Shared2016-07-16-190740.sagewsOpen in CoCalc
Author: Илья Некрасов
Views : 20
R.<t> = QQ[] s = SymmetricFunctions(R).s() p = SymmetricFunctions(R).p() e = s([2]) h = s([3]) aaa = p([3]) aa = p([2,1]) a = p([1,1,1]) aaa.scalar(s([3]))*s([3]) + aaa.scalar(s([2,1]))*s([2,1]) + aaa.scalar(s([1,1,1]))*s([1,1,1]) aa.scalar(s([3]))*s([3]) + aa.scalar(s([2,1]))*s([2,1]) + aa.scalar(s([1,1,1]))*s([1,1,1]) a.scalar(s([3]))*s([3]) + a.scalar(s([2,1]))*s([2,1]) + aa.scalar(s([1,1,1]))*s([1,1,1])
s[1, 1, 1] - s[2, 1] + s[3] -s[1, 1, 1] + s[3] -s[1, 1, 1] + 2*s[2, 1] + s[3]
R.<t> = QQ[] s = SymmetricFunctions(R).s() e= s([1,1]) h = s([3]) h(e) print e= s([1,1,1]) h = s([3]) h(e) print 1, 1, 1, 1, 2, 1, 1] + s[2, 2, 2, 2, 1, 1]\n"}
import sage.libs.lrcalc.lrcalc as lrcalc lrcalc.mult([1,1,1],1],)
R.<t> = QQ[] s = SymmetricFunctions(R).s() e= s([1,1,1,1]) h = s([3]) h(e)
s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2] + s[3, 2, 2, 2, 1, 1, 1] + s[3, 3, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 2, 1, 1] + s[3, 3, 3, 3]
R.<t> = QQ[] s = SymmetricFunctions(R).s() e= s([1,1,1]) h = s([1,1,1]) h(e)
s[1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1] + s[3, 2, 2, 2] + s[3, 3, 1, 1, 1]
R.<t> = QQ[] s = SymmetricFunctions(R).s() e= s([1,1]) h = s([1,1,1]) h(e) print e= s([1,1,1]) h = s([1,1,1]) h(e) print e= s([1,1,1,1]) h = s([1,1,1]) h(e) print e= s([1,1,1]) h = s([1,1,1]) h(e) print e= s([1,1,1]) h = s([2,1]) h(e) print
s[2, 1, 1, 1, 1] + s[2, 2, 1, 1] + s[3, 2, 1] s[2, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1] + s[2, 2, 2, 2, 1] + s[3, 2, 1, 1, 1, 1] + s[3, 2, 2, 1, 1] + s[3, 3, 2, 1] s[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 1, 1] + s[3, 2, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 1, 1, 1] + s[3, 2, 2, 2, 2, 1] + s[3, 3, 2, 1, 1, 1, 1] + s[3, 3, 2, 2, 1, 1] + s[3, 3, 3, 2, 1] s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 1, 1] + s[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 2, 1, 1, 1, 1, 1] + s[3, 3, 2, 2, 2, 1, 1, 1] + s[3, 3, 3, 2, 2, 2] + s[3, 3, 3, 3, 1, 1, 1]
R.<t> = QQ[] s = SymmetricFunctions(R).s()
R.<t> = QQ[] s = SymmetricFunctions(R).s() e= s([1,1]) h = s([4]) h(e) print e= s([1,1,1]) h = s([4]) h(e) print e= s([1,1,1,1]) h = s([4]) h(e) print e= s([1,1,1,1,1]) h = s([4]) h(e) print e= s([1,1,1,1,1,1]) h = s([4]) h(e) print e= s([1,1,1,1,1,1,1]) h = s([4]) h(e) print e= s([1,1,1,1,1,1,1,1]) h = s([4]) h(e) print
s[1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1] + s[2, 2, 2, 2] + s[3, 3, 1, 1] + s[4, 4] s[2, 2, 2, 2, 2, 2] + s[3, 2, 2, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 1, 1, 1] + s[3, 3, 2, 2, 1, 1] + s[3, 3, 3, 1, 1, 1] + s[4, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 1, 1, 1, 1] + s[4, 2, 2, 2, 2] + s[4, 3, 3, 1, 1] + s[4, 4, 4] s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2] + s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 2, 2, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 1, 1] + s[3, 3, 3, 2, 1, 1, 1, 1, 1] + s[3, 3, 3, 2, 2, 2, 1] + 2*s[3, 3, 3, 3, 1, 1, 1, 1] + s[3, 3, 3, 3, 2, 2] + s[4, 2, 2, 2, 2, 2, 2] + s[4, 3, 2, 2, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 1, 1, 1] + s[4, 3, 3, 2, 2, 1, 1] + s[4, 3, 3, 3, 1, 1, 1] + s[4, 4, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 2] + s[4, 4, 3, 3, 1, 1] + s[4, 4, 4, 4] s[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 2, 2, 1, 1] + s[3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 2, 2, 1, 1, 1] + s[3, 3, 3, 2, 2, 2, 2, 2, 1] + s[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 2, 2, 1, 1, 1, 1] + s[3, 3, 3, 3, 2, 2, 2, 1, 1] + s[3, 3, 3, 3, 3, 1, 1, 1, 1, 1] + s[3, 3, 3, 3, 3, 2, 1, 1, 1] + s[3, 3, 3, 3, 3, 2, 2, 1] + s[4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 2, 1, 1] + s[4, 3, 3, 3, 2, 1, 1, 1, 1, 1] + s[4, 3, 3, 3, 2, 2, 2, 1] + 2*s[4, 3, 3, 3, 3, 1, 1, 1, 1] + s[4, 3, 3, 3, 3, 2, 2] + s[4, 4, 2, 2, 2, 2, 2, 2] + s[4, 4, 3, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 1, 1, 1] + s[4, 4, 3, 3, 2, 2, 1, 1] + s[4, 4, 3, 3, 3, 1, 1, 1] + s[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 2, 2, 1, 1, 1, 1] + s[4, 4, 4, 2, 2, 2, 2] + s[4, 4, 4, 3, 3, 1, 1] + s[4, 4, 4, 4, 4] s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1] + 2*s[3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1] + s[3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1] + 2*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2] + 2*s[3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1] + s[3, 3, 3, 3, 3, 2, 2, 2, 2, 1] + 3*s[3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 2, 2, 1, 1] + s[3, 3, 3, 3, 3, 3, 3, 3] + s[4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1] + s[4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1] + s[4, 3, 3, 3, 2, 2, 2, 2, 2, 1] + s[4, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1] + s[4, 3, 3, 3, 3, 2, 2, 2, 1, 1] + s[4, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1] + s[4, 3, 3, 3, 3, 3, 2, 1, 1, 1] + s[4, 3, 3, 3, 3, 3, 2, 2, 1] + s[4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 2, 2, 2, 2, 1, 1] + s[4, 4, 3, 3, 3, 2, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 2, 2, 2, 1] + 2*s[4, 4, 3, 3, 3, 3, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 2, 2] + s[4, 4, 4, 2, 2, 2, 2, 2, 2] + s[4, 4, 4, 3, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 2, 2, 2, 1, 1, 1] + s[4, 4, 4, 3, 3, 2, 2, 1, 1] + s[4, 4, 4, 3, 3, 3, 1, 1, 1] + s[4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 2, 2, 1, 1, 1, 1] + s[4, 4, 4, 4, 2, 2, 2, 2] + s[4, 4, 4, 4, 3, 3, 1, 1] + s[4, 4, 4, 4, 4, 4] s[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2] + s[3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1] + s[3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1] + s[3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 1] + s[3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1] + s[4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 3*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[4, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1] + 2*s[4, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1] + 2*s[4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2] + 2*s[4, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1] + s[4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1] + 3*s[4, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1] + s[4, 3, 3, 3, 3, 3, 3, 3, 3] + s[4, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1] + s[4, 4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 1] + s[4, 4, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 2, 2, 2, 1, 1] + s[4, 4, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 3, 2, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 3, 2, 2, 1] + s[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 4, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 3, 2, 2, 2, 2, 1, 1] + s[4, 4, 4, 3, 3, 3, 2, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 3, 2, 2, 2, 1] + 2*s[4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 3, 3, 2, 2] + s[4, 4, 4, 4, 2, 2, 2, 2, 2, 2] + s[4, 4, 4, 4, 3, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 3, 2, 2, 2, 1, 1, 1] + s[4, 4, 4, 4, 3, 3, 2, 2, 1, 1] + s[4, 4, 4, 4, 3, 3, 3, 1, 1, 1] + s[4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 4, 2, 2, 1, 1, 1, 1] + s[4, 4, 4, 4, 4, 2, 2, 2, 2] + s[4, 4, 4, 4, 4, 3, 3, 1, 1] + s[4, 4, 4, 4, 4, 4, 4] s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 3*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 7*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1] + 2*s[3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 7*s[3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 8*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 7*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] + 2*s[3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + 2*s[3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1] + 3*s[3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 7*s[3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1] + 3*s[3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1] + 4*s[3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1] + s[3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2] + s[3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1] + s[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 3*s[4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[4, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1] + s[4, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1] + s[4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 1] + s[4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1] + s[4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 3*s[4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[4, 4, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1] + 2*s[4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[4, 4, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 4*s[4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1] + 2*s[4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2] + 2*s[4, 4, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1] + 3*s[4, 4, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1] + s[4, 4, 3, 3, 3, 3, 3, 3, 3, 3] + s[4, 4, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 4, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[4, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1] + s[4, 4, 4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 1] + s[4, 4, 4, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 1, 1] + s[4, 4, 4, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 3, 3, 3, 3, 2, 1, 1, 1] + s[4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 1] + s[4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2] + s[4, 4, 4, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 4, 4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 4, 4, 4, 3, 3, 2, 2, 2, 2, 1, 1] + s[4, 4, 4, 4, 3, 3, 3, 2, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 3, 3, 3, 2, 2, 2, 1] + 2*s[4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1] + s[4, 4, 4, 4, 3, 3, 3, 3, 2, 2] + s[4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2] + s[4, 4, 4, 4, 4, 3, 2, 2, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 4, 3, 2, 2, 2, 1, 1, 1] + s[4, 4, 4, 4, 4, 3, 3, 2, 2, 1, 1] + s[4, 4, 4, 4, 4, 3, 3, 3, 1, 1, 1] + s[4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 1, 1] + s[4, 4, 4, 4, 4, 4, 2, 2, 2, 2] + s[4, 4, 4, 4, 4, 4, 3, 3, 1, 1] + s[4, 4, 4, 4, 4, 4, 4, 4]
R.<t> = QQ[] s = SymmetricFunctions(R).s() h = s([1]) h*h*h print h = s([1,1]) h*h print h = s([1,1]) h*h*h print h = s([1,1]) h*h*h*h print h = s([1,1,1]) h*h*h print h = s([1,1,1,1]) h*h*h print h = s([1,1,1,1,1]) h*h*h print
s[1, 1, 1] + 2*s[2, 1] + s[3] s[1, 1, 1, 1] + s[2, 1, 1] + s[2, 2] s[1, 1, 1, 1, 1, 1] + 2*s[2, 1, 1, 1, 1] + 3*s[2, 2, 1, 1] + s[2, 2, 2] + s[3, 1, 1, 1] + 2*s[3, 2, 1] + s[3, 3] s[1, 1, 1, 1, 1, 1, 1, 1] + 3*s[2, 1, 1, 1, 1, 1, 1] + 6*s[2, 2, 1, 1, 1, 1] + 6*s[2, 2, 2, 1, 1] + 3*s[2, 2, 2, 2] + 3*s[3, 1, 1, 1, 1, 1] + 8*s[3, 2, 1, 1, 1] + 7*s[3, 2, 2, 1] + 6*s[3, 3, 1, 1] + 3*s[3, 3, 2] + s[4, 1, 1, 1, 1] + 3*s[4, 2, 1, 1] + 2*s[4, 2, 2] + 3*s[4, 3, 1] + s[4, 4] s[1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 1, 1, 1, 1, 1, 1, 1] + 3*s[2, 2, 1, 1, 1, 1, 1] + 4*s[2, 2, 2, 1, 1, 1] + 2*s[2, 2, 2, 2, 1] + s[3, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 1, 1, 1, 1] + 3*s[3, 2, 2, 1, 1] + s[3, 2, 2, 2] + s[3, 3, 1, 1, 1] + 2*s[3, 3, 2, 1] + s[3, 3, 3] s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[2, 2, 2, 1, 1, 1, 1, 1, 1] + 5*s[2, 2, 2, 2, 1, 1, 1, 1] + 3*s[2, 2, 2, 2, 2, 1, 1] + s[2, 2, 2, 2, 2, 2] + s[3, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 1, 1, 1, 1, 1] + 4*s[3, 2, 2, 2, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 1] + s[3, 3, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 1, 1] + s[3, 3, 2, 2, 2] + s[3, 3, 3, 1, 1, 1] + 2*s[3, 3, 3, 2, 1] + s[3, 3, 3, 3] s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 6*s[2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 4*s[2, 2, 2, 2, 2, 2, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 1] + s[3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 5*s[3, 2, 2, 2, 2, 1, 1, 1, 1] + 3*s[3, 2, 2, 2, 2, 2, 1, 1] + s[3, 2, 2, 2, 2, 2, 2] + s[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 1] + s[3, 3, 3, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 2, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 1, 1] + s[3, 3, 3, 2, 2, 2] + s[3, 3, 3, 3, 1, 1, 1] + 2*s[3, 3, 3, 3, 2, 1] + s[3, 3, 3, 3, 3]
R.<t> = QQ[] s = SymmetricFunctions(R).s() h = s([1]) h*h print h = s([1,1]) h*h print h = s([1,1,1]) h*h print h = s([1,1,1,1]) h*h print
s[1, 1] + s[2] s[1, 1, 1, 1] + s[2, 1, 1] + s[2, 2] s[1, 1, 1, 1, 1, 1] + s[2, 1, 1, 1, 1] + s[2, 2, 1, 1] + s[2, 2, 2] s[1, 1, 1, 1, 1, 1, 1, 1] + s[2, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1] + s[2, 2, 2, 1, 1] + s[2, 2, 2, 2]
# general stabilization rule: e is any Schur polynomial, h is an e_{\infty} R.<t> = QQ[] s = SymmetricFunctions(R).s() e = s([2,1]) h = s([1]) h*e print h = s([1,1]) h*(e+e) print h = s([1,1,1]) h*e print h = s([1,1,1,1]) h*e print h = s([1,1,1,1,1]) h*e print h = s([1,1,1,1,1,1]) h*e print h = s([1,1,1,1,1,1,1]) h*e print
s[2, 1, 1] + s[2, 2] + s[3, 1] 2*s[2, 1, 1, 1] + 2*s[2, 2, 1] + 2*s[3, 1, 1] + 2*s[3, 2] s[2, 1, 1, 1, 1] + s[2, 2, 1, 1] + s[3, 1, 1, 1] + s[3, 2, 1] s[2, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1] + s[3, 1, 1, 1, 1] + s[3, 2, 1, 1] s[2, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1] + s[3, 1, 1, 1, 1, 1] + s[3, 2, 1, 1, 1] s[2, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1] + s[3, 1, 1, 1, 1, 1, 1] + s[3, 2, 1, 1, 1, 1] s[2, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1, 1] + s[3, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 1, 1, 1, 1, 1]
# symmetric stabilization rule: h is an h_{\infty} R.<t> = QQ[] s = SymmetricFunctions(R).s() h = s([2]) h*h*h print h = s([3]) h*h*h print h = s([4]) h*h*h print h = s([5]) h*h*h print h = s([6]) h*h*h print h = s([7]) h*h*h print
s[2, 2, 2] + 2*s[3, 2, 1] + s[3, 3] + s[4, 1, 1] + 3*s[4, 2] + 2*s[5, 1] + s[6] s[3, 3, 3] + 2*s[4, 3, 2] + s[4, 4, 1] + s[5, 2, 2] + 3*s[5, 3, 1] + 2*s[5, 4] + 2*s[6, 2, 1] + 4*s[6, 3] + s[7, 1, 1] + 3*s[7, 2] + 2*s[8, 1] + s[9] s[4, 4, 4] + 2*s[5, 4, 3] + s[5, 5, 2] + s[6, 3, 3] + 3*s[6, 4, 2] + 2*s[6, 5, 1] + s[6, 6] + 2*s[7, 3, 2] + 4*s[7, 4, 1] + 3*s[7, 5] + s[8, 2, 2] + 3*s[8, 3, 1] + 5*s[8, 4] + 2*s[9, 2, 1] + 4*s[9, 3] + s[10, 1, 1] + 3*s[10, 2] + 2*s[11, 1] + s[12] s[5, 5, 5] + 2*s[6, 5, 4] + s[6, 6, 3] + s[7, 4, 4] + 3*s[7, 5, 3] + 2*s[7, 6, 2] + s[7, 7, 1] + 2*s[8, 4, 3] + 4*s[8, 5, 2] + 3*s[8, 6, 1] + 2*s[8, 7] + s[9, 3, 3] + 3*s[9, 4, 2] + 5*s[9, 5, 1] + 4*s[9, 6] + 2*s[10, 3, 2] + 4*s[10, 4, 1] + 6*s[10, 5] + s[11, 2, 2] + 3*s[11, 3, 1] + 5*s[11, 4] + 2*s[12, 2, 1] + 4*s[12, 3] + s[13, 1, 1] + 3*s[13, 2] + 2*s[14, 1] + s[15] s[6, 6, 6] + 2*s[7, 6, 5] + s[7, 7, 4] + s[8, 5, 5] + 3*s[8, 6, 4] + 2*s[8, 7, 3] + s[8, 8, 2] + 2*s[9, 5, 4] + 4*s[9, 6, 3] + 3*s[9, 7, 2] + 2*s[9, 8, 1] + s[9, 9] + s[10, 4, 4] + 3*s[10, 5, 3] + 5*s[10, 6, 2] + 4*s[10, 7, 1] + 3*s[10, 8] + 2*s[11, 4, 3] + 4*s[11, 5, 2] + 6*s[11, 6, 1] + 5*s[11, 7] + s[12, 3, 3] + 3*s[12, 4, 2] + 5*s[12, 5, 1] + 7*s[12, 6] + 2*s[13, 3, 2] + 4*s[13, 4, 1] + 6*s[13, 5] + s[14, 2, 2] + 3*s[14, 3, 1] + 5*s[14, 4] + 2*s[15, 2, 1] + 4*s[15, 3] + s[16, 1, 1] + 3*s[16, 2] + 2*s[17, 1] + s[18] s[7, 7, 7] + 2*s[8, 7, 6] + s[8, 8, 5] + s[9, 6, 6] + 3*s[9, 7, 5] + 2*s[9, 8, 4] + s[9, 9, 3] + 2*s[10, 6, 5] + 4*s[10, 7, 4] + 3*s[10, 8, 3] + 2*s[10, 9, 2] + s[10, 10, 1] + s[11, 5, 5] + 3*s[11, 6, 4] + 5*s[11, 7, 3] + 4*s[11, 8, 2] + 3*s[11, 9, 1] + 2*s[11, 10] + 2*s[12, 5, 4] + 4*s[12, 6, 3] + 6*s[12, 7, 2] + 5*s[12, 8, 1] + 4*s[12, 9] + s[13, 4, 4] + 3*s[13, 5, 3] + 5*s[13, 6, 2] + 7*s[13, 7, 1] + 6*s[13, 8] + 2*s[14, 4, 3] + 4*s[14, 5, 2] + 6*s[14, 6, 1] + 8*s[14, 7] + s[15, 3, 3] + 3*s[15, 4, 2] + 5*s[15, 5, 1] + 7*s[15, 6] + 2*s[16, 3, 2] + 4*s[16, 4, 1] + 6*s[16, 5] + s[17, 2, 2] + 3*s[17, 3, 1] + 5*s[17, 4] + 2*s[18, 2, 1] + 4*s[18, 3] + s[19, 1, 1] + 3*s[19, 2] + 2*s[20, 1] + s[21]
R.<t> = QQ[] s = SymmetricFunctions(R).s() i=5 a= s([1,1,1,1]) b = s([i]) e= s([1,1]) f= s([1,1]) h = s([i]) h(f(e)) print b(a) print
s[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] + s[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 6*s[3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 2, 2, 1, 1] + 3*s[3, 3, 2, 2, 2, 2, 2, 2, 2] + 2*s[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 8*s[3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1] + 9*s[3, 3, 3, 2, 2, 2, 2, 1, 1, 1] + 6*s[3, 3, 3, 2, 2, 2, 2, 2, 1] + 2*s[3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1] + 8*s[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1] + 10*s[3, 3, 3, 3, 2, 2, 1, 1, 1, 1] + 11*s[3, 3, 3, 3, 2, 2, 2, 1, 1] + 3*s[3, 3, 3, 3, 2, 2, 2, 2] + 5*s[3, 3, 3, 3, 3, 1, 1, 1, 1, 1] + 8*s[3, 3, 3, 3, 3, 2, 1, 1, 1] + 7*s[3, 3, 3, 3, 3, 2, 2, 1] + 3*s[3, 3, 3, 3, 3, 3, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 2] + s[4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 3*s[4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 5*s[4, 2, 2, 2, 2, 2, 2, 2, 1, 1] + 3*s[4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 8*s[4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 14*s[4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 15*s[4, 3, 2, 2, 2, 2, 2, 1, 1, 1] + 10*s[4, 3, 2, 2, 2, 2, 2, 2, 1] + s[4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 9*s[4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 17*s[4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + 30*s[4, 3, 3, 2, 2, 2, 1, 1, 1, 1] + 25*s[4, 3, 3, 2, 2, 2, 2, 1, 1] + 14*s[4, 3, 3, 2, 2, 2, 2, 2] + 11*s[4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1] + 25*s[4, 3, 3, 3, 2, 1, 1, 1, 1, 1] + 37*s[4, 3, 3, 3, 2, 2, 1, 1, 1] + 27*s[4, 3, 3, 3, 2, 2, 2, 1] + 15*s[4, 3, 3, 3, 3, 1, 1, 1, 1] + 26*s[4, 3, 3, 3, 3, 2, 1, 1] + 10*s[4, 3, 3, 3, 3, 2, 2] + 9*s[4, 3, 3, 3, 3, 3, 1] + 2*s[4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 15*s[4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 17*s[4, 4, 2, 2, 2, 2, 1, 1, 1, 1] + 21*s[4, 4, 2, 2, 2, 2, 2, 1, 1] + 5*s[4, 4, 2, 2, 2, 2, 2, 2] + 4*s[4, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 17*s[4, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1] + 36*s[4, 4, 3, 2, 2, 1, 1, 1, 1, 1] + 46*s[4, 4, 3, 2, 2, 2, 1, 1, 1] + 34*s[4, 4, 3, 2, 2, 2, 2, 1] + 19*s[4, 4, 3, 3, 1, 1, 1, 1, 1, 1] + 48*s[4, 4, 3, 3, 2, 1, 1, 1, 1] + 51*s[4, 4, 3, 3, 2, 2, 1, 1] + 27*s[4, 4, 3, 3, 2, 2, 2] + 29*s[4, 4, 3, 3, 3, 1, 1, 1] + 31*s[4, 4, 3, 3, 3, 2, 1] + 4*s[4, 4, 3, 3, 3, 3] + 3*s[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1] + 16*s[4, 4, 4, 2, 1, 1, 1, 1, 1, 1] + 25*s[4, 4, 4, 2, 2, 1, 1, 1, 1] + 34*s[4, 4, 4, 2, 2, 2, 1, 1] + 10*s[4, 4, 4, 2, 2, 2, 2] + 21*s[4, 4, 4, 3, 1, 1, 1, 1, 1] + 42*s[4, 4, 4, 3, 2, 1, 1, 1] + 37*s[4, 4, 4, 3, 2, 2, 1] + 19*s[4, 4, 4, 3, 3, 1, 1] + 17*s[4, 4, 4, 3, 3, 2] + 7*s[4, 4, 4, 4, 1, 1, 1, 1] + 20*s[4, 4, 4, 4, 2, 1, 1] + 6*s[4, 4, 4, 4, 2, 2] + 9*s[4, 4, 4, 4, 3, 1] + s[4, 4, 4, 4, 4] + s[5, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[5, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 5*s[5, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 6*s[5, 2, 2, 2, 2, 2, 2, 1, 1, 1] + 4*s[5, 2, 2, 2, 2, 2, 2, 2, 1] + s[5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 15*s[5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 24*s[5, 3, 2, 2, 2, 2, 1, 1, 1, 1] + 22*s[5, 3, 2, 2, 2, 2, 2, 1, 1] + 10*s[5, 3, 2, 2, 2, 2, 2, 2] + 4*s[5, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 17*s[5, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1] + 38*s[5, 3, 3, 2, 2, 1, 1, 1, 1, 1] + 48*s[5, 3, 3, 2, 2, 2, 1, 1, 1] + 36*s[5, 3, 3, 2, 2, 2, 2, 1] + 19*s[5, 3, 3, 3, 1, 1, 1, 1, 1, 1] + 46*s[5, 3, 3, 3, 2, 1, 1, 1, 1] + 54*s[5, 3, 3, 3, 2, 2, 1, 1] + 24*s[5, 3, 3, 3, 2, 2, 2] + 28*s[5, 3, 3, 3, 3, 1, 1, 1] + 30*s[5, 3, 3, 3, 3, 2, 1] + 6*s[5, 3, 3, 3, 3, 3] + 5*s[5, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 17*s[5, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 33*s[5, 4, 2, 2, 2, 1, 1, 1, 1, 1] + 42*s[5, 4, 2, 2, 2, 2, 1, 1, 1] + 30*s[5, 4, 2, 2, 2, 2, 2, 1] + 13*s[5, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1] + 45*s[5, 4, 3, 2, 1, 1, 1, 1, 1, 1] + 85*s[5, 4, 3, 2, 2, 1, 1, 1, 1] + 91*s[5, 4, 3, 2, 2, 2, 1, 1] + 40*s[5, 4, 3, 2, 2, 2, 2] + 47*s[5, 4, 3, 3, 1, 1, 1, 1, 1] + 97*s[5, 4, 3, 3, 2, 1, 1, 1] + 85*s[5, 4, 3, 3, 2, 2, 1] + 49*s[5, 4, 3, 3, 3, 1, 1] + 30*s[5, 4, 3, 3, 3, 2] + 11*s[5, 4, 4, 1, 1, 1, 1, 1, 1, 1] + 39*s[5, 4, 4, 2, 1, 1, 1, 1, 1] + 64*s[5, 4, 4, 2, 2, 1, 1, 1] + 52*s[5, 4, 4, 2, 2, 2, 1] + 46*s[5, 4, 4, 3, 1, 1, 1, 1] + 80*s[5, 4, 4, 3, 2, 1, 1] + 41*s[5, 4, 4, 3, 2, 2] + 33*s[5, 4, 4, 3, 3, 1] + 19*s[5, 4, 4, 4, 1, 1, 1] + 26*s[5, 4, 4, 4, 2, 1] + 7*s[5, 4, 4, 4, 3] + 2*s[5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 7*s[5, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 17*s[5, 5, 2, 2, 1, 1, 1, 1, 1, 1] + 30*s[5, 5, 2, 2, 2, 1, 1, 1, 1] + 27*s[5, 5, 2, 2, 2, 2, 1, 1] + 15*s[5, 5, 2, 2, 2, 2, 2] + 13*s[5, 5, 3, 1, 1, 1, 1, 1, 1, 1] + 40*s[5, 5, 3, 2, 1, 1, 1, 1, 1] + 64*s[5, 5, 3, 2, 2, 1, 1, 1] + 51*s[5, 5, 3, 2, 2, 2, 1] + 37*s[5, 5, 3, 3, 1, 1, 1, 1] + 64*s[5, 5, 3, 3, 2, 1, 1] + 31*s[5, 5, 3, 3, 2, 2] + 24*s[5, 5, 3, 3, 3, 1] + 11*s[5, 5, 4, 1, 1, 1, 1, 1, 1] + 38*s[5, 5, 4, 2, 1, 1, 1, 1] + 49*s[5, 5, 4, 2, 2, 1, 1] + 27*s[5, 5, 4, 2, 2, 2] + 40*s[5, 5, 4, 3, 1, 1, 1] + 50*s[5, 5, 4, 3, 2, 1] + 10*s[5, 5, 4, 3, 3] + 14*s[5, 5, 4, 4, 1, 1] + 13*s[5, 5, 4, 4, 2] + 5*s[5, 5, 5, 1, 1, 1, 1, 1] + 13*s[5, 5, 5, 2, 1, 1, 1] + 13*s[5, 5, 5, 2, 2, 1] + 13*s[5, 5, 5, 3, 1, 1] + 9*s[5, 5, 5, 3, 2] + 4*s[5, 5, 5, 4, 1] + s[5, 5, 5, 5] + s[6, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[6, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[6, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 5*s[6, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 8*s[6, 2, 2, 2, 2, 2, 2, 1, 1] + s[6, 2, 2, 2, 2, 2, 2, 2] + 3*s[6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 10*s[6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 22*s[6, 3, 2, 2, 2, 1, 1, 1, 1, 1] + 27*s[6, 3, 2, 2, 2, 2, 1, 1, 1] + 20*s[6, 3, 2, 2, 2, 2, 2, 1] + 8*s[6, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1] + 23*s[6, 3, 3, 2, 1, 1, 1, 1, 1, 1] + 49*s[6, 3, 3, 2, 2, 1, 1, 1, 1] + 45*s[6, 3, 3, 2, 2, 2, 1, 1] + 25*s[6, 3, 3, 2, 2, 2, 2] + 21*s[6, 3, 3, 3, 1, 1, 1, 1, 1] + 49*s[6, 3, 3, 3, 2, 1, 1, 1] + 40*s[6, 3, 3, 3, 2, 2, 1] + 27*s[6, 3, 3, 3, 3, 1, 1] + 12*s[6, 3, 3, 3, 3, 2] + 2*s[6, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 8*s[6, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 28*s[6, 4, 2, 2, 1, 1, 1, 1, 1, 1] + 41*s[6, 4, 2, 2, 2, 1, 1, 1, 1] + 47*s[6, 4, 2, 2, 2, 2, 1, 1] + 15*s[6, 4, 2, 2, 2, 2, 2] + 18*s[6, 4, 3, 1, 1, 1, 1, 1, 1, 1] + 60*s[6, 4, 3, 2, 1, 1, 1, 1, 1] + 94*s[6, 4, 3, 2, 2, 1, 1, 1] + 75*s[6, 4, 3, 2, 2, 2, 1] + 56*s[6, 4, 3, 3, 1, 1, 1, 1] + 89*s[6, 4, 3, 3, 2, 1, 1] + 48*s[6, 4, 3, 3, 2, 2] + 31*s[6, 4, 3, 3, 3, 1] + 17*s[6, 4, 4, 1, 1, 1, 1, 1, 1] + 43*s[6, 4, 4, 2, 1, 1, 1, 1] + 66*s[6, 4, 4, 2, 2, 1, 1] + 24*s[6, 4, 4, 2, 2, 2] + 44*s[6, 4, 4, 3, 1, 1, 1] + 58*s[6, 4, 4, 3, 2, 1] + 16*s[6, 4, 4, 3, 3] + 18*s[6, 4, 4, 4, 1, 1] + 9*s[6, 4, 4, 4, 2] + 4*s[6, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 12*s[6, 5, 2, 1, 1, 1, 1, 1, 1, 1] + 28*s[6, 5, 2, 2, 1, 1, 1, 1, 1] + 38*s[6, 5, 2, 2, 2, 1, 1, 1] + 31*s[6, 5, 2, 2, 2, 2, 1] + 19*s[6, 5, 3, 1, 1, 1, 1, 1, 1] + 58*s[6, 5, 3, 2, 1, 1, 1, 1] + 70*s[6, 5, 3, 2, 2, 1, 1] + 37*s[6, 5, 3, 2, 2, 2] + 48*s[6, 5, 3, 3, 1, 1, 1] + 55*s[6, 5, 3, 3, 2, 1] + 10*s[6, 5, 3, 3, 3] + 18*s[6, 5, 4, 1, 1, 1, 1, 1] + 47*s[6, 5, 4, 2, 1, 1, 1] + 47*s[6, 5, 4, 2, 2, 1] + 41*s[6, 5, 4, 3, 1, 1] + 28*s[6, 5, 4, 3, 2] + 12*s[6, 5, 4, 4, 1] + 8*s[6, 5, 5, 1, 1, 1, 1] + 14*s[6, 5, 5, 2, 1, 1] + 11*s[6, 5, 5, 2, 2] + 9*s[6, 5, 5, 3, 1] + 4*s[6, 5, 5, 4] + 2*s[6, 6, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[6, 6, 2, 1, 1, 1, 1, 1, 1] + 10*s[6, 6, 2, 2, 1, 1, 1, 1] + 15*s[6, 6, 2, 2, 2, 1, 1] + 4*s[6, 6, 2, 2, 2, 2] + 9*s[6, 6, 3, 1, 1, 1, 1, 1] + 21*s[6, 6, 3, 2, 1, 1, 1] + 21*s[6, 6, 3, 2, 2, 1] + 13*s[6, 6, 3, 3, 1, 1] + 11*s[6, 6, 3, 3, 2] + 7*s[6, 6, 4, 1, 1, 1, 1] + 18*s[6, 6, 4, 2, 1, 1] + 7*s[6, 6, 4, 2, 2] + 11*s[6, 6, 4, 3, 1] + s[6, 6, 4, 4] + 3*s[6, 6, 5, 1, 1, 1] + 5*s[6, 6, 5, 2, 1] + 2*s[6, 6, 5, 3] + s[6, 6, 6, 1, 1] + s[7, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[7, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 5*s[7, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 6*s[7, 2, 2, 2, 2, 2, 1, 1, 1] + 4*s[7, 2, 2, 2, 2, 2, 2, 1] + s[7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[7, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 13*s[7, 3, 2, 2, 1, 1, 1, 1, 1, 1] + 21*s[7, 3, 2, 2, 2, 1, 1, 1, 1] + 20*s[7, 3, 2, 2, 2, 2, 1, 1] + 9*s[7, 3, 2, 2, 2, 2, 2] + 7*s[7, 3, 3, 1, 1, 1, 1, 1, 1, 1] + 23*s[7, 3, 3, 2, 1, 1, 1, 1, 1] + 33*s[7, 3, 3, 2, 2, 1, 1, 1] + 26*s[7, 3, 3, 2, 2, 2, 1] + 20*s[7, 3, 3, 3, 1, 1, 1, 1] + 28*s[7, 3, 3, 3, 2, 1, 1] + 14*s[7, 3, 3, 3, 2, 2] + 9*s[7, 3, 3, 3, 3, 1] + 3*s[7, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 10*s[7, 4, 2, 1, 1, 1, 1, 1, 1, 1] + 23*s[7, 4, 2, 2, 1, 1, 1, 1, 1] + 32*s[7, 4, 2, 2, 2, 1, 1, 1] + 23*s[7, 4, 2, 2, 2, 2, 1] + 15*s[7, 4, 3, 1, 1, 1, 1, 1, 1] + 44*s[7, 4, 3, 2, 1, 1, 1, 1] + 54*s[7, 4, 3, 2, 2, 1, 1] + 25*s[7, 4, 3, 2, 2, 2] + 34*s[7, 4, 3, 3, 1, 1, 1] + 39*s[7, 4, 3, 3, 2, 1] + 7*s[7, 4, 3, 3, 3] + 11*s[7, 4, 4, 1, 1, 1, 1, 1] + 29*s[7, 4, 4, 2, 1, 1, 1] + 27*s[7, 4, 4, 2, 2, 1] + 24*s[7, 4, 4, 3, 1, 1] + 15*s[7, 4, 4, 3, 2] + 6*s[7, 4, 4, 4, 1] + 2*s[7, 5, 1, 1, 1, 1, 1, 1, 1, 1] + 9*s[7, 5, 2, 1, 1, 1, 1, 1, 1] + 18*s[7, 5, 2, 2, 1, 1, 1, 1] + 20*s[7, 5, 2, 2, 2, 1, 1] + 10*s[7, 5, 2, 2, 2, 2] + 15*s[7, 5, 3, 1, 1, 1, 1, 1] + 35*s[7, 5, 3, 2, 1, 1, 1] + 33*s[7, 5, 3, 2, 2, 1] + 22*s[7, 5, 3, 3, 1, 1] + 15*s[7, 5, 3, 3, 2] + 13*s[7, 5, 4, 1, 1, 1, 1] + 26*s[7, 5, 4, 2, 1, 1] + 15*s[7, 5, 4, 2, 2] + 16*s[7, 5, 4, 3, 1] + 2*s[7, 5, 4, 4] + 5*s[7, 5, 5, 1, 1, 1] + 7*s[7, 5, 5, 2, 1] + 3*s[7, 5, 5, 3] + 3*s[7, 6, 2, 1, 1, 1, 1, 1] + 6*s[7, 6, 2, 2, 1, 1, 1] + 6*s[7, 6, 2, 2, 2, 1] + 7*s[7, 6, 3, 1, 1, 1, 1] + 13*s[7, 6, 3, 2, 1, 1] + 7*s[7, 6, 3, 2, 2] + 6*s[7, 6, 3, 3, 1] + 6*s[7, 6, 4, 1, 1, 1] + 9*s[7, 6, 4, 2, 1] + 3*s[7, 6, 4, 3] + 2*s[7, 6, 5, 1, 1] + 2*s[7, 6, 5, 2] + s[7, 7, 2, 2, 1, 1] + s[7, 7, 2, 2, 2] + s[7, 7, 3, 1, 1, 1] + 2*s[7, 7, 3, 2, 1] + s[7, 7, 4, 1, 1] + s[7, 7, 4, 2] + s[8, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[8, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 3*s[8, 2, 2, 2, 2, 1, 1, 1, 1] + 5*s[8, 2, 2, 2, 2, 2, 1, 1] + 2*s[8, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 5*s[8, 3, 2, 1, 1, 1, 1, 1, 1, 1] + 11*s[8, 3, 2, 2, 1, 1, 1, 1, 1] + 11*s[8, 3, 2, 2, 2, 1, 1, 1] + 8*s[8, 3, 2, 2, 2, 2, 1] + 3*s[8, 3, 3, 1, 1, 1, 1, 1, 1] + 13*s[8, 3, 3, 2, 1, 1, 1, 1] + 11*s[8, 3, 3, 2, 2, 1, 1] + 8*s[8, 3, 3, 2, 2, 2] + 10*s[8, 3, 3, 3, 1, 1, 1] + 8*s[8, 3, 3, 3, 2, 1] + s[8, 4, 1, 1, 1, 1, 1, 1, 1, 1] + 6*s[8, 4, 2, 1, 1, 1, 1, 1, 1] + 9*s[8, 4, 2, 2, 1, 1, 1, 1] + 12*s[8, 4, 2, 2, 2, 1, 1] + 3*s[8, 4, 2, 2, 2, 2] + 8*s[8, 4, 3, 1, 1, 1, 1, 1] + 17*s[8, 4, 3, 2, 1, 1, 1] + 15*s[8, 4, 3, 2, 2, 1] + 9*s[8, 4, 3, 3, 1, 1] + 7*s[8, 4, 3, 3, 2] + 3*s[8, 4, 4, 1, 1, 1, 1] + 12*s[8, 4, 4, 2, 1, 1] + 3*s[8, 4, 4, 2, 2] + 6*s[8, 4, 4, 3, 1] + 2*s[8, 5, 2, 1, 1, 1, 1, 1] + 4*s[8, 5, 2, 2, 1, 1, 1] + 4*s[8, 5, 2, 2, 2, 1] + 7*s[8, 5, 3, 1, 1, 1, 1] + 9*s[8, 5, 3, 2, 1, 1] + 7*s[8, 5, 3, 2, 2] + 3*s[8, 5, 3, 3, 1] + 6*s[8, 5, 4, 1, 1, 1] + 8*s[8, 5, 4, 2, 1] + 2*s[8, 5, 4, 3] + s[8, 5, 5, 1, 1] + 3*s[8, 5, 5, 2] + s[8, 6, 2, 2, 1, 1] + 2*s[8, 6, 3, 1, 1, 1] + 3*s[8, 6, 3, 2, 1] + s[8, 6, 3, 3] + 3*s[8, 6, 4, 1, 1] + s[8, 6, 4, 2] + s[8, 6, 5, 1] + s[8, 7, 3, 2] + s[9, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[9, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[9, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[9, 2, 2, 2, 2, 1, 1, 1] + s[9, 2, 2, 2, 2, 2, 1] + s[9, 3, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[9, 3, 2, 1, 1, 1, 1, 1, 1] + 3*s[9, 3, 2, 2, 1, 1, 1, 1] + 3*s[9, 3, 2, 2, 2, 1, 1] + s[9, 3, 2, 2, 2, 2] + 2*s[9, 3, 3, 1, 1, 1, 1, 1] + 3*s[9, 3, 3, 2, 1, 1, 1] + 3*s[9, 3, 3, 2, 2, 1] + s[9, 3, 3, 3, 1, 1] + s[9, 3, 3, 3, 2] + s[9, 4, 2, 1, 1, 1, 1, 1] + s[9, 4, 2, 2, 1, 1, 1] + s[9, 4, 2, 2, 2, 1] + 2*s[9, 4, 3, 1, 1, 1, 1] + 3*s[9, 4, 3, 2, 1, 1] + 2*s[9, 4, 3, 2, 2] + s[9, 4, 3, 3, 1] + 2*s[9, 4, 4, 1, 1, 1] + 2*s[9, 4, 4, 2, 1] + s[9, 5, 3, 1, 1, 1] + s[9, 5, 3, 2, 1] + 2*s[9, 5, 4, 1, 1] + s[9, 5, 4, 2] + s[9, 5, 5, 1] + s[9, 6, 4, 1] + s[10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[10, 2, 2, 1, 1, 1, 1, 1, 1] + s[10, 2, 2, 2, 2, 1, 1] + s[10, 3, 3, 1, 1, 1, 1] + s[10, 3, 3, 2, 2] + s[10, 4, 4, 1, 1] + s[10, 5, 5] s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1] + s[3, 2, 2, 2, 2, 2, 2, 2, 2, 1] + s[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1] + 3*s[3, 3, 2, 2, 2, 2, 2, 2, 1, 1] + 2*s[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 3*s[3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[3, 3, 3, 2, 2, 2, 2, 1, 1, 1] + s[3, 3, 3, 2, 2, 2, 2, 2, 1] + 3*s[3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1] + s[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1] + 4*s[3, 3, 3, 3, 2, 2, 1, 1, 1, 1] + s[3, 3, 3, 3, 2, 2, 2, 1, 1] + 2*s[3, 3, 3, 3, 2, 2, 2, 2] + s[3, 3, 3, 3, 3, 2, 1, 1, 1] + 2*s[3, 3, 3, 3, 3, 3, 1, 1] + s[4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 3, 2, 2, 2, 2, 2, 1, 1, 1] + s[4, 3, 2, 2, 2, 2, 2, 2, 1] + s[4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 1, 1, 1, 1] + 2*s[4, 3, 3, 2, 2, 2, 2, 1, 1] + 2*s[4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 1, 1, 1, 1, 1] + 3*s[4, 3, 3, 3, 2, 2, 1, 1, 1] + 2*s[4, 3, 3, 3, 2, 2, 2, 1] + s[4, 3, 3, 3, 3, 2, 1, 1] + s[4, 3, 3, 3, 3, 2, 2] + s[4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 3*s[4, 4, 2, 2, 2, 2, 1, 1, 1, 1] + s[4, 4, 2, 2, 2, 2, 2, 1, 1] + 2*s[4, 4, 2, 2, 2, 2, 2, 2] + s[4, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1] + s[4, 4, 3, 2, 2, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 2, 2, 2, 1, 1, 1] + s[4, 4, 3, 2, 2, 2, 2, 1] + 3*s[4, 4, 3, 3, 1, 1, 1, 1, 1, 1] + 2*s[4, 4, 3, 3, 2, 1, 1, 1, 1] + 3*s[4, 4, 3, 3, 2, 2, 1, 1] + s[4, 4, 3, 3, 3, 2, 1] + s[4, 4, 3, 3, 3, 3] + s[4, 4, 4, 2, 2, 2, 2] + s[4, 4, 4, 3, 1, 1, 1, 1, 1] + s[4, 4, 4, 3, 2, 1, 1, 1] + s[4, 4, 4, 3, 2, 2, 1] + 2*s[4, 4, 4, 4, 1, 1, 1, 1] + s[4, 4, 4, 4, 2, 2] + s[5, 3, 2, 2, 2, 2, 2, 1, 1] + s[5, 3, 3, 2, 2, 1, 1, 1, 1, 1] + s[5, 3, 3, 2, 2, 2, 2, 1] + s[5, 3, 3, 3, 2, 1, 1, 1, 1] + s[5, 3, 3, 3, 2, 2, 2] + s[5, 3, 3, 3, 3, 1, 1, 1] + s[5, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[5, 4, 2, 2, 2, 1, 1, 1, 1, 1] + s[5, 4, 2, 2, 2, 2, 1, 1, 1] + s[5, 4, 3, 2, 2, 1, 1, 1, 1] + s[5, 4, 3, 2, 2, 2, 1, 1] + s[5, 4, 3, 3, 1, 1, 1, 1, 1] + s[5, 4, 3, 3, 2, 1, 1, 1] + s[5, 4, 3, 3, 2, 2, 1] + s[5, 4, 4, 3, 2, 1, 1] + s[5, 4, 4, 4, 1, 1, 1] + s[5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + s[5, 5, 2, 2, 1, 1, 1, 1, 1, 1] + s[5, 5, 2, 2, 2, 2, 1, 1] + s[5, 5, 3, 3, 1, 1, 1, 1] + s[5, 5, 3, 3, 2, 2] + s[5, 5, 4, 4, 1, 1] + s[5, 5, 5, 5]
SemistandardTableaux([1,1,1,1], max_entry=8).cardinality() SemistandardTableaux([2,1,1], max_entry=8).cardinality() SemistandardTableaux([2,2], max_entry=8).cardinality() SemistandardTableaux([3,1], max_entry=8).cardinality() SemistandardTableaux([4], max_entry=8).cardinality() SemistandardTableaux([1,1,1,1], max_entry=8).cardinality() SemistandardTableaux([1,1,1,1], max_entry=8).cardinality() SemistandardTableaux([1,1,1,1], max_entry=8).cardinality() SemistandardTableaux([1,1,1,1], max_entry=8).cardinality()
70 378 336 630 330 70 70 70 70
binom(8,4)
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1191, in execute flags=compile_flags), namespace, locals) File "", line 1, in <module> NameError: name 'binom' is not defined