xref: /dports/math/frobby/frobby-0.9.1/test/commonIdeals/t16.alexdual

R = QQ[x1, x2, x3, x4, x5, x6, x7, x8];
I = monomialIdeal(
 x1^94,
 x1^88*x4,
 x1^88*x5^8,
 x1^88*x6,
 x1^87*x3^45*x4,
 x1^87*x3^45*x5^8,
 x1^87*x3^45*x6,
 x1^87*x4^33,
 x1^87*x4*x8,
 x1^87*x5^27,
 x1^87*x5^8*x8,
 x1^87*x6*x8,
 x1^83*x2^77,
 x1^83*x2^67*x4,
 x1^83*x2^60*x4^33,
 x1^83*x2^60*x4*x8,
 x1^83*x4^33*x7^5,
 x1^83*x4*x7^11,
 x1^83*x4*x7^5*x8,
 x1^83*x7^23,
 x1^82*x3^58,
 x1^82*x3^47*x4,
 x1^82*x3^47*x5^8,
 x1^82*x3^47*x6,
 x1^82*x3^45*x4*x7^5,
 x1^82*x3^45*x5^8*x7^5,
 x1^82*x3^45*x6^54,
 x1^82*x3^45*x6*x7^5,
 x1^82*x3^22*x4*x7^11,
 x1^82*x3^22*x4*x7^5*x8,
 x1^82*x4*x5^5*x7^11,
 x1^82*x4*x5^5*x7^5*x8,
 x1^82*x4*x7^5*x8^12,
 x1^82*x5^43,
 x1^82*x5^27*x6^54,
 x1^82*x5^27*x7^5,
 x1^82*x5^8*x7^11,
 x1^82*x5^8*x7^5*x8,
 x1^82*x6^59,
 x1^82*x6^54*x8,
 x1^82*x6*x7^11,
 x1^82*x6*x7^5*x8,
 x1^77*x2^21*x4*x5^5*x7^5*x8,
 x1^77*x2^21*x4*x7^5*x8^12,
 x1^77*x2^21*x5^43,
 x1^77*x2^21*x5^27*x7^5,
 x1^77*x2^21*x5^8*x7^5*x8,
 x1^77*x2^21*x6*x7^5*x8,
 x1^77*x4^2*x5^43,
 x1^77*x4^2*x5^27*x7^5,
 x1^77*x4^2*x5^5*x7^5*x8,
 x1^77*x4^2*x6*x7^5*x8,
 x1^77*x4^2*x7^5*x8^12,
 x1^77*x4*x7^5*x8^17,
 x1^77*x4*x8^20,
 x1^77*x5^43*x8^17,
 x1^77*x5^8*x7^5*x8^17,
 x1^77*x5^8*x8^20,
 x1^77*x6*x7^5*x8^17,
 x1^77*x6*x8^20,
 x1^77*x8^54,
 x1^72*x2^49*x4*x5^5*x7^5*x8,
 x1^72*x2^49*x4*x7^5*x8^12,
 x1^72*x2^49*x4*x8^20,
 x1^72*x2^49*x5^43,
 x1^72*x2^49*x5^27*x7^5,
 x1^72*x2^49*x5^8*x7^5*x8,
 x1^72*x2^49*x5^8*x8^20,
 x1^72*x2^49*x6*x7^5*x8,
 x1^72*x2^49*x6*x8^20,
 x1^72*x2^21*x3^22*x4*x7^11,
 x1^72*x2^21*x3^22*x4*x7^5*x8,
 x1^72*x2^21*x3^10*x4*x5^5*x7^5*x8,
 x1^72*x2^21*x3^10*x4*x7^5*x8^12,
 x1^72*x2^21*x3^10*x5^43,
 x1^72*x2^21*x3^10*x5^27*x7^5,
 x1^72*x2^21*x3^10*x5^8*x7^5*x8,
 x1^72*x2^21*x3^10*x6*x7^5*x8,
 x1^72*x2^21*x4*x5^5*x7^11,
 x1^72*x2^21*x4*x5^5*x7^7*x8,
 x1^72*x2^21*x4*x7^7*x8^12,
 x1^72*x2^21*x5^47,
 x1^72*x2^21*x5^43*x6^43,
 x1^72*x2^21*x5^27*x6^54,
 x1^72*x2^21*x5^27*x6^43*x7^5,
 x1^72*x2^21*x5^27*x7^7,
 x1^72*x2^21*x5^8*x7^11,
 x1^72*x2^21*x5^8*x7^7*x8,
 x1^72*x2^21*x6^59,
 x1^72*x2^21*x6^54*x8,
 x1^72*x2^21*x6^43*x7^5*x8,
 x1^72*x2^21*x6*x7^11,
 x1^72*x2^21*x6*x7^7*x8,
 x1^72*x3^22*x4^33*x7^5,
 x1^72*x3^22*x4^2*x7^11,
 x1^72*x3^22*x4^2*x7^5*x8,
 x1^72*x3^22*x4*x7^17,
 x1^72*x3^22*x7^23,
 x1^72*x3^10*x4^2*x5^43,
 x1^72*x3^10*x4^2*x5^27*x7^5,
 x1^72*x3^10*x4^2*x5^5*x7^5*x8,
 x1^72*x3^10*x4^2*x6*x7^5*x8,
 x1^72*x3^10*x4^2*x7^5*x8^12,
 x1^72*x3^10*x4*x7^5*x8^17,
 x1^72*x3^10*x4*x8^20,
 x1^72*x3^10*x5^43*x8^17,
 x1^72*x3^10*x5^8*x7^5*x8^17,
 x1^72*x3^10*x5^8*x8^20,
 x1^72*x3^10*x6*x7^5*x8^17,
 x1^72*x3^10*x6*x8^20,
 x1^72*x4^33*x5^5*x7^5,
 x1^72*x4^33*x6^54,
 x1^72*x4^33*x6*x7^5,
 x1^72*x4^10*x5^43,
 x1^72*x4^10*x5^27*x7^5,
 x1^72*x4^10*x5^5*x7^5*x8,
 x1^72*x4^10*x6*x7^5*x8,
 x1^72*x4^10*x7^5*x8^12,
 x1^72*x4^10*x8^20,
 x1^72*x4^2*x5^47,
 x1^72*x4^2*x5^43*x6^43,
 x1^72*x4^2*x5^27*x6^54,
 x1^72*x4^2*x5^27*x6^43*x7^5,
 x1^72*x4^2*x5^27*x7^7,
 x1^72*x4^2*x5^5*x7^11,
 x1^72*x4^2*x5^5*x7^7*x8,
 x1^72*x4^2*x6^59,
 x1^72*x4^2*x6^54*x8,
 x1^72*x4^2*x6^43*x7^5*x8,
 x1^72*x4^2*x6*x7^11,
 x1^72*x4^2*x6*x7^7*x8,
 x1^72*x4^2*x7^7*x8^12,
 x1^72*x4*x5^5*x7^17,
 x1^72*x4*x7^17*x8^12,
 x1^72*x4*x7^7*x8^17,
 x1^72*x5^51,
 x1^72*x5^47*x8^17,
 x1^72*x5^43*x6^43*x8^17,
 x1^72*x5^8*x7^17,
 x1^72*x5^8*x7^7*x8^17,
 x1^72*x5^5*x7^23,
 x1^72*x6^54*x8^17,
 x1^72*x6^43*x7^5*x8^17,
 x1^72*x6^43*x8^20,
 x1^72*x6*x7^17,
 x1^72*x6*x7^7*x8^17,
 x1^72*x7^23*x8^12,
 x1^71*x5^61,
 x1^71*x5^5*x7^43,
 x1^71*x6*x7^43,
 x1^59*x2^77*x3^22,
 x1^59*x2^77*x5^5,
 x1^59*x2^77*x8^12,
 x1^59*x2^67*x3^22*x4,
 x1^59*x2^67*x4*x5^5,
 x1^59*x2^67*x5^8,
 x1^59*x2^67*x6,
 x1^59*x2^60*x3^45*x4,
 x1^59*x2^60*x3^45*x5^8,
 x1^59*x2^60*x3^45*x6,
 x1^59*x2^60*x3^22*x4*x8,
 x1^59*x2^60*x4*x5^5*x8,
 x1^59*x2^60*x4*x8^12,
 x1^59*x2^60*x5^8*x8,
 x1^59*x2^60*x6*x8,
 x1^59*x2^59*x3^22*x4*x7^11,
 x1^59*x2^59*x3^22*x4*x7^5*x8,
 x1^59*x2^59*x3^22*x7^23,
 x1^59*x2^59*x4*x5^5*x7^11,
 x1^59*x2^59*x4*x5^5*x7^5*x8,
 x1^59*x2^59*x4*x7^5*x8^12,
 x1^59*x2^59*x5^8*x7^11,
 x1^59*x2^59*x5^8*x7^5*x8,
 x1^59*x2^59*x5^5*x7^23,
 x1^59*x2^59*x6*x7^11,
 x1^59*x2^59*x6*x7^5*x8,
 x1^59*x2^59*x7^23*x8^12,
 x1^59*x2^45*x5^5*x7^43,
 x1^59*x2^45*x6*x7^43,
 x1^59*x2^21*x3^58,
 x1^59*x2^21*x3^47*x4,
 x1^59*x2^21*x3^47*x5^8,
 x1^59*x2^21*x3^47*x6,
 x1^59*x2^21*x3^45*x4*x7^5,
 x1^59*x2^21*x3^45*x5^8*x7^5,
 x1^59*x2^21*x3^45*x6*x7^5,
 x1^59*x2^21*x3^26*x4*x7^11,
 x1^59*x2^21*x3^26*x4*x7^5*x8,
 x1^59*x2^21*x3^26*x5^8*x7^11,
 x1^59*x2^21*x3^26*x5^8*x7^5*x8,
 x1^59*x2^21*x3^26*x6*x7^11,
 x1^59*x2^21*x3^26*x6*x7^5*x8,
 x1^59*x3^58*x7^17,
 x1^59*x3^58*x8^17,
 x1^59*x3^47*x4^2,
 x1^59*x3^47*x4*x8^17,
 x1^59*x3^47*x5^8*x8^17,
 x1^59*x3^47*x6*x8^17,
 x1^59*x3^45*x4^2*x7^5,
 x1^59*x3^26*x4^2*x7^11,
 x1^59*x3^26*x4^2*x7^5*x8,
 x1^59*x3^26*x4*x7^17,
 x1^59*x3^26*x4*x7^5*x8^17,
 x1^59*x3^26*x5^8*x7^17,
 x1^59*x3^26*x5^8*x7^5*x8^17,
 x1^59*x3^26*x6*x7^17,
 x1^59*x3^26*x6*x7^5*x8^17,
 x1^59*x3^26*x7^23,
 x1^59*x3^22*x7^43,
 x1^59*x3*x5^5*x7^43,
 x1^59*x3*x6*x7^43,
 x1^59*x5^5*x7^43*x8^11,
 x1^59*x6*x7^43*x8^11,
 x1^59*x7^43*x8^12,
 x1^56*x2^49*x4*x8^29,
 x1^56*x2^49*x5^8*x8^29,
 x1^56*x2^49*x6*x8^29,
 x1^56*x3^10*x4*x8^29,
 x1^56*x3^10*x5^8*x8^29,
 x1^56*x3^10*x6*x8^29,
 x1^56*x4^49,
 x1^56*x4^43*x5^5*x7^5,
 x1^56*x4^43*x6*x7^5,
 x1^56*x4^43*x7^5*x8^12,
 x1^56*x4^43*x8^20,
 x1^56*x4^10*x8^29,
 x1^56*x4*x7^7*x8^29,
 x1^56*x5^8*x7^7*x8^29,
 x1^56*x6^43*x8^29,
 x1^56*x6*x7^7*x8^29,
 x1^53*x2^21*x3^26*x5^43,
 x1^53*x2^21*x3^26*x5^27*x6^54,
 x1^53*x2^21*x3^26*x5^27*x7^5,
 x1^53*x2^21*x3^26*x5^21*x7^11,
 x1^53*x2^21*x3^26*x5^21*x7^5*x8,
 x1^53*x2^21*x3^26*x6^54*x8,
 x1^53*x2^21*x3^26*x6^41*x7^11,
 x1^53*x2^21*x3^26*x6^41*x7^5*x8,
 x1^53*x3^26*x4^4*x7^11,
 x1^53*x3^26*x4^4*x7^5*x8,
 x1^53*x3^26*x4^2*x5^43,
 x1^53*x3^26*x4^2*x5^27*x6^54,
 x1^53*x3^26*x4^2*x5^27*x7^5,
 x1^53*x3^26*x4^2*x5^21*x7^11,
 x1^53*x3^26*x4^2*x5^21*x7^5*x8,
 x1^53*x3^26*x4^2*x6^54*x8,
 x1^53*x3^26*x4^2*x6^41*x7^11,
 x1^53*x3^26*x4^2*x6^41*x7^5*x8,
 x1^53*x3^26*x4*x7^5*x8^18,
 x1^53*x3^26*x4*x8^20,
 x1^53*x3^26*x5^43*x8^17,
 x1^53*x3^26*x5^21*x7^17,
 x1^53*x3^26*x5^21*x7^5*x8^17,
 x1^53*x3^26*x5^8*x7^5*x8^18,
 x1^53*x3^26*x5^8*x8^20,
 x1^53*x3^26*x6^54*x8^17,
 x1^53*x3^26*x6^41*x7^17,
 x1^53*x3^26*x6^41*x7^5*x8^17,
 x1^53*x3^26*x6*x7^5*x8^18,
 x1^53*x3^26*x6*x8^20,
 x1^53*x3^26*x7^23*x8^18,
 x1^53*x3^22*x4^4*x7^43,
 x1^53*x3^22*x7^45,
 x1^53*x3^14*x4*x8^29,
 x1^53*x3^14*x5^8*x8^29,
 x1^53*x3^14*x6*x8^29,
 x1^53*x3^10*x4*x8^32,
 x1^53*x3^10*x5^13*x8^29,
 x1^53*x3^10*x5^8*x8^32,
 x1^53*x3^10*x6*x8^32,
 x1^53*x3*x4^4*x5^5*x7^43,
 x1^53*x3*x4^4*x6*x7^43,
 x1^53*x3*x5^21*x7^43,
 x1^53*x3*x5^5*x7^45,
 x1^53*x3*x6*x7^45,
 x1^53*x4^10*x5^13*x8^29,
 x1^53*x4^10*x8^32,
 x1^53*x4^4*x5^5*x7^43*x8^11,
 x1^53*x4^4*x6*x7^43*x8^11,
 x1^53*x4^4*x7^43*x8^12,
 x1^53*x4*x7^18*x8^29,
 x1^53*x4*x7^7*x8^32,
 x1^53*x5^47*x8^29,
 x1^53*x5^21*x7^43*x8^11,
 x1^53*x5^13*x6^43*x8^29,
 x1^53*x5^13*x7^7*x8^29,
 x1^53*x5^8*x7^18*x8^29,
 x1^53*x5^8*x7^7*x8^32,
 x1^53*x5^5*x7^45*x8^11,
 x1^53*x6^46*x8^29,
 x1^53*x6^43*x8^32,
 x1^53*x6^41*x7^43,
 x1^53*x6*x7^45*x8^11,
 x1^53*x6*x7^18*x8^29,
 x1^53*x6*x7^7*x8^32,
 x1^53*x7^45*x8^12,
 x1^53*x7^43*x8^18,
 x1^53*x7^23*x8^29,
 x1^32*x2^22*x3^26*x4^4*x7^11,
 x1^32*x2^22*x3^26*x4^4*x7^5*x8,
 x1^32*x2^22*x3^26*x6^54*x8,
 x1^32*x2^22*x3^26*x6^41*x7^11,
 x1^32*x2^22*x3^26*x6^41*x7^5*x8,
 x1^32*x2^22*x3^22*x4^4*x7^43,
 x1^32*x2^22*x3^22*x7^45,
 x1^32*x2^22*x3*x4^4*x5^5*x7^43,
 x1^32*x2^22*x3*x4^4*x6*x7^43,
 x1^32*x2^22*x3*x5^5*x7^45,
 x1^32*x2^22*x3*x6*x7^45,
 x1^32*x2^22*x6^41*x7^43,
 x1^32*x2^21*x3^27*x6^54*x8,
 x1^32*x2^21*x3^27*x6^41*x7^11,
 x1^32*x2^21*x3^27*x6^41*x7^5*x8,
 x1^32*x2^21*x3^26*x6^59,
 x1^32*x2^21*x3^26*x6^56*x7^11,
 x1^32*x2^21*x3^26*x6^56*x8,
 x1^32*x2^21*x6^64,
 x1^32*x3^27*x4^4*x7^11,
 x1^32*x3^27*x4^4*x7^5*x8,
 x1^32*x3^27*x4^2*x6^54*x8,
 x1^32*x3^27*x4^2*x6^41*x7^11,
 x1^32*x3^27*x4^2*x6^41*x7^5*x8,
 x1^32*x3^27*x6^41*x7^17,
 x1^32*x3^27*x7^45,
 x1^32*x3^26*x4^33*x6^54,
 x1^32*x3^26*x4^33*x7^5,
 x1^32*x3^26*x4^26*x6^54*x8,
 x1^32*x3^26*x4^26*x7^11,
 x1^32*x3^26*x4^26*x7^5*x8,
 x1^32*x3^26*x4^2*x6^59,
 x1^32*x3^26*x4^2*x6^56*x7^11,
 x1^32*x3^26*x4^2*x6^56*x8,
 x1^32*x3^26*x6^56*x7^17,
 x1^32*x3^22*x4^43*x7^5,
 x1^32*x3^22*x4^26*x7^43,
 x1^32*x3^22*x7^62,
 x1^32*x3^14*x4^49,
 x1^32*x3^14*x4^43*x5^5*x7^5,
 x1^32*x3^14*x4^43*x6*x7^5,
 x1^32*x3*x4^26*x5^5*x7^43,
 x1^32*x3*x4^26*x6*x7^43,
 x1^32*x3*x5^5*x7^62,
 x1^32*x3*x6*x7^62,
 x1^32*x4^49*x5^13,
 x1^32*x4^49*x6^46,
 x1^32*x4^49*x7^18,
 x1^32*x4^43*x5^13*x7^5,
 x1^32*x4^43*x5^5*x7^18,
 x1^32*x4^43*x6^54,
 x1^32*x4^43*x6^46*x7^5,
 x1^32*x4^43*x6*x7^18,
 x1^32*x4^30*x5^5*x7^43,
 x1^32*x4^30*x6*x7^43,
 x1^32*x4^26*x6^41*x7^43,
 x1^32*x4^2*x6^64,
 x1^32*x6^64*x7^17,
 x1^32*x6^56*x7^43,
 x1^32*x6^41*x7^62,
 x1^26*x3^47*x4^4,
 x1^26*x3^47*x4^2*x6^41,
 x1^26*x3^47*x4*x8^18,
 x1^26*x3^47*x6^41*x8^17,
 x1^26*x3^47*x6*x8^18,
 x1^26*x3^45*x4^2*x6^54,
 x1^26*x3^28*x4^2*x6^59,
 x1^26*x3^28*x4^2*x6^54*x8,
 x1^26*x3^27*x4^2*x6^54*x8^10,
 x1^26*x3^27*x4*x8^20,
 x1^26*x3^27*x6^54*x8^17,
 x1^26*x3^27*x6*x8^20,
 x1^26*x3^26*x4^2*x6^56*x8^10,
 x1^26*x3^26*x6^56*x8^17,
 x1^26*x4^2*x6^79,
 x1^26*x4^2*x6^64*x8^10,
 x1^26*x6^64*x8^17,
 x1^26*x6^56*x8^29,
 x1^19*x4^10*x8^35,
 x1^19*x4*x7^7*x8^35,
 x1^19*x6*x7^7*x8^35,
 x1^19*x7^23*x8^35,
 x1^6*x3^28*x4^33*x7^5,
 x1^6*x3^28*x4^4*x7^11,
 x1^6*x3^28*x4^4*x7^5*x8,
 x1^6*x3^28*x4^2*x6^41*x7^11,
 x1^6*x3^28*x4^2*x6^41*x7^5*x8,
 x1^6*x3^28*x6^41*x7^17,
 x1^6*x3^28*x7^45,
 x1^6*x3^27*x4^14*x8^20,
 x1^6*x3^27*x4^4*x7^5*x8^10,
 x1^6*x3^27*x4^2*x6^41*x7^5*x8^10,
 x1^6*x3^27*x4*x5*x8^20,
 x1^6*x3^27*x4*x7^5*x8^18,
 x1^6*x3^27*x4*x7*x8^20,
 x1^6*x3^27*x4*x8^31,
 x1^6*x3^27*x5^8*x7^5*x8^18,
 x1^6*x3^27*x5^8*x8^20,
 x1^6*x3^27*x5*x6*x8^20,
 x1^6*x3^27*x6^41*x7^17*x8^10,
 x1^6*x3^27*x6^41*x7^5*x8^17,
 x1^6*x3^27*x6*x7^5*x8^18,
 x1^6*x3^27*x6*x7*x8^20,
 x1^6*x3^27*x6*x8^31,
 x1^6*x3^27*x7^45*x8^10,
 x1^6*x3^27*x7^23*x8^18,
 x1^6*x3^26*x4^26*x7^5*x8^10,
 x1^6*x3^26*x4^26*x8^20,
 x1^6*x3^22*x4^26*x7^43*x8^10,
 x1^6*x3^22*x7^93,
 x1^6*x3^22*x7^62*x8^10,
 x1^6*x3^14*x4^26*x8^29,
 x1^6*x3^10*x4*x8^35,
 x1^6*x3^10*x5^8*x8^35,
 x1^6*x3^10*x6*x8^35,
 x1^6*x3^10*x8^54,
 x1^6*x3^5*x4^10*x8^35,
 x1^6*x3^5*x4*x7^7*x8^35,
 x1^6*x3^5*x6*x7^7*x8^35,
 x1^6*x3^5*x7^23*x8^35,
 x1^6*x3*x4^26*x5^5*x7^43*x8^10,
 x1^6*x3*x4^26*x6*x7^43*x8^10,
 x1^6*x3*x5^5*x7^62*x8^10,
 x1^6*x3*x6*x7^62*x8^10,
 x1^6*x4^30*x5^5*x7^43*x8^10,
 x1^6*x4^30*x6*x7^43*x8^10,
 x1^6*x4^26*x5^13*x8^29,
 x1^6*x4^26*x5^5*x7^43*x8^11,
 x1^6*x4^26*x6^41*x7^43*x8^10,
 x1^6*x4^26*x6*x7^43*x8^11,
 x1^6*x4^26*x7^43*x8^12,
 x1^6*x4^26*x7^18*x8^29,
 x1^6*x4^26*x8^32,
 x1^6*x4^11*x8^35,
 x1^6*x4^10*x5^4*x8^35,
 x1^6*x4^10*x6^14*x8^35,
 x1^6*x4^10*x8^38,
 x1^6*x4*x5^4*x7^7*x8^35,
 x1^6*x4*x7^7*x8^38,
 x1^6*x5^8*x7^7*x8^35,
 x1^6*x5^5*x7^93,
 x1^6*x5^5*x7^62*x8^11,
 x1^6*x5^4*x6*x7^7*x8^35,
 x1^6*x5^4*x7^23*x8^35,
 x1^6*x6^43*x8^35,
 x1^6*x6^41*x7^62*x8^10,
 x1^6*x6^14*x7^7*x8^35,
 x1^6*x6*x7^93,
 x1^6*x6*x7^62*x8^11,
 x1^6*x6*x7^7*x8^38,
 x1^6*x7^98,
 x1^6*x7^62*x8^12,
 x1^6*x7^37*x8^35,
 x1^6*x7^23*x8^38,
 x1^6*x7^7*x8^54,
 x1^6*x8^55,
 x1*x2^21*x3^59,
 x1*x2^21*x3^47*x5^21,
 x1*x2^21*x3^47*x6^41,
 x1*x2^21*x3^45*x5^21*x7^5,
 x1*x2^21*x3^45*x6^54,
 x1*x2^21*x3^45*x6^41*x7^5,
 x1*x2^21*x3^28*x6^59,
 x1*x2^21*x3^28*x6^54*x8,
 x1*x2^21*x3^28*x6^41*x7^11,
 x1*x2^21*x3^28*x6^41*x7^5*x8,
 x1*x2^21*x3^27*x5^21*x7^11,
 x1*x2^21*x3^27*x5^21*x7^5*x8,
 x1*x2^21*x3^27*x5^17*x6^54*x8,
 x1*x2^21*x3^27*x5^17*x6^41*x7^11,
 x1*x2^21*x3^27*x5^17*x6^41*x7^5*x8,
 x1*x2^21*x3^27*x6^54*x8^10,
 x1*x2^21*x3^27*x6^41*x7^5*x8^10,
 x1*x2^21*x3^26*x5^17*x6^59,
 x1*x2^21*x3^26*x5^17*x6^56*x7^11,
 x1*x2^21*x3^26*x5^17*x6^56*x8,
 x1*x2^21*x3^26*x6^56*x8^10,
 x1*x2^21*x5^17*x6^64,
 x1*x2^21*x6^79,
 x1*x2^21*x6^64*x8^10,
 x1*x2^12*x4^10*x8^35,
 x1*x2^12*x4*x7^7*x8^35,
 x1*x2^12*x6*x7^7*x8^35,
 x1*x2^12*x7^23*x8^35,
 x1*x2^11*x3^47*x4^4,
 x1*x2^11*x3^47*x4^2*x6^41,
 x1*x2^11*x3^47*x4*x8^18,
 x1*x2^11*x3^47*x6^41*x8^17,
 x1*x2^11*x3^47*x6*x8^18,
 x1*x2^11*x3^45*x4^2*x6^54,
 x1*x2^11*x3^28*x4^2*x6^59,
 x1*x2^11*x3^28*x4^2*x6^54*x8,
 x1*x2^11*x3^27*x4^2*x6^54*x8^10,
 x1*x2^11*x3^27*x4*x8^20,
 x1*x2^11*x3^27*x6^54*x8^17,
 x1*x2^11*x3^27*x6*x8^20,
 x1*x2^11*x3^26*x4^2*x6^56*x8^10,
 x1*x2^11*x3^26*x6^56*x8^17,
 x1*x2^11*x4^2*x6^79,
 x1*x2^11*x4^2*x6^64*x8^10,
 x1*x2^11*x6^64*x8^17,
 x1*x2^11*x6^56*x8^29,
 x1*x2*x3^28*x4^4*x7^11,
 x1*x2*x3^28*x4^4*x7^5*x8,
 x1*x2*x3^28*x4^2*x6^41*x7^11,
 x1*x2*x3^28*x4^2*x6^41*x7^5*x8,
 x1*x2*x3^28*x6^41*x7^17,
 x1*x2*x3^28*x7^45,
 x1*x2*x3^27*x4^14*x8^20,
 x1*x2*x3^27*x4^4*x7^5*x8^10,
 x1*x2*x3^27*x4^2*x6^41*x7^5*x8^10,
 x1*x2*x3^27*x4*x5*x8^20,
 x1*x2*x3^27*x4*x7^5*x8^18,
 x1*x2*x3^27*x4*x7*x8^20,
 x1*x2*x3^27*x4*x8^31,
 x1*x2*x3^27*x5^8*x7^5*x8^18,
 x1*x2*x3^27*x5^8*x8^20,
 x1*x2*x3^27*x5*x6*x8^20,
 x1*x2*x3^27*x6^41*x7^17*x8^10,
 x1*x2*x3^27*x6^41*x7^5*x8^17,
 x1*x2*x3^27*x6*x7^5*x8^18,
 x1*x2*x3^27*x6*x7*x8^20,
 x1*x2*x3^27*x6*x8^31,
 x1*x2*x3^27*x7^45*x8^10,
 x1*x2*x3^27*x7^23*x8^18,
 x1*x2*x3^22*x7^62*x8^10,
 x1*x2*x3^10*x4*x8^35,
 x1*x2*x3^10*x5^8*x8^35,
 x1*x2*x3^10*x6*x8^35,
 x1*x2*x3^5*x4^10*x8^35,
 x1*x2*x3^5*x4*x7^7*x8^35,
 x1*x2*x3^5*x6*x7^7*x8^35,
 x1*x2*x3^5*x7^23*x8^35,
 x1*x2*x3*x5^5*x7^62*x8^10,
 x1*x2*x3*x6*x7^62*x8^10,
 x1*x2*x4^11*x8^35,
 x1*x2*x4^10*x5^4*x8^35,
 x1*x2*x4^10*x6^14*x8^35,
 x1*x2*x4^10*x8^38,
 x1*x2*x4*x5^4*x7^7*x8^35,
 x1*x2*x4*x7^7*x8^38,
 x1*x2*x5^8*x7^7*x8^35,
 x1*x2*x5^5*x7^62*x8^11,
 x1*x2*x5^4*x6*x7^7*x8^35,
 x1*x2*x5^4*x7^23*x8^35,
 x1*x2*x6^43*x8^35,
 x1*x2*x6^41*x7^62*x8^10,
 x1*x2*x6^14*x7^7*x8^35,
 x1*x2*x6*x7^62*x8^11,
 x1*x2*x6*x7^7*x8^38,
 x1*x2*x7^62*x8^12,
 x1*x2*x7^37*x8^35,
 x1*x2*x7^23*x8^38,
 x1*x3^59*x4^2,
 x1*x3^59*x7^17,
 x1*x3^59*x8^17,
 x1*x3^58*x4^4,
 x1*x3^58*x4^2*x6^41,
 x1*x3^58*x6^41*x8^17,
 x1*x3^58*x8^18,
 x1*x3^47*x4^14,
 x1*x3^47*x4^4*x5,
 x1*x3^47*x4^4*x7,
 x1*x3^47*x4^2*x5^21,
 x1*x3^47*x4^2*x5*x6^41,
 x1*x3^47*x4^2*x6^41*x7,
 x1*x3^47*x4*x5*x8^18,
 x1*x3^47*x4*x7*x8^18,
 x1*x3^47*x5^21*x8^17,
 x1*x3^47*x5^8*x8^18,
 x1*x3^47*x5*x6^41*x8^17,
 x1*x3^47*x5*x6*x8^18,
 x1*x3^47*x6^41*x7*x8^17,
 x1*x3^47*x6*x7*x8^18,
 x1*x3^45*x4^14*x6^54,
 x1*x3^45*x4^4*x7^5,
 x1*x3^45*x4^2*x5^21*x7^5,
 x1*x3^45*x4^2*x5*x6^54,
 x1*x3^45*x4^2*x6^54*x7,
 x1*x3^45*x4^2*x6^41*x7^5,
 x1*x3^44*x4^14*x8^20,
 x1*x3^44*x4^4*x7^11,
 x1*x3^44*x4^4*x7^5*x8,
 x1*x3^44*x4^2*x6^41*x7^11,
 x1*x3^44*x4^2*x6^41*x7^5*x8,
 x1*x3^44*x4*x5*x8^20,
 x1*x3^44*x4*x7^5*x8^18,
 x1*x3^44*x4*x7*x8^20,
 x1*x3^44*x4*x8^31,
 x1*x3^44*x5^8*x7^5*x8^18,
 x1*x3^44*x5^8*x8^20,
 x1*x3^44*x5*x6*x8^20,
 x1*x3^44*x6^41*x7^17,
 x1*x3^44*x6^41*x7^5*x8^17,
 x1*x3^44*x6*x7^5*x8^18,
 x1*x3^44*x6*x7*x8^20,
 x1*x3^44*x6*x8^31,
 x1*x3^44*x7^45,
 x1*x3^44*x7^23*x8^18,
 x1*x3^28*x4^14*x6^59,
 x1*x3^28*x4^14*x6^54*x8,
 x1*x3^28*x4^2*x5*x6^59,
 x1*x3^28*x4^2*x5*x6^54*x8,
 x1*x3^28*x4^2*x6^59*x7,
 x1*x3^28*x4^2*x6^54*x7*x8,
 x1*x3^28*x4^2*x6^46*x7^11,
 x1*x3^28*x4^2*x6^46*x7^5*x8,
 x1*x3^28*x6^46*x7^17,
 x1*x3^27*x4^14*x6^54*x8^10,
 x1*x3^27*x4^14*x6^46*x8^20,
 x1*x3^27*x4^4*x5^17*x7^11,
 x1*x3^27*x4^4*x5^17*x7^5*x8,
 x1*x3^27*x4^2*x5^21*x7^11,
 x1*x3^27*x4^2*x5^21*x7^5*x8,
 x1*x3^27*x4^2*x5^17*x6^54*x8,
 x1*x3^27*x4^2*x5^17*x6^41*x7^11,
 x1*x3^27*x4^2*x5^17*x6^41*x7^5*x8,
 x1*x3^27*x4^2*x5*x6^54*x8^10,
 x1*x3^27*x4^2*x6^54*x7*x8^10,
 x1*x3^27*x4^2*x6^46*x7^5*x8^10,
 x1*x3^27*x5^21*x7^17,
 x1*x3^27*x5^21*x7^5*x8^17,
 x1*x3^27*x5^17*x6^41*x7^17,
 x1*x3^27*x5^17*x6^41*x7^5*x8^17,
 x1*x3^27*x5^17*x7^45,
 x1*x3^27*x5^17*x7^5*x8^18,
 x1*x3^27*x5^17*x8^20,
 x1*x3^27*x5*x6^54*x8^17,
 x1*x3^27*x5*x6^46*x8^20,
 x1*x3^27*x6^54*x7*x8^17,
 x1*x3^27*x6^46*x7^17*x8^10,
 x1*x3^27*x6^46*x7^5*x8^17,
 x1*x3^27*x6^46*x7*x8^20,
 x1*x3^27*x6^46*x8^31,
 x1*x3^26*x4^14*x6^56*x8^10,
 x1*x3^26*x4^2*x5^17*x6^59,
 x1*x3^26*x4^2*x5^17*x6^56*x7^11,
 x1*x3^26*x4^2*x5^17*x6^56*x8,
 x1*x3^26*x4^2*x5*x6^56*x8^10,
 x1*x3^26*x4^2*x6^56*x7*x8^10,
 x1*x3^26*x5^17*x6^56*x7^17,
 x1*x3^26*x5*x6^56*x8^17,
 x1*x3^26*x6^56*x7^17*x8^10,
 x1*x3^26*x6^56*x7*x8^17,
 x1*x3^10*x5^17*x8^35,
 x1*x3*x5^17*x7^62,
 x1*x4^14*x6^79,
 x1*x4^14*x6^64*x8^10,
 x1*x4^14*x6^56*x8^29,
 x1*x4^10*x5^17*x8^35,
 x1*x4^2*x5^17*x6^64,
 x1*x4^2*x5*x6^79,
 x1*x4^2*x5*x6^64*x8^10,
 x1*x4^2*x6^79*x7,
 x1*x4^2*x6^64*x7*x8^10,
 x1*x5^17*x6^64*x7^17,
 x1*x5^17*x6^56*x7^43,
 x1*x5^17*x6^43*x8^35,
 x1*x5^17*x6^41*x7^62,
 x1*x5^17*x7^62*x8^11,
 x1*x5^17*x7^7*x8^35,
 x1*x5*x6^64*x8^17,
 x1*x5*x6^56*x8^29,
 x1*x6^79*x7^17,
 x1*x6^64*x7^17*x8^10,
 x1*x6^64*x7*x8^17,
 x1*x6^56*x7^43*x8^10,
 x1*x6^56*x7*x8^29,
 x1*x6^56*x8^31,
 x1*x6^46*x7^62*x8^10,
 x1*x6^46*x8^35,
 x2^78*x3^22,
 x2^78*x5^5,
 x2^78*x6,
 x2^78*x8^12,
 x2^77*x8^18,
 x2^67*x3^22*x4^4,
 x2^67*x4^4*x5^5,
 x2^67*x4^4*x6,
 x2^67*x5^21,
 x2^67*x6^41,
 x2^60*x3^45*x4^4,
 x2^60*x3^45*x5^21,
 x2^60*x3^45*x6^41,
 x2^60*x3^22*x4^33,
 x2^60*x3^22*x4^4*x8,
 x2^60*x4^33*x5^5,
 x2^60*x4^33*x6,
 x2^60*x4^4*x5^5*x8,
 x2^60*x4^4*x6*x8,
 x2^60*x4^4*x8^12,
 x2^60*x4*x8^18,
 x2^60*x5^27,
 x2^60*x5^21*x8,
 x2^60*x5^8*x8^18,
 x2^60*x6^41*x8,
 x2^60*x6*x8^18,
 x2^59*x3^22*x4^33*x7^5,
 x2^59*x3^22*x4^4*x7^11,
 x2^59*x3^22*x4^4*x7^5*x8,
 x2^59*x4^33*x5^5*x7^5,
 x2^59*x4^33*x6^54,
 x2^59*x4^33*x6*x7^5,
 x2^59*x4^4*x5^5*x7^11,
 x2^59*x4^4*x5^5*x7^5*x8,
 x2^59*x4^4*x6*x7^11,
 x2^59*x4^4*x6*x7^5*x8,
 x2^59*x4^4*x7^5*x8^12,
 x2^59*x4*x7^5*x8^18,
 x2^59*x4*x8^20,
 x2^59*x5^43,
 x2^59*x5^27*x6^54,
 x2^59*x5^27*x7^5,
 x2^59*x5^21*x7^11,
 x2^59*x5^21*x7^5*x8,
 x2^59*x5^8*x7^5*x8^18,
 x2^59*x5^8*x8^20,
 x2^59*x6^59,
 x2^59*x6^54*x8,
 x2^59*x6^41*x7^11,
 x2^59*x6^41*x7^5*x8,
 x2^59*x6*x7^5*x8^18,
 x2^59*x6*x8^20,
 x2^59*x7^23*x8^18,
 x2^56*x4^49,
 x2^56*x4^43*x5^5*x7^5,
 x2^56*x4^43*x6*x7^5,
 x2^56*x4^43*x7^5*x8^12,
 x2^56*x4^43*x8^20,
 x2^56*x4*x8^29,
 x2^56*x5^8*x8^29,
 x2^56*x6*x8^29,
 x2^49*x4*x8^32,
 x2^49*x5^13*x8^29,
 x2^49*x5^8*x8^32,
 x2^49*x6*x8^32,
 x2^49*x8^54,
 x2^45*x4^4*x5^5*x7^43,
 x2^45*x4^4*x6*x7^43,
 x2^45*x5^61,
 x2^45*x5^21*x7^43,
 x2^45*x5^5*x7^45,
 x2^45*x6*x7^45,
 x2^40*x3^26*x4^33*x6^54,
 x2^40*x3^26*x4^33*x7^5,
 x2^40*x3^26*x4^4*x7^11,
 x2^40*x3^26*x4^4*x7^5*x8,
 x2^40*x3^26*x6^59,
 x2^40*x3^26*x6^54*x8,
 x2^40*x3^26*x6^41*x7^11,
 x2^40*x3^26*x6^41*x7^5*x8,
 x2^40*x3^22*x4^43*x7^5,
 x2^40*x3^22*x4^4*x7^43,
 x2^40*x3^22*x7^45,
 x2^40*x3^14*x4^49,
 x2^40*x3^14*x4^43*x5^5*x7^5,
 x2^40*x3^14*x4^43*x6*x7^5,
 x2^40*x3*x4^4*x5^5*x7^43,
 x2^40*x3*x4^4*x6*x7^43,
 x2^40*x3*x5^5*x7^45,
 x2^40*x3*x6*x7^45,
 x2^40*x4^49*x5^13,
 x2^40*x4^49*x6^46,
 x2^40*x4^49*x7^18,
 x2^40*x4^43*x5^13*x7^5,
 x2^40*x4^43*x5^5*x7^18,
 x2^40*x4^43*x6^54,
 x2^40*x4^43*x6^46*x7^5,
 x2^40*x4^43*x6*x7^18,
 x2^40*x4^30*x5^5*x7^43,
 x2^40*x4^30*x6*x7^43,
 x2^40*x6^64,
 x2^40*x6^41*x7^43,
 x2^22*x3^59,
 x2^22*x3^58*x8^18,
 x2^22*x3^47*x4^4,
 x2^22*x3^47*x4*x8^18,
 x2^22*x3^47*x5^21,
 x2^22*x3^47*x5^8*x8^18,
 x2^22*x3^47*x6^41,
 x2^22*x3^47*x6*x8^18,
 x2^22*x3^45*x4^4*x7^5,
 x2^22*x3^45*x5^21*x7^5,
 x2^22*x3^45*x6^54,
 x2^22*x3^45*x6^41*x7^5,
 x2^22*x3^28*x4^4*x7^11,
 x2^22*x3^28*x4^4*x7^5*x8,
 x2^22*x3^28*x6^59,
 x2^22*x3^28*x6^54*x8,
 x2^22*x3^28*x6^41*x7^11,
 x2^22*x3^28*x6^41*x7^5*x8,
 x2^22*x3^28*x7^45,
 x2^22*x3^26*x4^4*x5^17*x7^11,
 x2^22*x3^26*x4^4*x5^17*x7^5*x8,
 x2^22*x3^26*x4^4*x7^5*x8^10,
 x2^22*x3^26*x4*x7^5*x8^18,
 x2^22*x3^26*x4*x8^20,
 x2^22*x3^26*x5^43,
 x2^22*x3^26*x5^27*x6^54,
 x2^22*x3^26*x5^27*x7^5,
 x2^22*x3^26*x5^21*x7^11,
 x2^22*x3^26*x5^21*x7^5*x8,
 x2^22*x3^26*x5^17*x6^59,
 x2^22*x3^26*x5^17*x6^54*x8,
 x2^22*x3^26*x5^17*x6^41*x7^11,
 x2^22*x3^26*x5^17*x6^41*x7^5*x8,
 x2^22*x3^26*x5^8*x7^5*x8^18,
 x2^22*x3^26*x5^8*x8^20,
 x2^22*x3^26*x6^54*x8^10,
 x2^22*x3^26*x6^41*x7^5*x8^10,
 x2^22*x3^26*x6*x7^5*x8^18,
 x2^22*x3^26*x6*x8^20,
 x2^22*x3^26*x7^23*x8^18,
 x2^22*x3^22*x4^4*x7^43*x8^10,
 x2^22*x3^22*x7^45*x8^10,
 x2^22*x3^14*x4*x8^29,
 x2^22*x3^14*x5^8*x8^29,
 x2^22*x3^14*x6*x8^29,
 x2^22*x3^10*x4*x8^32,
 x2^22*x3^10*x5^13*x8^29,
 x2^22*x3^10*x5^8*x8^32,
 x2^22*x3^10*x6*x8^32,
 x2^22*x3*x4^4*x5^17*x7^43,
 x2^22*x3*x4^4*x5^5*x7^43*x8^10,
 x2^22*x3*x4^4*x6*x7^43*x8^10,
 x2^22*x3*x5^21*x7^43,
 x2^22*x3*x5^17*x7^45,
 x2^22*x3*x5^5*x7^45*x8^10,
 x2^22*x3*x6*x7^45*x8^10,
 x2^22*x4^10*x5^13*x8^29,
 x2^22*x4^10*x8^32,
 x2^22*x4^4*x5^5*x7^43*x8^11,
 x2^22*x4^4*x6*x7^43*x8^11,
 x2^22*x4^4*x7^43*x8^12,
 x2^22*x4*x7^18*x8^29,
 x2^22*x4*x7^7*x8^32,
 x2^22*x5^47*x8^29,
 x2^22*x5^21*x7^43*x8^11,
 x2^22*x5^17*x6^64,
 x2^22*x5^17*x6^41*x7^43,
 x2^22*x5^13*x6^43*x8^29,
 x2^22*x5^13*x7^7*x8^29,
 x2^22*x5^8*x7^18*x8^29,
 x2^22*x5^8*x7^7*x8^32,
 x2^22*x5^5*x7^45*x8^11,
 x2^22*x6^79,
 x2^22*x6^64*x8^10,
 x2^22*x6^46*x8^29,
 x2^22*x6^43*x8^32,
 x2^22*x6^41*x7^43*x8^10,
 x2^22*x6*x7^45*x8^11,
 x2^22*x6*x7^18*x8^29,
 x2^22*x6*x7^7*x8^32,
 x2^22*x7^45*x8^12,
 x2^22*x7^43*x8^18,
 x2^22*x7^23*x8^29,
 x2^21*x3^66,
 x2^21*x3^47*x5^27,
 x2^21*x3^27*x5^43,
 x2^21*x3^27*x5^27*x6^54,
 x2^21*x3^27*x5^27*x7^5,
 x2^21*x3^26*x5^50,
 x2^21*x3^26*x5^27*x6^56,
 x2^21*x5^27*x6^64,
 x2^21*x6^88,
 x2^11*x4^2*x6^88,
 x2^11*x6^88*x8^17,
 x2*x3^28*x4^33*x7^5,
 x2*x3^28*x4^23*x7^11,
 x2*x3^28*x4^23*x7^5*x8,
 x2*x3^28*x7^82,
 x2*x3^27*x4^23*x7^5*x8^10,
 x2*x3^27*x4^23*x8^20,
 x2*x3^26*x4^26*x7^5*x8^10,
 x2*x3^26*x4^26*x8^20,
 x2*x3^22*x4^26*x7^43*x8^10,
 x2*x3^22*x4^23*x7^62*x8^10,
 x2*x3^22*x7^93,
 x2*x3^22*x7^82*x8^10,
 x2*x3^14*x4^26*x8^29,
 x2*x3^10*x4*x8^48,
 x2*x3^10*x5^8*x8^48,
 x2*x3^10*x6*x8^48,
 x2*x3^10*x8^54,
 x2*x3*x4^26*x5^5*x7^43*x8^10,
 x2*x3*x4^26*x6*x7^43*x8^10,
 x2*x3*x4^23*x5^5*x7^62*x8^10,
 x2*x3*x4^23*x6*x7^62*x8^10,
 x2*x3*x5^5*x7^82*x8^10,
 x2*x3*x6*x7^82*x8^10,
 x2*x4^30*x5^5*x7^43*x8^10,
 x2*x4^30*x6*x7^43*x8^10,
 x2*x4^26*x5^13*x8^29,
 x2*x4^26*x5^5*x7^43*x8^11,
 x2*x4^26*x6^41*x7^43*x8^10,
 x2*x4^26*x6*x7^43*x8^11,
 x2*x4^26*x7^43*x8^12,
 x2*x4^26*x7^18*x8^29,
 x2*x4^26*x8^32,
 x2*x4^23*x5^5*x7^62*x8^11,
 x2*x4^23*x6^41*x7^62*x8^10,
 x2*x4^23*x6*x7^62*x8^11,
 x2*x4^23*x7^62*x8^12,
 x2*x4^23*x8^35,
 x2*x4^10*x8^48,
 x2*x4*x7^7*x8^48,
 x2*x5^8*x7^7*x8^48,
 x2*x5^5*x7^93,
 x2*x5^5*x7^82*x8^11,
 x2*x6^43*x8^48,
 x2*x6^41*x7^82*x8^10,
 x2*x6*x7^93,
 x2*x6*x7^82*x8^11,
 x2*x6*x7^7*x8^48,
 x2*x7^98,
 x2*x7^82*x8^12,
 x2*x7^23*x8^48,
 x2*x7^7*x8^54,
 x2*x8^55,
 x3^78,
 x3^66*x4^2,
 x3^66*x7^17,
 x3^66*x8^17,
 x3^58*x4^2*x6^88,
 x3^58*x6^88*x8^17,
 x3^58*x8^48,
 x3^47*x4^23,
 x3^47*x4^2*x5^27,
 x3^47*x5^27*x8^17,
 x3^45*x4^23*x6^54,
 x3^45*x4^23*x7^5,
 x3^44*x4^33*x7^5,
 x3^44*x4^23*x7^11,
 x3^44*x4^23*x7^5*x8,
 x3^44*x4^23*x8^20,
 x3^44*x4*x8^48,
 x3^44*x5^8*x8^48,
 x3^44*x6*x8^48,
 x3^44*x7^82,
 x3^44*x7^23*x8^48,
 x3^44*x8^54,
 x3^28*x4^49,
 x3^28*x4^36*x7^5,
 x3^28*x4^33*x6^54,
 x3^28*x4^33*x6^46*x7^5,
 x3^28*x4^23*x6^59,
 x3^28*x4^23*x6^54*x8,
 x3^28*x4^23*x6^46*x7^11,
 x3^28*x4^23*x6^46*x7^5*x8,
 x3^28*x6^46*x7^82,
 x3^27*x4^23*x5^17*x6^54*x8,
 x3^27*x4^23*x5^17*x7^11,
 x3^27*x4^23*x5^17*x7^5*x8,
 x3^27*x4^23*x5^17*x8^20,
 x3^27*x4^23*x6^54*x8^10,
 x3^27*x4^23*x6^46*x7^5*x8^10,
 x3^27*x4^23*x6^46*x8^20,
 x3^27*x4^2*x5^43,
 x3^27*x4^2*x5^27*x6^54,
 x3^27*x4^2*x5^27*x7^5,
 x3^27*x5^43*x8^17,
 x3^27*x5^27*x6^54*x8^17,
 x3^27*x5^27*x7^17,
 x3^27*x5^27*x7^5*x8^17,
 x3^27*x5^27*x8^20,
 x3^26*x4^36*x7^5*x8^10,
 x3^26*x4^36*x8^20,
 x3^26*x4^33*x5^17*x6^54,
 x3^26*x4^33*x5^17*x7^5,
 x3^26*x4^26*x5^43,
 x3^26*x4^26*x5^27*x6^54,
 x3^26*x4^26*x5^27*x7^5,
 x3^26*x4^26*x5^17*x6^54*x8,
 x3^26*x4^26*x5^17*x7^11,
 x3^26*x4^26*x5^17*x7^5*x8,
 x3^26*x4^26*x5^17*x8^20,
 x3^26*x4^26*x6^54*x8^10,
 x3^26*x4^26*x6^46*x7^5*x8^10,
 x3^26*x4^26*x6^46*x8^20,
 x3^26*x4^23*x5^17*x6^59,
 x3^26*x4^23*x5^17*x6^56*x7^11,
 x3^26*x4^23*x5^17*x6^56*x8,
 x3^26*x4^23*x6^56*x8^10,
 x3^26*x4^2*x5^50,
 x3^26*x4^2*x5^27*x6^56,
 x3^26*x5^51,
 x3^26*x5^50*x7^17,
 x3^26*x5^50*x8^17,
 x3^26*x5^27*x6^56*x7^17,
 x3^26*x5^27*x6^56*x8^17,
 x3^22*x4^43*x7^5*x8^10,
 x3^22*x4^36*x7^93,
 x3^22*x4^36*x7^43*x8^10,
 x3^14*x4^61,
 x3^14*x4^49*x8^10,
 x3^14*x4^43*x5^5*x7^5*x8^10,
 x3^14*x4^43*x6*x7^5*x8^10,
 x3^14*x4^43*x7^5*x8^12,
 x3^14*x4^43*x8^20,
 x3^14*x4^36*x8^29,
 x3^10*x5^27*x8^35,
 x3^10*x5^17*x8^48,
 x3*x4^26*x5^17*x7^43,
 x3*x4^23*x5^17*x7^62,
 x3*x5^61,
 x3*x5^50*x7^43,
 x3*x5^27*x7^62,
 x3*x5^17*x7^82,
 x4^65,
 x4^61*x5^13,
 x4^61*x6^46,
 x4^61*x7^18,
 x4^49*x5^17,
 x4^49*x5^13*x8^10,
 x4^49*x6^46*x8^10,
 x4^49*x7^93,
 x4^49*x7^18*x8^10,
 x4^43*x5^43,
 x4^43*x5^17*x6^54,
 x4^43*x5^17*x7^5,
 x4^43*x5^13*x7^5*x8^10,
 x4^43*x5^13*x8^20,
 x4^43*x5^5*x7^18*x8^10,
 x4^43*x6^54*x8^10,
 x4^43*x6^46*x7^5*x8^10,
 x4^43*x6^46*x8^20,
 x4^43*x6*x7^18*x8^10,
 x4^43*x7^18*x8^12,
 x4^36*x5^13*x8^29,
 x4^36*x5^5*x7^93,
 x4^36*x5^5*x7^43*x8^10,
 x4^36*x6*x7^93,
 x4^36*x6*x7^43*x8^10,
 x4^36*x7^98,
 x4^36*x7^43*x8^12,
 x4^36*x7^18*x8^29,
 x4^36*x8^32,
 x4^30*x5^61,
 x4^30*x5^17*x7^43,
 x4^26*x5^17*x6^41*x7^43,
 x4^26*x5^17*x7^43*x8^11,
 x4^26*x5^17*x8^29,
 x4^26*x6^46*x7^43*x8^10,
 x4^26*x6^46*x8^29,
 x4^23*x5^17*x6^64,
 x4^23*x5^17*x6^56*x7^43,
 x4^23*x5^17*x6^41*x7^62,
 x4^23*x5^17*x7^62*x8^11,
 x4^23*x5^17*x8^35,
 x4^23*x6^79,
 x4^23*x6^64*x8^10,
 x4^23*x6^56*x7^43*x8^10,
 x4^23*x6^56*x8^29,
 x4^23*x6^46*x7^62*x8^10,
 x4^23*x6^46*x8^35,
 x4^14*x6^88,
 x4^10*x5^27*x8^35,
 x4^10*x5^17*x8^48,
 x4^2*x5^27*x6^64,
 x4^2*x5*x6^88,
 x4^2*x6^95,
 x4^2*x6^88*x7,
 x5^73,
 x5^61*x6^41,
 x5^61*x8^11,
 x5^51*x6^64,
 x5^50*x6^41*x7^43,
 x5^50*x7^43*x8^11,
 x5^50*x8^29,
 x5^47*x8^35,
 x5^27*x6^64*x7^17,
 x5^27*x6^64*x8^17,
 x5^27*x6^56*x7^43,
 x5^27*x6^56*x8^29,
 x5^27*x6^43*x8^35,
 x5^27*x6^41*x7^62,
 x5^27*x7^62*x8^11,
 x5^27*x7^7*x8^35,
 x5^17*x6^43*x8^48,
 x5^17*x6^41*x7^82,
 x5^17*x7^93,
 x5^17*x7^82*x8^11,
 x5^17*x7^7*x8^48,
 x5^17*x8^55,
 x5*x6^88*x8^17,
 x6^96,
 x6^95*x8^17,
 x6^88*x7^17,
 x6^88*x7*x8^17,
 x6^88*x8^31,
 x6^79*x7^82,
 x6^46*x7^93,
 x6^46*x7^82*x8^10,
 x6^46*x8^48,
 x8^63
);