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* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* 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: St000769
-----------------------------------------------------------------------------
Collection: Integer compositions
-----------------------------------------------------------------------------
Description: The major index of a composition regarded as a word.
This is the sum of the positions of the descents of the composition.
For the statistic which interprets the composition as a descent set, see [[St000008]].
-----------------------------------------------------------------------------
References: [1] MacMahon, P. A. Two Applications of General Theorems in Combinatory Analysis: (1) To the Theory of Inversions of Permutations; (2) To the Ascertainment of the Numbers of Terms in the Development of a Determinant which has Amongst its Elements an Arbitrary Number of Zeros [[MathSciNet:1576566]]
-----------------------------------------------------------------------------
Code:
def statistic(w):
return sum(i+1 for i in range(len(w)-1) if w[i] > w[i+1])
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 0
[1,1] => 0
[2] => 0
[1,1,1] => 0
[1,2] => 0
[2,1] => 1
[3] => 0
[1,1,1,1] => 0
[1,1,2] => 0
[1,2,1] => 2
[1,3] => 0
[2,1,1] => 1
[2,2] => 0
[3,1] => 1
[4] => 0
[1,1,1,1,1] => 0
[1,1,1,2] => 0
[1,1,2,1] => 3
[1,1,3] => 0
[1,2,1,1] => 2
[1,2,2] => 0
[1,3,1] => 2
[1,4] => 0
[2,1,1,1] => 1
[2,1,2] => 1
[2,2,1] => 2
[2,3] => 0
[3,1,1] => 1
[3,2] => 1
[4,1] => 1
[5] => 0
[1,1,1,1,1,1] => 0
[1,1,1,1,2] => 0
[1,1,1,2,1] => 4
[1,1,1,3] => 0
[1,1,2,1,1] => 3
[1,1,2,2] => 0
[1,1,3,1] => 3
[1,1,4] => 0
[1,2,1,1,1] => 2
[1,2,1,2] => 2
[1,2,2,1] => 3
[1,2,3] => 0
[1,3,1,1] => 2
[1,3,2] => 2
[1,4,1] => 2
[1,5] => 0
[2,1,1,1,1] => 1
[2,1,1,2] => 1
[2,1,2,1] => 4
[2,1,3] => 1
[2,2,1,1] => 2
[2,2,2] => 0
[2,3,1] => 2
[2,4] => 0
[3,1,1,1] => 1
[3,1,2] => 1
[3,2,1] => 3
[3,3] => 0
[4,1,1] => 1
[4,2] => 1
[5,1] => 1
[6] => 0
[1,1,1,1,1,1,1] => 0
[1,1,1,1,1,2] => 0
[1,1,1,1,2,1] => 5
[1,1,1,1,3] => 0
[1,1,1,2,1,1] => 4
[1,1,1,2,2] => 0
[1,1,1,3,1] => 4
[1,1,1,4] => 0
[1,1,2,1,1,1] => 3
[1,1,2,1,2] => 3
[1,1,2,2,1] => 4
[1,1,2,3] => 0
[1,1,3,1,1] => 3
[1,1,3,2] => 3
[1,1,4,1] => 3
[1,1,5] => 0
[1,2,1,1,1,1] => 2
[1,2,1,1,2] => 2
[1,2,1,2,1] => 6
[1,2,1,3] => 2
[1,2,2,1,1] => 3
[1,2,2,2] => 0
[1,2,3,1] => 3
[1,2,4] => 0
[1,3,1,1,1] => 2
[1,3,1,2] => 2
[1,3,2,1] => 5
[1,3,3] => 0
[1,4,1,1] => 2
[1,4,2] => 2
[1,5,1] => 2
[1,6] => 0
[2,1,1,1,1,1] => 1
[2,1,1,1,2] => 1
[2,1,1,2,1] => 5
[2,1,1,3] => 1
[2,1,2,1,1] => 4
[2,1,2,2] => 1
[2,1,3,1] => 4
[2,1,4] => 1
[2,2,1,1,1] => 2
[2,2,1,2] => 2
[2,2,2,1] => 3
[2,2,3] => 0
[2,3,1,1] => 2
[2,3,2] => 2
[2,4,1] => 2
[2,5] => 0
[3,1,1,1,1] => 1
[3,1,1,2] => 1
[3,1,2,1] => 4
[3,1,3] => 1
[3,2,1,1] => 3
[3,2,2] => 1
[3,3,1] => 2
[3,4] => 0
[4,1,1,1] => 1
[4,1,2] => 1
[4,2,1] => 3
[4,3] => 1
[5,1,1] => 1
[5,2] => 1
[6,1] => 1
[7] => 0
[1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,2] => 0
[1,1,1,1,1,2,1] => 6
[1,1,1,1,1,3] => 0
[1,1,1,1,2,1,1] => 5
[1,1,1,1,2,2] => 0
[1,1,1,1,3,1] => 5
[1,1,1,1,4] => 0
[1,1,1,2,1,1,1] => 4
[1,1,1,2,1,2] => 4
[1,1,1,2,2,1] => 5
[1,1,1,2,3] => 0
[1,1,1,3,1,1] => 4
[1,1,1,3,2] => 4
[1,1,1,4,1] => 4
[1,1,1,5] => 0
[1,1,2,1,1,1,1] => 3
[1,1,2,1,1,2] => 3
[1,1,2,1,2,1] => 8
[1,1,2,1,3] => 3
[1,1,2,2,1,1] => 4
[1,1,2,2,2] => 0
[1,1,2,3,1] => 4
[1,1,2,4] => 0
[1,1,3,1,1,1] => 3
[1,1,3,1,2] => 3
[1,1,3,2,1] => 7
[1,1,3,3] => 0
[1,1,4,1,1] => 3
[1,1,4,2] => 3
[1,1,5,1] => 3
[1,1,6] => 0
[1,2,1,1,1,1,1] => 2
[1,2,1,1,1,2] => 2
[1,2,1,1,2,1] => 7
[1,2,1,1,3] => 2
[1,2,1,2,1,1] => 6
[1,2,1,2,2] => 2
[1,2,1,3,1] => 6
[1,2,1,4] => 2
[1,2,2,1,1,1] => 3
[1,2,2,1,2] => 3
[1,2,2,2,1] => 4
[1,2,2,3] => 0
[1,2,3,1,1] => 3
[1,2,3,2] => 3
[1,2,4,1] => 3
[1,2,5] => 0
[1,3,1,1,1,1] => 2
[1,3,1,1,2] => 2
[1,3,1,2,1] => 6
[1,3,1,3] => 2
[1,3,2,1,1] => 5
[1,3,2,2] => 2
[1,3,3,1] => 3
[1,3,4] => 0
[1,4,1,1,1] => 2
[1,4,1,2] => 2
[1,4,2,1] => 5
[1,4,3] => 2
[1,5,1,1] => 2
[1,5,2] => 2
[1,6,1] => 2
[1,7] => 0
[2,1,1,1,1,1,1] => 1
[2,1,1,1,1,2] => 1
[2,1,1,1,2,1] => 6
[2,1,1,1,3] => 1
[2,1,1,2,1,1] => 5
[2,1,1,2,2] => 1
[2,1,1,3,1] => 5
[2,1,1,4] => 1
[2,1,2,1,1,1] => 4
[2,1,2,1,2] => 4
[2,1,2,2,1] => 5
[2,1,2,3] => 1
[2,1,3,1,1] => 4
[2,1,3,2] => 4
[2,1,4,1] => 4
[2,1,5] => 1
[2,2,1,1,1,1] => 2
[2,2,1,1,2] => 2
[2,2,1,2,1] => 6
[2,2,1,3] => 2
[2,2,2,1,1] => 3
[2,2,2,2] => 0
[2,2,3,1] => 3
[2,2,4] => 0
[2,3,1,1,1] => 2
[2,3,1,2] => 2
[2,3,2,1] => 5
[2,3,3] => 0
[2,4,1,1] => 2
[2,4,2] => 2
[2,5,1] => 2
[2,6] => 0
[3,1,1,1,1,1] => 1
[3,1,1,1,2] => 1
[3,1,1,2,1] => 5
[3,1,1,3] => 1
[3,1,2,1,1] => 4
[3,1,2,2] => 1
[3,1,3,1] => 4
[3,1,4] => 1
[3,2,1,1,1] => 3
[3,2,1,2] => 3
[3,2,2,1] => 4
[3,2,3] => 1
[3,3,1,1] => 2
[3,3,2] => 2
[3,4,1] => 2
[3,5] => 0
[4,1,1,1,1] => 1
[4,1,1,2] => 1
[4,1,2,1] => 4
[4,1,3] => 1
[4,2,1,1] => 3
[4,2,2] => 1
[4,3,1] => 3
[4,4] => 0
[5,1,1,1] => 1
[5,1,2] => 1
[5,2,1] => 3
[5,3] => 1
[6,1,1] => 1
[6,2] => 1
[7,1] => 1
[8] => 0
[1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,2] => 0
[1,1,1,1,1,1,2,1] => 7
[1,1,1,1,1,1,3] => 0
[1,1,1,1,1,2,1,1] => 6
[1,1,1,1,1,2,2] => 0
[1,1,1,1,1,3,1] => 6
[1,1,1,1,1,4] => 0
[1,1,1,1,2,1,1,1] => 5
[1,1,1,1,2,1,2] => 5
[1,1,1,1,2,2,1] => 6
[1,1,1,1,2,3] => 0
[1,1,1,1,3,1,1] => 5
[1,1,1,1,3,2] => 5
[1,1,1,1,4,1] => 5
[1,1,1,1,5] => 0
[1,1,1,2,1,1,1,1] => 4
[1,1,1,2,1,1,2] => 4
[1,1,1,2,1,2,1] => 10
[1,1,1,2,1,3] => 4
[1,1,1,2,2,1,1] => 5
[1,1,1,2,2,2] => 0
[1,1,1,2,3,1] => 5
[1,1,1,2,4] => 0
[1,1,1,3,1,1,1] => 4
[1,1,1,3,1,2] => 4
[1,1,1,3,2,1] => 9
[1,1,1,3,3] => 0
[1,1,1,4,1,1] => 4
[1,1,1,4,2] => 4
[1,1,1,5,1] => 4
[1,1,1,6] => 0
[1,1,2,1,1,1,1,1] => 3
[1,1,2,1,1,1,2] => 3
[1,1,2,1,1,2,1] => 9
[1,1,2,1,1,3] => 3
[1,1,2,1,2,1,1] => 8
[1,1,2,1,2,2] => 3
[1,1,2,1,3,1] => 8
[1,1,2,1,4] => 3
[1,1,2,2,1,1,1] => 4
[1,1,2,2,1,2] => 4
[1,1,2,2,2,1] => 5
[1,1,2,2,3] => 0
[1,1,2,3,1,1] => 4
[1,1,2,3,2] => 4
[1,1,2,4,1] => 4
[1,1,2,5] => 0
[1,1,3,1,1,1,1] => 3
[1,1,3,1,1,2] => 3
[1,1,3,1,2,1] => 8
[1,1,3,1,3] => 3
[1,1,3,2,1,1] => 7
[1,1,3,2,2] => 3
[1,1,3,3,1] => 4
[1,1,3,4] => 0
[1,1,4,1,1,1] => 3
[1,1,4,1,2] => 3
[1,1,4,2,1] => 7
[1,1,4,3] => 3
[1,1,5,1,1] => 3
[1,1,5,2] => 3
[1,1,6,1] => 3
[1,1,7] => 0
[1,2,1,1,1,1,1,1] => 2
[1,2,1,1,1,1,2] => 2
[1,2,1,1,1,2,1] => 8
[1,2,1,1,1,3] => 2
[1,2,1,1,2,1,1] => 7
[1,2,1,1,2,2] => 2
[1,2,1,1,3,1] => 7
[1,2,1,1,4] => 2
[1,2,1,2,1,1,1] => 6
[1,2,1,2,1,2] => 6
[1,2,1,2,2,1] => 7
[1,2,1,2,3] => 2
[1,2,1,3,1,1] => 6
[1,2,1,3,2] => 6
[1,2,1,4,1] => 6
[1,2,1,5] => 2
[1,2,2,1,1,1,1] => 3
[1,2,2,1,1,2] => 3
[1,2,2,1,2,1] => 8
[1,2,2,1,3] => 3
[1,2,2,2,1,1] => 4
[1,2,2,2,2] => 0
[1,2,2,3,1] => 4
[1,2,2,4] => 0
[1,2,3,1,1,1] => 3
[1,2,3,1,2] => 3
[1,2,3,2,1] => 7
[1,2,3,3] => 0
[1,2,4,1,1] => 3
[1,2,4,2] => 3
[1,2,5,1] => 3
[1,2,6] => 0
[1,3,1,1,1,1,1] => 2
[1,3,1,1,1,2] => 2
[1,3,1,1,2,1] => 7
[1,3,1,1,3] => 2
[1,3,1,2,1,1] => 6
[1,3,1,2,2] => 2
[1,3,1,3,1] => 6
[1,3,1,4] => 2
[1,3,2,1,1,1] => 5
[1,3,2,1,2] => 5
[1,3,2,2,1] => 6
[1,3,2,3] => 2
[1,3,3,1,1] => 3
[1,3,3,2] => 3
[1,3,4,1] => 3
[1,3,5] => 0
[1,4,1,1,1,1] => 2
[1,4,1,1,2] => 2
[1,4,1,2,1] => 6
[1,4,1,3] => 2
[1,4,2,1,1] => 5
[1,4,2,2] => 2
[1,4,3,1] => 5
[1,4,4] => 0
[1,5,1,1,1] => 2
[1,5,1,2] => 2
[1,5,2,1] => 5
[1,5,3] => 2
[1,6,1,1] => 2
[1,6,2] => 2
[1,7,1] => 2
[1,8] => 0
[2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2] => 1
[2,1,1,1,1,2,1] => 7
[2,1,1,1,1,3] => 1
[2,1,1,1,2,1,1] => 6
[2,1,1,1,2,2] => 1
[2,1,1,1,3,1] => 6
[2,1,1,1,4] => 1
[2,1,1,2,1,1,1] => 5
[2,1,1,2,1,2] => 5
[2,1,1,2,2,1] => 6
[2,1,1,2,3] => 1
[2,1,1,3,1,1] => 5
[2,1,1,3,2] => 5
[2,1,1,4,1] => 5
[2,1,1,5] => 1
[2,1,2,1,1,1,1] => 4
[2,1,2,1,1,2] => 4
[2,1,2,1,2,1] => 9
[2,1,2,1,3] => 4
[2,1,2,2,1,1] => 5
[2,1,2,2,2] => 1
[2,1,2,3,1] => 5
[2,1,2,4] => 1
[2,1,3,1,1,1] => 4
[2,1,3,1,2] => 4
[2,1,3,2,1] => 8
[2,1,3,3] => 1
[2,1,4,1,1] => 4
[2,1,4,2] => 4
[2,1,5,1] => 4
[2,1,6] => 1
[2,2,1,1,1,1,1] => 2
[2,2,1,1,1,2] => 2
[2,2,1,1,2,1] => 7
[2,2,1,1,3] => 2
[2,2,1,2,1,1] => 6
[2,2,1,2,2] => 2
[2,2,1,3,1] => 6
[2,2,1,4] => 2
[2,2,2,1,1,1] => 3
[2,2,2,1,2] => 3
[2,2,2,2,1] => 4
[2,2,2,3] => 0
[2,2,3,1,1] => 3
[2,2,3,2] => 3
[2,2,4,1] => 3
[2,2,5] => 0
[2,3,1,1,1,1] => 2
[2,3,1,1,2] => 2
[2,3,1,2,1] => 6
[2,3,1,3] => 2
[2,3,2,1,1] => 5
[2,3,2,2] => 2
[2,3,3,1] => 3
[2,3,4] => 0
[2,4,1,1,1] => 2
[2,4,1,2] => 2
[2,4,2,1] => 5
[2,4,3] => 2
[2,5,1,1] => 2
[2,5,2] => 2
[2,6,1] => 2
[2,7] => 0
[3,1,1,1,1,1,1] => 1
[3,1,1,1,1,2] => 1
[3,1,1,1,2,1] => 6
[3,1,1,1,3] => 1
[3,1,1,2,1,1] => 5
[3,1,1,2,2] => 1
[3,1,1,3,1] => 5
[3,1,1,4] => 1
[3,1,2,1,1,1] => 4
[3,1,2,1,2] => 4
[3,1,2,2,1] => 5
[3,1,2,3] => 1
[3,1,3,1,1] => 4
[3,1,3,2] => 4
[3,1,4,1] => 4
[3,1,5] => 1
[3,2,1,1,1,1] => 3
[3,2,1,1,2] => 3
[3,2,1,2,1] => 7
[3,2,1,3] => 3
[3,2,2,1,1] => 4
[3,2,2,2] => 1
[3,2,3,1] => 4
[3,2,4] => 1
[3,3,1,1,1] => 2
[3,3,1,2] => 2
[3,3,2,1] => 5
[3,3,3] => 0
[3,4,1,1] => 2
[3,4,2] => 2
[3,5,1] => 2
[3,6] => 0
[4,1,1,1,1,1] => 1
[4,1,1,1,2] => 1
[4,1,1,2,1] => 5
[4,1,1,3] => 1
[4,1,2,1,1] => 4
[4,1,2,2] => 1
[4,1,3,1] => 4
[4,1,4] => 1
[4,2,1,1,1] => 3
[4,2,1,2] => 3
[4,2,2,1] => 4
[4,2,3] => 1
[4,3,1,1] => 3
[4,3,2] => 3
[4,4,1] => 2
[4,5] => 0
[5,1,1,1,1] => 1
[5,1,1,2] => 1
[5,1,2,1] => 4
[5,1,3] => 1
[5,2,1,1] => 3
[5,2,2] => 1
[5,3,1] => 3
[5,4] => 1
[6,1,1,1] => 1
[6,1,2] => 1
[6,2,1] => 3
[6,3] => 1
[7,1,1] => 1
[7,2] => 1
[8,1] => 1
[9] => 0
[1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,2] => 0
[1,1,1,1,1,1,2,2] => 0
[1,1,1,1,2,1,1,2] => 5
[1,1,1,1,2,2,1,1] => 6
[1,1,1,1,3,3] => 0
[1,1,1,1,5,1] => 5
[1,1,1,2,1,1,1,2] => 4
[1,1,2,1,1,1,1,2] => 3
[1,1,2,1,1,2,1,1] => 9
[1,1,2,1,2,3] => 3
[1,1,2,2,1,1,1,1] => 4
[1,1,2,2,2,2] => 0
[1,1,3,1,1,1,2] => 3
[1,1,3,1,1,3] => 3
[1,1,3,2,1,2] => 7
[1,1,3,3,1,1] => 4
[1,1,4,4] => 0
[1,1,7,1] => 3
[1,2,1,1,1,1,1,1,1] => 2
[1,2,1,1,1,1,1,2] => 2
[1,2,1,1,4,1] => 7
[1,2,1,2,1,1,2] => 6
[1,2,2,1,1,1,2] => 3
[1,2,2,1,2,1,1] => 8
[1,2,3,1,1,2] => 3
[1,2,6,1] => 3
[1,3,1,1,1,1,2] => 2
[1,3,1,1,3,1] => 7
[1,3,1,2,1,2] => 6
[1,3,2,1,1,2] => 5
[1,3,3,1,2] => 3
[1,3,5,1] => 3
[1,4,1,1,1,2] => 2
[1,4,1,1,2,1] => 7
[1,4,1,2,2] => 2
[1,4,2,1,2] => 5
[1,4,3,2] => 5
[1,4,4,1] => 3
[1,5,1,1,1,1] => 2
[1,5,1,1,2] => 2
[1,5,1,3] => 2
[1,5,2,2] => 2
[1,5,3,1] => 5
[1,5,4] => 2
[1,6,1,2] => 2
[1,6,2,1] => 5
[1,6,3] => 2
[1,7,1,1] => 2
[1,7,2] => 2
[1,8,1] => 2
[1,9] => 0
[2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,2] => 1
[2,1,1,1,1,2,1,1] => 7
[2,1,1,1,2,3] => 1
[2,1,1,2,1,1,1,1] => 5
[2,1,1,2,2,2] => 1
[2,1,2,1,1,3] => 4
[2,1,2,2,1,2] => 5
[2,1,2,3,1,1] => 5
[2,1,3,4] => 1
[2,1,6,1] => 4
[2,2,1,1,1,1,1,1] => 2
[2,2,1,1,2,1,1] => 7
[2,2,1,1,2,2] => 2
[2,2,2,1,1,1,1] => 3
[2,2,2,1,1,2] => 3
[2,2,2,1,2,1] => 8
[2,2,2,2,1,1] => 4
[2,2,2,2,2] => 0
[2,2,3,3] => 0
[3,1,1,1,1,1,1,1] => 1
[3,1,1,1,1,3] => 1
[3,1,1,2,1,2] => 5
[3,1,1,3,1,1] => 5
[3,1,2,4] => 1
[3,1,3,1,1,1] => 4
[3,2,1,1,1,1,1] => 3
[3,2,1,1,1,2] => 3
[3,2,1,2,1,1] => 7
[3,2,2,1,1,1] => 4
[3,2,2,2,1] => 5
[3,2,2,3] => 1
[3,3,1,1,1,1] => 2
[3,3,2,1,1] => 5
[3,3,2,2] => 2
[3,3,3,1] => 3
[4,1,1,1,1,1,1] => 1
[4,1,1,4] => 1
[4,2,1,1,1,1] => 3
[4,2,1,3] => 3
[4,2,2,1,1] => 4
[4,2,2,2] => 1
[4,3,1,1,1] => 3
[4,3,1,2] => 3
[4,3,2,1] => 6
[4,3,3] => 1
[4,4,1,1] => 2
[4,4,2] => 2
[5,1,1,1,1,1] => 1
[5,2,1,1,1] => 3
[5,2,2,1] => 4
[5,3,1,1] => 3
[5,3,2] => 3
[5,4,1] => 3
[5,5] => 0
[6,1,1,1,1] => 1
[6,2,1,1] => 3
[6,2,2] => 1
[6,3,1] => 3
[6,4] => 1
[7,1,1,1] => 1
[7,2,1] => 3
[7,3] => 1
[8,1,1] => 1
[8,2] => 1
[9,1] => 1
[10] => 0
[1,10] => 0
[1,8,1,1] => 2
[1,7,2,1] => 5
[1,6,3,1] => 5
[1,5,4,1] => 5
[1,4,5,1] => 3
[1,3,6,1] => 3
[1,2,7,1] => 3
[1,1,8,1] => 3
[10,1] => 1
[1,8,2] => 2
[1,7,1,2] => 2
[1,6,1,1,2] => 2
[1,5,1,1,1,2] => 2
[1,4,1,1,1,1,2] => 2
[1,3,1,1,1,1,1,2] => 2
[1,2,1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,1,1,1,2] => 0
[1,7,3] => 2
[1,6,2,2] => 2
[1,5,2,1,2] => 5
[1,4,2,1,1,2] => 5
[1,3,2,1,1,1,2] => 5
[1,2,2,1,1,1,1,2] => 3
[1,1,2,1,1,1,1,1,2] => 3
[1,2,2,2,2,2] => 0
[1,2,2,2,1,3] => 4
[1,2,2,1,3,2] => 8
[1,2,2,1,2,3] => 3
[1,2,2,1,1,4] => 3
[1,2,1,3,2,2] => 6
[1,2,1,3,1,3] => 6
[1,2,1,2,3,2] => 7
[1,2,1,2,2,3] => 2
[1,2,1,2,1,4] => 6
[1,2,1,1,4,2] => 7
[1,2,1,1,3,3] => 2
[1,2,1,1,2,4] => 2
[1,2,1,1,1,5] => 2
[1,1,3,2,2,2] => 3
[1,1,3,2,1,3] => 7
[1,1,3,1,3,2] => 8
[1,1,3,1,2,3] => 3
[1,1,3,1,1,4] => 3
[1,1,2,3,2,2] => 4
[1,1,2,3,1,3] => 4
[1,1,2,2,3,2] => 5
[1,1,2,2,2,3] => 0
[1,1,2,2,1,4] => 4
[1,1,2,1,4,2] => 8
[1,1,2,1,3,3] => 3
[1,1,2,1,2,4] => 3
[1,1,2,1,1,5] => 3
[1,1,1,4,2,2] => 4
[1,1,1,4,1,3] => 4
[1,1,1,3,3,2] => 5
[1,1,1,3,2,3] => 4
[1,1,1,3,1,4] => 4
[1,1,1,2,4,2] => 5
[1,1,1,2,3,3] => 0
[1,1,1,2,2,4] => 0
[1,1,1,2,1,5] => 4
[1,1,1,1,5,2] => 5
[1,1,1,1,4,3] => 5
[1,1,1,1,3,4] => 0
[1,1,1,1,2,5] => 0
[1,1,1,1,1,6] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,2,2] => 0
[1,1,1,1,1,1,2,2,1,1] => 8
[1,1,1,1,1,1,2,1,1,2] => 7
[1,1,1,1,1,1,3,3] => 0
[1,1,1,1,2,2,1,1,1,1] => 6
[1,1,1,1,2,2,2,2] => 0
[1,1,1,1,2,1,1,2,1,1] => 13
[1,1,1,1,2,1,1,1,1,2] => 5
[1,1,1,1,2,1,2,3] => 5
[1,1,1,1,3,3,1,1] => 6
[1,1,1,1,3,2,1,2] => 11
[1,1,1,1,3,1,1,3] => 5
[1,1,1,1,4,4] => 0
[1,1,2,2,1,1,1,1,1,1] => 4
[1,1,2,2,1,1,2,2] => 4
[1,1,2,2,2,2,1,1] => 6
[1,1,2,2,2,1,1,2] => 5
[1,1,2,2,3,3] => 0
[1,1,2,1,1,2,1,1,1,1] => 9
[1,1,2,1,1,2,2,2] => 3
[1,1,2,1,1,1,1,2,1,1] => 11
[1,1,2,1,1,1,1,1,1,2] => 3
[1,1,2,1,1,1,2,3] => 3
[1,1,2,1,2,3,1,1] => 9
[1,1,2,1,2,2,1,2] => 9
[1,1,2,1,2,1,1,3] => 8
[1,1,2,1,3,4] => 3
[1,1,3,3,1,1,1,1] => 4
[1,1,3,3,2,2] => 4
[1,1,3,2,1,2,1,1] => 13
[1,1,3,2,1,1,1,2] => 7
[1,1,3,2,2,3] => 3
[1,1,3,1,1,3,1,1] => 9
[1,1,3,1,1,2,1,2] => 9
[1,1,3,1,1,1,1,3] => 3
[1,1,3,1,2,4] => 3
[1,1,4,4,1,1] => 4
[1,1,4,3,1,2] => 7
[1,1,4,2,1,3] => 7
[1,1,4,1,1,4] => 3
[1,1,5,5] => 0
[2,2,1,1,1,1,1,1,1,1] => 2
[2,2,1,1,1,1,2,2] => 2
[2,2,1,1,2,2,1,1] => 8
[2,2,1,1,2,1,1,2] => 7
[2,2,1,1,3,3] => 2
[2,2,2,2,1,1,1,1] => 4
[2,2,2,2,2,2] => 0
[2,2,2,1,1,2,1,1] => 9
[2,2,2,1,1,1,1,2] => 3
[2,2,2,1,2,3] => 3
[2,2,3,3,1,1] => 4
[2,2,3,2,1,2] => 7
[2,2,3,1,1,3] => 3
[2,2,4,4] => 0
[2,1,1,2,1,1,1,1,1,1] => 5
[2,1,1,2,1,1,2,2] => 5
[2,1,1,2,2,2,1,1] => 7
[2,1,1,2,2,1,1,2] => 6
[2,1,1,2,3,3] => 1
[2,1,1,1,1,2,1,1,1,1] => 7
[2,1,1,1,1,2,2,2] => 1
[2,1,1,1,1,1,1,2,1,1] => 9
[2,1,1,1,1,1,1,1,1,2] => 1
[2,1,1,1,1,1,2,3] => 1
[2,1,1,1,2,3,1,1] => 7
[2,1,1,1,2,2,1,2] => 7
[2,1,1,1,2,1,1,3] => 6
[2,1,1,1,3,4] => 1
[2,1,2,3,1,1,1,1] => 5
[2,1,2,3,2,2] => 5
[2,1,2,2,1,2,1,1] => 11
[2,1,2,2,1,1,1,2] => 5
[2,1,2,2,2,3] => 1
[2,1,2,1,1,3,1,1] => 10
[2,1,2,1,1,2,1,2] => 10
[2,1,2,1,1,1,1,3] => 4
[2,1,2,1,2,4] => 4
[2,1,3,4,1,1] => 5
[2,1,3,3,1,2] => 5
[2,1,3,2,1,3] => 8
[2,1,3,1,1,4] => 4
[2,1,4,5] => 1
[3,3,1,1,1,1,1,1] => 2
[3,3,1,1,2,2] => 2
[3,3,2,2,1,1] => 6
[3,3,2,1,1,2] => 5
[3,3,3,3] => 0
[3,2,1,2,1,1,1,1] => 7
[3,2,1,2,2,2] => 3
[3,2,1,1,1,2,1,1] => 9
[3,2,1,1,1,1,1,2] => 3
[3,2,1,1,2,3] => 3
[3,2,2,3,1,1] => 5
[3,2,2,2,1,2] => 5
[3,2,2,1,1,3] => 4
[3,2,3,4] => 1
[3,1,1,3,1,1,1,1] => 5
[3,1,1,3,2,2] => 5
[3,1,1,2,1,2,1,1] => 11
[3,1,1,2,1,1,1,2] => 5
[3,1,1,2,2,3] => 1
[3,1,1,1,1,3,1,1] => 7
[3,1,1,1,1,2,1,2] => 7
[3,1,1,1,1,1,1,3] => 1
[3,1,1,1,2,4] => 1
[3,1,2,4,1,1] => 5
[3,1,2,3,1,2] => 5
[3,1,2,2,1,3] => 5
[3,1,2,1,1,4] => 4
[3,1,3,5] => 1
[4,4,1,1,1,1] => 2
[4,4,2,2] => 2
[4,3,1,2,1,1] => 7
[4,3,1,1,1,2] => 3
[4,3,2,3] => 3
[4,2,1,3,1,1] => 7
[4,2,1,2,1,2] => 7
[4,2,1,1,1,3] => 3
[4,2,2,4] => 1
[4,1,1,4,1,1] => 5
[4,1,1,3,1,2] => 5
[4,1,1,2,1,3] => 5
[4,1,1,1,1,4] => 1
[4,1,2,5] => 1
[5,5,1,1] => 2
[5,4,1,2] => 3
[5,3,1,3] => 3
[5,2,1,4] => 3
[5,1,1,5] => 1
[6,6] => 0
[1,11] => 0
[1,9,2] => 2
[1,8,1,2] => 2
[1,7,1,1,2] => 2
[1,6,1,1,1,2] => 2
[1,5,1,1,1,1,2] => 2
[1,4,1,1,1,1,1,2] => 2
[1,3,1,1,1,1,1,1,2] => 2
[1,2,1,1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,1,1,1,1,2] => 0
[1,2,2,2,2,2,2] => 0
[1,2,2,2,2,1,3] => 5
[1,2,2,2,1,3,2] => 10
[1,2,2,2,1,2,3] => 4
[1,2,2,2,1,1,4] => 4
[1,2,2,1,3,2,2] => 8
[1,2,2,1,3,1,3] => 8
[1,2,2,1,2,3,2] => 9
[1,2,2,1,2,2,3] => 3
[1,2,2,1,2,1,4] => 8
[1,2,2,1,1,4,2] => 9
[1,2,2,1,1,3,3] => 3
[1,2,2,1,1,2,4] => 3
[1,2,2,1,1,1,5] => 3
[1,2,1,3,2,2,2] => 6
[1,2,1,3,2,1,3] => 11
[1,2,1,3,1,3,2] => 12
[1,2,1,3,1,2,3] => 6
[1,2,1,3,1,1,4] => 6
[1,2,1,2,3,2,2] => 7
[1,2,1,2,3,1,3] => 7
[1,2,1,2,2,3,2] => 8
[1,2,1,2,2,2,3] => 2
[1,2,1,2,2,1,4] => 7
[1,2,1,2,1,4,2] => 12
[1,2,1,2,1,3,3] => 6
[1,2,1,2,1,2,4] => 6
[1,2,1,2,1,1,5] => 6
[1,2,1,1,4,2,2] => 7
[1,2,1,1,4,1,3] => 7
[1,2,1,1,3,3,2] => 8
[1,2,1,1,3,2,3] => 7
[1,2,1,1,3,1,4] => 7
[1,2,1,1,2,4,2] => 8
[1,2,1,1,2,3,3] => 2
[1,2,1,1,2,2,4] => 2
[1,2,1,1,2,1,5] => 7
[1,2,1,1,1,5,2] => 8
[1,2,1,1,1,4,3] => 8
[1,2,1,1,1,3,4] => 2
[1,2,1,1,1,2,5] => 2
[1,2,1,1,1,1,6] => 2
[1,1,3,2,2,2,2] => 3
[1,1,3,2,2,1,3] => 8
[1,1,3,2,1,3,2] => 13
[1,1,3,2,1,2,3] => 7
[1,1,3,2,1,1,4] => 7
[1,1,3,1,3,2,2] => 8
[1,1,3,1,3,1,3] => 8
[1,1,3,1,2,3,2] => 9
[1,1,3,1,2,2,3] => 3
[1,1,3,1,2,1,4] => 8
[1,1,3,1,1,4,2] => 9
[1,1,3,1,1,3,3] => 3
[1,1,3,1,1,2,4] => 3
[1,1,3,1,1,1,5] => 3
[1,1,2,3,2,2,2] => 4
[1,1,2,3,2,1,3] => 9
[1,1,2,3,1,3,2] => 10
[1,1,2,3,1,2,3] => 4
[1,1,2,3,1,1,4] => 4
[1,1,2,2,3,2,2] => 5
[1,1,2,2,3,1,3] => 5
[1,1,2,2,2,3,2] => 6
[1,1,2,2,2,2,3] => 0
[1,1,2,2,2,1,4] => 5
[1,1,2,2,1,4,2] => 10
[1,1,2,2,1,3,3] => 4
[1,1,2,2,1,2,4] => 4
[1,1,2,2,1,1,5] => 4
[1,1,2,1,4,2,2] => 8
[1,1,2,1,4,1,3] => 8
[1,1,2,1,3,3,2] => 9
[1,1,2,1,3,2,3] => 8
[1,1,2,1,3,1,4] => 8
[1,1,2,1,2,4,2] => 9
[1,1,2,1,2,3,3] => 3
[1,1,2,1,2,2,4] => 3
[1,1,2,1,2,1,5] => 8
[1,1,2,1,1,5,2] => 9
[1,1,2,1,1,4,3] => 9
[1,1,2,1,1,3,4] => 3
[1,1,2,1,1,2,5] => 3
[1,1,2,1,1,1,6] => 3
[1,1,1,4,2,2,2] => 4
[1,1,1,4,2,1,3] => 9
[1,1,1,4,1,3,2] => 10
[1,1,1,4,1,2,3] => 4
[1,1,1,4,1,1,4] => 4
[1,1,1,3,3,2,2] => 5
[1,1,1,3,3,1,3] => 5
[1,1,1,3,2,3,2] => 10
[1,1,1,3,2,2,3] => 4
[1,1,1,3,2,1,4] => 9
[1,1,1,3,1,4,2] => 10
[1,1,1,3,1,3,3] => 4
[1,1,1,3,1,2,4] => 4
[1,1,1,3,1,1,5] => 4
[1,1,1,2,4,2,2] => 5
[1,1,1,2,4,1,3] => 5
[1,1,1,2,3,3,2] => 6
[1,1,1,2,3,2,3] => 5
[1,1,1,2,3,1,4] => 5
[1,1,1,2,2,4,2] => 6
[1,1,1,2,2,3,3] => 0
[1,1,1,2,2,2,4] => 0
[1,1,1,2,2,1,5] => 5
[1,1,1,2,1,5,2] => 10
[1,1,1,2,1,4,3] => 10
[1,1,1,2,1,3,4] => 4
[1,1,1,2,1,2,5] => 4
[1,1,1,2,1,1,6] => 4
[1,1,1,1,5,2,2] => 5
[1,1,1,1,5,1,3] => 5
[1,1,1,1,4,3,2] => 11
[1,1,1,1,4,2,3] => 5
[1,1,1,1,4,1,4] => 5
[1,1,1,1,3,4,2] => 6
[1,1,1,1,3,3,3] => 0
[1,1,1,1,3,2,4] => 5
[1,1,1,1,3,1,5] => 5
[1,1,1,1,2,5,2] => 6
[1,1,1,1,2,4,3] => 6
[1,1,1,1,2,3,4] => 0
[1,1,1,1,2,2,5] => 0
[1,1,1,1,2,1,6] => 5
[1,1,1,1,1,6,2] => 6
[1,1,1,1,1,5,3] => 6
[1,1,1,1,1,4,4] => 0
[1,1,1,1,1,3,5] => 0
[1,1,1,1,1,2,6] => 0
[1,1,1,1,1,1,7] => 0
-----------------------------------------------------------------------------
Created: Apr 10, 2017 at 09:50 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Sep 25, 2020 at 00:22 by Martin Rubey