0123_0231_0321_1032_2031<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 55, 159, 464, 1356, 3958, 11550, 33709, 98385, 287148, 838069, 2445988, 7138867, 20835514, 60810572, 177481855, 517998900, 1511832636, 4412437776, 12878149775, 37586193866, 109699141111, 320168134157, 934443361091, 2727268275429, 7959810680755, 23231519482064, 67803559543229, 197891605423471, 577566838096638, 1685687736754210, 4919851623074099, 14359088854541605, 41908465646732303, 122314132230461074, 356986272640054018, 1041900854214633092, 3040893931256958104, 8875159151420078027, 25903057371842135105, 75600715408194822570, 220648400232624813671, 643984865253527008576, 1879535524564767914275, 5485616166942379049056, 16010330391593853241146, 46727782521989618697837, 136379800167571001856176, 398038359406288704487764, 1161715557319925823194880, 3390585365019026534265919, 9895769274195312571736744, 28881812131445480529965661, 84294515048092819205399193, 246022141368922702940776445, 718040717230742536714332289, 2095675083276740713571247725, 6116441518253972348556397308, 17851458532267491289261986029, 52101302820963802780145612073, 152062967333177859925144560242, 443811282678081991208797190294, 1295308503357009238202243823507, 3780490006347997754739107026755, 11033745745555362065577670585515, 32203112552377011049682045006856, 93988069144950593839940125121776, 274313767876576483117830534732750, 800612715328740241923754132648946, 2336669883206367079317416487878981, 6819809426636087545054414480568417, 19904309526091001928971225628735136, 58092757865501816159300018979311149, 169549640091564248476431322625565180, 494847921004802653593673398147544099, 1444264138753302259007105720923856134, 4215232223777643434610835203225730676, 12302585256815295784329877988694678123, 35906350105088086841510252280227994880, 104796345723752751214835981581217079904, 305858825664825099547261177923114475620, 892680184513936373459687099534051284163, 2605378184172762314318652458133006853434, 7604062014952665432964118360012187312403, 22193230709654179079825502017313555047817, 64773207841204507709062118529805428346459, 189047214843523500854148055650726060185637, 551753581939454256131678518358879042765055, 1610349115351949796605873120142823292537860, 4699968170934992464023473569883534828518441, 13717336568334255100872990563346459910386751, 40035446131867603187084774823149644470296950, 116847533702551034928902475647653487407313786, 341031447168037054468786233696244449108398491, 995335068462694597488475292080842073940343897, 2904986935188682155940656378101391932087170971, 8478500719010109411012884010440326463474982834<br /><br />


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



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



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



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



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



Explicit closed form in Maple syntax:<br />
781153/3782610891*((((RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-278/131)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-278/131*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+83/131)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(-278/131*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+83/131)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+83/131*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+187/131)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+((-278/131*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+83/131)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+83/131*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+187/131)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(83/131*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+187/131)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+187/131*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-1684/131)*((((-6237/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-1)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(4738/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+5691/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-6103/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-8299/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-6237/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-1)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(5012/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+23448/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-5150/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+18117/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-2196/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-67309/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((4738/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+5691/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(-5150/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+18117/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(9588/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-52937/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+20807/5963+54778/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-6103/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-8299/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(-2196/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-67309/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(20807/5963+54778/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-54801/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-101760/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+1)+(((6237/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-4738/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+6103/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-4738/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+2548/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-1359/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-1359/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+6103/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+4511/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-4738/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+2548/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-1359/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-29144/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+2548/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+2101/89)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-77650/5963-1359/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+2101/89*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-1359/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+6103/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+4511/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-77650/5963-1359/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+2101/89*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-77650/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+4511/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-83422/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+1)+(((1+6237/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^4+((-17757/5963-274/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-17757/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-28612/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-132/5963-18437/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-132/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+63994/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((57861/5963+26951/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+57861/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+9413/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(34273/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-71399/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-71399/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-252976/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+1)+(((-6237/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-1)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(4738/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+5691/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-6103/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-8299/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((4738/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+5691/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(33466/5963-2548/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+1359/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-80119/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-6103/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-8299/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(1359/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-80119/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-4511/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+18338/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+2)+(((1+6237/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-17757/5963-274/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-17757/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-28612/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((15349/5963+2602/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+15349/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+27596/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(3555/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-12810/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-12810/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-57270/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+2)+(((1+6237/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-5691/5963-4738/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-5691/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-32107/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(6103/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+8299/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+8299/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+75608/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+3)+(((28310/5963+32640/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+28310/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-59605/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(28310/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-59605/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-59605/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-212570/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+1)+(((15481/5963+21039/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+15481/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-36398/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(15481/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-36398/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-36398/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-138082/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+2)+(((12066/5963-4464/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+12066/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-3495/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(12066/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-3495/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-3495/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+35202/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+3)+(((-1-6237/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(-RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+11794/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+454/67)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+4)+(((-RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(5691/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+32107/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-8299/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-75608/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3-((RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-5691/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-32107/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+8299/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+75608/5963)*(RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-1)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((5691/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+32107/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(-13990/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-107715/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(69321/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-54227/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+140752/5963-61355/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-8299/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-75608/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(8299/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+75608/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(140752/5963-61355/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-26371/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-449164/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n)+(((RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-5691/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+8299/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-5691/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-33466/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+80119/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+80119/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+8299/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-18338/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-5691/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-33466/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+80119/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(263025/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-33466/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-159812/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-8033/5963+80119/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-159812/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(80119/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+8299/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-18338/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-8033/5963+80119/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-159812/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-8033/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-18338/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-390161/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n)+(((RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-11794/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-454/67)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^4+((-RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+11794/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+11794/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+454/67)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3+((23588/5963-2*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+23588/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+908/67)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-65621/5963+72404/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-65621/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-80289/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-77953/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-10464/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-342556/5963-10464/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n)+(((-53827/5963+66441/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-53827/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-39883/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(-53827/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-39883/5963)*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-475568/5963-39883/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n)-472413/5963*RootOf(_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 5)^(-n))<br /><br />



Explicit closed form in latex syntax:<br />
\frac{781153 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{278}{131}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{278 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{131}+\frac{83}{131}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{278 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{131}+\frac{83}{131}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{83 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{131}+\frac{187}{131}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(-\frac{278 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{131}+\frac{83}{131}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{83 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{131}+\frac{187}{131}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{83 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{131}+\frac{187}{131}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{131}-\frac{1684}{131}\right) \left(\left(\left(\left(-\frac{6237 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{4738 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{5691}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{6103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{8299}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{6237 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{5012 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{23448}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{5150 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{18117}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{2196 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{67309}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{4738 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{5691}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{5150 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{18117}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{9588 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{52937}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{20807}{5963}+\frac{54778 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{6103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{8299}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{2196 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{67309}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{20807}{5963}+\frac{54778 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{54801 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{101760}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(\frac{6237 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{4738 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{6103}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{4738 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2548 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{1359}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1359 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{6103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}+\frac{4511}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4738 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2548 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{1359}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{29144 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{2548 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2101}{89}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{77650}{5963}-\frac{1359 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2101 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{89}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{1359 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{6103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}+\frac{4511}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{77650}{5963}-\frac{1359 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2101 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{89}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{77650 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{4511 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{83422}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1+\frac{6237 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{17757}{5963}-\frac{274 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{17757 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{28612}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{132}{5963}-\frac{18437 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{132 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{63994}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{57861}{5963}+\frac{26951 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{57861 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{9413}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{34273 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{71399}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{71399 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{252976}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-\frac{6237 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{4738 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{5691}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{6103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{8299}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{4738 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{5691}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{33466}{5963}-\frac{2548 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1359 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{80119}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{6103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{8299}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1359 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{80119}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{4511 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{18338}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1+\frac{6237 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{17757}{5963}-\frac{274 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{17757 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{28612}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{15349}{5963}+\frac{2602 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{15349 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{27596}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{3555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{12810}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{12810 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{57270}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1+\frac{6237 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{5691}{5963}-\frac{4738 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{5691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{32107}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{6103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{8299}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{8299 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{75608}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{28310}{5963}+\frac{32640 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{28310 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{59605}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{28310 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{59605}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{59605 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{212570}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{15481}{5963}+\frac{21039 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{15481 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{36398}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{15481 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{36398}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{36398 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{138082}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{12066}{5963}-\frac{4464 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{12066 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{3495}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{12066 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{3495}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{3495 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{35202}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1-\frac{6237 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{11794 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{454}{67}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \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}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{5691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{32107}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{8299 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{75608}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{5691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{32107}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{8299 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{75608}{5963}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{5691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{32107}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{13990 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{107715}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{69321 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{54227}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{140752}{5963}-\frac{61355 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{8299 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{75608}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{8299 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}+\frac{75608}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{140752}{5963}-\frac{61355 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{26371 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{5963}-\frac{449164}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}-\frac{5691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{8299}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{5691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{33466 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{80119}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{80119 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{8299 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{18338}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{5691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{33466 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{80119}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{263025 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{33466 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{159812}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{8033}{5963}+\frac{80119 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{159812 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{80119 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{8299 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{18338}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{8033}{5963}+\frac{80119 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{159812 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{8033 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{18338 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5963}-\frac{390161}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{11794 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{454}{67}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{11794}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{11794 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{454}{67}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{23588}{5963}-2 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{23588 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}+\frac{908}{67}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{65621}{5963}+\frac{72404 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{65621 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{80289}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{77953 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{10464}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{342556}{5963}-\frac{10464 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(-\frac{53827}{5963}+\frac{66441 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{53827 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{39883}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{53827 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}-\frac{39883}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{475568}{5963}-\frac{39883 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}-\frac{472413 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{5963}\right)}{3782610891}<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)+a(n+1)+2*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)+a \! \left(n +1\right)+2 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/17076/<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[4,x]<br />
  
    F[20,x] = F[2,x]+F[21,x]<br />
  
    F[21,x] = F[22,x]+F[23,x]+F[60,x]<br />
  
    F[22,x] = 0<br />
  
    F[23,x] = F[24,x]*F[4,x]<br />
  
    F[24,x] = F[25,x]+F[31,x]<br />
  
    F[25,x] = F[15,x]+F[26,x]<br />
  
    F[26,x] = F[27,x]<br />
  
    F[27,x] = F[28,x]*F[4,x]<br />
  
    F[28,x] = F[29,x]+F[30,x]<br />
  
    F[29,x] = F[4,x]<br />
  
    F[30,x] = F[18,x]<br />
  
    F[31,x] = F[32,x]+F[54,x]<br />
  
    F[32,x] = F[22,x]+F[23,x]+F[33,x]<br />
  
    F[33,x] = F[34,x]*F[4,x]<br />
  
    F[34,x] = F[2,x]+F[35,x]<br />
  
    F[35,x] = F[22,x]+F[36,x]+F[53,x]<br />
  
    F[36,x] = F[37,x]*F[4,x]<br />
  
    F[37,x] = F[38,x]+F[40,x]<br />
  
    F[38,x] = F[39,x]+F[4,x]<br />
  
    F[39,x] = F[27,x]<br />
  
    F[40,x] = F[35,x]+F[41,x]<br />
  
    F[41,x] = 2*F[22,x]+F[42,x]+F[49,x]<br />
  
    F[42,x] = F[4,x]*F[43,x]<br />
  
    F[43,x] = F[44,x]+F[45,x]<br />
  
    F[44,x] = F[18,x]<br />
  
    F[45,x] = F[46,x]<br />
  
    F[46,x] = 2*F[22,x]+F[42,x]+F[47,x]<br />
  
    F[47,x] = F[4,x]*F[48,x]<br />
  
    F[48,x] = F[35,x]<br />
  
    F[49,x] = F[4,x]*F[50,x]<br />
  
    F[50,x] = F[51,x]+F[52,x]<br />
  
    F[51,x] = F[35,x]<br />
  
    F[52,x] = F[46,x]<br />
  
    F[53,x] = F[2,x]*F[4,x]<br />
  
    F[54,x] = 2*F[22,x]+F[49,x]+F[55,x]<br />
  
    F[55,x] = F[4,x]*F[56,x]<br />
  
    F[56,x] = F[57,x]+F[58,x]<br />
  
    F[57,x] = F[18,x]<br />
  
    F[58,x] = F[59,x]<br />
  
    F[59,x] = 2*F[22,x]+F[47,x]+F[55,x]<br />
  
    F[60,x] = F[4,x]*F[61,x]<br />
  
    F[61,x] = F[62,x]+F[65,x]<br />
  
    F[62,x] = F[2,x]+F[63,x]<br />
  
    F[63,x] = F[22,x]+F[36,x]+F[64,x]<br />
  
    F[64,x] = F[34,x]*F[4,x]<br />
  
    F[65,x] = F[32,x]+F[66,x]<br />
  
    F[66,x] = 2*F[22,x]+F[42,x]+F[47,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_{4}\! \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_{60}\! \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_{31}\! \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_{27}\! \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_{30}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{4}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{18}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{54}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{33}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{22}\! \left(x \right)+F_{36}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{40}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{27}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{35}\! \left(x \right)+F_{41}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{49}\! \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_{45}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{18}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{46}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{47}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{35}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{35}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{46}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{49}\! \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_{57}\! \left(x \right)+F_{58}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = F_{18}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = F_{59}\! \left(x \right)<br />
  
    F_{59}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{47}\! \left(x \right)+F_{55}\! \left(x \right)<br />
  
    F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)<br />
  
    F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)<br />
  
    F_{62}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)<br />
  
    F_{63}\! \left(x \right) = F_{22}\! \left(x \right)+F_{36}\! \left(x \right)+F_{64}\! \left(x \right)<br />
  
    F_{64}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{65}\! \left(x \right) = F_{32}\! \left(x \right)+F_{66}\! \left(x \right)<br />
  
    F_{66}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{47}\! \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_4(x))<br />
  
    Eq(F_20(x), F_2(x) + F_21(x))<br />
  
    Eq(F_21(x), F_22(x) + F_23(x) + F_60(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_31(x))<br />
  
    Eq(F_25(x), F_15(x) + F_26(x))<br />
  
    Eq(F_26(x), F_27(x))<br />
  
    Eq(F_27(x), F_28(x)*F_4(x))<br />
  
    Eq(F_28(x), F_29(x) + F_30(x))<br />
  
    Eq(F_29(x), F_4(x))<br />
  
    Eq(F_30(x), F_18(x))<br />
  
    Eq(F_31(x), F_32(x) + F_54(x))<br />
  
    Eq(F_32(x), F_22(x) + F_23(x) + F_33(x))<br />
  
    Eq(F_33(x), F_34(x)*F_4(x))<br />
  
    Eq(F_34(x), F_2(x) + F_35(x))<br />
  
    Eq(F_35(x), F_22(x) + F_36(x) + F_53(x))<br />
  
    Eq(F_36(x), F_37(x)*F_4(x))<br />
  
    Eq(F_37(x), F_38(x) + F_40(x))<br />
  
    Eq(F_38(x), F_39(x) + F_4(x))<br />
  
    Eq(F_39(x), F_27(x))<br />
  
    Eq(F_40(x), F_35(x) + F_41(x))<br />
  
    Eq(F_41(x), 2*F_22(x) + F_42(x) + F_49(x))<br />
  
    Eq(F_42(x), F_4(x)*F_43(x))<br />
  
    Eq(F_43(x), F_44(x) + F_45(x))<br />
  
    Eq(F_44(x), F_18(x))<br />
  
    Eq(F_45(x), F_46(x))<br />
  
    Eq(F_46(x), 2*F_22(x) + F_42(x) + F_47(x))<br />
  
    Eq(F_47(x), F_4(x)*F_48(x))<br />
  
    Eq(F_48(x), F_35(x))<br />
  
    Eq(F_49(x), F_4(x)*F_50(x))<br />
  
    Eq(F_50(x), F_51(x) + F_52(x))<br />
  
    Eq(F_51(x), F_35(x))<br />
  
    Eq(F_52(x), F_46(x))<br />
  
    Eq(F_53(x), F_2(x)*F_4(x))<br />
  
    Eq(F_54(x), 2*F_22(x) + F_49(x) + F_55(x))<br />
  
    Eq(F_55(x), F_4(x)*F_56(x))<br />
  
    Eq(F_56(x), F_57(x) + F_58(x))<br />
  
    Eq(F_57(x), F_18(x))<br />
  
    Eq(F_58(x), F_59(x))<br />
  
    Eq(F_59(x), 2*F_22(x) + F_47(x) + F_55(x))<br />
  
    Eq(F_60(x), F_4(x)*F_61(x))<br />
  
    Eq(F_61(x), F_62(x) + F_65(x))<br />
  
    Eq(F_62(x), F_2(x) + F_63(x))<br />
  
    Eq(F_63(x), F_22(x) + F_36(x) + F_64(x))<br />
  
    Eq(F_64(x), F_34(x)*F_4(x))<br />
  
    Eq(F_65(x), F_32(x) + F_66(x))<br />
  
    Eq(F_66(x), 2*F_22(x) + F_42(x) + F_47(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, 3, 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, 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;: [2, 0, 3, 1], &#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, 3, 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, 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;: [2, 0, 3, 1], &#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, 3, 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, 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;: [2, 0, 3, 1], &#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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [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, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#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.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2]]], &#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, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[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;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], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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], &#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], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[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;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: 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[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, 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, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0]]}, {&#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, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [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, 1]]}, {&#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, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 2, 3, 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, 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;: [2, 0, 3, 1], &#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, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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;: &#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, 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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#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;: 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[[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;: &#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, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], 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{&#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;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 2]]}, {&#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, 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, 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, 4], [1, 4]]}, {&#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, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [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, 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, 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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [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, 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, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#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], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [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, 1]]}, {&#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, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 2, 3, 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, 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;: [2, 0, 3, 1], &#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, 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;: [], &#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, 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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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, &#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;: &#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, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#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, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 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], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#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, 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;: [[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;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 2]]}, {&#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, 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, 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, 4], [1, 4]]}, {&#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, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [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, 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, 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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [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, 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, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#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, 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, 2, 3, 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, 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;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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, 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, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#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], &#34;pos&#34;: [[1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [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, 1]]}, {&#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, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 2, 3, 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, 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;: [2, 0, 3, 1], &#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, 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, 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[[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, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[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;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#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, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], 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{&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 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], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], 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{&#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;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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;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;: [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, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, 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{&#34;patt&#34;: [0, 2, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [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, 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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#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, 3, 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, 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;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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;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;: [[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, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0]]}, {&#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, 3, 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, 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;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [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;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;: &#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, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 0]]}, {&#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, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[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;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#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, 3], [0, 3]]}, {&#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;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#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, 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, 0]]}, {&#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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [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, 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], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 2, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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;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, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#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;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#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, 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, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], 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[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 2, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#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_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;, 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[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, 3, 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, 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;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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], 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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, 3, 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, 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, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [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, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0]]}, {&#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], 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2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 3, 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, 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;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [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, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 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