***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * 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. * ***************************************************************************** ----------------------------------------------------------------------------- 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. = 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. = 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. = PolynomialRing(QQ) R. = 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