0132_0231_1023_1032_1302<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 59, 180, 545, 1647, 4977, 15043, 45473, 137464, 415553, 1256212, 3797508, 11479796, 34703205, 104907130, 317132270, 958684865, 2898086256, 8760860065, 26483914652, 80060374207, 242021000371, 731624916824, 2211688316710, 6685892043586, 20211325475112, 61098455493741, 184699477939605, 558343036259833, 1687860461856762, 5102370323776270, 15424369199521011, 46627577009552335, 140954285368717024, 426102144654341469, 1288098742114050735, 3893898189087405097, 11771180742008411151, 35584057243546862741, 107569933523591049440, 325181879038491058773, 983018683671617109176, 2971646929726662244704, 8983232589202585475944, 27156142590309067059441, 82092506574034926933826, 248164098166611826900274, 750195385535062094263721, 2267826493178935728950816, 6855596691648668965204193, 20724339423631493100493488, 62649286978782089427598719, 189387612252397439997886315, 572515177815383865105434476, 1730702578329968621200996622, 5231881233380839489964408838, 15815878235193725305386052320, 47811101436037936800303550137, 144532057375131235989682638601, 436917681911896212834994928257, 1320793907138496397433444635314, 3992735055950310851319517622630, 12069962725337500795806251162771, 36487269540693934547993925133843, 110300327252918249353290900747772, 333435807755689839796621752574937, 1007970154419898554456639796963727, 3047074754927657496535085745214785, 9211249481350867112086783841279195, 27845433352258214199313137466446745, 84176219539473730752043719180187416, 254463123138395936015172365619636857, 769237219152872389614978771143189372, 2325389596858086799731968336462102876, 7029608867770063455789400052428341900, 21250374948180015531102631590768488941, 64239482442425956374491971941840498378, 194194743129658713804583681111809854406, 587047043739693923177064819338881784769, 1774632134781411616932579956672936452320, 5364679453518019842286093712201543958097, 16217324748570113553170023571602811600468, 49024666670086867290362817080207426003903, 148200642175895025994835877762945517350259, 448007744532998338613541315994356164501376, 1354318957156247235324335300427061774888822, 4094080649486824161359278690852058713473674, 12376328542057533083802355446595663393720552, 37413407623063702785562106738931156708881253, 113100025198330275019547176372568058228792477, 341899241810240259151102015305431566863424025, 1033554955849319240008019625070196533981261098, 3124417126825852476695228272745308735867537422, 9445054012034463155196619047924219357554070323, 28552220036278340140043647563606275996337400327, 86312822347159245334638926483949628237246841736, 260922033105182509449144120053201739044792147157<br /><br />


Generating function in Maple syntax:<br />
-(x-1)*(x^3-2*x^2+3*x-1)/(x^5-3*x^4+7*x^3-8*x^2+5*x-1)<br /><br />



Generating function in latex syntax:<br />
-\frac{\left(x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right)}{x^{5}-3 x^{4}+7 x^{3}-8 x^{2}+5 x -1}<br /><br />



Generating function in sympy syntax:<br />
(1 - x)*(x**3 - 2*x**2 + 3*x - 1)/(x**5 - 3*x**4 + 7*x**3 - 8*x**2 + 5*x - 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^5-3*x^4+7*x^3-8*x^2+5*x-1)*F(x)+(x-1)*(x^3-2*x^2+3*x-1) = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{5}-3 x^{4}+7 x^{3}-8 x^{2}+5 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) = 0<br /><br />



Explicit closed form in Maple syntax:<br />
29241/6848689*((((-1+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-1-35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+56/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((-1+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(49/171-214/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(2213/171+14/9*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-310/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1454/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-1-35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(2213/171+14/9*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-6491/171+232/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-91/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+196/9)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+56/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-310/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1454/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-91/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+196/9)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+1021/171-134/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+1)+(((-122/171+35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-122/171+142/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-53/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-122/171+142/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(1061/171+142/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-116/9*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+1061/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+910/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-53/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(1061/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+910/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-680/171-53/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+910/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n+1)+(((-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+293/171+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^4+((179/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-220/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-2467/171-220/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((-1367/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+106/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+6815/171+106/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((764/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+364/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-11642/171+364/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-526/171-959/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-526/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3341/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+1)+(((-1+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-1-35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+56/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-1-35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-142/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+1766/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-1127/171+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+56/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-1127/171+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+53/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-63/19)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+2)+(((-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+293/171+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((179/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-220/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-2467/171-220/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-136/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-149/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+1697/57-149/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(109/57+48/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+109/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1475/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+2)+(((-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+293/171+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-548/57+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-56/171-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1286/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+3)+(((-1409/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+409/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+202/19+409/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(202/19+409/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+202/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-2681/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+1)+(((959/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-85/19)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1724/171-85/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-1724/171-85/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1724/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+6691/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+2)+(((-48/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+391/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+823/171+391/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(823/171+391/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+823/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-3478/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+3)+(((122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-293/171-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-293/171-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-293/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1588/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+4)+(((-293/171-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(548/57-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1286/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3-((293/171+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-548/57+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+1286/171)*(RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-3)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((548/57-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-6218/171+569/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(13576/171-854/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+1679/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-6983/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1286/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-56/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+1286/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(1679/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-6983/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-3472/171+895/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n)+(((-56/171+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(1127/171-1766/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+1127/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+63/19)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((1127/171-1766/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-1135/171-1766/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+4990/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-1135/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1127/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-806/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(1127/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+63/19)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-1135/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1127/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-806/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-1012/171+63/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-806/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n)+(((293/171+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+293/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1588/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^4+((-3*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-293/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+1588/57-293/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((7*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+2051/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-11116/171+2051/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-7*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1790/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+13087/171-1790/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(673/57+143/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+673/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-13358/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n)+(((RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+554/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+383/171+554/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(383/171+554/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+383/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-5711/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n)-2617/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 5)^(-n))*((((RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-22/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-22/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-22/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+31/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+((-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-22/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-22/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+31/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-22/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+31/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+31/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-250/171)<br /><br />



Explicit closed form in latex syntax:<br />
\frac{29241 \left(\left(\left(\left(-1+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-1-\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}+\frac{56}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-1+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{49}{171}-\frac{214 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{2213}{171}+\frac{14 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{9}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{310 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{1454}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-1-\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{2213}{171}+\frac{14 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{9}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{6491}{171}+\frac{232 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{91 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}+\frac{196}{9}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}+\frac{56}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{310 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{1454}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{91 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}+\frac{196}{9}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1021}{171}-\frac{134 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{122}{171}+\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{122}{171}+\frac{142 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{53}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{122}{171}+\frac{142 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{1061}{171}+\frac{142 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{116 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{9}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1061 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{910}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{53}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{1061 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{910}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{680}{171}-\frac{53 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{57}+\frac{910 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{293}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(\frac{179 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{220}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2467}{171}-\frac{220 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{1367 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{106}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{6815}{171}+\frac{106 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{364}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{11642}{171}+\frac{364 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{526}{171}-\frac{959 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{526 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{3341}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-1+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-1-\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}+\frac{56}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-1-\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{142 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}+\frac{1766}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1127}{171}+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}+\frac{56}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{1127}{171}+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{53 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}-\frac{63}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{293}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{179 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{220}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2467}{171}-\frac{220 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{136 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{149}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1697}{57}-\frac{149 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{109}{57}+\frac{48 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{109 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{1475}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{293}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{548}{57}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{56}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{1286}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{1409 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{409}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{202}{19}+\frac{409 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{202}{19}+\frac{409 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{202 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}-\frac{2681}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{959 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{85}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1724}{171}-\frac{85 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{1724}{171}-\frac{85 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1724 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{6691}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{48 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}+\frac{391}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{823}{171}+\frac{391 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{823}{171}+\frac{391 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{823 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{3478}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{293}{171}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{293}{171}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{1588}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\frac{293}{171}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{548}{57}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{1286}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-\left(\left(\frac{293}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{548}{57}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}+\frac{1286}{171}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-3\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{548}{57}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{6218}{171}+\frac{569 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{13576}{171}-\frac{854 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1679 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{6983}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{1286}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}+\frac{1286}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{1679 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{6983}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{3472}{171}+\frac{895 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(-\frac{56}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{1127}{171}-\frac{1766 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{63}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1127}{171}-\frac{1766 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{1135}{171}-\frac{1766 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{4990 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1135 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{1127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{806}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{1127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{63}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{1135 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{1127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{806}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1012}{171}+\frac{63 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{19}-\frac{806 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\frac{293}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{1588}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(-3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{293}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1588}{57}-\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(7 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{2051}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{11116}{171}+\frac{2051 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-7 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{1790}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{13087}{171}-\frac{1790 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{673}{57}+\frac{143 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{673 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{13358}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{554}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{383}{171}+\frac{554 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{383}{171}+\frac{554 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{383 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{5711}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}-\frac{2617 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{171}\right) \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{122}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{22}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{22}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{22 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{31}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{22}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{22 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{31}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{22 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{31}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{31 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{250}{171}\right)}{6848689}<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)-3*a(n+1)+7*a(n+2)-8*a(n+3)+5*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)-3 a \! \left(n +1\right)+7 a \! \left(n +2\right)-8 a \! \left(n +3\right)+5 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/18749/<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[21,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[13,x]<br />
  
    F[10,x] = F[1,x]+F[11,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[10,x]*F[4,x]<br />
  
    F[13,x] = F[14,x]+F[7,x]<br />
  
    F[14,x] = F[15,x]<br />
  
    F[15,x] = F[16,x]*F[4,x]<br />
  
    F[16,x] = F[17,x]+F[20,x]<br />
  
    F[17,x] = F[18,x]+F[4,x]<br />
  
    F[18,x] = F[19,x]<br />
  
    F[19,x] = F[17,x]*F[4,x]<br />
  
    F[20,x] = F[15,x]<br />
  
    F[21,x] = F[2,x]+F[22,x]<br />
  
    F[22,x] = F[23,x]+F[24,x]+F[62,x]<br />
  
    F[23,x] = 0<br />
  
    F[24,x] = F[25,x]*F[4,x]<br />
  
    F[25,x] = F[26,x]+F[29,x]<br />
  
    F[26,x] = F[27,x]+F[4,x]<br />
  
    F[27,x] = F[15,x]+F[23,x]+F[28,x]<br />
  
    F[28,x] = F[4,x]*F[7,x]<br />
  
    F[29,x] = F[30,x]+F[32,x]<br />
  
    F[30,x] = F[23,x]+F[24,x]+F[31,x]<br />
  
    F[31,x] = F[2,x]*F[4,x]<br />
  
    F[32,x] = F[23,x]+F[33,x]+F[34,x]+F[46,x]<br />
  
    F[33,x] = 0<br />
  
    F[34,x] = F[35,x]*F[4,x]<br />
  
    F[35,x] = F[36,x]+F[39,x]<br />
  
    F[36,x] = F[30,x]+F[37,x]<br />
  
    F[37,x] = F[38,x]<br />
  
    F[38,x] = F[36,x]*F[4,x]<br />
  
    F[39,x] = F[40,x]<br />
  
    F[40,x] = F[4,x]*F[41,x]<br />
  
    F[41,x] = F[42,x]+F[45,x]<br />
  
    F[42,x] = F[30,x]+F[43,x]<br />
  
    F[43,x] = F[44,x]<br />
  
    F[44,x] = F[4,x]*F[42,x]<br />
  
    F[45,x] = F[40,x]<br />
  
    F[46,x] = F[4,x]*F[47,x]<br />
  
    F[47,x] = F[48,x]<br />
  
    F[48,x] = F[4,x]*F[49,x]<br />
  
    F[49,x] = F[50,x]+F[53,x]<br />
  
    F[50,x] = F[2,x]+F[51,x]<br />
  
    F[51,x] = F[52,x]<br />
  
    F[52,x] = F[4,x]*F[50,x]<br />
  
    F[53,x] = F[47,x]+F[54,x]<br />
  
    F[54,x] = F[55,x]<br />
  
    F[55,x] = F[4,x]*F[56,x]<br />
  
    F[56,x] = F[57,x]+F[61,x]<br />
  
    F[57,x] = F[58,x]+F[59,x]<br />
  
    F[58,x] = F[31,x]<br />
  
    F[59,x] = F[60,x]<br />
  
    F[60,x] = F[4,x]*F[57,x]<br />
  
    F[61,x] = F[55,x]<br />
  
    F[62,x] = F[4,x]*F[63,x]<br />
  
    F[63,x] = F[64,x]+F[67,x]<br />
  
    F[64,x] = F[2,x]+F[65,x]<br />
  
    F[65,x] = F[23,x]+F[24,x]+F[66,x]<br />
  
    F[66,x] = F[4,x]*F[64,x]<br />
  
    F[67,x] = F[47,x]+F[68,x]<br />
  
    F[68,x] = F[40,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_{21}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)<br />
  
    F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = F_{19}\! \left(x \right)<br />
  
    F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{62}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = 0<br />
  
    F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)<br />
  
    F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)+F_{28}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{32}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{31}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{23}\! \left(x \right)+F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{46}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = 0<br />
  
    F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{38}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{40}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = F_{30}\! \left(x \right)+F_{43}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{44}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{40}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{48}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = F_{2}\! \left(x \right)+F_{51}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{52}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{47}\! \left(x \right)+F_{54}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{55}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = F_{31}\! \left(x \right)<br />
  
    F_{59}\! \left(x \right) = F_{60}\! \left(x \right)<br />
  
    F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)<br />
  
    F_{61}\! \left(x \right) = F_{55}\! \left(x \right)<br />
  
    F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)<br />
  
    F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)<br />
  
    F_{64}\! \left(x \right) = F_{2}\! \left(x \right)+F_{65}\! \left(x \right)<br />
  
    F_{65}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{66}\! \left(x \right)<br />
  
    F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)<br />
  
    F_{67}\! \left(x \right) = F_{47}\! \left(x \right)+F_{68}\! \left(x \right)<br />
  
    F_{68}\! \left(x \right) = F_{40}\! \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_21(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_13(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_10(x)*F_4(x))<br />
  
    Eq(F_13(x), F_14(x) + F_7(x))<br />
  
    Eq(F_14(x), F_15(x))<br />
  
    Eq(F_15(x), F_16(x)*F_4(x))<br />
  
    Eq(F_16(x), F_17(x) + F_20(x))<br />
  
    Eq(F_17(x), F_18(x) + F_4(x))<br />
  
    Eq(F_18(x), F_19(x))<br />
  
    Eq(F_19(x), F_17(x)*F_4(x))<br />
  
    Eq(F_20(x), F_15(x))<br />
  
    Eq(F_21(x), F_2(x) + F_22(x))<br />
  
    Eq(F_22(x), F_23(x) + F_24(x) + F_62(x))<br />
  
    Eq(F_23(x), 0)<br />
  
    Eq(F_24(x), F_25(x)*F_4(x))<br />
  
    Eq(F_25(x), F_26(x) + F_29(x))<br />
  
    Eq(F_26(x), F_27(x) + F_4(x))<br />
  
    Eq(F_27(x), F_15(x) + F_23(x) + F_28(x))<br />
  
    Eq(F_28(x), F_4(x)*F_7(x))<br />
  
    Eq(F_29(x), F_30(x) + F_32(x))<br />
  
    Eq(F_30(x), F_23(x) + F_24(x) + F_31(x))<br />
  
    Eq(F_31(x), F_2(x)*F_4(x))<br />
  
    Eq(F_32(x), F_23(x) + F_33(x) + F_34(x) + F_46(x))<br />
  
    Eq(F_33(x), 0)<br />
  
    Eq(F_34(x), F_35(x)*F_4(x))<br />
  
    Eq(F_35(x), F_36(x) + F_39(x))<br />
  
    Eq(F_36(x), F_30(x) + F_37(x))<br />
  
    Eq(F_37(x), F_38(x))<br />
  
    Eq(F_38(x), F_36(x)*F_4(x))<br />
  
    Eq(F_39(x), F_40(x))<br />
  
    Eq(F_40(x), F_4(x)*F_41(x))<br />
  
    Eq(F_41(x), F_42(x) + F_45(x))<br />
  
    Eq(F_42(x), F_30(x) + F_43(x))<br />
  
    Eq(F_43(x), F_44(x))<br />
  
    Eq(F_44(x), F_4(x)*F_42(x))<br />
  
    Eq(F_45(x), F_40(x))<br />
  
    Eq(F_46(x), F_4(x)*F_47(x))<br />
  
    Eq(F_47(x), F_48(x))<br />
  
    Eq(F_48(x), F_4(x)*F_49(x))<br />
  
    Eq(F_49(x), F_50(x) + F_53(x))<br />
  
    Eq(F_50(x), F_2(x) + F_51(x))<br />
  
    Eq(F_51(x), F_52(x))<br />
  
    Eq(F_52(x), F_4(x)*F_50(x))<br />
  
    Eq(F_53(x), F_47(x) + F_54(x))<br />
  
    Eq(F_54(x), F_55(x))<br />
  
    Eq(F_55(x), F_4(x)*F_56(x))<br />
  
    Eq(F_56(x), F_57(x) + F_61(x))<br />
  
    Eq(F_57(x), F_58(x) + F_59(x))<br />
  
    Eq(F_58(x), F_31(x))<br />
  
    Eq(F_59(x), F_60(x))<br />
  
    Eq(F_60(x), F_4(x)*F_57(x))<br />
  
    Eq(F_61(x), F_55(x))<br />
  
    Eq(F_62(x), F_4(x)*F_63(x))<br />
  
    Eq(F_63(x), F_64(x) + F_67(x))<br />
  
    Eq(F_64(x), F_2(x) + F_65(x))<br />
  
    Eq(F_65(x), F_23(x) + F_24(x) + F_66(x))<br />
  
    Eq(F_66(x), F_4(x)*F_64(x))<br />
  
    Eq(F_67(x), F_47(x) + F_68(x))<br />
  
    Eq(F_68(x), F_40(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, 3, 2], &#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;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#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, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#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, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#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, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}], &#34;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, 2, 1], &#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;: [1, 0, 2, 3], &#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, 0], [0, 1], [0, 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[[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;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;: 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0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 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&#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, 2, 1], &#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;: [1, 0, 2, 3], &#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], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#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;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]]], &#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;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[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, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#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, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, &#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]]], &#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;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [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, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 2], [1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 4], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 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, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 4]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#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, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 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, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#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;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#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, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [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, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#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, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 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0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 4]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1]]], &#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, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], 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[1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 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, 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{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#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, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 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[[1, 0], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;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, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#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;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#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;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, &#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], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#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, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [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, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 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, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1], [1, 4]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, 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