CoCalc Public Files2016-07-16-190740.sagewsOpen with one click!
Author: Илья Некрасов
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Compute Environment: Ubuntu 18.04 (Deprecated)
SemistandardTableaux([1,1,1,1], max_entry=n).cardinality()
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1230, in execute exec( File "", line 1, in <module> File "sage/misc/lazy_import.pyx", line 361, in sage.misc.lazy_import.LazyImport.__call__ (build/cythonized/sage/misc/lazy_import.c:4027) return self.get_object()(*args, **kwds) File "sage/misc/classcall_metaclass.pyx", line 322, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__ (build/cythonized/sage/misc/classcall_metaclass.c:1762) return cls.classcall(cls, *args, **kwds) File "/ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/combinat/tableau.py", line 5870, in __classcall_private__ raise ValueError( "max_entry must be an integer or PlusInfinity" ) ValueError: max_entry must be an integer or PlusInfinity
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([3]) h = s([4]) h(e)
s[4, 4, 4] + s[5, 4, 2, 1] + s[6, 2, 2, 2] + s[6, 4, 2] + s[6, 6] + s[7, 3, 2] + s[7, 4, 1] + s[8, 2, 2] + s[8, 4] + s[9, 3] + s[10, 2] + s[12]
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]) h(e+e) print h = s([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] 3*s[2, 2, 1, 1] + s[2, 2, 2] + s[3, 1, 1, 1] + 4*s[3, 2, 1] + 3*s[3, 3] + 3*s[4, 1, 1] + s[4, 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]
# working place 12/01/2020 R.<t> = QQ[] s = SymmetricFunctions(R).s() e = s([4]) h = s([1,1]) e(h+h)-2*e(h) print e = s([4]) h = s([1,1]) e(h+h+h)-3*e(h) print e = s([4]) h = s([1,1]) e(h+h+h+h)-4*e(h) print e = s([4]) h = s([1,1]) e(h+h+h+h+h)-5*e(h) print e = s([4]) h = s([1,1]) e(h+h+h+h+h+h)-6*e(h) print e = s([4]) h = s([1,1]) e(h+h+h+h+h+h+h)-7*e(h) print e = s([4]) h = s([1,1]) e(h+h+h+h+h+h+h+h)-8*e(h) print
3*s[1, 1, 1, 1, 1, 1, 1, 1] + 3*s[2, 1, 1, 1, 1, 1, 1] + 7*s[2, 2, 1, 1, 1, 1] + 3*s[2, 2, 2, 1, 1] + 4*s[2, 2, 2, 2] + 4*s[3, 2, 1, 1, 1] + 3*s[3, 2, 2, 1] + 7*s[3, 3, 1, 1] + s[4, 2, 2] + 3*s[4, 3, 1] + 3*s[4, 4] <built-in function print> 12*s[1, 1, 1, 1, 1, 1, 1, 1] + 15*s[2, 1, 1, 1, 1, 1, 1] + 33*s[2, 2, 1, 1, 1, 1] + 18*s[2, 2, 2, 1, 1] + 18*s[2, 2, 2, 2] + 3*s[3, 1, 1, 1, 1, 1] + 24*s[3, 2, 1, 1, 1] + 18*s[3, 2, 2, 1] + 33*s[3, 3, 1, 1] + 3*s[3, 3, 2] + 3*s[4, 2, 1, 1] + 6*s[4, 2, 2] + 15*s[4, 3, 1] + 12*s[4, 4] <built-in function print> 31*s[1, 1, 1, 1, 1, 1, 1, 1] + 45*s[2, 1, 1, 1, 1, 1, 1] + 96*s[2, 2, 1, 1, 1, 1] + 60*s[2, 2, 2, 1, 1] + 51*s[2, 2, 2, 2] + 15*s[3, 1, 1, 1, 1, 1] + 80*s[3, 2, 1, 1, 1] + 61*s[3, 2, 2, 1] + 96*s[3, 3, 1, 1] + 15*s[3, 3, 2] + s[4, 1, 1, 1, 1] + 15*s[4, 2, 1, 1] + 20*s[4, 2, 2] + 45*s[4, 3, 1] + 31*s[4, 4] <built-in function print> 65*s[1, 1, 1, 1, 1, 1, 1, 1] + 105*s[2, 1, 1, 1, 1, 1, 1] + 220*s[2, 2, 1, 1, 1, 1] + 150*s[2, 2, 2, 1, 1] + 115*s[2, 2, 2, 2] + 45*s[3, 1, 1, 1, 1, 1] + 200*s[3, 2, 1, 1, 1] + 155*s[3, 2, 2, 1] + 220*s[3, 3, 1, 1] + 45*s[3, 3, 2] + 5*s[4, 1, 1, 1, 1] + 45*s[4, 2, 1, 1] + 50*s[4, 2, 2] + 105*s[4, 3, 1] + 65*s[4, 4] <built-in function print> 120*s[1, 1, 1, 1, 1, 1, 1, 1] + 210*s[2, 1, 1, 1, 1, 1, 1] + 435*s[2, 2, 1, 1, 1, 1] + 315*s[2, 2, 2, 1, 1] + 225*s[2, 2, 2, 2] + 105*s[3, 1, 1, 1, 1, 1] + 420*s[3, 2, 1, 1, 1] + 330*s[3, 2, 2, 1] + 435*s[3, 3, 1, 1] + 105*s[3, 3, 2] + 15*s[4, 1, 1, 1, 1] + 105*s[4, 2, 1, 1] + 105*s[4, 2, 2] + 210*s[4, 3, 1] + 120*s[4, 4] <built-in function print> 203*s[1, 1, 1, 1, 1, 1, 1, 1] + 378*s[2, 1, 1, 1, 1, 1, 1] + 777*s[2, 2, 1, 1, 1, 1] + 588*s[2, 2, 2, 1, 1] + 399*s[2, 2, 2, 2] + 210*s[3, 1, 1, 1, 1, 1] + 784*s[3, 2, 1, 1, 1] + 623*s[3, 2, 2, 1] + 777*s[3, 3, 1, 1] + 210*s[3, 3, 2] + 35*s[4, 1, 1, 1, 1] + 210*s[4, 2, 1, 1] + 196*s[4, 2, 2] + 378*s[4, 3, 1] + 203*s[4, 4] <built-in function print> 322*s[1, 1, 1, 1, 1, 1, 1, 1] + 630*s[2, 1, 1, 1, 1, 1, 1] + 1288*s[2, 2, 1, 1, 1, 1] + 1008*s[2, 2, 2, 1, 1] + 658*s[2, 2, 2, 2] + 378*s[3, 1, 1, 1, 1, 1] + 1344*s[3, 2, 1, 1, 1] + 1078*s[3, 2, 2, 1] + 1288*s[3, 3, 1, 1] + 378*s[3, 3, 2] + 70*s[4, 1, 1, 1, 1] + 378*s[4, 2, 1, 1] + 336*s[4, 2, 2] + 630*s[4, 3, 1] + 322*s[4, 4] <built-in function print>
# working place 12/01/2020 R.<t> = QQ[] s = SymmetricFunctions(R).s() e = s([3]) h = s([1,1]) e(h+h)-2*e(h) print e = s([3]) h = s([1,1]) e(h+h+h)-3*e(h) print e = s([3]) h = s([1,1]) e(h+h+h+h)-4*e(h) print e = s([3]) h = s([1,1]) e(h+h+h+h+h)-5*e(h) print e = s([3]) h = s([1,1]) e(h+h+h+h+h+h)-6*e(h) print e = s([3]) h = s([1,1]) e(h+h+h+h+h+h+h)-7*e(h) print
2*s[1, 1, 1, 1, 1, 1] + 2*s[2, 1, 1, 1, 1] + 4*s[2, 2, 1, 1] + 2*s[3, 2, 1] + 2*s[3, 3] <built-in function print> 7*s[1, 1, 1, 1, 1, 1] + 8*s[2, 1, 1, 1, 1] + 15*s[2, 2, 1, 1] + s[2, 2, 2] + s[3, 1, 1, 1] + 8*s[3, 2, 1] + 7*s[3, 3] <built-in function print> 16*s[1, 1, 1, 1, 1, 1] + 20*s[2, 1, 1, 1, 1] + 36*s[2, 2, 1, 1] + 4*s[2, 2, 2] + 4*s[3, 1, 1, 1] + 20*s[3, 2, 1] + 16*s[3, 3] <built-in function print> 30*s[1, 1, 1, 1, 1, 1] + 40*s[2, 1, 1, 1, 1] + 70*s[2, 2, 1, 1] + 10*s[2, 2, 2] + 10*s[3, 1, 1, 1] + 40*s[3, 2, 1] + 30*s[3, 3] <built-in function print> 50*s[1, 1, 1, 1, 1, 1] + 70*s[2, 1, 1, 1, 1] + 120*s[2, 2, 1, 1] + 20*s[2, 2, 2] + 20*s[3, 1, 1, 1] + 70*s[3, 2, 1] + 50*s[3, 3] <built-in function print> 77*s[1, 1, 1, 1, 1, 1] + 112*s[2, 1, 1, 1, 1] + 189*s[2, 2, 1, 1] + 35*s[2, 2, 2] + 35*s[3, 1, 1, 1] + 112*s[3, 2, 1] + 77*s[3, 3] <built-in function print>
# working place 12/02/2020 R.<t> = QQ[] s = SymmetricFunctions(R).s() e = s([3]) h = s([]) e(h+h+h)-3*e(h) print e = s([3]) h = s([1]) e(h+h+h)-3*e(h) print e = s([3]) h = s([1,1]) e(h+h+h)-3*e(h) print e = s([3]) h = s([1,1,1]) e(h+h+h)-3*e(h) print e = s([3]) h = s([1,1,1,1]) e(h+h+h)-3*e(h) print
7*s[] <built-in function print> s[1, 1, 1] + 8*s[2, 1] + 7*s[3] <built-in function print> 7*s[1, 1, 1, 1, 1, 1] + 8*s[2, 1, 1, 1, 1] + 15*s[2, 2, 1, 1] + s[2, 2, 2] + s[3, 1, 1, 1] + 8*s[3, 2, 1] + 7*s[3, 3] <built-in function print> s[1, 1, 1, 1, 1, 1, 1, 1, 1] + 8*s[2, 1, 1, 1, 1, 1, 1, 1] + 9*s[2, 2, 1, 1, 1, 1, 1] + 16*s[2, 2, 2, 1, 1, 1] + 8*s[2, 2, 2, 2, 1] + 7*s[3, 1, 1, 1, 1, 1, 1] + 8*s[3, 2, 1, 1, 1, 1] + 15*s[3, 2, 2, 1, 1] + s[3, 2, 2, 2] + s[3, 3, 1, 1, 1] + 8*s[3, 3, 2, 1] + 7*s[3, 3, 3] <built-in function print> 7*s[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 8*s[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 15*s[2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 16*s[2, 2, 2, 1, 1, 1, 1, 1, 1] + 23*s[2, 2, 2, 2, 1, 1, 1, 1] + 9*s[2, 2, 2, 2, 2, 1, 1] + 7*s[2, 2, 2, 2, 2, 2] + s[3, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 8*s[3, 2, 1, 1, 1, 1, 1, 1, 1] + 9*s[3, 2, 2, 1, 1, 1, 1, 1] + 16*s[3, 2, 2, 2, 1, 1, 1] + 8*s[3, 2, 2, 2, 2, 1] + 7*s[3, 3, 1, 1, 1, 1, 1, 1] + 8*s[3, 3, 2, 1, 1, 1, 1] + 15*s[3, 3, 2, 2, 1, 1] + s[3, 3, 2, 2, 2] + s[3, 3, 3, 1, 1, 1] + 8*s[3, 3, 3, 2, 1] + 7*s[3, 3, 3, 3] <built-in function print>
# working place 12/02/2020 R.<t> = QQ[] s = SymmetricFunctions(R).s() e = s([3]) h = s([]) e(h)-e(h) print e = s([3]) h = s([]) e(h+h)-2*e(h) print e = s([3]) h = s([]) e(h+h+h)-3*e(h) print e = s([3]) h = s([]) e(h+h+h+h)-4*e(h) print e = s([3]) h = s([]) e(h+h+h+h+h)-5*e(h) print e = s([3]) h = s([]) e(h+h+h+h+h+h)-6*e(h) print e = s([3]) h = s([]) e(h+h+h+h+h+h+h)-7*e(h) print e = s([3]) h = s([]) e(h+h+h+h+h+h+h+h)-8*e(h) print
0 <built-in function print> 2*s[] <built-in function print> 7*s[] <built-in function print> 16*s[] <built-in function print> 30*s[] <built-in function print> 50*s[] <built-in function print> 77*s[] <built-in function print> 112*s[] <built-in function print>