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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001527
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The cyclic permutation representation number of an integer partition.
This is the size of the largest cyclic group $C$ such that the fake degree is the character of a permutation representation of $C$.
-----------------------------------------------------------------------------
References: [1] Alexandersson, P., Amini, N. The cone of cyclic sieving phenomena [[MathSciNet:3922156]]
-----------------------------------------------------------------------------
Code:
def fdeg(p):
R.<q> = QQ[]
f = prod([ 1-q*q^j for j in range(p.size()) ])
b = sum([ j*k for j, k in enumerate(p) ])
return (q^b)*(f/p.hook_polynomial(q,q))
def fake_degree(a):
R.<q> = QQ[]
if a == 0:
return R(0)
else:
z = SymmetricFunctions(QQ).schur()(a)
return R(sum([z.coefficient(p)*fdeg(p) for p in z.support()]))
def standard_CSP(p, r):
P = parent(p)
q = P.gen()
PP.<q> = PolynomialRing(QQ)
R.<q> = PP.quo(q^r-1)
return R(p).lift()
def orbit_lengths(p, r):
p = standard_CSP(p, r)
p = {k: p[k] for k in range(r)}
divs = sorted(divisors(r))
O = dict()
for d in divs:
count = p[r-d]
if count:
O[r//d] = count
if count:
for k in range(0, r, d):
p[k] -= count
assert all(c == 0 for c in p.values()), "%s" % p
return O
def has_cyclic_permutation_representation(p, r):
if p == 0:
return True
try:
lo = orbit_lengths(p, r)
except AssertionError:
return False
return all(v in ZZ and ZZ(v) >= 0 for v in lo.values())
def statistic(la):
s = SymmetricFunctions(QQ).schur()
f = fake_degree(s(la))
for r in reversed(divisors(la.size())):
if has_cyclic_permutation_representation(f, r):
return r
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 2
[1,1] => 1
[3] => 3
[2,1] => 1
[1,1,1] => 3
[4] => 4
[3,1] => 1
[2,2] => 4
[2,1,1] => 1
[1,1,1,1] => 2
[5] => 5
[4,1] => 1
[3,2] => 5
[3,1,1] => 5
[2,2,1] => 5
[2,1,1,1] => 1
[1,1,1,1,1] => 5
[6] => 6
[5,1] => 1
[4,2] => 6
[4,1,1] => 3
[3,3] => 3
[3,2,1] => 2
[3,1,1,1] => 3
[2,2,2] => 6
[2,2,1,1] => 3
[2,1,1,1,1] => 2
[1,1,1,1,1,1] => 3
[7] => 7
[6,1] => 1
[5,2] => 7
[5,1,1] => 7
[4,3] => 7
[4,2,1] => 7
[4,1,1,1] => 1
[3,3,1] => 7
[3,2,2] => 7
[3,2,1,1] => 7
[3,1,1,1,1] => 7
[2,2,2,1] => 7
[2,2,1,1,1] => 7
[2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1] => 7
[8] => 8
[7,1] => 1
[6,2] => 8
[6,1,1] => 1
[5,3] => 1
[5,2,1] => 8
[5,1,1,1] => 2
[4,4] => 8
[4,3,1] => 1
[4,2,2] => 8
[4,2,1,1] => 1
[4,1,1,1,1] => 2
[3,3,2] => 1
[3,3,1,1] => 8
[3,2,2,1] => 1
[3,2,1,1,1] => 8
[3,1,1,1,1,1] => 1
[2,2,2,2] => 8
[2,2,2,1,1] => 1
[2,2,1,1,1,1] => 8
[2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1] => 4
[9] => 9
[8,1] => 1
[7,2] => 9
[7,1,1] => 9
[6,3] => 9
[6,2,1] => 1
[6,1,1,1] => 3
[5,4] => 1
[5,3,1] => 9
[5,2,2] => 9
[5,2,1,1] => 9
[5,1,1,1,1] => 1
[4,4,1] => 9
[4,3,2] => 1
[4,3,1,1] => 9
[4,2,2,1] => 9
[4,2,1,1,1] => 9
[4,1,1,1,1,1] => 3
[3,3,3] => 9
[3,3,2,1] => 1
[3,3,1,1,1] => 9
[3,2,2,2] => 9
[3,2,2,1,1] => 9
[3,2,1,1,1,1] => 1
[3,1,1,1,1,1,1] => 9
[2,2,2,2,1] => 1
[2,2,2,1,1,1] => 9
[2,2,1,1,1,1,1] => 9
[2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1] => 9
[10] => 10
[9,1] => 1
[8,2] => 10
[8,1,1] => 5
[7,3] => 5
[7,2,1] => 10
[7,1,1,1] => 2
[6,4] => 10
[6,3,1] => 5
[6,2,2] => 10
[6,2,1,1] => 5
[6,1,1,1,1] => 10
[5,5] => 5
[5,4,1] => 2
[5,3,2] => 5
[5,3,1,1] => 10
[5,2,2,1] => 5
[5,2,1,1,1] => 2
[5,1,1,1,1,1] => 5
[4,4,2] => 10
[4,4,1,1] => 5
[4,3,3] => 5
[4,3,2,1] => 2
[4,3,1,1,1] => 10
[4,2,2,2] => 10
[4,2,2,1,1] => 5
[4,2,1,1,1,1] => 10
[4,1,1,1,1,1,1] => 1
[3,3,3,1] => 10
[3,3,2,2] => 5
[3,3,2,1,1] => 10
[3,3,1,1,1,1] => 5
[3,2,2,2,1] => 2
[3,2,2,1,1,1] => 10
[3,2,1,1,1,1,1] => 10
[3,1,1,1,1,1,1,1] => 5
[2,2,2,2,2] => 10
[2,2,2,2,1,1] => 5
[2,2,2,1,1,1,1] => 10
[2,2,1,1,1,1,1,1] => 5
[2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1] => 5
[11] => 11
[10,1] => 1
[9,2] => 11
[9,1,1] => 11
[8,3] => 11
[8,2,1] => 11
[8,1,1,1] => 1
[7,4] => 11
[7,3,1] => 11
[7,2,2] => 11
[7,2,1,1] => 11
[7,1,1,1,1] => 11
[6,5] => 11
[6,4,1] => 11
[6,3,2] => 11
[6,3,1,1] => 11
[6,2,2,1] => 11
[6,2,1,1,1] => 11
[6,1,1,1,1,1] => 1
[5,5,1] => 11
[5,4,2] => 11
[5,4,1,1] => 11
[5,3,3] => 11
[5,3,2,1] => 11
[5,3,1,1,1] => 11
[5,2,2,2] => 11
[5,2,2,1,1] => 11
[5,2,1,1,1,1] => 11
[5,1,1,1,1,1,1] => 11
[4,4,3] => 11
[4,4,2,1] => 11
[4,4,1,1,1] => 11
[4,3,3,1] => 11
[4,3,2,2] => 11
[4,3,2,1,1] => 11
[4,3,1,1,1,1] => 11
[4,2,2,2,1] => 11
[4,2,2,1,1,1] => 11
[4,2,1,1,1,1,1] => 11
[4,1,1,1,1,1,1,1] => 1
[3,3,3,2] => 11
[3,3,3,1,1] => 11
[3,3,2,2,1] => 11
[3,3,2,1,1,1] => 11
[3,3,1,1,1,1,1] => 11
[3,2,2,2,2] => 11
[3,2,2,2,1,1] => 11
[3,2,2,1,1,1,1] => 11
[3,2,1,1,1,1,1,1] => 11
[3,1,1,1,1,1,1,1,1] => 11
[2,2,2,2,2,1] => 11
[2,2,2,2,1,1,1] => 11
[2,2,2,1,1,1,1,1] => 11
[2,2,1,1,1,1,1,1,1] => 11
[2,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => 11
[12] => 12
[11,1] => 1
[10,2] => 12
[10,1,1] => 3
[9,3] => 3
[9,2,1] => 4
[9,1,1,1] => 3
[8,4] => 4
[8,3,1] => 3
[8,2,2] => 12
[8,2,1,1] => 3
[8,1,1,1,1] => 2
[7,5] => 3
[7,4,1] => 12
[7,3,2] => 1
[7,3,1,1] => 12
[7,2,2,1] => 3
[7,2,1,1,1] => 12
[7,1,1,1,1,1] => 3
[6,6] => 12
[6,5,1] => 1
[6,4,2] => 6
[6,4,1,1] => 3
[6,3,3] => 3
[6,3,2,1] => 4
[6,3,1,1,1] => 4
[6,2,2,2] => 12
[6,2,2,1,1] => 3
[6,2,1,1,1,1] => 4
[6,1,1,1,1,1,1] => 3
[5,5,2] => 3
[5,5,1,1] => 6
[5,4,3] => 4
[5,4,2,1] => 3
[5,4,1,1,1] => 4
[5,3,3,1] => 12
[5,3,2,2] => 3
[5,3,2,1,1] => 12
[5,3,1,1,1,1] => 3
[5,2,2,2,1] => 4
[5,2,2,1,1,1] => 4
[5,2,1,1,1,1,1] => 12
[5,1,1,1,1,1,1,1] => 4
[4,4,4] => 12
[4,4,3,1] => 3
[4,4,2,2] => 4
[4,4,2,1,1] => 3
[4,4,1,1,1,1] => 6
[4,3,3,2] => 3
[4,3,3,1,1] => 12
[4,3,2,2,1] => 3
[4,3,2,1,1,1] => 4
[4,3,1,1,1,1,1] => 3
[4,2,2,2,2] => 12
[4,2,2,2,1,1] => 3
[4,2,2,1,1,1,1] => 12
[4,2,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1] => 4
[3,3,3,3] => 6
[3,3,3,2,1] => 4
[3,3,3,1,1,1] => 3
[3,3,2,2,2] => 3
[3,3,2,2,1,1] => 12
[3,3,2,1,1,1,1] => 1
[3,3,1,1,1,1,1,1] => 12
[3,2,2,2,2,1] => 1
[3,2,2,2,1,1,1] => 12
[3,2,2,1,1,1,1,1] => 3
[3,2,1,1,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2] => 12
[2,2,2,2,2,1,1] => 3
[2,2,2,2,1,1,1,1] => 2
[2,2,2,1,1,1,1,1,1] => 3
[2,2,1,1,1,1,1,1,1,1] => 12
[2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1] => 6
[13] => 13
[12,1] => 1
[11,2] => 13
[11,1,1] => 13
[10,3] => 13
[10,2,1] => 13
[10,1,1,1] => 1
[9,4] => 13
[9,3,1] => 13
[9,2,2] => 13
[9,2,1,1] => 13
[9,1,1,1,1] => 13
[8,5] => 13
[8,4,1] => 13
[8,3,2] => 13
[8,3,1,1] => 13
[8,2,2,1] => 13
[8,2,1,1,1] => 13
[8,1,1,1,1,1] => 1
[7,6] => 13
[7,5,1] => 13
[7,4,2] => 13
[7,4,1,1] => 13
[7,3,3] => 13
[7,3,2,1] => 13
[7,3,1,1,1] => 13
[7,2,2,2] => 13
[7,2,2,1,1] => 13
[7,2,1,1,1,1] => 13
[7,1,1,1,1,1,1] => 13
[6,6,1] => 13
[6,5,2] => 13
[6,5,1,1] => 13
[6,4,3] => 13
[6,4,2,1] => 13
[6,4,1,1,1] => 13
[6,3,3,1] => 13
[6,3,2,2] => 13
[6,3,2,1,1] => 13
[6,3,1,1,1,1] => 13
[6,2,2,2,1] => 13
[6,2,2,1,1,1] => 13
[6,2,1,1,1,1,1] => 13
[6,1,1,1,1,1,1,1] => 1
[5,5,3] => 13
[5,5,2,1] => 13
[5,5,1,1,1] => 13
[5,4,4] => 13
[5,4,3,1] => 13
[5,4,2,2] => 13
[5,4,2,1,1] => 13
[5,4,1,1,1,1] => 13
[5,3,3,2] => 13
[5,3,3,1,1] => 13
[5,3,2,2,1] => 13
[5,3,2,1,1,1] => 13
[5,3,1,1,1,1,1] => 13
[5,2,2,2,2] => 13
[5,2,2,2,1,1] => 13
[5,2,2,1,1,1,1] => 13
[5,2,1,1,1,1,1,1] => 13
[5,1,1,1,1,1,1,1,1] => 13
[4,4,4,1] => 13
[4,4,3,2] => 13
[4,4,3,1,1] => 13
[4,4,2,2,1] => 13
[4,4,2,1,1,1] => 13
[4,4,1,1,1,1,1] => 13
[4,3,3,3] => 13
[4,3,3,2,1] => 13
[4,3,3,1,1,1] => 13
[4,3,2,2,2] => 13
[4,3,2,2,1,1] => 13
[4,3,2,1,1,1,1] => 13
[4,3,1,1,1,1,1,1] => 13
[4,2,2,2,2,1] => 13
[4,2,2,2,1,1,1] => 13
[4,2,2,1,1,1,1,1] => 13
[4,2,1,1,1,1,1,1,1] => 13
[4,1,1,1,1,1,1,1,1,1] => 1
[3,3,3,3,1] => 13
[3,3,3,2,2] => 13
[3,3,3,2,1,1] => 13
[3,3,3,1,1,1,1] => 13
[3,3,2,2,2,1] => 13
[3,3,2,2,1,1,1] => 13
[3,3,2,1,1,1,1,1] => 13
[3,3,1,1,1,1,1,1,1] => 13
[3,2,2,2,2,2] => 13
[3,2,2,2,2,1,1] => 13
[3,2,2,2,1,1,1,1] => 13
[3,2,2,1,1,1,1,1,1] => 13
[3,2,1,1,1,1,1,1,1,1] => 13
[3,1,1,1,1,1,1,1,1,1,1] => 13
[2,2,2,2,2,2,1] => 13
[2,2,2,2,2,1,1,1] => 13
[2,2,2,2,1,1,1,1,1] => 13
[2,2,2,1,1,1,1,1,1,1] => 13
[2,2,1,1,1,1,1,1,1,1,1] => 13
[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] => 13
[14] => 14
[13,1] => 1
[12,2] => 14
[12,1,1] => 7
[11,3] => 7
[11,2,1] => 14
[11,1,1,1] => 2
[10,4] => 14
[10,3,1] => 7
[10,2,2] => 14
[10,2,1,1] => 7
[10,1,1,1,1] => 14
[9,5] => 7
[9,4,1] => 14
[9,3,2] => 7
[9,3,1,1] => 14
[9,2,2,1] => 7
[9,2,1,1,1] => 14
[9,1,1,1,1,1] => 1
[8,6] => 14
[8,5,1] => 7
[8,4,2] => 14
[8,4,1,1] => 7
[8,3,3] => 7
[8,3,2,1] => 14
[8,3,1,1,1] => 14
[8,2,2,2] => 14
[8,2,2,1,1] => 7
[8,2,1,1,1,1] => 14
[8,1,1,1,1,1,1] => 7
[7,7] => 7
[7,6,1] => 2
[7,5,2] => 7
[7,5,1,1] => 14
[7,4,3] => 14
[7,4,2,1] => 7
[7,4,1,1,1] => 2
[7,3,3,1] => 14
[7,3,2,2] => 7
[7,3,2,1,1] => 14
[7,3,1,1,1,1] => 7
[7,2,2,2,1] => 14
[7,2,2,1,1,1] => 14
[7,2,1,1,1,1,1] => 2
[7,1,1,1,1,1,1,1] => 7
[6,6,2] => 14
[6,6,1,1] => 7
[6,5,3] => 7
[6,5,2,1] => 2
[6,5,1,1,1] => 14
[6,4,4] => 14
[6,4,3,1] => 7
[6,4,2,2] => 14
[6,4,2,1,1] => 7
[6,4,1,1,1,1] => 14
[6,3,3,2] => 7
[6,3,3,1,1] => 14
[6,3,2,2,1] => 7
[6,3,2,1,1,1] => 2
[6,3,1,1,1,1,1] => 7
[6,2,2,2,2] => 14
[6,2,2,2,1,1] => 7
[6,2,2,1,1,1,1] => 14
[6,2,1,1,1,1,1,1] => 7
[6,1,1,1,1,1,1,1,1] => 2
[5,5,4] => 7
[5,5,3,1] => 14
[5,5,2,2] => 7
[5,5,2,1,1] => 14
[5,5,1,1,1,1] => 7
[5,4,4,1] => 7
[5,4,3,2] => 14
[5,4,3,1,1] => 14
[5,4,2,2,1] => 2
[5,4,2,1,1,1] => 14
[5,4,1,1,1,1,1] => 14
[5,3,3,3] => 14
[5,3,3,2,1] => 14
[5,3,3,1,1,1] => 7
[5,3,2,2,2] => 7
[5,3,2,2,1,1] => 14
[5,3,2,1,1,1,1] => 7
[5,3,1,1,1,1,1,1] => 14
[5,2,2,2,2,1] => 7
[5,2,2,2,1,1,1] => 2
[5,2,2,1,1,1,1,1] => 7
[5,2,1,1,1,1,1,1,1] => 14
[5,1,1,1,1,1,1,1,1,1] => 7
[4,4,4,2] => 14
[4,4,4,1,1] => 7
[4,4,3,3] => 7
[4,4,3,2,1] => 14
[4,4,3,1,1,1] => 14
[4,4,2,2,2] => 14
[4,4,2,2,1,1] => 7
[4,4,2,1,1,1,1] => 14
[4,4,1,1,1,1,1,1] => 7
[4,3,3,3,1] => 14
[4,3,3,2,2] => 7
[4,3,3,2,1,1] => 14
[4,3,3,1,1,1,1] => 7
[4,3,2,2,2,1] => 2
[4,3,2,2,1,1,1] => 14
[4,3,2,1,1,1,1,1] => 14
[4,3,1,1,1,1,1,1,1] => 14
[4,2,2,2,2,2] => 14
[4,2,2,2,2,1,1] => 7
[4,2,2,2,1,1,1,1] => 14
[4,2,2,1,1,1,1,1,1] => 7
[4,2,1,1,1,1,1,1,1,1] => 14
[4,1,1,1,1,1,1,1,1,1,1] => 1
[3,3,3,3,2] => 14
[3,3,3,3,1,1] => 7
[3,3,3,2,2,1] => 14
[3,3,3,2,1,1,1] => 14
[3,3,3,1,1,1,1,1] => 14
[3,3,2,2,2,2] => 7
[3,3,2,2,2,1,1] => 14
[3,3,2,2,1,1,1,1] => 7
[3,3,2,1,1,1,1,1,1] => 14
[3,3,1,1,1,1,1,1,1,1] => 7
[3,2,2,2,2,2,1] => 2
[3,2,2,2,2,1,1,1] => 14
[3,2,2,2,1,1,1,1,1] => 14
[3,2,2,1,1,1,1,1,1,1] => 14
[3,2,1,1,1,1,1,1,1,1,1] => 14
[3,1,1,1,1,1,1,1,1,1,1,1] => 7
[2,2,2,2,2,2,2] => 14
[2,2,2,2,2,2,1,1] => 7
[2,2,2,2,2,1,1,1,1] => 14
[2,2,2,2,1,1,1,1,1,1] => 7
[2,2,2,1,1,1,1,1,1,1,1] => 14
[2,2,1,1,1,1,1,1,1,1,1,1] => 7
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 7
[15] => 15
[14,1] => 1
[13,2] => 15
[13,1,1] => 15
[12,3] => 15
[12,2,1] => 5
[12,1,1,1] => 3
[11,4] => 5
[11,3,1] => 15
[11,2,2] => 15
[11,2,1,1] => 15
[11,1,1,1,1] => 5
[10,5] => 15
[10,4,1] => 3
[10,3,2] => 5
[10,3,1,1] => 15
[10,2,2,1] => 15
[10,2,1,1,1] => 3
[10,1,1,1,1,1] => 5
[9,6] => 3
[9,5,1] => 5
[9,4,2] => 15
[9,4,1,1] => 15
[9,3,3] => 15
[9,3,2,1] => 1
[9,3,1,1,1] => 15
[9,2,2,2] => 15
[9,2,2,1,1] => 15
[9,2,1,1,1,1] => 5
[9,1,1,1,1,1,1] => 3
[8,7] => 5
[8,6,1] => 15
[8,5,2] => 3
[8,5,1,1] => 15
[8,4,3] => 5
[8,4,2,1] => 15
[8,4,1,1,1] => 5
[8,3,3,1] => 15
[8,3,2,2] => 15
[8,3,2,1,1] => 15
[8,3,1,1,1,1] => 15
[8,2,2,2,1] => 1
[8,2,2,1,1,1] => 15
[8,2,1,1,1,1,1] => 15
[8,1,1,1,1,1,1,1] => 5
[7,7,1] => 15
[7,6,2] => 5
[7,6,1,1] => 3
[7,5,3] => 15
[7,5,2,1] => 15
[7,5,1,1,1] => 15
[7,4,4] => 15
[7,4,3,1] => 15
[7,4,2,2] => 1
[7,4,2,1,1] => 15
[7,4,1,1,1,1] => 15
[7,3,3,2] => 15
[7,3,3,1,1] => 15
[7,3,2,2,1] => 15
[7,3,2,1,1,1] => 5
[7,3,1,1,1,1,1] => 15
[7,2,2,2,2] => 15
[7,2,2,2,1,1] => 15
[7,2,2,1,1,1,1] => 15
[7,2,1,1,1,1,1,1] => 15
[7,1,1,1,1,1,1,1,1] => 3
[6,6,3] => 15
[6,6,2,1] => 5
[6,6,1,1,1] => 15
[6,5,4] => 5
[6,5,3,1] => 15
[6,5,2,2] => 15
[6,5,2,1,1] => 3
[6,5,1,1,1,1] => 5
[6,4,4,1] => 15
[6,4,3,2] => 5
[6,4,3,1,1] => 15
[6,4,2,2,1] => 15
[6,4,2,1,1,1] => 15
[6,4,1,1,1,1,1] => 15
[6,3,3,3] => 15
[6,3,3,2,1] => 5
[6,3,3,1,1,1] => 15
[6,3,2,2,2] => 3
[6,3,2,2,1,1] => 15
[6,3,2,1,1,1,1] => 5
[6,3,1,1,1,1,1,1] => 15
[6,2,2,2,2,1] => 5
[6,2,2,2,1,1,1] => 15
[6,2,2,1,1,1,1,1] => 15
[6,2,1,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1,1] => 5
[5,5,5] => 15
[5,5,4,1] => 3
[5,5,3,2] => 15
[5,5,3,1,1] => 15
[5,5,2,2,1] => 5
[5,5,2,1,1,1] => 3
[5,5,1,1,1,1,1] => 15
[5,4,4,2] => 15
[5,4,4,1,1] => 5
[5,4,3,3] => 5
[5,4,3,2,1] => 3
[5,4,3,1,1,1] => 5
[5,4,2,2,2] => 5
[5,4,2,2,1,1] => 15
[5,4,2,1,1,1,1] => 15
[5,4,1,1,1,1,1,1] => 1
[5,3,3,3,1] => 5
[5,3,3,2,2] => 15
[5,3,3,2,1,1] => 15
[5,3,3,1,1,1,1] => 15
[5,3,2,2,2,1] => 3
[5,3,2,2,1,1,1] => 15
[5,3,2,1,1,1,1,1] => 15
[5,3,1,1,1,1,1,1,1] => 15
[5,2,2,2,2,2] => 15
[5,2,2,2,2,1,1] => 15
[5,2,2,2,1,1,1,1] => 5
[5,2,2,1,1,1,1,1,1] => 15
[5,2,1,1,1,1,1,1,1,1] => 3
[5,1,1,1,1,1,1,1,1,1,1] => 5
[4,4,4,3] => 3
[4,4,4,2,1] => 5
[4,4,4,1,1,1] => 15
[4,4,3,3,1] => 15
[4,4,3,2,2] => 15
[4,4,3,2,1,1] => 5
[4,4,3,1,1,1,1] => 15
[4,4,2,2,2,1] => 15
[4,4,2,2,1,1,1] => 1
[4,4,2,1,1,1,1,1] => 15
[4,4,1,1,1,1,1,1,1] => 15
[4,3,3,3,2] => 3
[4,3,3,3,1,1] => 15
[4,3,3,2,2,1] => 15
[4,3,3,2,1,1,1] => 15
[4,3,3,1,1,1,1,1] => 15
[4,3,2,2,2,2] => 5
[4,3,2,2,2,1,1] => 15
[4,3,2,2,1,1,1,1] => 15
[4,3,2,1,1,1,1,1,1] => 1
[4,3,1,1,1,1,1,1,1,1] => 15
[4,2,2,2,2,2,1] => 3
[4,2,2,2,2,1,1,1] => 15
[4,2,2,2,1,1,1,1,1] => 15
[4,2,2,1,1,1,1,1,1,1] => 15
[4,2,1,1,1,1,1,1,1,1,1] => 15
[4,1,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,3] => 15
[3,3,3,3,2,1] => 5
[3,3,3,3,1,1,1] => 15
[3,3,3,2,2,2] => 15
[3,3,3,2,2,1,1] => 15
[3,3,3,2,1,1,1,1] => 5
[3,3,3,1,1,1,1,1,1] => 15
[3,3,2,2,2,2,1] => 5
[3,3,2,2,2,1,1,1] => 3
[3,3,2,2,1,1,1,1,1] => 15
[3,3,2,1,1,1,1,1,1,1] => 5
[3,3,1,1,1,1,1,1,1,1,1] => 15
[3,2,2,2,2,2,2] => 15
[3,2,2,2,2,2,1,1] => 15
[3,2,2,2,2,1,1,1,1] => 5
[3,2,2,2,1,1,1,1,1,1] => 3
[3,2,2,1,1,1,1,1,1,1,1] => 15
[3,2,1,1,1,1,1,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 15
[2,2,2,2,2,2,2,1] => 5
[2,2,2,2,2,2,1,1,1] => 3
[2,2,2,2,2,1,1,1,1,1] => 15
[2,2,2,2,1,1,1,1,1,1,1] => 5
[2,2,2,1,1,1,1,1,1,1,1,1] => 15
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 15
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 15
[16] => 16
[15,1] => 1
[14,2] => 16
[14,1,1] => 1
[13,3] => 1
[13,2,1] => 16
[13,1,1,1] => 2
[12,4] => 16
[12,3,1] => 1
[12,2,2] => 16
[12,2,1,1] => 1
[12,1,1,1,1] => 2
[11,5] => 1
[11,4,1] => 16
[11,3,2] => 1
[11,3,1,1] => 16
[11,2,2,1] => 1
[11,2,1,1,1] => 16
[11,1,1,1,1,1] => 1
[10,6] => 16
[10,5,1] => 1
[10,4,2] => 2
[10,4,1,1] => 1
[10,3,3] => 1
[10,3,2,1] => 16
[10,3,1,1,1] => 16
[10,2,2,2] => 16
[10,2,2,1,1] => 1
[10,2,1,1,1,1] => 16
[10,1,1,1,1,1,1] => 1
[9,7] => 1
[9,6,1] => 16
[9,5,2] => 1
[9,5,1,1] => 2
[9,4,3] => 16
[9,4,2,1] => 1
[9,4,1,1,1] => 16
[9,3,3,1] => 16
[9,3,2,2] => 1
[9,3,2,1,1] => 16
[9,3,1,1,1,1] => 1
[9,2,2,2,1] => 16
[9,2,2,1,1,1] => 16
[9,2,1,1,1,1,1] => 16
[9,1,1,1,1,1,1,1] => 4
[8,8] => 16
[8,7,1] => 1
[8,6,2] => 16
[8,6,1,1] => 1
[8,5,3] => 1
[8,5,2,1] => 16
[8,5,1,1,1] => 2
[8,4,4] => 16
[8,4,3,1] => 1
[8,4,2,2] => 16
[8,4,2,1,1] => 1
[8,4,1,1,1,1] => 2
[8,3,3,2] => 1
[8,3,3,1,1] => 16
[8,3,2,2,1] => 1
[8,3,2,1,1,1] => 16
[8,3,1,1,1,1,1] => 1
[8,2,2,2,2] => 16
[8,2,2,2,1,1] => 1
[8,2,2,1,1,1,1] => 16
[8,2,1,1,1,1,1,1] => 1
[8,1,1,1,1,1,1,1,1] => 4
[7,7,2] => 1
[7,7,1,1] => 16
[7,6,3] => 16
[7,6,2,1] => 1
[7,6,1,1,1] => 16
[7,5,4] => 1
[7,5,3,1] => 16
[7,5,2,2] => 1
[7,5,2,1,1] => 2
[7,5,1,1,1,1] => 1
[7,4,4,1] => 1
[7,4,3,2] => 16
[7,4,3,1,1] => 16
[7,4,2,2,1] => 16
[7,4,2,1,1,1] => 2
[7,4,1,1,1,1,1] => 16
[7,3,3,3] => 2
[7,3,3,2,1] => 16
[7,3,3,1,1,1] => 1
[7,3,2,2,2] => 1
[7,3,2,2,1,1] => 16
[7,3,2,1,1,1,1] => 1
[7,3,1,1,1,1,1,1] => 16
[7,2,2,2,2,1] => 1
[7,2,2,2,1,1,1] => 16
[7,2,2,1,1,1,1,1] => 1
[7,2,1,1,1,1,1,1,1] => 16
[7,1,1,1,1,1,1,1,1,1] => 1
[6,6,4] => 16
[6,6,3,1] => 1
[6,6,2,2] => 16
[6,6,2,1,1] => 1
[6,6,1,1,1,1] => 16
[6,5,5] => 1
[6,5,4,1] => 16
[6,5,3,2] => 1
[6,5,3,1,1] => 16
[6,5,2,2,1] => 1
[6,5,2,1,1,1] => 16
[6,5,1,1,1,1,1] => 1
[6,4,4,2] => 16
[6,4,4,1,1] => 1
[6,4,3,3] => 1
[6,4,3,2,1] => 16
[6,4,3,1,1,1] => 16
[6,4,2,2,2] => 16
[6,4,2,2,1,1] => 1
[6,4,2,1,1,1,1] => 16
[6,4,1,1,1,1,1,1] => 1
[6,3,3,3,1] => 16
[6,3,3,2,2] => 1
[6,3,3,2,1,1] => 16
[6,3,3,1,1,1,1] => 1
[6,3,2,2,2,1] => 16
[6,3,2,2,1,1,1] => 2
[6,3,2,1,1,1,1,1] => 16
[6,3,1,1,1,1,1,1,1] => 16
[6,2,2,2,2,2] => 16
[6,2,2,2,2,1,1] => 1
[6,2,2,2,1,1,1,1] => 2
[6,2,2,1,1,1,1,1,1] => 1
[6,2,1,1,1,1,1,1,1,1] => 16
[6,1,1,1,1,1,1,1,1,1,1] => 1
[5,5,5,1] => 2
[5,5,4,2] => 1
[5,5,4,1,1] => 16
[5,5,3,3] => 16
[5,5,3,2,1] => 16
[5,5,3,1,1,1] => 1
[5,5,2,2,2] => 1
[5,5,2,2,1,1] => 16
[5,5,2,1,1,1,1] => 1
[5,5,1,1,1,1,1,1] => 16
[5,4,4,3] => 1
[5,4,4,2,1] => 16
[5,4,4,1,1,1] => 16
[5,4,3,3,1] => 16
[5,4,3,2,2] => 16
[5,4,3,2,1,1] => 16
[5,4,3,1,1,1,1] => 16
[5,4,2,2,2,1] => 1
[5,4,2,2,1,1,1] => 16
[5,4,2,1,1,1,1,1] => 1
[5,4,1,1,1,1,1,1,1] => 16
[5,3,3,3,2] => 16
[5,3,3,3,1,1] => 1
[5,3,3,2,2,1] => 16
[5,3,3,2,1,1,1] => 16
[5,3,3,1,1,1,1,1] => 16
[5,3,2,2,2,2] => 1
[5,3,2,2,2,1,1] => 2
[5,3,2,2,1,1,1,1] => 1
[5,3,2,1,1,1,1,1,1] => 16
[5,3,1,1,1,1,1,1,1,1] => 1
[5,2,2,2,2,2,1] => 16
[5,2,2,2,2,1,1,1] => 2
[5,2,2,2,1,1,1,1,1] => 16
[5,2,2,1,1,1,1,1,1,1] => 16
[5,2,1,1,1,1,1,1,1,1,1] => 16
[5,1,1,1,1,1,1,1,1,1,1,1] => 2
[4,4,4,4] => 16
[4,4,4,3,1] => 1
[4,4,4,2,2] => 16
[4,4,4,2,1,1] => 1
[4,4,4,1,1,1,1] => 2
[4,4,3,3,2] => 1
[4,4,3,3,1,1] => 16
[4,4,3,2,2,1] => 1
[4,4,3,2,1,1,1] => 16
[4,4,3,1,1,1,1,1] => 1
[4,4,2,2,2,2] => 16
[4,4,2,2,2,1,1] => 1
[4,4,2,2,1,1,1,1] => 16
[4,4,2,1,1,1,1,1,1] => 1
[4,4,1,1,1,1,1,1,1,1] => 16
[4,3,3,3,3] => 2
[4,3,3,3,2,1] => 16
[4,3,3,3,1,1,1] => 1
[4,3,3,2,2,2] => 1
[4,3,3,2,2,1,1] => 16
[4,3,3,2,1,1,1,1] => 1
[4,3,3,1,1,1,1,1,1] => 16
[4,3,2,2,2,2,1] => 1
[4,3,2,2,2,1,1,1] => 16
[4,3,2,2,1,1,1,1,1] => 1
[4,3,2,1,1,1,1,1,1,1] => 16
[4,3,1,1,1,1,1,1,1,1,1] => 1
[4,2,2,2,2,2,2] => 16
[4,2,2,2,2,2,1,1] => 1
[4,2,2,2,2,1,1,1,1] => 2
[4,2,2,2,1,1,1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1,1,1] => 16
[4,2,1,1,1,1,1,1,1,1,1,1] => 1
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[3,3,3,3,3,1] => 1
[3,3,3,3,2,2] => 16
[3,3,3,3,2,1,1] => 1
[3,3,3,3,1,1,1,1] => 16
[3,3,3,2,2,2,1] => 16
[3,3,3,2,2,1,1,1] => 1
[3,3,3,2,1,1,1,1,1] => 16
[3,3,3,1,1,1,1,1,1,1] => 1
[3,3,2,2,2,2,2] => 1
[3,3,2,2,2,2,1,1] => 16
[3,3,2,2,2,1,1,1,1] => 1
[3,3,2,2,1,1,1,1,1,1] => 2
[3,3,2,1,1,1,1,1,1,1,1] => 1
[3,3,1,1,1,1,1,1,1,1,1,1] => 16
[3,2,2,2,2,2,2,1] => 1
[3,2,2,2,2,2,1,1,1] => 16
[3,2,2,2,2,1,1,1,1,1] => 1
[3,2,2,2,1,1,1,1,1,1,1] => 16
[3,2,2,1,1,1,1,1,1,1,1,1] => 1
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 16
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,2,2] => 16
[2,2,2,2,2,2,2,1,1] => 1
[2,2,2,2,2,2,1,1,1,1] => 16
[2,2,2,2,2,1,1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1,1] => 16
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 16
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 8
[17] => 17
[16,1] => 1
[15,2] => 17
[15,1,1] => 17
[14,3] => 17
[14,2,1] => 17
[14,1,1,1] => 1
[13,4] => 17
[13,3,1] => 17
[13,2,2] => 17
[13,2,1,1] => 17
[13,1,1,1,1] => 17
[12,5] => 17
[12,4,1] => 17
[12,3,2] => 17
[12,3,1,1] => 17
[12,2,2,1] => 17
[12,2,1,1,1] => 17
[12,1,1,1,1,1] => 1
[11,6] => 17
[11,5,1] => 17
[11,4,2] => 17
[11,4,1,1] => 17
[11,3,3] => 17
[11,3,2,1] => 17
[11,3,1,1,1] => 17
[11,2,2,2] => 17
[11,2,2,1,1] => 17
[11,2,1,1,1,1] => 17
[11,1,1,1,1,1,1] => 17
[10,7] => 17
[10,6,1] => 17
[10,5,2] => 17
[10,5,1,1] => 17
[10,4,3] => 17
[10,4,2,1] => 17
[10,4,1,1,1] => 17
[10,3,3,1] => 17
[10,3,2,2] => 17
[10,3,2,1,1] => 17
[10,3,1,1,1,1] => 17
[10,2,2,2,1] => 17
[10,2,2,1,1,1] => 17
[10,2,1,1,1,1,1] => 17
[10,1,1,1,1,1,1,1] => 1
[9,8] => 17
[9,7,1] => 17
[9,6,2] => 17
[9,6,1,1] => 17
[9,5,3] => 17
[9,5,2,1] => 17
[9,5,1,1,1] => 17
[9,4,4] => 17
[9,4,3,1] => 17
[9,4,2,2] => 17
[9,4,2,1,1] => 17
[9,4,1,1,1,1] => 17
[9,3,3,2] => 17
[9,3,3,1,1] => 17
[9,3,2,2,1] => 17
[9,3,2,1,1,1] => 17
[9,3,1,1,1,1,1] => 17
[9,2,2,2,2] => 17
[9,2,2,2,1,1] => 17
[9,2,2,1,1,1,1] => 17
[9,2,1,1,1,1,1,1] => 17
[9,1,1,1,1,1,1,1,1] => 17
[8,8,1] => 17
[8,7,2] => 17
[8,7,1,1] => 17
[8,6,3] => 17
[8,6,2,1] => 17
[8,6,1,1,1] => 17
[8,5,4] => 17
[8,5,3,1] => 17
[8,5,2,2] => 17
[8,5,2,1,1] => 17
[8,5,1,1,1,1] => 17
[8,4,4,1] => 17
[8,4,3,2] => 17
[8,4,3,1,1] => 17
[8,4,2,2,1] => 17
[8,4,2,1,1,1] => 17
[8,4,1,1,1,1,1] => 17
[8,3,3,3] => 17
[8,3,3,2,1] => 17
[8,3,3,1,1,1] => 17
[8,3,2,2,2] => 17
[8,3,2,2,1,1] => 17
[8,3,2,1,1,1,1] => 17
[8,3,1,1,1,1,1,1] => 17
[8,2,2,2,2,1] => 17
[8,2,2,2,1,1,1] => 17
[8,2,2,1,1,1,1,1] => 17
[8,2,1,1,1,1,1,1,1] => 17
[8,1,1,1,1,1,1,1,1,1] => 1
[7,7,3] => 17
[7,7,2,1] => 17
[7,7,1,1,1] => 17
[7,6,4] => 17
[7,6,3,1] => 17
[7,6,2,2] => 17
[7,6,2,1,1] => 17
[7,6,1,1,1,1] => 17
[7,5,5] => 17
[7,5,4,1] => 17
[7,5,3,2] => 17
[7,5,3,1,1] => 17
[7,5,2,2,1] => 17
[7,5,2,1,1,1] => 17
[7,5,1,1,1,1,1] => 17
[7,4,4,2] => 17
[7,4,4,1,1] => 17
[7,4,3,3] => 17
[7,4,3,2,1] => 17
[7,4,3,1,1,1] => 17
[7,4,2,2,2] => 17
[7,4,2,2,1,1] => 17
[7,4,2,1,1,1,1] => 17
[7,4,1,1,1,1,1,1] => 17
[7,3,3,3,1] => 17
[7,3,3,2,2] => 17
[7,3,3,2,1,1] => 17
[7,3,3,1,1,1,1] => 17
[7,3,2,2,2,1] => 17
[7,3,2,2,1,1,1] => 17
[7,3,2,1,1,1,1,1] => 17
[7,3,1,1,1,1,1,1,1] => 17
[7,2,2,2,2,2] => 17
[7,2,2,2,2,1,1] => 17
[7,2,2,2,1,1,1,1] => 17
[7,2,2,1,1,1,1,1,1] => 17
[7,2,1,1,1,1,1,1,1,1] => 17
[7,1,1,1,1,1,1,1,1,1,1] => 17
[6,6,5] => 17
[6,6,4,1] => 17
[6,6,3,2] => 17
[6,6,3,1,1] => 17
[6,6,2,2,1] => 17
[6,6,2,1,1,1] => 17
[6,6,1,1,1,1,1] => 17
[6,5,5,1] => 17
[6,5,4,2] => 17
[6,5,4,1,1] => 17
[6,5,3,3] => 17
[6,5,3,2,1] => 17
[6,5,3,1,1,1] => 17
[6,5,2,2,2] => 17
[6,5,2,2,1,1] => 17
[6,5,2,1,1,1,1] => 17
[6,5,1,1,1,1,1,1] => 17
[6,4,4,3] => 17
[6,4,4,2,1] => 17
[6,4,4,1,1,1] => 17
[6,4,3,3,1] => 17
[6,4,3,2,2] => 17
[6,4,3,2,1,1] => 17
[6,4,3,1,1,1,1] => 17
[6,4,2,2,2,1] => 17
[6,4,2,2,1,1,1] => 17
[6,4,2,1,1,1,1,1] => 17
[6,4,1,1,1,1,1,1,1] => 17
[6,3,3,3,2] => 17
[6,3,3,3,1,1] => 17
[6,3,3,2,2,1] => 17
[6,3,3,2,1,1,1] => 17
[6,3,3,1,1,1,1,1] => 17
[6,3,2,2,2,2] => 17
[6,3,2,2,2,1,1] => 17
[6,3,2,2,1,1,1,1] => 17
[6,3,2,1,1,1,1,1,1] => 17
[6,3,1,1,1,1,1,1,1,1] => 17
[6,2,2,2,2,2,1] => 17
[6,2,2,2,2,1,1,1] => 17
[6,2,2,2,1,1,1,1,1] => 17
[6,2,2,1,1,1,1,1,1,1] => 17
[6,2,1,1,1,1,1,1,1,1,1] => 17
[6,1,1,1,1,1,1,1,1,1,1,1] => 1
[5,5,5,2] => 17
[5,5,5,1,1] => 17
[5,5,4,3] => 17
[5,5,4,2,1] => 17
[5,5,4,1,1,1] => 17
[5,5,3,3,1] => 17
[5,5,3,2,2] => 17
[5,5,3,2,1,1] => 17
[5,5,3,1,1,1,1] => 17
[5,5,2,2,2,1] => 17
[5,5,2,2,1,1,1] => 17
[5,5,2,1,1,1,1,1] => 17
[5,5,1,1,1,1,1,1,1] => 17
[5,4,4,4] => 17
[5,4,4,3,1] => 17
[5,4,4,2,2] => 17
[5,4,4,2,1,1] => 17
[5,4,4,1,1,1,1] => 17
[5,4,3,3,2] => 17
[5,4,3,3,1,1] => 17
[5,4,3,2,2,1] => 17
[5,4,3,2,1,1,1] => 17
[5,4,3,1,1,1,1,1] => 17
[5,4,2,2,2,2] => 17
[5,4,2,2,2,1,1] => 17
[5,4,2,2,1,1,1,1] => 17
[5,4,2,1,1,1,1,1,1] => 17
[5,4,1,1,1,1,1,1,1,1] => 17
[5,3,3,3,3] => 17
[5,3,3,3,2,1] => 17
[5,3,3,3,1,1,1] => 17
[5,3,3,2,2,2] => 17
[5,3,3,2,2,1,1] => 17
[5,3,3,2,1,1,1,1] => 17
[5,3,3,1,1,1,1,1,1] => 17
[5,3,2,2,2,2,1] => 17
[5,3,2,2,2,1,1,1] => 17
[5,3,2,2,1,1,1,1,1] => 17
[5,3,2,1,1,1,1,1,1,1] => 17
[5,3,1,1,1,1,1,1,1,1,1] => 17
[5,2,2,2,2,2,2] => 17
[5,2,2,2,2,2,1,1] => 17
[5,2,2,2,2,1,1,1,1] => 17
[5,2,2,2,1,1,1,1,1,1] => 17
[5,2,2,1,1,1,1,1,1,1,1] => 17
[5,2,1,1,1,1,1,1,1,1,1,1] => 17
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 17
[4,4,4,4,1] => 17
[4,4,4,3,2] => 17
[4,4,4,3,1,1] => 17
[4,4,4,2,2,1] => 17
[4,4,4,2,1,1,1] => 17
[4,4,4,1,1,1,1,1] => 17
[4,4,3,3,3] => 17
[4,4,3,3,2,1] => 17
[4,4,3,3,1,1,1] => 17
[4,4,3,2,2,2] => 17
[4,4,3,2,2,1,1] => 17
[4,4,3,2,1,1,1,1] => 17
[4,4,3,1,1,1,1,1,1] => 17
[4,4,2,2,2,2,1] => 17
[4,4,2,2,2,1,1,1] => 17
[4,4,2,2,1,1,1,1,1] => 17
[4,4,2,1,1,1,1,1,1,1] => 17
[4,4,1,1,1,1,1,1,1,1,1] => 17
[4,3,3,3,3,1] => 17
[4,3,3,3,2,2] => 17
[4,3,3,3,2,1,1] => 17
[4,3,3,3,1,1,1,1] => 17
[4,3,3,2,2,2,1] => 17
[4,3,3,2,2,1,1,1] => 17
[4,3,3,2,1,1,1,1,1] => 17
[4,3,3,1,1,1,1,1,1,1] => 17
[4,3,2,2,2,2,2] => 17
[4,3,2,2,2,2,1,1] => 17
[4,3,2,2,2,1,1,1,1] => 17
[4,3,2,2,1,1,1,1,1,1] => 17
[4,3,2,1,1,1,1,1,1,1,1] => 17
[4,3,1,1,1,1,1,1,1,1,1,1] => 17
[4,2,2,2,2,2,2,1] => 17
[4,2,2,2,2,2,1,1,1] => 17
[4,2,2,2,2,1,1,1,1,1] => 17
[4,2,2,2,1,1,1,1,1,1,1] => 17
[4,2,2,1,1,1,1,1,1,1,1,1] => 17
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 17
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[3,3,3,3,3,2] => 17
[3,3,3,3,3,1,1] => 17
[3,3,3,3,2,2,1] => 17
[3,3,3,3,2,1,1,1] => 17
[3,3,3,3,1,1,1,1,1] => 17
[3,3,3,2,2,2,2] => 17
[3,3,3,2,2,2,1,1] => 17
[3,3,3,2,2,1,1,1,1] => 17
[3,3,3,2,1,1,1,1,1,1] => 17
[3,3,3,1,1,1,1,1,1,1,1] => 17
[3,3,2,2,2,2,2,1] => 17
[3,3,2,2,2,2,1,1,1] => 17
[3,3,2,2,2,1,1,1,1,1] => 17
[3,3,2,2,1,1,1,1,1,1,1] => 17
[3,3,2,1,1,1,1,1,1,1,1,1] => 17
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 17
[3,2,2,2,2,2,2,2] => 17
[3,2,2,2,2,2,2,1,1] => 17
[3,2,2,2,2,2,1,1,1,1] => 17
[3,2,2,2,2,1,1,1,1,1,1] => 17
[3,2,2,2,1,1,1,1,1,1,1,1] => 17
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 17
-----------------------------------------------------------------------------
Created: Mar 25, 2020 at 10:08 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Mar 25, 2020 at 10:08 by Martin Rubey