813211920133497332, 14192308877623970341473, 40358479214731118522562, 114766868348948533045273, 326361010793915689771990, 928068447790857461978873, 2639135850479443495913553, 7504875371924554663101760, 21341513866323960801869307, 60688577962314570472605470, 172579298645712334808897096, 490761446734516060586245092, 1395571771880873784363080504, 3968568809612122807455235149, 11285366123019120797734058757, 32092044926149433156473614714, 91259719562068532987281936450, 259514045730418658433653643187, 737976625991762994258165490190, 2098574275536218602843337934504, 5967687640545299105523592214695, 16970233643990210491865629549695, 48258026773214658302999311706087, 137230706241279737734084408162079, 390241126600169144999323388824731, 1109723479979877477445092736902896, 3155705839483182131184172223908515, 8973838550779182878271916828265451, 25518784839793302533341233367278117, 72567427641443492662826817582458476, 206359024834302845118334387919276896, 586820402963333528850877240975272716, 1668733342825948656285534702495290511, 4745354720791908967916373656227514548, 13494301844540273973888305465418621165, 38373565936747225822617497536554907994, 109122396969181876245600752964488925671, 310309902914096546167620279432290228769, 882424126678143627059737820143546396412, 2509337704118470388928540623570529080961, 7135770116592980612562088338392754018588, 20291894181197626291907102017651370903082, 57703788481560559360039613698986690335674, 164091492661635829551571170844698965888038, 466624786213612046422776636905976557187737, 1326934672706563141048050469269127383798423, 3773386407349636698701118067126426569863836, 10730328532397670101221183097006540124421224, 30513691942315525009304463796129575335685695, 86771378261098055861066650660140890662908806, 246750609515369022931470856946283362533391196, 701681412884770241446391632101725425951929089<br /><br />


Generating function in Maple syntax:<br />
-(2*x-1)/(x^5-2*x^4-x^3+x^2-3*x+1)<br /><br />



Generating function in latex syntax:<br />
-\frac{2 x -1}{x^{5}-2 x^{4}-x^{3}+x^{2}-3 x +1}<br /><br />



Generating function in sympy syntax:<br />
(1 - 2*x)/(x**5 - 2*x**4 - x**3 + x**2 - 3*x + 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^5-2*x^4-x^3+x^2-3*x+1)*F(x)+2*x-1 = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{5}-2 x^{4}-x^{3}+x^{2}-3 x +1\right) F \! \left(x \right)+2 x -1 = 0<br /><br />



Explicit closed form in Maple syntax:<br />
-139/489731*((((RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-56/33)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-56/33*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+127/33)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+(-56/33*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+127/33)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+127/33*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-42/11)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+((-56/33*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+127/33)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+127/33*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-42/11)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+(127/33*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-42/11)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-42/11*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-63/11)*((((-1+20/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(218/139-109/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+108/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+165/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-1+20/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^3+(606/139-288/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-1118/139+544/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-51/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+684/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+((218/139-109/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^3+(-1118/139+544/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-117/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+2022/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+7/139-686/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(108/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+165/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^3+(-51/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+684/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(7/139-686/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+2035/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-998/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+1)+(((-108/139-20/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2+109/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+109/139*(RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-2)*(RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-364/109)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-1408/139-108/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2+728/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+(109/139*(RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-2)*(RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-364/109)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(4078/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-582/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2-5972/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+10715/139+728/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2-5972/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(-1408/139-108/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2+728/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(10715/139+728/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2-5972/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+10715/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-1408/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2-12726/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+1)+(((1-20/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-110/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^4+((-388/139+179/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-388/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+1232/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^3+((81/139-258/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+81/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-1914/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-138/139+261/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-138/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+1188/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(-248/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+2200/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+16/139+2200/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+1)+(((-1+20/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(218/139-109/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+108/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+165/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+((218/139-109/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-1575/139+582/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-728/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+2422/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(108/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+165/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-728/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+2422/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-5864/139+1408/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+2)+(((1-20/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-110/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-388/139+179/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-388/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+1232/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-457/139+38/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-457/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-286/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(-677/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+1738/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-3836/139+1738/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+2)+(((1-20/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-110/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-218/139+109/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-218/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+847/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(-108/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-165/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-1014/139-165/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+3)+(((-387/139+420/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-387/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+2310/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+(-387/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+2310/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-996/139+2310/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+1)+(((-538/139+296/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-538/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+1628/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+(-538/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+1628/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-2824/139+1628/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+2)+(((170/139-70/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+170/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-385/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+(170/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-385/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+1010/139-385/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+3)+(((-1+20/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+110/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+(-RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+110/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-1012/139+110/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+4)+(((-RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+110/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-847/139+218/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+165/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+1014/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^3-((-110/139+RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(847/139-218/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-165/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-1014/139)*(RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-2)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-847/139+218/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^3+(2708/139-271/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-2787/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+5298/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-13902/139+6027/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(165/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+1014/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^3+(-330/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-2028/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-13902/139+6027/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-12369/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+39513/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n)+(((-165/139+RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2-218/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-2422/139+1575/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-218/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+5864/139-165/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2-2422/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-2422/139+1575/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-218/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-10781/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+1575/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2+16735/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-24097/139-2422/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2+16735/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(5864/139-165/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2-2422/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-24097/139-2422/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2+16735/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)-24097/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+5864/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^2+32634/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)^(-n)+(((RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-110/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+1012/139-110/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^4+((220/139-2*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+220/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-2024/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)+110/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)-1012/139+110/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^2+((6479/139-2239/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+6479/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-12067/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)+(6192/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-12888/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+37896/139-12888/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n)+(((6589/139-2378/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+6589/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-13079/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)+(6589/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)-13079/139)*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)+40822/139-13079/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n)+6963/139*RootOf(_Z^5-2*_Z^4-_Z^3+_Z^2-3*_Z+1,index = 5)^(-n))<br /><br />



Explicit closed form in latex syntax:<br />
-\frac{139 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{56}{33}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{33}+\frac{127}{33}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{33}+\frac{127}{33}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{127 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{33}-\frac{42}{11}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{33}+\frac{127}{33}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{127 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{33}-\frac{42}{11}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{127 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{33}-\frac{42}{11}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{42 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{11}-\frac{63}{11}\right) \left(\left(\left(\left(-1+\frac{20 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{218}{139}-\frac{109 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{108 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{165}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-1+\frac{20 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{606}{139}-\frac{288 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1118}{139}+\frac{544 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{51 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{684}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{218}{139}-\frac{109 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{1118}{139}+\frac{544 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{117 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{2022}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{7}{139}-\frac{686 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{108 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{165}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{51 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{684}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{7}{139}-\frac{686 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{2035 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}-\frac{998}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{108}{139}-\frac{20 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}+\frac{109 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\frac{109 \left(\mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-2\right) \left(\mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{364}{109}\right) \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)}{139}-\frac{1408}{139}-\frac{108 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}+\frac{728 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\frac{109 \left(\mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-2\right) \left(\mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{364}{109}\right) \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}}{139}+\left(\frac{4078 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{582 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}-\frac{5972}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{10715}{139}+\frac{728 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}-\frac{5972 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{1408}{139}-\frac{108 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}+\frac{728 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{10715}{139}+\frac{728 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}-\frac{5972 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{10715 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{1408 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}-\frac{12726}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{20 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{110}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{388}{139}+\frac{179 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{388 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{1232}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{81}{139}-\frac{258 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{81 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{1914}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{138}{139}+\frac{261 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{138 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{1188}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{248 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{2200}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{16}{139}+\frac{2200 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-1+\frac{20 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{218}{139}-\frac{109 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{108 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{165}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{218}{139}-\frac{109 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1575}{139}+\frac{582 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{728 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{2422}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{108 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{165}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{728 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{2422}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{5864}{139}+\frac{1408 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{20 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{110}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{388}{139}+\frac{179 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{388 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{1232}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{457}{139}+\frac{38 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{457 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{286}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{677 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{1738}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{3836}{139}+\frac{1738 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{20 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{110}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{218}{139}+\frac{109 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{218 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{847}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{108 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{165}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1014}{139}-\frac{165 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{387}{139}+\frac{420 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{387 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{2310}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{387 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{2310}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{996}{139}+\frac{2310 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{538}{139}+\frac{296 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{538 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{1628}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{538 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{1628}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{2824}{139}+\frac{1628 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{170}{139}-\frac{70 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{170 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{385}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{170 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{385}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1010}{139}-\frac{385 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{20 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{110}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{110}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1012}{139}+\frac{110 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{110}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{847}{139}+\frac{218 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{165 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{1014}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(\left(-\frac{110}{139}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{847}{139}-\frac{218 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{165 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}-\frac{1014}{139}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-2\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{847}{139}+\frac{218 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{2708}{139}-\frac{271 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{2787 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{5298}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{13902}{139}+\frac{6027 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{165 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{1014}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{330 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}-\frac{2028}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{13902}{139}+\frac{6027 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{12369 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{139}+\frac{39513}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(-\frac{165}{139}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}-\frac{218 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{2422}{139}+\frac{1575 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{218 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{5864}{139}-\frac{165 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}-\frac{2422 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{2422}{139}+\frac{1575 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{218 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{10781 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{1575 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}+\frac{16735}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{24097}{139}-\frac{2422 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}+\frac{16735 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{5864}{139}-\frac{165 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}-\frac{2422 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{24097}{139}-\frac{2422 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}+\frac{16735 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{24097 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}+\frac{5864 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}+\frac{32634}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{110}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1012}{139}-\frac{110 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(\frac{220}{139}-2 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{220 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{2024}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{110}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1012}{139}+\frac{110 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{6479}{139}-\frac{2239 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{6479 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{12067}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{6192 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{12888}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{37896}{139}-\frac{12888 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{6589}{139}-\frac{2378 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{6589 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{13079}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{6589 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{13079}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{40822}{139}-\frac{13079 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}+\frac{6963 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{139}\right)}{489731}<br /><br />



  
    Recurrence in maple format:<br />
    
      a(0) = 1<br />
    
      a(1) = 1<br />
    
      a(2) = 2<br />
    
      a(3) = 6<br />
    
      a(4) = 19<br />
    
    a(n+5) = -a(n)+2*a(n+1)+a(n+2)-a(n+3)+3*a(n+4), n >= 5<br /><br />

    Recurrence in latex format:<br />
    
      a \! \left(0\right) = 1<br />
    
      a \! \left(1\right) = 1<br />
    
      a \! \left(2\right) = 2<br />
    
      a \! \left(3\right) = 6<br />
    
      a \! \left(4\right) = 19<br />
    
    a \! \left(n +5\right) = -a \! \left(n \right)+2 a \! \left(n +1\right)+a \! \left(n +2\right)-a \! \left(n +3\right)+3 a \! \left(n +4\right), \quad n \geq 5<br /><br />
  



  Specification 1<br />
  Strategy pack name: point_placements<br />
  Tree: http://permpal.com/tree/16820/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[3,x]<br />
  
    F[3,x] = F[4,x]*F[5,x]<br />
  
    F[4,x] = x<br />
  
    F[5,x] = F[20,x]+F[6,x]<br />
  
    F[6,x] = F[1,x]+F[7,x]<br />
  
    F[7,x] = F[8,x]<br />
  
    F[8,x] = F[4,x]*F[9,x]<br />
  
    F[9,x] = F[10,x]+F[14,x]<br />
  
    F[10,x] = F[1,x]+F[11,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[13,x]*F[4,x]<br />
  
    F[13,x] = F[1,x]+F[4,x]<br />
  
    F[14,x] = F[15,x]+F[17,x]<br />
  
    F[15,x] = F[16,x]<br />
  
    F[16,x] = F[13,x]*F[4,x]<br />
  
    F[17,x] = F[18,x]<br />
  
    F[18,x] = F[19,x]*F[4,x]<br />
  
    F[19,x] = F[15,x]<br />
  
    F[20,x] = F[2,x]+F[21,x]<br />
  
    F[21,x] = F[22,x]+F[23,x]+F[88,x]<br />
  
    F[22,x] = 0<br />
  
    F[23,x] = F[24,x]*F[4,x]<br />
  
    F[24,x] = F[25,x]+F[37,x]<br />
  
    F[25,x] = F[15,x]+F[26,x]<br />
  
    F[26,x] = F[22,x]+F[27,x]+F[35,x]<br />
  
    F[27,x] = F[28,x]*F[4,x]<br />
  
    F[28,x] = F[29,x]+F[32,x]<br />
  
    F[29,x] = F[30,x]+F[4,x]<br />
  
    F[30,x] = F[31,x]<br />
  
    F[31,x] = x^2<br />
  
    F[32,x] = F[33,x]<br />
  
    F[33,x] = F[34,x]<br />
  
    F[34,x] = F[15,x]*F[4,x]<br />
  
    F[35,x] = F[36,x]*F[4,x]<br />
  
    F[36,x] = F[15,x]+F[33,x]<br />
  
    F[37,x] = F[38,x]+F[77,x]<br />
  
    F[38,x] = F[22,x]+F[23,x]+F[39,x]<br />
  
    F[39,x] = F[4,x]*F[40,x]<br />
  
    F[40,x] = F[2,x]+F[41,x]<br />
  
    F[41,x] = F[22,x]+F[42,x]+F[70,x]<br />
  
    F[42,x] = F[4,x]*F[43,x]<br />
  
    F[43,x] = F[44,x]+F[46,x]<br />
  
    F[44,x] = F[4,x]+F[45,x]<br />
  
    F[45,x] = F[22,x]+F[27,x]+F[34,x]<br />
  
    F[46,x] = F[41,x]+F[47,x]<br />
  
    F[47,x] = F[22,x]+F[48,x]+F[65,x]+F[71,x]<br />
  
    F[48,x] = F[4,x]*F[49,x]<br />
  
    F[49,x] = F[50,x]+F[57,x]<br />
  
    F[50,x] = F[51,x]+F[54,x]<br />
  
    F[51,x] = F[52,x]<br />
  
    F[52,x] = F[4,x]*F[53,x]<br />
  
    F[53,x] = F[4,x]<br />
  
    F[54,x] = F[55,x]<br />
  
    F[55,x] = F[4,x]*F[56,x]<br />
  
    F[56,x] = F[33,x]<br />
  
    F[57,x] = F[58,x]+F[61,x]<br />
  
    F[58,x] = 2*F[22,x]+F[48,x]+F[59,x]<br />
  
    F[59,x] = F[4,x]*F[60,x]<br />
  
    F[60,x] = F[41,x]<br />
  
    F[61,x] = F[62,x]<br />
  
    F[62,x] = F[4,x]*F[63,x]<br />
  
    F[63,x] = F[64,x]<br />
  
    F[64,x] = F[65,x]<br />
  
    F[65,x] = F[4,x]*F[66,x]<br />
  
    F[66,x] = F[67,x]<br />
  
    F[67,x] = F[4,x]*F[68,x]<br />
  
    F[68,x] = F[2,x]+F[69,x]<br />
  
    F[69,x] = F[70,x]<br />
  
    F[70,x] = F[2,x]*F[4,x]<br />
  
    F[71,x] = F[4,x]*F[72,x]<br />
  
    F[72,x] = F[73,x]+F[76,x]<br />
  
    F[73,x] = F[41,x]+F[74,x]<br />
  
    F[74,x] = F[75,x]<br />
  
    F[75,x] = F[4,x]*F[69,x]<br />
  
    F[76,x] = F[64,x]<br />
  
    F[77,x] = F[22,x]+F[71,x]+F[78,x]+F[86,x]<br />
  
    F[78,x] = F[4,x]*F[79,x]<br />
  
    F[79,x] = F[80,x]+F[83,x]<br />
  
    F[80,x] = F[81,x]+F[82,x]<br />
  
    F[81,x] = F[52,x]<br />
  
    F[82,x] = F[55,x]<br />
  
    F[83,x] = F[84,x]+F[85,x]<br />
  
    F[84,x] = 2*F[22,x]+F[59,x]+F[78,x]<br />
  
    F[85,x] = F[62,x]<br />
  
    F[86,x] = F[4,x]*F[87,x]<br />
  
    F[87,x] = F[64,x]+F[66,x]<br />
  
    F[88,x] = F[4,x]*F[89,x]<br />
  
    F[89,x] = F[90,x]+F[93,x]<br />
  
    F[90,x] = F[2,x]+F[91,x]<br />
  
    F[91,x] = F[22,x]+F[42,x]+F[92,x]<br />
  
    F[92,x] = F[4,x]*F[68,x]<br />
  
    F[93,x] = F[66,x]+F[94,x]<br />
  
    F[94,x] = F[95,x]<br />
  
    F[95,x] = F[4,x]*F[96,x]<br />
  
    F[96,x] = F[66,x]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = x<br />
  
    F_{5}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)<br />
  
    F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{7}\! \left(x \right) = F_{8}\! \left(x \right)<br />
  
    F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)<br />
  
    F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)<br />
  
    F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)<br />
  
    F_{11}\! \left(x \right) = F_{12}\! \left(x \right)<br />
  
    F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{16}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{17}\! \left(x \right) = F_{18}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{19}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)<br />
  
    F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{88}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = 0<br />
  
    F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{37}\! \left(x \right)<br />
  
    F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)<br />
  
    F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{35}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{31}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = x^{2}<br />
  
    F_{32}\! \left(x \right) = F_{33}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{34}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{77}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{39}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{70}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{4}\! \left(x \right)+F_{45}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{34}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{41}\! \left(x \right)+F_{47}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{22}\! \left(x \right)+F_{48}\! \left(x \right)+F_{65}\! \left(x \right)+F_{71}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{52}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{4}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{55}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{33}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{48}\! \left(x \right)+F_{59}\! \left(x \right)<br />
  
    F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)<br />
  
    F_{60}\! \left(x \right) = F_{41}\! \left(x \right)<br />
  
    F_{61}\! \left(x \right) = F_{62}\! \left(x \right)<br />
  
    F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)<br />
  
    F_{63}\! \left(x \right) = F_{64}\! \left(x \right)<br />
  
    F_{64}\! \left(x \right) = F_{65}\! \left(x \right)<br />
  
    F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)<br />
  
    F_{66}\! \left(x \right) = F_{67}\! \left(x \right)<br />
  
    F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)<br />
  
    F_{68}\! \left(x \right) = F_{2}\! \left(x \right)+F_{69}\! \left(x \right)<br />
  
    F_{69}\! \left(x \right) = F_{70}\! \left(x \right)<br />
  
    F_{70}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)<br />
  
    F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)<br />
  
    F_{73}\! \left(x \right) = F_{41}\! \left(x \right)+F_{74}\! \left(x \right)<br />
  
    F_{74}\! \left(x \right) = F_{75}\! \left(x \right)<br />
  
    F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)<br />
  
    F_{76}\! \left(x \right) = F_{64}\! \left(x \right)<br />
  
    F_{77}\! \left(x \right) = F_{22}\! \left(x \right)+F_{71}\! \left(x \right)+F_{78}\! \left(x \right)+F_{86}\! \left(x \right)<br />
  
    F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)<br />
  
    F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)<br />
  
    F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)<br />
  
    F_{81}\! \left(x \right) = F_{52}\! \left(x \right)<br />
  
    F_{82}\! \left(x \right) = F_{55}\! \left(x \right)<br />
  
    F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)<br />
  
    F_{84}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{59}\! \left(x \right)+F_{78}\! \left(x \right)<br />
  
    F_{85}\! \left(x \right) = F_{62}\! \left(x \right)<br />
  
    F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)<br />
  
    F_{87}\! \left(x \right) = F_{64}\! \left(x \right)+F_{66}\! \left(x \right)<br />
  
    F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)<br />
  
    F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{93}\! \left(x \right)<br />
  
    F_{90}\! \left(x \right) = F_{2}\! \left(x \right)+F_{91}\! \left(x \right)<br />
  
    F_{91}\! \left(x \right) = F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{92}\! \left(x \right)<br />
  
    F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)<br />
  
    F_{93}\! \left(x \right) = F_{66}\! \left(x \right)+F_{94}\! \left(x \right)<br />
  
    F_{94}\! \left(x \right) = F_{95}\! \left(x \right)<br />
  
    F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)<br />
  
    F_{96}\! \left(x \right) = F_{66}\! \left(x \right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_3(x))<br />
  
    Eq(F_3(x), F_4(x)*F_5(x))<br />
  
    Eq(F_4(x), x)<br />
  
    Eq(F_5(x), F_20(x) + F_6(x))<br />
  
    Eq(F_6(x), F_1(x) + F_7(x))<br />
  
    Eq(F_7(x), F_8(x))<br />
  
    Eq(F_8(x), F_4(x)*F_9(x))<br />
  
    Eq(F_9(x), F_10(x) + F_14(x))<br />
  
    Eq(F_10(x), F_1(x) + F_11(x))<br />
  
    Eq(F_11(x), F_12(x))<br />
  
    Eq(F_12(x), F_13(x)*F_4(x))<br />
  
    Eq(F_13(x), F_1(x) + F_4(x))<br />
  
    Eq(F_14(x), F_15(x) + F_17(x))<br />
  
    Eq(F_15(x), F_16(x))<br />
  
    Eq(F_16(x), F_13(x)*F_4(x))<br />
  
    Eq(F_17(x), F_18(x))<br />
  
    Eq(F_18(x), F_19(x)*F_4(x))<br />
  
    Eq(F_19(x), F_15(x))<br />
  
    Eq(F_20(x), F_2(x) + F_21(x))<br />
  
    Eq(F_21(x), F_22(x) + F_23(x) + F_88(x))<br />
  
    Eq(F_22(x), 0)<br />
  
    Eq(F_23(x), F_24(x)*F_4(x))<br />
  
    Eq(F_24(x), F_25(x) + F_37(x))<br />
  
    Eq(F_25(x), F_15(x) + F_26(x))<br />
  
    Eq(F_26(x), F_22(x) + F_27(x) + F_35(x))<br />
  
    Eq(F_27(x), F_28(x)*F_4(x))<br />
  
    Eq(F_28(x), F_29(x) + F_32(x))<br />
  
    Eq(F_29(x), F_30(x) + F_4(x))<br />
  
    Eq(F_30(x), F_31(x))<br />
  
    Eq(F_31(x), x**2)<br />
  
    Eq(F_32(x), F_33(x))<br />
  
    Eq(F_33(x), F_34(x))<br />
  
    Eq(F_34(x), F_15(x)*F_4(x))<br />
  
    Eq(F_35(x), F_36(x)*F_4(x))<br />
  
    Eq(F_36(x), F_15(x) + F_33(x))<br />
  
    Eq(F_37(x), F_38(x) + F_77(x))<br />
  
    Eq(F_38(x), F_22(x) + F_23(x) + F_39(x))<br />
  
    Eq(F_39(x), F_4(x)*F_40(x))<br />
  
    Eq(F_40(x), F_2(x) + F_41(x))<br />
  
    Eq(F_41(x), F_22(x) + F_42(x) + F_70(x))<br />
  
    Eq(F_42(x), F_4(x)*F_43(x))<br />
  
    Eq(F_43(x), F_44(x) + F_46(x))<br />
  
    Eq(F_44(x), F_4(x) + F_45(x))<br />
  
    Eq(F_45(x), F_22(x) + F_27(x) + F_34(x))<br />
  
    Eq(F_46(x), F_41(x) + F_47(x))<br />
  
    Eq(F_47(x), F_22(x) + F_48(x) + F_65(x) + F_71(x))<br />
  
    Eq(F_48(x), F_4(x)*F_49(x))<br />
  
    Eq(F_49(x), F_50(x) + F_57(x))<br />
  
    Eq(F_50(x), F_51(x) + F_54(x))<br />
  
    Eq(F_51(x), F_52(x))<br />
  
    Eq(F_52(x), F_4(x)*F_53(x))<br />
  
    Eq(F_53(x), F_4(x))<br />
  
    Eq(F_54(x), F_55(x))<br />
  
    Eq(F_55(x), F_4(x)*F_56(x))<br />
  
    Eq(F_56(x), F_33(x))<br />
  
    Eq(F_57(x), F_58(x) + F_61(x))<br />
  
    Eq(F_58(x), 2*F_22(x) + F_48(x) + F_59(x))<br />
  
    Eq(F_59(x), F_4(x)*F_60(x))<br />
  
    Eq(F_60(x), F_41(x))<br />
  
    Eq(F_61(x), F_62(x))<br />
  
    Eq(F_62(x), F_4(x)*F_63(x))<br />
  
    Eq(F_63(x), F_64(x))<br />
  
    Eq(F_64(x), F_65(x))<br />
  
    Eq(F_65(x), F_4(x)*F_66(x))<br />
  
    Eq(F_66(x), F_67(x))<br />
  
    Eq(F_67(x), F_4(x)*F_68(x))<br />
  
    Eq(F_68(x), F_2(x) + F_69(x))<br />
  
    Eq(F_69(x), F_70(x))<br />
  
    Eq(F_70(x), F_2(x)*F_4(x))<br />
  
    Eq(F_71(x), F_4(x)*F_72(x))<br />
  
    Eq(F_72(x), F_73(x) + F_76(x))<br />
  
    Eq(F_73(x), F_41(x) + F_74(x))<br />
  
    Eq(F_74(x), F_75(x))<br />
  
    Eq(F_75(x), F_4(x)*F_69(x))<br />
  
    Eq(F_76(x), F_64(x))<br />
  
    Eq(F_77(x), F_22(x) + F_71(x) + F_78(x) + F_86(x))<br />
  
    Eq(F_78(x), F_4(x)*F_79(x))<br />
  
    Eq(F_79(x), F_80(x) + F_83(x))<br />
  
    Eq(F_80(x), F_81(x) + F_82(x))<br />
  
    Eq(F_81(x), F_52(x))<br />
  
    Eq(F_82(x), F_55(x))<br />
  
    Eq(F_83(x), F_84(x) + F_85(x))<br />
  
    Eq(F_84(x), 2*F_22(x) + F_59(x) + F_78(x))<br />
  
    Eq(F_85(x), F_62(x))<br />
  
    Eq(F_86(x), F_4(x)*F_87(x))<br />
  
    Eq(F_87(x), F_64(x) + F_66(x))<br />
  
    Eq(F_88(x), F_4(x)*F_89(x))<br />
  
    Eq(F_89(x), F_90(x) + F_93(x))<br />
  
    Eq(F_90(x), F_2(x) + F_91(x))<br />
  
    Eq(F_91(x), F_22(x) + F_42(x) + F_92(x))<br />
  
    Eq(F_92(x), F_4(x)*F_68(x))<br />
  
    Eq(F_93(x), F_66(x) + F_94(x))<br />
  
    Eq(F_94(x), F_95(x))<br />
  
    Eq(F_95(x), F_4(x)*F_96(x))<br />
  
    Eq(F_96(x), F_66(x))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;extra_basis&#34;: [], &#34;ignore_parent&#34;: false, &#34;maxreqlen&#34;: 1, &#34;one_cell_only&#34;: false, &#34;strategy_class&#34;: &#34;CellInsertionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;point_only&#34;: false, &#34;strategy_class&#34;: &#34;PatternPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;point_placements&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, 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&#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 1]]}, 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0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], 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1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 3], [0, 1], [0, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 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[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 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&#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: 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{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 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{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: 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[1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], 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1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], 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[[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 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0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], &#34;own_col&#34;: true, 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&#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], 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&#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 5]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 5], [1, 5]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 5], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 5]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 2], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 2], [1, 5]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 4], [1, 2], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 4], [1, 2], [1, 5]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 5], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 5], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 5], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 5], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 5]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 5]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 5]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 5]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 5]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 5], [1, 5]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 5], [1, 5]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 5], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 5], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 3], [1, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 5], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 5]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 5], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 5], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 5], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 5]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], 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[0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], 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1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, &#34;rule_class&#34;: &#34;EquivalenceRule&#34;}]}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, 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