The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{12,2})$.

There are 72 possibilities.
Here are their Poincaré polynomials: $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 2 x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + x^{10} y^{4} + 5 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 5 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{11} y^{2} + 6 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 6 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 2 x^{10} y^{3} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 2 x^{10} y^{4} + 4 x^{10} y^{3} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 5 x^{10} y^{3} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + x^{10} y^{4} + 5 x^{10} y^{3} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{11} y^{2} + 4 x^{10} y^{3} + 2 x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 4 x^{10} y^{3} + 2 x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 5 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{11} y^{2} + 6 x^{10} y^{3} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 6 x^{10} y^{3} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 2 x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + x^{10} y^{4} + 5 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 5 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{11} y^{2} + 6 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 6 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 2 x^{10} y^{3} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 2 x^{10} y^{4} + 4 x^{10} y^{3} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 5 x^{10} y^{3} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + x^{10} y^{4} + 5 x^{10} y^{3} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{11} y^{2} + 4 x^{10} y^{3} + 2 x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 4 x^{10} y^{3} + 2 x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 5 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{11} y^{2} + 6 x^{10} y^{3} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 6 x^{10} y^{3} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 72 possibilities:
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 2 2 1 3 3 3 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
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