x7, x6, x5, x4, x3, x2, x1, 
x1^7+x1^6-12*x1^5-7*x1^4+28*x1^3+14*x1^2-9*x1+1
x1^6+x1^5*x2+x1^4*x2^2+x1^3*x2^3+x1^2*x2^4+x1*x2^5+x2^6+x1^5+x1^4*x2+x1^3*x2^2+x1^2*x2^3+x1*x2^4+x2^5-12*x1^4-12*x1^3*x2-12*x1^2*x2^2-12*x1*x2^3-12*x2^4-7*x1^3-7*x1^2*x2-7*x1*x2^2-7*x2^3+28*x1^2+28*x1*x2+28*x2^2+14*x1+14*x2-9
x1^5+x1^4*x2+x1^4*x3+x1^3*x2^2+x1^3*x2*x3+x1^3*x3^2+x1^2*x2^3+x1^2*x2^2*x3+x1^2*x2*x3^2+x1^2*x3^3+x1*x2^4+x1*x2^3*x3+x1*x2^2*x3^2+x1*x2*x3^3+x1*x3^4+x2^5+x2^4*x3+x2^3*x3^2+x2^2*x3^3+x2*x3^4+x3^5+x1^4+x1^3*x2+x1^3*x3+x1^2*x2^2+x1^2*x2*x3+x1^2*x3^2+x1*x2^3+x1*x2^2*x3+x1*x2*x3^2+x1*x3^3+x2^4+x2^3*x3+x2^2*x3^2+x2*x3^3+x3^4-12*x1^3-12*x1^2*x2-12*x1^2*x3-12*x1*x2^2-12*x1*x2*x3-12*x1*x3^2-12*x2^3-12*x2^2*x3-12*x2*x3^2-12*x3^3-7*x1^2-7*x1*x2-7*x1*x3-7*x2^2-7*x2*x3-7*x3^2+28*x1+28*x2+28*x3+14
x1^4+x1^3*x2+x1^3*x3+x1^3*x4+x1^2*x2^2+x1^2*x2*x3+x1^2*x2*x4+x1^2*x3^2+x1^2*x3*x4+x1^2*x4^2+x1*x2^3+x1*x2^2*x3+x1*x2^2*x4+x1*x2*x3^2+x1*x2*x3*x4+x1*x2*x4^2+x1*x3^3+x1*x3^2*x4+x1*x3*x4^2+x1*x4^3+x2^4+x2^3*x3+x2^3*x4+x2^2*x3^2+x2^2*x3*x4+x2^2*x4^2+x2*x3^3+x2*x3^2*x4+x2*x3*x4^2+x2*x4^3+x3^4+x3^3*x4+x3^2*x4^2+x3*x4^3+x4^4+x1^3+x1^2*x2+x1^2*x3+x1^2*x4+x1*x2^2+x1*x2*x3+x1*x2*x4+x1*x3^2+x1*x3*x4+x1*x4^2+x2^3+x2^2*x3+x2^2*x4+x2*x3^2+x2*x3*x4+x2*x4^2+x3^3+x3^2*x4+x3*x4^2+x4^3-12*x1^2-12*x1*x2-12*x1*x3-12*x1*x4-12*x2^2-12*x2*x3-12*x2*x4-12*x3^2-12*x3*x4-12*x4^2-7*x1-7*x2-7*x3-7*x4+28
x1^3+x1^2*x2+x1^2*x3+x1^2*x4+x1^2*x5+x1*x2^2+x1*x2*x3+x1*x2*x4+x1*x2*x5+x1*x3^2+x1*x3*x4+x1*x3*x5+x1*x4^2+x1*x4*x5+x1*x5^2+x2^3+x2^2*x3+x2^2*x4+x2^2*x5+x2*x3^2+x2*x3*x4+x2*x3*x5+x2*x4^2+x2*x4*x5+x2*x5^2+x3^3+x3^2*x4+x3^2*x5+x3*x4^2+x3*x4*x5+x3*x5^2+x4^3+x4^2*x5+x4*x5^2+x5^3+x1^2+x1*x2+x1*x3+x1*x4+x1*x5+x2^2+x2*x3+x2*x4+x2*x5+x3^2+x3*x4+x3*x5+x4^2+x4*x5+x5^2-12*x1-12*x2-12*x3-12*x4-12*x5-7
x1^2+x1*x2+x1*x3+x1*x4+x1*x5+x1*x6+x2^2+x2*x3+x2*x4+x2*x5+x2*x6+x3^2+x3*x4+x3*x5+x3*x6+x4^2+x4*x5+x4*x6+x5^2+x5*x6+x6^2+x1+x2+x3+x4+x5+x6-12
x7+x6+x5+x4+x3+x2+x1+1
-2*x1^3-4*x1^2*x2-2*x1^2*x3-2*x1^2*x4-4*x1*x2^2-4*x1*x2*x3-4*x1*x2*x4-2*x1*x2*x5-2*x1*x2*x6-2*x1*x3^2-4*x1*x3*x4+2*x1*x3*x5-2*x1*x4^2+2*x1*x4*x6-2*x2^3-2*x2^2*x3-2*x2^2*x4-2*x2*x3^2-4*x2*x3*x4+2*x2*x3*x6-2*x2*x4^2+2*x2*x4*x5-2*x3^3-4*x3^2*x4-4*x3*x4^2-2*x3*x4*x5-2*x3*x4*x6-2*x4^3-2*x1^2-4*x1*x2-2*x1*x3-2*x1*x4-2*x2^2-2*x2*x3-2*x2*x4-2*x3^2-4*x3*x4-2*x4^2+24*x1+24*x2+24*x3+24*x4-12
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