-- at the beginning we add the [SX] case for a test, then 78 from the paper
LL = {
{x1,x2,x3,x4,x5,x6,y3*x4*x5*x6, y2*x4*x5*x6, x2*y3*x5*x6, y2*x3*x4*x6, y2*x3*x4*x5, y1*x4*x5*x6, x1*y3*x5*x6, y1*x3*x4*x6, y1*x3*x4*x5, y1*x2*x5*x6, x1*y2*x4*x6, x1*y2*x4*x5, y1*x2*x3*x6, y1*x2*x3*x5, x1*y2*x3*x4, 
x1^2*y2*y3*x4*x5*x6, x1*x2*y2*y3*x4*x5*x6, x1*y2*y3*x3*x4*x5*x6, x1*y2*y3*x4^2*x5*x6, x1*y2*y3*x4*x5^2*x6, x1*y2*y3*x4*x5*x6^2},
{x1,x2,x3,x4,x5,x6,x4*x5*x6*y3,x4*x5*x6*y2,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x4*x5*x6*y1,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x3*x4^2*x5*x6*y1*y2,x3*x4*x5^2*x6*y1*y2,x3*x4*x5*x6^2*y1*y2},
{x1,x2,x3,x4,x5,x6,x4*x5*x6*y3,x4*x5*x6*y2,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x4*x5*x6*y1,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x4^2*x5*x6*y1*y3,x3*x4*x5^2*x6*y1*y2,x3*x4*x5*x6^2*y1*y2},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x4*x5*x6*y2,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x4*x5*x6*y1,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x3*x4*x5*x6*y1*y4,x3*x4*x5^2*x6*y1*y2,x3*x4*x5*x6^2*y1*y2},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x4*x5*x6*y1,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x3*x4*x5*x6^2*y1*y2},
{x1,x2,x3,x4,x5,x6,x3*x4*x5*y6,x2*x4*x5*y6,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x4*x5*x6*y1,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x3*x4^2*x5*y1*y6,x2*x3*x4*x5^2*y1*y6,x3*x4*x5*x6^2*y1*y2},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x4*x5*x6*y1,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x3*x5*x6*y2,x3*x4*x6*y2,x2*x3*x5*y4,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x3*x5*x6*y2,x2*x3*x6*y4,x2*x3*x5*y4,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x2*x3^2*x5*x6*y1*y4,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x2*x5*x6*y3,x2*x3*x6*y4,x2*x3*x5*y4,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2^2*x4*x5*x6*y1*y3,x2*x3^2*x5*x6*y1*y4,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x3*x5*x6*y2,x2*x3*x6*y4,x2*x3*x5*y4,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2^2*x3*x5*x6*y1*y4,x2*x3^2*x5*x6*y1*y4,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x2*x3*x6*y5,x2*x3*x6*y4,x2*x3*x5*y4,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2^2*x3*x5*x6*y1*y4,x2*x3^2*x5*x6*y1*y4,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x2*x3*x6*y5,x2*x3*x6*y4,x2*x3*x5*y4,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2^2*x3*x4*x6*y1*y5,x2*x3^2*x5*x6*y1*y4,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x2*x3*x5*y6,x2*x3*x4*y6,x2*x3*x5*y4,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2^2*x3*x4*x5*y1*y6,x2*x3^2*x4*x5*y1*y6,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x2*x3*x5*x6^2*y1*y4},
{x1,x2,x3,x4,x5,x6,x3*x5*x6*y4,x2*x5*x6*y4,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x1*x5*x6*y4,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x1*x3*x6*y2,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x3*x4*x5*x6*y1*y4,x2*x3*x5^2*x6*y1*y4,x1*x3*x5*x6^2*y2*y4},
{x1,x2,x3,x4,x5,x6,x3*x4*x5*y6,x2*x4*x5*y6,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x1*x4*x5*y6,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x1*x3*x6*y2,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x3*x4^2*x5*y1*y6,x2*x3*x4*x5^2*y1*y6,x1*x3*x4*x5*x6*y2*y6},
{x1,x2,x3,x4,x5,x6,x3*x4*x5*y6,x2*x4*x5*y6,x2*x3*x5*y6,x2*x3*x4*y6,x3*x4*x5*y2,x1*x4*x5*y6,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x1*x2*x3*y6,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2^2*x3*x4*x5*y1*y6,x2*x3^2*x4*x5*y1*y6,x2*x3*x4^2*x5*y1*y6,x2*x3*x4*x5^2*y1*y6,x1*x2*x3*x4*x5*y6^2},
{x1,x2,x3,x4,x5,x6,x4*x5*x6*y3,x4*x5*x6*y2,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x4*x5*x6*y1,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x3^2*x4*x5*x6*y1*y2,x2*x4^2*x5*x6*y1*y3,x2*x4*x5^2*x6*y1*y3,x2*x4*x5*x6^2*y1*y3},
{x1,x2,x3,x4,x5,x6,x4*x5*x6*y3,x4*x5*x6*y2,x3*x5*x6*y2,x3*x4*x6*y2,x3*x4*x5*y2,x4*x5*x6*y1,x3*x5*x6*y1,x3*x4*x6*y1,x3*x4*x5*y1,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x2*x3*x4*x5*x6*y1*y3,x2*x4^2*x5*x6*y1*y3,x2*x4*x5^2*x6*y1*y3,x2*x4*x5*x6^2*y1*y3},
{x1,x2,x3,x4,x5,x6,x4*x5*x6*y3,x4*x5*x6*y2,x2*x5*x6*y3,x2*x4*x6*y3,x2*x4*x5*y3,x4*x5*x6*y1,x1*x5*x6*y3,x1*x4*x6*y3,x1*x4*x5*y3,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2*x3*x4*x5*x6*y1*y2,x2*x3*x4*x5*x6*y1*y3,x2*x4^2*x5*x6*y1*y3,x2*x4*x5^2*x6*y1*y3,x2*x4*x5*x6^2*y1*y3},
{x1,x2,x3,x4,x5,x6,x4*x5*x6*y3,x4*x5*x6*y2,x2*x5*x6*y3,x2*x4*x6*y3,x2*x4*x5*y3,x4*x5*x6*y1,x1*x5*x6*y3,x1*x4*x6*y3,x1*x4*x5*y3,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2^2*x4*x5*x6*y1*y3,x2*x3*x4*x5*x6*y1*y3,x2*x4^2*x5*x6*y1*y3,x2*x4*x5^2*x6*y1*y3,x2*x4*x5*x6^2*y1*y3},
{x1,x2,x3,x4,x5,x6,x4*x5*x6*y3,x2*x5*x6*y4,x2*x5*x6*y3,x2*x4*x6*y3,x2*x4*x5*y3,x4*x5*x6*y1,x1*x5*x6*y3,x1*x4*x6*y3,x1*x4*x5*y3,x2*x5*x6*y1,x2*x4*x6*y1,x2*x4*x5*y1,x2*x3*x6*y1,x2*x3*x5*y1,x2*x3*x4*y1,x2*x3*x4*x5*x6*y1^2,x2^2*x4*x5*x6*y1*y3,x2*x3*x4*x5*x6*y1*y3,x2*x4^2*x5*x6*y1*y3,x2*x4*x5^2*x6*y1*y3,x2*x4*x5*x6^2*y1*y3},
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