//This is the ideal Fourier invariants.



// This is the inverse of the Fourier transform.

matrix ptoq[136][116] =
1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/128,1/64,1/128,1/64,1/128,1/128,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/128,1/64,1/128,1/64,1/128,1/128,1/128,1/128,1/128,1/128,1/128,1/64,1/128,1/64,1/64,1/64,1/64,1/128,1/64,1/128,1/128,1/128,1/128,1/128,1/128,1/64,1/128,1/64,1/128,1/128,1/128,1/128,1/128,1/128,1/128,1/64,1/128,1/64,1/64,1/64,1/64,1/128,1/64,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/128,1/64,1/128,1/64,1/128,1/128,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/256,1/128,1/256,
1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,0,1/64,0,-1/64,1/64,0,-1/64,0,0,-1/64,0,1/64,-1/64,1/64,-1/128,0,1/128,0,-1/64,0,1/64,1/128,0,-1/128,0,1/64,0,-1/64,1/64,0,-1/64,0,0,-1/64,0,1/64,-1/64,1/64,1/64,0,-1/64,0,1/32,0,-1/32,-1/64,0,1/64,0,-1/64,0,1/64,-1/64,0,1/64,0,0,1/64,0,-1/64,1/64,-1/64,-1/64,0,1/64,0,-1/32,0,1/32,1/64,0,-1/64,-1/128,0,1/128,0,-1/64,0,1/64,1/128,0,-1/128,0,-1/64,0,1/64,-1/64,0,1/64,0,0,1/64,0,-1/64,1/64,-1/64,1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,
1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/128,-1/64,1/128,-1/64,-1/128,1/128,-1/128,1/128,1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/128,-1/64,1/128,-1/64,-1/128,1/128,-1/128,1/128,1/128,1/128,1/128,-1/64,1/128,-1/64,1/64,-1/64,1/64,1/128,-1/64,1/128,-1/128,1/128,-1/128,1/128,1/128,-1/64,1/128,-1/64,-1/128,1/128,-1/128,1/128,1/128,1/128,1/128,-1/64,1/128,-1/64,1/64,-1/64,1/64,1/128,-1/64,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/128,-1/64,1/128,-1/64,-1/128,1/128,-1/128,1/128,1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/256,-1/128,1/256,
1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,-1/64,1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,-1/64,1/64,0,-1/64,1/32,0,-1/32,0,1/64,0,-1/64,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,-1/64,1/64,0,-1/64,1/32,0,-1/32,0,1/64,0,-1/64,1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,-1/64,1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,
1/128,1/64,1/128,0,0,0,0,-1/128,-1/64,-1/128,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-1/64,-1/64,-1/128,-1/64,-1/128,0,0,0,0,1/128,1/64,1/128,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-1/64,-1/64,1/64,1/32,1/64,0,0,0,0,-1/64,-1/32,-1/64,0,0,0,0,-1/64,0,-1/64,0,0,0,0,0,1/64,1/64,-1/64,-1/32,-1/64,0,0,0,0,1/64,1/32,1/64,-1/128,-1/64,-1/128,0,0,0,0,1/128,1/64,1/128,0,0,0,0,-1/64,0,-1/64,0,0,0,0,0,1/64,1/64,1/128,1/64,1/128,0,0,0,0,-1/128,-1/64,-1/128,
1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,-1/64,0,1/64,0,1/64,0,-1/64,0,-1/64,0,1/64,0,1/64,-1/64,1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,-1/64,0,1/64,0,1/64,0,-1/64,0,-1/64,0,1/64,0,1/64,-1/64,1/64,0,-1/64,-1/32,0,1/32,0,1/64,0,-1/64,-1/64,0,1/64,0,1/64,0,-1/64,0,-1/64,0,1/64,0,1/64,-1/64,1/64,0,-1/64,-1/32,0,1/32,0,1/64,0,-1/64,1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,-1/64,0,1/64,0,1/64,0,-1/64,0,-1/64,0,1/64,0,1/64,-1/64,1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,
1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-1/64,-1/64,-1/128,1/64,-1/128,0,0,0,0,1/128,-1/64,1/128,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-1/64,-1/64,1/64,-1/32,1/64,0,0,0,0,-1/64,1/32,-1/64,0,0,0,0,-1/64,0,-1/64,0,0,0,0,0,1/64,1/64,-1/64,1/32,-1/64,0,0,0,0,1/64,-1/32,1/64,-1/128,1/64,-1/128,0,0,0,0,1/128,-1/64,1/128,0,0,0,0,-1/64,0,-1/64,0,0,0,0,0,1/64,1/64,1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,
1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/128,-1/64,1/128,-1/64,1/128,-1/128,1/128,-1/128,1/128,1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/128,-1/64,1/128,-1/64,1/128,-1/128,1/128,-1/128,1/128,1/128,1/128,-1/64,1/128,1/64,-1/64,1/64,-1/64,1/128,-1/64,1/128,1/128,-1/128,1/128,-1/128,1/128,-1/64,1/128,-1/64,1/128,-1/128,1/128,-1/128,1/128,1/128,1/128,-1/64,1/128,1/64,-1/64,1/64,-1/64,1/128,-1/64,1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/128,-1/64,1/128,-1/64,1/128,-1/128,1/128,-1/128,1/128,1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/256,-1/128,1/256,
1/128,0,-1/128,0,-1/64,0,1/64,-1/128,0,1/128,0,-1/64,0,1/64,1/64,0,-1/64,0,0,1/64,0,-1/64,-1/64,1/64,-1/128,0,1/128,0,1/64,0,-1/64,1/128,0,-1/128,0,-1/64,0,1/64,1/64,0,-1/64,0,0,1/64,0,-1/64,-1/64,1/64,1/64,0,-1/64,0,-1/32,0,1/32,-1/64,0,1/64,0,1/64,0,-1/64,-1/64,0,1/64,0,0,-1/64,0,1/64,1/64,-1/64,-1/64,0,1/64,0,1/32,0,-1/32,1/64,0,-1/64,-1/128,0,1/128,0,1/64,0,-1/64,1/128,0,-1/128,0,1/64,0,-1/64,-1/64,0,1/64,0,0,-1/64,0,1/64,1/64,-1/64,1/128,0,-1/128,0,-1/64,0,1/64,-1/128,0,1/128,
1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/128,1/64,1/128,1/64,-1/128,-1/128,-1/128,-1/128,1/128,1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/128,1/64,1/128,1/64,-1/128,-1/128,-1/128,-1/128,1/128,1/128,1/128,1/64,1/128,-1/64,-1/64,-1/64,-1/64,1/128,1/64,1/128,-1/128,-1/128,-1/128,-1/128,1/128,1/64,1/128,1/64,-1/128,-1/128,-1/128,-1/128,1/128,1/128,1/128,1/64,1/128,-1/64,-1/64,-1/64,-1/64,1/128,1/64,1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/128,1/64,1/128,1/64,-1/128,-1/128,-1/128,-1/128,1/128,1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/256,1/128,1/256,
1/128,1/64,1/128,0,0,0,0,-1/128,-1/64,-1/128,1/64,1/64,1/64,1/64,0,0,0,0,-1/64,-1/64,-1/64,-1/64,0,0,1/128,1/64,1/128,0,0,0,0,-1/128,-1/64,-1/128,1/64,1/64,1/64,1/64,0,0,0,0,-1/64,-1/64,-1/64,-1/64,0,0,1/64,1/32,1/64,0,0,0,0,-1/64,-1/32,-1/64,1/64,1/64,1/64,1/64,0,0,0,0,-1/64,-1/64,-1/64,-1/64,0,0,1/64,1/32,1/64,0,0,0,0,-1/64,-1/32,-1/64,1/128,1/64,1/128,0,0,0,0,-1/128,-1/64,-1/128,1/64,1/64,1/64,1/64,0,0,0,0,-1/64,-1/64,-1/64,-1/64,0,0,1/128,1/64,1/128,0,0,0,0,-1/128,-1/64,-1/128,
1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,0,1/64,0,-1/64,0,0,0,0,0,1/64,0,-1/64,0,0,-1/128,0,1/128,-1/64,0,1/64,0,-1/128,0,1/128,0,1/64,0,-1/64,0,0,0,0,0,1/64,0,-1/64,0,0,1/64,0,-1/64,1/32,0,-1/32,0,1/64,0,-1/64,0,-1/64,0,1/64,0,0,0,0,0,-1/64,0,1/64,0,0,-1/64,0,1/64,-1/32,0,1/32,0,-1/64,0,1/64,-1/128,0,1/128,-1/64,0,1/64,0,-1/128,0,1/128,0,-1/64,0,1/64,0,0,0,0,0,-1/64,0,1/64,0,0,1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,
1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,-1/64,1/64,-1/64,1/64,0,0,0,0,1/64,-1/64,1/64,-1/64,0,0,1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,-1/64,1/64,-1/64,1/64,0,0,0,0,1/64,-1/64,1/64,-1/64,0,0,1/64,-1/32,1/64,0,0,0,0,-1/64,1/32,-1/64,-1/64,1/64,-1/64,1/64,0,0,0,0,1/64,-1/64,1/64,-1/64,0,0,1/64,-1/32,1/64,0,0,0,0,-1/64,1/32,-1/64,1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,-1/64,1/64,-1/64,1/64,0,0,0,0,1/64,-1/64,1/64,-1/64,0,0,1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,
1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,0,1/64,0,-1/64,0,0,0,0,0,1/64,0,-1/64,0,0,-1/128,0,1/128,1/64,0,-1/64,0,-1/128,0,1/128,0,1/64,0,-1/64,0,0,0,0,0,1/64,0,-1/64,0,0,1/64,0,-1/64,-1/32,0,1/32,0,1/64,0,-1/64,0,-1/64,0,1/64,0,0,0,0,0,-1/64,0,1/64,0,0,-1/64,0,1/64,1/32,0,-1/32,0,-1/64,0,1/64,-1/128,0,1/128,1/64,0,-1/64,0,-1/128,0,1/128,0,-1/64,0,1/64,0,0,0,0,0,-1/64,0,1/64,0,0,1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,
1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,1/64,0,-1/64,0,0,1/32,0,-1/32,-1/64,0,1/64,0,0,0,1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,1/64,0,-1/64,0,0,1/32,0,-1/32,-1/64,0,1/64,0,0,0,1/64,0,-1/64,0,1/32,0,-1/32,-1/64,0,1/64,1/64,0,-1/64,0,0,1/32,0,-1/32,-1/64,0,1/64,0,0,0,1/64,0,-1/64,0,1/32,0,-1/32,-1/64,0,1/64,1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,1/64,0,-1/64,0,0,1/32,0,-1/32,-1/64,0,1/64,0,0,0,1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,
1/128,1/64,1/128,1/64,1/64,1/64,1/64,1/128,1/64,1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/128,-1/64,-1/128,-1/64,-1/64,-1/64,-1/64,-1/128,-1/64,-1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,1/32,1/64,1/32,1/32,1/32,1/32,1/64,1/32,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/64,-1/32,-1/64,-1/32,-1/32,-1/32,-1/32,-1/64,-1/32,-1/64,-1/128,-1/64,-1/128,-1/64,-1/64,-1/64,-1/64,-1/128,-1/64,-1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/128,1/64,1/128,1/64,1/64,1/64,1/64,1/128,1/64,1/128,
1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,-1/64,0,1/64,0,0,-1/32,0,1/32,1/64,0,-1/64,0,0,0,1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,-1/64,0,1/64,0,0,-1/32,0,1/32,1/64,0,-1/64,0,0,0,1/64,0,-1/64,0,1/32,0,-1/32,-1/64,0,1/64,-1/64,0,1/64,0,0,-1/32,0,1/32,1/64,0,-1/64,0,0,0,1/64,0,-1/64,0,1/32,0,-1/32,-1/64,0,1/64,1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,-1/64,0,1/64,0,0,-1/32,0,1/32,1/64,0,-1/64,0,0,0,1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,
1/128,-1/64,1/128,-1/64,1/64,-1/64,1/64,1/128,-1/64,1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/128,1/64,-1/128,1/64,-1/64,1/64,-1/64,-1/128,1/64,-1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,-1/32,1/64,-1/32,1/32,-1/32,1/32,1/64,-1/32,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/64,1/32,-1/64,1/32,-1/32,1/32,-1/32,-1/64,1/32,-1/64,-1/128,1/64,-1/128,1/64,-1/64,1/64,-1/64,-1/128,1/64,-1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/128,-1/64,1/128,-1/64,1/64,-1/64,1/64,1/128,-1/64,1/128,
1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,1/64,-1/64,1/64,-1/64,0,0,0,0,-1/64,1/64,-1/64,1/64,0,0,1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,1/64,-1/64,1/64,-1/64,0,0,0,0,-1/64,1/64,-1/64,1/64,0,0,1/64,-1/32,1/64,0,0,0,0,-1/64,1/32,-1/64,1/64,-1/64,1/64,-1/64,0,0,0,0,-1/64,1/64,-1/64,1/64,0,0,1/64,-1/32,1/64,0,0,0,0,-1/64,1/32,-1/64,1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,1/64,-1/64,1/64,-1/64,0,0,0,0,-1/64,1/64,-1/64,1/64,0,0,1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,
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1/128,0,-1/128,0,-1/64,0,1/64,-1/128,0,1/128,1/64,0,-1/64,0,0,-1/32,0,1/32,-1/64,0,1/64,0,0,0,1/128,0,-1/128,0,-1/64,0,1/64,-1/128,0,1/128,-1/64,0,1/64,0,0,1/32,0,-1/32,1/64,0,-1/64,0,0,0,-1/64,0,1/64,0,1/32,0,-1/32,1/64,0,-1/64,-1/64,0,1/64,0,0,1/32,0,-1/32,1/64,0,-1/64,0,0,0,-1/64,0,1/64,0,1/32,0,-1/32,1/64,0,-1/64,1/128,0,-1/128,0,-1/64,0,1/64,-1/128,0,1/128,1/64,0,-1/64,0,0,-1/32,0,1/32,-1/64,0,1/64,0,0,0,1/128,0,-1/128,0,-1/64,0,1/64,-1/128,0,1/128,
1/128,1/64,1/128,-1/64,-1/64,-1/64,-1/64,1/128,1/64,1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/128,-1/64,-1/128,1/64,1/64,1/64,1/64,-1/128,-1/64,-1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/64,-1/32,-1/64,1/32,1/32,1/32,1/32,-1/64,-1/32,-1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,1/32,1/64,-1/32,-1/32,-1/32,-1/32,1/64,1/32,1/64,-1/128,-1/64,-1/128,1/64,1/64,1/64,1/64,-1/128,-1/64,-1/128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/128,1/64,1/128,-1/64,-1/64,-1/64,-1/64,1/128,1/64,1/128,
1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/128,1/64,1/128,1/64,-1/128,-1/128,-1/128,-1/128,1/128,1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,-1/128,-1/64,-1/128,-1/64,1/128,1/128,1/128,1/128,-1/128,-1/128,-1/128,-1/64,-1/128,1/64,1/64,1/64,1/64,-1/128,-1/64,-1/128,1/128,1/128,1/128,1/128,-1/128,-1/64,-1/128,-1/64,1/128,1/128,1/128,1/128,-1/128,-1/128,-1/128,-1/64,-1/128,1/64,1/64,1/64,1/64,-1/128,-1/64,-1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/128,1/64,1/128,1/64,-1/128,-1/128,-1/128,-1/128,1/128,1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,1/256,1/128,1/256,
1/128,0,-1/128,0,-1/64,0,1/64,-1/128,0,1/128,0,-1/64,0,1/64,1/64,0,-1/64,0,0,1/64,0,-1/64,-1/64,1/64,-1/128,0,1/128,0,1/64,0,-1/64,1/128,0,-1/128,0,1/64,0,-1/64,-1/64,0,1/64,0,0,-1/64,0,1/64,1/64,-1/64,-1/64,0,1/64,0,1/32,0,-1/32,1/64,0,-1/64,0,-1/64,0,1/64,1/64,0,-1/64,0,0,1/64,0,-1/64,-1/64,1/64,1/64,0,-1/64,0,-1/32,0,1/32,-1/64,0,1/64,-1/128,0,1/128,0,1/64,0,-1/64,1/128,0,-1/128,0,1/64,0,-1/64,-1/64,0,1/64,0,0,-1/64,0,1/64,1/64,-1/64,1/128,0,-1/128,0,-1/64,0,1/64,-1/128,0,1/128,
1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/128,-1/64,1/128,-1/64,1/128,-1/128,1/128,-1/128,1/128,1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,-1/128,1/64,-1/128,1/64,-1/128,1/128,-1/128,1/128,-1/128,-1/128,-1/128,1/64,-1/128,-1/64,1/64,-1/64,1/64,-1/128,1/64,-1/128,-1/128,1/128,-1/128,1/128,-1/128,1/64,-1/128,1/64,-1/128,1/128,-1/128,1/128,-1/128,-1/128,-1/128,1/64,-1/128,-1/64,1/64,-1/64,1/64,-1/128,1/64,-1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/128,-1/64,1/128,-1/64,1/128,-1/128,1/128,-1/128,1/128,1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,1/256,-1/128,1/256,
1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,-1/64,0,1/64,0,1/64,0,-1/64,0,-1/64,0,1/64,0,1/64,-1/64,1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,1/64,0,-1/64,0,-1/64,0,1/64,0,1/64,0,-1/64,0,-1/64,1/64,-1/64,0,1/64,1/32,0,-1/32,0,-1/64,0,1/64,1/64,0,-1/64,0,-1/64,0,1/64,0,1/64,0,-1/64,0,-1/64,1/64,-1/64,0,1/64,1/32,0,-1/32,0,-1/64,0,1/64,1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,-1/64,0,1/64,0,1/64,0,-1/64,0,-1/64,0,1/64,0,1/64,-1/64,1/128,0,-1/128,-1/64,0,1/64,0,1/128,0,-1/128,
1/128,1/64,1/128,0,0,0,0,-1/128,-1/64,-1/128,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-1/64,-1/64,-1/128,-1/64,-1/128,0,0,0,0,1/128,1/64,1/128,0,0,0,0,-1/64,0,-1/64,0,0,0,0,0,1/64,1/64,-1/64,-1/32,-1/64,0,0,0,0,1/64,1/32,1/64,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-1/64,-1/64,1/64,1/32,1/64,0,0,0,0,-1/64,-1/32,-1/64,-1/128,-1/64,-1/128,0,0,0,0,1/128,1/64,1/128,0,0,0,0,-1/64,0,-1/64,0,0,0,0,0,1/64,1/64,1/128,1/64,1/128,0,0,0,0,-1/128,-1/64,-1/128,
1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,-1/64,1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,1/64,-1/64,0,1/64,-1/32,0,1/32,0,-1/64,0,1/64,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,1/64,-1/64,0,1/64,-1/32,0,1/32,0,-1/64,0,1/64,1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,0,-1/64,0,1/64,-1/64,1/128,0,-1/128,1/64,0,-1/64,0,1/128,0,-1/128,
1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-1/64,-1/64,-1/128,1/64,-1/128,0,0,0,0,1/128,-1/64,1/128,0,0,0,0,-1/64,0,-1/64,0,0,0,0,0,1/64,1/64,-1/64,1/32,-1/64,0,0,0,0,1/64,-1/32,1/64,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-1/64,-1/64,1/64,-1/32,1/64,0,0,0,0,-1/64,1/32,-1/64,-1/128,1/64,-1/128,0,0,0,0,1/128,-1/64,1/128,0,0,0,0,-1/64,0,-1/64,0,0,0,0,0,1/64,1/64,1/128,-1/64,1/128,0,0,0,0,-1/128,1/64,-1/128,
1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/128,-1/64,1/128,-1/64,-1/128,1/128,-1/128,1/128,1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/256,-1/128,1/256,1/128,-1/128,1/128,-1/128,-1/128,1/64,-1/128,1/64,1/128,-1/128,1/128,-1/128,-1/128,-1/128,-1/128,1/64,-1/128,1/64,-1/64,1/64,-1/64,-1/128,1/64,-1/128,1/128,-1/128,1/128,-1/128,-1/128,1/64,-1/128,1/64,1/128,-1/128,1/128,-1/128,-1/128,-1/128,-1/128,1/64,-1/128,1/64,-1/64,1/64,-1/64,-1/128,1/64,-1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/128,-1/64,1/128,-1/64,-1/128,1/128,-1/128,1/128,1/128,1/128,1/256,-1/128,1/256,-1/128,1/128,-1/128,1/128,1/256,-1/128,1/256,
1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,0,1/64,0,-1/64,1/64,0,-1/64,0,0,-1/64,0,1/64,-1/64,1/64,-1/128,0,1/128,0,-1/64,0,1/64,1/128,0,-1/128,0,-1/64,0,1/64,-1/64,0,1/64,0,0,1/64,0,-1/64,1/64,-1/64,-1/64,0,1/64,0,-1/32,0,1/32,1/64,0,-1/64,0,1/64,0,-1/64,1/64,0,-1/64,0,0,-1/64,0,1/64,-1/64,1/64,1/64,0,-1/64,0,1/32,0,-1/32,-1/64,0,1/64,-1/128,0,1/128,0,-1/64,0,1/64,1/128,0,-1/128,0,-1/64,0,1/64,-1/64,0,1/64,0,0,1/64,0,-1/64,1/64,-1/64,1/128,0,-1/128,0,1/64,0,-1/64,-1/128,0,1/128,
1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/128,1/64,1/128,1/64,1/128,1/128,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/256,1/128,1/256,-1/128,-1/128,-1/128,-1/128,-1/128,-1/64,-1/128,-1/64,-1/128,-1/128,-1/128,-1/128,-1/128,-1/128,-1/128,-1/64,-1/128,-1/64,-1/64,-1/64,-1/64,-1/128,-1/64,-1/128,-1/128,-1/128,-1/128,-1/128,-1/128,-1/64,-1/128,-1/64,-1/128,-1/128,-1/128,-1/128,-1/128,-1/128,-1/128,-1/64,-1/128,-1/64,-1/64,-1/64,-1/64,-1/128,-1/64,-1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/128,1/64,1/128,1/64,1/128,1/128,1/128,1/128,1/128,1/128,1/256,1/128,1/256,1/128,1/128,1/128,1/128,1/256,1/128,1/256;

// This is the ring of probability distributions. 

ring rP = 0,(p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36,p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49,p50,p51,p52,p53,p54,p55,p56,p57,p58,p59,p60,p61,p62,p63,p64,p65,p66,p67,p68,p69,p70,p71,p72,p73,p74,p75,p76,p77,p78,p79,p80,p81,p82,p83,p84,p85,p86,p87,p88,p89,p90,p91,p92,p93,p94,p95,p96,p97,p98,p99,p100,p101,p102,p103,p104,p105,p106,p107,p108,p109,p110,p111,p112,p113,p114,p115,p116,p117,p118,p119,p120,p121,p122,p123,p124,p125,p126,p127,p128,p129,p130,p131,p132,p133,p134,p135,p136),dp;

//This is the Fourier transform.

matrix qtop[116][136] =
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,0,-1,0,1,0,-1,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,
1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,
1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,-1,0,1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,-1,0,1,
1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,
1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,1,0,-1,0,-1,0,1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,1,0,-1,0,-1,0,1,
1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,-1,1,-1,0,0,0,0,1,-1,1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,-1,1,-1,0,0,0,0,1,-1,1,
1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,
1,0,-1,0,-1,0,1,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,
1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,
1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,
1,1,1,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,
1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,1,0,-1,0,-1,0,1,
1,-1,1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,-1,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,
1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,
1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,-1,0,1,0,0,0,0,1,0,-1,0,1,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,-1,0,1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,1,0,-1,0,0,0,0,-1,0,1,
1,-1,1,-1,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,1,-1,1,
1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,1,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,1,0,-1,0,0,0,0,-1,0,1,
1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,-1,0,1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,-1,0,1,-1,0,1,0,-1,0,1,
1,-1,1,0,0,0,0,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,-1,1,-1,0,0,0,0,1,-1,1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,
1,0,-1,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,1,0,-1,0,-1,0,1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,1,1,0,-1,0,-1,0,1,
1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,
1,-1,1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,-1,1,-1,1,-1,1,
1,1,1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,-1,1,1,1,
1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,
1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,-1,0,1,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,-1,0,1,-1,0,1,
1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,
1,0,-1,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,1,0,-1,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,-1,0,1,0,-1,0,1,
1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,1,-1,1,
1,0,-1,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,1,0,-1,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,-1,0,1,
1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,1,1,1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,1,1,1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,
1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,
1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,
1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,
1,1,1,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,
1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,
1,-1,1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,
1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,-1,0,1,0,0,0,0,1,0,-1,1,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,-1,0,1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,-1,0,1,0,0,0,0,1,0,-1,
1,-1,1,-1,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,-1,1,-1,
1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,1,0,-1,1,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,1,0,-1,
1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,1,0,-1,0,1,0,-1,
1,-1,1,0,0,0,0,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,
1,0,-1,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,0,1,0,1,0,-1,
1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,
1,-1,1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,
1,1,1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-1,-1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
1,0,-1,0,1,0,-1,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,-1,0,1,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,-1,0,1,1,0,-1,
1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,
1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,1,0,-1,1,0,-1,0,1,0,-1,
1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,
1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,1,0,-1,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,1,0,-1,-1,0,1,0,1,0,-1,
1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,1,-1,1,0,0,0,0,-1,1,-1,
1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,
1,0,-1,0,-1,0,1,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,1,0,-1,1,0,-1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,
1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,
1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,
1,-1,1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,
1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,
1,1,1,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,
1,-1,1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,
1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,-1,0,1,0,0,0,0,1,0,-1,-1,0,1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,1,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,-1,0,1,0,0,0,0,1,0,-1,
1,1,1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-1,-1,
1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,1,0,-1,-1,0,1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,1,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,1,0,-1,
1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,1,0,-1,0,1,0,-1,
1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,
1,0,-1,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,0,1,0,1,0,-1,
1,-1,1,0,0,0,0,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,
1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
1,-1,1,-1,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,-1,1,-1,
1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,
1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,-1,0,1,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,1,0,-1,1,0,-1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,-1,0,1,0,1,0,-1,1,0,-1,
1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,
1,0,-1,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,-1,0,1,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,-1,0,1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,1,0,-1,0,1,0,-1,
1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,1,-1,1,0,0,0,0,-1,1,-1,
1,0,-1,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,1,0,-1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,1,0,-1,-1,0,1,0,1,0,-1,
1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,1,1,1,0,0,0,0,-1,-1,-1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,-1,0,1,1,0,-1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,-1,0,1,0,-1,0,1,1,0,-1,
1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,
1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,
1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,-1,0,1,-1,0,1,
1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,
1,0,-1,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,-1,0,1,0,-1,0,1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,-1,0,1,0,-1,0,1,
1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,1,-1,1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,1,-1,1,
1,0,-1,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,-1,0,1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,1,0,-1,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,-1,0,1,
1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,1,1,1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,
1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,
1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,
1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,
1,-1,1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,
1,0,-1,-1,0,1,0,1,0,-1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,1,0,-1,0,-1,0,1,
1,1,1,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,1,1,1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,
1,-1,1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,-1,1,-1,1,-1,1,
1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,-1,0,1,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,1,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,1,0,-1,0,0,0,0,-1,0,1,
1,1,1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,-1,1,1,1,
1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,1,0,-1,0,1,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,0,0,-1,0,1,0,1,0,-1,0,0,0,0,-1,0,1,
1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,-1,0,1,0,-1,0,1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,-1,0,1,-1,0,1,0,-1,0,1,
1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,
1,0,-1,-1,0,1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,-1,0,1,1,0,-1,0,-1,0,1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,1,1,0,-1,0,-1,0,1,
1,-1,1,0,0,0,0,-1,1,-1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,-1,1,-1,0,0,0,0,1,-1,1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,1,-1,1,
1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,
1,-1,1,-1,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,-1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,1,-1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,0,-1,0,1,0,-1,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,1,0,-1,0,1,0,-1,-1,0,1,1,0,-1,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,
1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,
1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,1,0,-1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-1,0,1,-1,0,1,0,-1,0,1,
1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,
1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,1,0,-1,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,-1,0,1,1,0,-1,0,-1,0,1,
1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,-1,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,1,-1,1,0,0,0,0,-1,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,-1,1,-1,0,0,0,0,1,-1,1,
1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,
1,0,-1,0,-1,0,1,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,-1,0,1,-1,0,1,-1,0,1,0,0,1,0,-1,1,0,-1,0,0,-1,0,1,1,0,-1,0,-1,0,1,-1,0,1,
1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1;

ideal Fourier = qtop*transpose(maxideal(1));

// This is the list of polynomial invariants.

map F = rQ, Fourier;
ideal PInvariants =  F(Invariants); 

// This is the polynomial parametrization.

ring r = 0,(a0,a1,b0,b1,c0,c1,d0,d1,e0,e1,f0,f1,g0,g1),dp;

ideal P = 
a0*b0*c0*d0*e0*f0*g0+2*a0*b0*c0*d0*e1*f1*g1+a0*b0*c0*d0*e2*f2*g2+2*a0*b1*c1*d0*e0*f1*g1+2*a0*b1*c1*d0*e1*f0*g0+2*a0*b1*c1*d0*e1*f2*g2+2*a0*b1*c1*d0*e2*f1*g1+a0*b2*c2*d0*e0*f2*g2+2*a0*b2*c2*d0*e1*f1*g1+a0*b2*c2*d0*e2*f0*g0+2*a1*b0*c1*d1*e0*f0*g0+4*a1*b0*c1*d1*e1*f1*g1+2*a1*b0*c1*d1*e2*f2*g2+2*a1*b1*c0*d1*e0*f1*g1+2*a1*b1*c0*d1*e1*f0*g0+2*a1*b1*c0*d1*e1*f2*g2+2*a1*b1*c0*d1*e2*f1*g1+2*a1*b1*c2*d1*e0*f1*g1+2*a1*b1*c2*d1*e1*f0*g0+2*a1*b1*c2*d1*e1*f2*g2+2*a1*b1*c2*d1*e2*f1*g1+2*a1*b2*c1*d1*e0*f2*g2+4*a1*b2*c1*d1*e1*f1*g1+2*a1*b2*c1*d1*e2*f0*g0+a2*b0*c2*d2*e0*f0*g0+2*a2*b0*c2*d2*e1*f1*g1+a2*b0*c2*d2*e2*f2*g2+2*a2*b1*c1*d2*e0*f1*g1+2*a2*b1*c1*d2*e1*f0*g0+2*a2*b1*c1*d2*e1*f2*g2+2*a2*b1*c1*d2*e2*f1*g1+a2*b2*c0*d2*e0*f2*g2+2*a2*b2*c0*d2*e1*f1*g1+a2*b2*c0*d2*e2*f0*g0,
2*a0*b0*c1*d0*e0*f1*g1+2*a0*b0*c1*d0*e1*f0*g0+2*a0*b0*c1*d0*e1*f2*g2+2*a0*b0*c1*d0*e2*f1*g1+2*a0*b1*c0*d0*e0*f0*g0+4*a0*b1*c0*d0*e1*f1*g1+2*a0*b1*c0*d0*e2*f2*g2+2*a0*b1*c2*d0*e0*f2*g2+4*a0*b1*c2*d0*e1*f1*g1+2*a0*b1*c2*d0*e2*f0*g0+2*a0*b2*c1*d0*e0*f1*g1+2*a0*b2*c1*d0*e1*f0*g0+2*a0*b2*c1*d0*e1*f2*g2+2*a0*b2*c1*d0*e2*f1*g1+2*a1*b0*c0*d1*e0*f1*g1+2*a1*b0*c0*d1*e1*f0*g0+2*a1*b0*c0*d1*e1*f2*g2+2*a1*b0*c0*d1*e2*f1*g1+2*a1*b0*c2*d1*e0*f1*g1+2*a1*b0*c2*d1*e1*f0*g0+2*a1*b0*c2*d1*e1*f2*g2+2*a1*b0*c2*d1*e2*f1*g1+4*a1*b1*c1*d1*e0*f0*g0+4*a1*b1*c1*d1*e0*f2*g2+16*a1*b1*c1*d1*e1*f1*g1+4*a1*b1*c1*d1*e2*f0*g0+4*a1*b1*c1*d1*e2*f2*g2+2*a1*b2*c0*d1*e0*f1*g1+2*a1*b2*c0*d1*e1*f0*g0+2*a1*b2*c0*d1*e1*f2*g2+2*a1*b2*c0*d1*e2*f1*g1+2*a1*b2*c2*d1*e0*f1*g1+2*a1*b2*c2*d1*e1*f0*g0+2*a1*b2*c2*d1*e1*f2*g2+2*a1*b2*c2*d1*e2*f1*g1+2*a2*b0*c1*d2*e0*f1*g1+2*a2*b0*c1*d2*e1*f0*g0+2*a2*b0*c1*d2*e1*f2*g2+2*a2*b0*c1*d2*e2*f1*g1+2*a2*b1*c0*d2*e0*f2*g2+4*a2*b1*c0*d2*e1*f1*g1+2*a2*b1*c0*d2*e2*f0*g0+2*a2*b1*c2*d2*e0*f0*g0+4*a2*b1*c2*d2*e1*f1*g1+2*a2*b1*c2*d2*e2*f2*g2+2*a2*b2*c1*d2*e0*f1*g1+2*a2*b2*c1*d2*e1*f0*g0+2*a2*b2*c1*d2*e1*f2*g2+2*a2*b2*c1*d2*e2*f1*g1,
a0*b0*c2*d0*e0*f2*g2+2*a0*b0*c2*d0*e1*f1*g1+a0*b0*c2*d0*e2*f0*g0+2*a0*b1*c1*d0*e0*f1*g1+2*a0*b1*c1*d0*e1*f0*g0+2*a0*b1*c1*d0*e1*f2*g2+2*a0*b1*c1*d0*e2*f1*g1+a0*b2*c0*d0*e0*f0*g0+2*a0*b2*c0*d0*e1*f1*g1+a0*b2*c0*d0*e2*f2*g2+2*a1*b0*c1*d1*e0*f2*g2+4*a1*b0*c1*d1*e1*f1*g1+2*a1*b0*c1*d1*e2*f0*g0+2*a1*b1*c0*d1*e0*f1*g1+2*a1*b1*c0*d1*e1*f0*g0+2*a1*b1*c0*d1*e1*f2*g2+2*a1*b1*c0*d1*e2*f1*g1+2*a1*b1*c2*d1*e0*f1*g1+2*a1*b1*c2*d1*e1*f0*g0+2*a1*b1*c2*d1*e1*f2*g2+2*a1*b1*c2*d1*e2*f1*g1+2*a1*b2*c1*d1*e0*f0*g0+4*a1*b2*c1*d1*e1*f1*g1+2*a1*b2*c1*d1*e2*f2*g2+a2*b0*c0*d2*e0*f2*g2+2*a2*b0*c0*d2*e1*f1*g1+a2*b0*c0*d2*e2*f0*g0+2*a2*b1*c1*d2*e0*f1*g1+2*a2*b1*c1*d2*e1*f0*g0+2*a2*b1*c1*d2*e1*f2*g2+2*a2*b1*c1*d2*e2*f1*g1+a2*b2*c2*d2*e0*f0*g0+2*a2*b2*c2*d2*e1*f1*g1+a2*b2*c2*d2*e2*f2*g2,
2*a0*b0*c0*d0*e0*f1*g0+2*a0*b0*c0*d0*e1*f0*g1+2*a0*b0*c0*d0*e1*f2*g1+2*a0*b0*c0*d0*e2*f1*g2+2*a0*b1*c1*d0*e0*f0*g1+2*a0*b1*c1*d0*e0*f2*g1+4*a0*b1*c1*d0*e1*f1*g0+4*a0*b1*c1*d0*e1*f1*g2+2*a0*b1*c1*d0*e2*f0*g1+2*a0*b1*c1*d0*e2*f2*g1+2*a0*b2*c2*d0*e0*f1*g2+2*a0*b2*c2*d0*e1*f0*g1+2*a0*b2*c2*d0*e1*f2*g1+2*a0*b2*c2*d0*e2*f1*g0+4*a1*b0*c1*d1*e0*f1*g0+4*a1*b0*c1*d1*e1*f0*g1+4*a1*b0*c1*d1*e1*f2*g1+4*a1*b0*c1*d1*e2*f1*g2+2*a1*b1*c0*d1*e0*f0*g1+2*a1*b1*c0*d1*e0*f2*g1+4*a1*b1*c0*d1*e1*f1*g0+4*a1*b1*c0*d1*e1*f1*g2+2*a1*b1*c0*d1*e2*f0*g1+2*a1*b1*c0*d1*e2*f2*g1+2*a1*b1*c2*d1*e0*f0*g1+2*a1*b1*c2*d1*e0*f2*g1+4*a1*b1*c2*d1*e1*f1*g0+4*a1*b1*c2*d1*e1*f1*g2+2*a1*b1*c2*d1*e2*f0*g1+2*a1*b1*c2*d1*e2*f2*g1+4*a1*b2*c1*d1*e0*f1*g2+4*a1*b2*c1*d1*e1*f0*g1+4*a1*b2*c1*d1*e1*f2*g1+4*a1*b2*c1*d1*e2*f1*g0+2*a2*b0*c2*d2*e0*f1*g0+2*a2*b0*c2*d2*e1*f0*g1+2*a2*b0*c2*d2*e1*f2*g1+2*a2*b0*c2*d2*e2*f1*g2+2*a2*b1*c1*d2*e0*f0*g1+2*a2*b1*c1*d2*e0*f2*g1+4*a2*b1*c1*d2*e1*f1*g0+4*a2*b1*c1*d2*e1*f1*g2+2*a2*b1*c1*d2*e2*f0*g1+2*a2*b1*c1*d2*e2*f2*g1+2*a2*b2*c0*d2*e0*f1*g2+2*a2*b2*c0*d2*e1*f0*g1+2*a2*b2*c0*d2*e1*f2*g1+2*a2*b2*c0*d2*e2*f1*g0,
2*a0*b0*c1*d0*e0*f0*g1+2*a0*b0*c1*d0*e1*f1*g0+2*a0*b0*c1*d0*e1*f1*g2+2*a0*b0*c1*d0*e2*f2*g1+2*a0*b1*c0*d0*e0*f1*g0+2*a0*b1*c0*d0*e1*f0*g1+2*a0*b1*c0*d0*e1*f2*g1+2*a0*b1*c0*d0*e2*f1*g2+2*a0*b1*c2*d0*e0*f1*g2+2*a0*b1*c2*d0*e1*f0*g1+2*a0*b1*c2*d0*e1*f2*g1+2*a0*b1*c2*d0*e2*f1*g0+2*a0*b2*c1*d0*e0*f2*g1+2*a0*b2*c1*d0*e1*f1*g0+2*a0*b2*c1*d0*e1*f1*g2+2*a0*b2*c1*d0*e2*f0*g1+2*a1*b0*c0*d1*e0*f0*g1+2*a1*b0*c0*d1*e1*f1*g0+2*a1*b0*c0*d1*e1*f1*g2+2*a1*b0*c0*d1*e2*f2*g1+2*a1*b0*c2*d1*e0*f0*g1+2*a1*b0*c2*d1*e1*f1*g0+2*a1*b0*c2*d1*e1*f1*g2+2*a1*b0*c2*d1*e2*f2*g1+4*a1*b1*c1*d1*e0*f1*g0+4*a1*b1*c1*d1*e0*f1*g2+8*a1*b1*c1*d1*e1*f0*g1+8*a1*b1*c1*d1*e1*f2*g1+4*a1*b1*c1*d1*e2*f1*g0+4*a1*b1*c1*d1*e2*f1*g2+2*a1*b2*c0*d1*e0*f2*g1+2*a1*b2*c0*d1*e1*f1*g0+2*a1*b2*c0*d1*e1*f1*g2+2*a1*b2*c0*d1*e2*f0*g1+2*a1*b2*c2*d1*e0*f2*g1+2*a1*b2*c2*d1*e1*f1*g0+2*a1*b2*c2*d1*e1*f1*g2+2*a1*b2*c2*d1*e2*f0*g1+2*a2*b0*c1*d2*e0*f0*g1+2*a2*b0*c1*d2*e1*f1*g0+2*a2*b0*c1*d2*e1*f1*g2+2*a2*b0*c1*d2*e2*f2*g1+2*a2*b1*c0*d2*e0*f1*g2+2*a2*b1*c0*d2*e1*f0*g1+2*a2*b1*c0*d2*e1*f2*g1+2*a2*b1*c0*d2*e2*f1*g0+2*a2*b1*c2*d2*e0*f1*g0+2*a2*b1*c2*d2*e1*f0*g1+2*a2*b1*c2*d2*e1*f2*g1+2*a2*b1*c2*d2*e2*f1*g2+2*a2*b2*c1*d2*e0*f2*g1+2*a2*b2*c1*d2*e1*f1*g0+2*a2*b2*c1*d2*e1*f1*g2+2*a2*b2*c1*d2*e2*f0*g1,
2*a0*b0*c2*d0*e0*f1*g2+2*a0*b0*c2*d0*e1*f0*g1+2*a0*b0*c2*d0*e1*f2*g1+2*a0*b0*c2*d0*e2*f1*g0+2*a0*b1*c1*d0*e0*f0*g1+2*a0*b1*c1*d0*e0*f2*g1+4*a0*b1*c1*d0*e1*f1*g0+4*a0*b1*c1*d0*e1*f1*g2+2*a0*b1*c1*d0*e2*f0*g1+2*a0*b1*c1*d0*e2*f2*g1+2*a0*b2*c0*d0*e0*f1*g0+2*a0*b2*c0*d0*e1*f0*g1+2*a0*b2*c0*d0*e1*f2*g1+2*a0*b2*c0*d0*e2*f1*g2+4*a1*b0*c1*d1*e0*f1*g2+4*a1*b0*c1*d1*e1*f0*g1+4*a1*b0*c1*d1*e1*f2*g1+4*a1*b0*c1*d1*e2*f1*g0+2*a1*b1*c0*d1*e0*f0*g1+2*a1*b1*c0*d1*e0*f2*g1+4*a1*b1*c0*d1*e1*f1*g0+4*a1*b1*c0*d1*e1*f1*g2+2*a1*b1*c0*d1*e2*f0*g1+2*a1*b1*c0*d1*e2*f2*g1+2*a1*b1*c2*d1*e0*f0*g1+2*a1*b1*c2*d1*e0*f2*g1+4*a1*b1*c2*d1*e1*f1*g0+4*a1*b1*c2*d1*e1*f1*g2+2*a1*b1*c2*d1*e2*f0*g1+2*a1*b1*c2*d1*e2*f2*g1+4*a1*b2*c1*d1*e0*f1*g0+4*a1*b2*c1*d1*e1*f0*g1+4*a1*b2*c1*d1*e1*f2*g1+4*a1*b2*c1*d1*e2*f1*g2+2*a2*b0*c0*d2*e0*f1*g2+2*a2*b0*c0*d2*e1*f0*g1+2*a2*b0*c0*d2*e1*f2*g1+2*a2*b0*c0*d2*e2*f1*g0+2*a2*b1*c1*d2*e0*f0*g1+2*a2*b1*c1*d2*e0*f2*g1+4*a2*b1*c1*d2*e1*f1*g0+4*a2*b1*c1*d2*e1*f1*g2+2*a2*b1*c1*d2*e2*f0*g1+2*a2*b1*c1*d2*e2*f2*g1+2*a2*b2*c2*d2*e0*f1*g0+2*a2*b2*c2*d2*e1*f0*g1+2*a2*b2*c2*d2*e1*f2*g1+2*a2*b2*c2*d2*e2*f1*g2,
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a0*b0*c2*d2*e0*f0*g0+2*a0*b0*c2*d2*e1*f1*g1+a0*b0*c2*d2*e2*f2*g2+2*a0*b1*c1*d2*e0*f1*g1+2*a0*b1*c1*d2*e1*f0*g0+2*a0*b1*c1*d2*e1*f2*g2+2*a0*b1*c1*d2*e2*f1*g1+a0*b2*c0*d2*e0*f2*g2+2*a0*b2*c0*d2*e1*f1*g1+a0*b2*c0*d2*e2*f0*g0+2*a1*b0*c1*d1*e0*f0*g0+4*a1*b0*c1*d1*e1*f1*g1+2*a1*b0*c1*d1*e2*f2*g2+2*a1*b1*c0*d1*e0*f1*g1+2*a1*b1*c0*d1*e1*f0*g0+2*a1*b1*c0*d1*e1*f2*g2+2*a1*b1*c0*d1*e2*f1*g1+2*a1*b1*c2*d1*e0*f1*g1+2*a1*b1*c2*d1*e1*f0*g0+2*a1*b1*c2*d1*e1*f2*g2+2*a1*b1*c2*d1*e2*f1*g1+2*a1*b2*c1*d1*e0*f2*g2+4*a1*b2*c1*d1*e1*f1*g1+2*a1*b2*c1*d1*e2*f0*g0+a2*b0*c0*d0*e0*f0*g0+2*a2*b0*c0*d0*e1*f1*g1+a2*b0*c0*d0*e2*f2*g2+2*a2*b1*c1*d0*e0*f1*g1+2*a2*b1*c1*d0*e1*f0*g0+2*a2*b1*c1*d0*e1*f2*g2+2*a2*b1*c1*d0*e2*f1*g1+a2*b2*c2*d0*e0*f2*g2+2*a2*b2*c2*d0*e1*f1*g1+a2*b2*c2*d0*e2*f0*g0;

// This checks that the polynomial parametrization
// lies on the probability simplex.
// It requires suma.sing. Most likely, you should 
// change the directory where you saved this file. 

// If you do have this file, you should uncomment
// the following two lines.

// < "/home/lgp/singular/suma.sing";

// Suma(Substitute(2,P));

// This checks that the PInvariants vanish at
// the polynomial parametrization.

map Evaluate = rP, P;

// The following command takes a lot of space and time to
// finish for larger models.

// ideal Z = Evaluate(PInvariants);

setring rP;
ideal Z;
int i;
for (i=1; i<= size(PInvariants); i++)
{
  i;
  Z = PInvariants[i];
  setring r;
  Evaluate(Z);
  setring rP;
}