***************************************************************************** * 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: St001805 ----------------------------------------------------------------------------- Collection: Semistandard tableaux ----------------------------------------------------------------------------- Description: The maximal overlap of a cylindrical tableau associated with a semistandard tableau. A cylindrical tableau associated with a semistandard Young tableau $T$ is the skew semistandard tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle. The overlap, recorded in this statistic, equals $\max_C\big(2\ell(T) - \ell(C)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(T): if not T: return 0 w = len(T[0]) l = len(T) d = 0 while d < l and len(T[d]) == w and T[0][w-1] <= T[l-1-d][0]: d += 1 return d ----------------------------------------------------------------------------- Statistic values: [[1,2]] => 0 [[2,2]] => 1 [[1],[2]] => 2 [[1,3]] => 0 [[2,3]] => 0 [[3,3]] => 1 [[1],[3]] => 2 [[2],[3]] => 2 [[1,4]] => 0 [[2,4]] => 0 [[3,4]] => 0 [[4,4]] => 1 [[1],[4]] => 2 [[2],[4]] => 2 [[3],[4]] => 2 [[1,5]] => 0 [[2,5]] => 0 [[3,5]] => 0 [[4,5]] => 0 [[5,5]] => 1 [[1],[5]] => 2 [[2],[5]] => 2 [[3],[5]] => 2 [[4],[5]] => 2 [[1,6]] => 0 [[2,6]] => 0 [[3,6]] => 0 [[4,6]] => 0 [[5,6]] => 0 [[6,6]] => 1 [[1],[6]] => 2 [[2],[6]] => 2 [[3],[6]] => 2 [[4],[6]] => 2 [[5],[6]] => 2 [[1,7]] => 0 [[2,7]] => 0 [[3,7]] => 0 [[4,7]] => 0 [[5,7]] => 0 [[6,7]] => 0 [[7,7]] => 1 [[1],[7]] => 2 [[2],[7]] => 2 [[3],[7]] => 2 [[4],[7]] => 2 [[5],[7]] => 2 [[6],[7]] => 2 [[1,8]] => 0 [[2,8]] => 0 [[3,8]] => 0 [[4,8]] => 0 [[5,8]] => 0 [[6,8]] => 0 [[7,8]] => 0 [[8,8]] => 1 [[1],[8]] => 2 [[2],[8]] => 2 [[3],[8]] => 2 [[4],[8]] => 2 [[5],[8]] => 2 [[6],[8]] => 2 [[7],[8]] => 2 [[1,1,2]] => 0 [[1,2,2]] => 0 [[2,2,2]] => 1 [[1,1],[2]] => 1 [[1,2],[2]] => 1 [[1,1,3]] => 0 [[1,2,3]] => 0 [[1,3,3]] => 0 [[2,2,3]] => 0 [[2,3,3]] => 0 [[3,3,3]] => 1 [[1,1],[3]] => 1 [[1,2],[3]] => 1 [[1,3],[2]] => 0 [[1,3],[3]] => 1 [[2,2],[3]] => 1 [[2,3],[3]] => 1 [[1],[2],[3]] => 3 [[1,1,4]] => 0 [[1,2,4]] => 0 [[1,3,4]] => 0 [[1,4,4]] => 0 [[2,2,4]] => 0 [[2,3,4]] => 0 [[2,4,4]] => 0 [[3,3,4]] => 0 [[3,4,4]] => 0 [[4,4,4]] => 1 [[1,1],[4]] => 1 [[1,2],[4]] => 1 [[1,4],[2]] => 0 [[1,3],[4]] => 1 [[1,4],[3]] => 0 [[1,4],[4]] => 1 [[2,2],[4]] => 1 [[2,3],[4]] => 1 [[2,4],[3]] => 0 [[2,4],[4]] => 1 [[3,3],[4]] => 1 [[3,4],[4]] => 1 [[1],[2],[4]] => 3 [[1],[3],[4]] => 3 [[2],[3],[4]] => 3 [[1,1,5]] => 0 [[1,2,5]] => 0 [[1,3,5]] => 0 [[1,4,5]] => 0 [[1,5,5]] => 0 [[2,2,5]] => 0 [[2,3,5]] => 0 [[2,4,5]] => 0 [[2,5,5]] => 0 [[3,3,5]] => 0 [[3,4,5]] => 0 [[3,5,5]] => 0 [[4,4,5]] => 0 [[4,5,5]] => 0 [[5,5,5]] => 1 [[1,1],[5]] => 1 [[1,2],[5]] => 1 [[1,5],[2]] => 0 [[1,3],[5]] => 1 [[1,5],[3]] => 0 [[1,4],[5]] => 1 [[1,5],[4]] => 0 [[1,5],[5]] => 1 [[2,2],[5]] => 1 [[2,3],[5]] => 1 [[2,5],[3]] => 0 [[2,4],[5]] => 1 [[2,5],[4]] => 0 [[2,5],[5]] => 1 [[3,3],[5]] => 1 [[3,4],[5]] => 1 [[3,5],[4]] => 0 [[3,5],[5]] => 1 [[4,4],[5]] => 1 [[4,5],[5]] => 1 [[1],[2],[5]] => 3 [[1],[3],[5]] => 3 [[1],[4],[5]] => 3 [[2],[3],[5]] => 3 [[2],[4],[5]] => 3 [[3],[4],[5]] => 3 [[1,1,6]] => 0 [[1,2,6]] => 0 [[1,3,6]] => 0 [[1,4,6]] => 0 [[1,5,6]] => 0 [[1,6,6]] => 0 [[2,2,6]] => 0 [[2,3,6]] => 0 [[2,4,6]] => 0 [[2,5,6]] => 0 [[2,6,6]] => 0 [[3,3,6]] => 0 [[3,4,6]] => 0 [[3,5,6]] => 0 [[3,6,6]] => 0 [[4,4,6]] => 0 [[4,5,6]] => 0 [[4,6,6]] => 0 [[5,5,6]] => 0 [[5,6,6]] => 0 [[6,6,6]] => 1 [[1,1],[6]] => 1 [[1,2],[6]] => 1 [[1,6],[2]] => 0 [[1,3],[6]] => 1 [[1,6],[3]] => 0 [[1,4],[6]] => 1 [[1,6],[4]] => 0 [[1,5],[6]] => 1 [[1,6],[5]] => 0 [[1,6],[6]] => 1 [[2,2],[6]] => 1 [[2,3],[6]] => 1 [[2,6],[3]] => 0 [[2,4],[6]] => 1 [[2,6],[4]] => 0 [[2,5],[6]] => 1 [[2,6],[5]] => 0 [[2,6],[6]] => 1 [[3,3],[6]] => 1 [[3,4],[6]] => 1 [[3,6],[4]] => 0 [[3,5],[6]] => 1 [[3,6],[5]] => 0 [[3,6],[6]] => 1 [[4,4],[6]] => 1 [[4,5],[6]] => 1 [[4,6],[5]] => 0 [[4,6],[6]] => 1 [[5,5],[6]] => 1 [[5,6],[6]] => 1 [[1],[2],[6]] => 3 [[1],[3],[6]] => 3 [[1],[4],[6]] => 3 [[1],[5],[6]] => 3 [[2],[3],[6]] => 3 [[2],[4],[6]] => 3 [[2],[5],[6]] => 3 [[3],[4],[6]] => 3 [[3],[5],[6]] => 3 [[4],[5],[6]] => 3 [[1,1,7]] => 0 [[1,2,7]] => 0 [[1,3,7]] => 0 [[1,4,7]] => 0 [[1,5,7]] => 0 [[1,6,7]] => 0 [[1,7,7]] => 0 [[2,2,7]] => 0 [[2,3,7]] => 0 [[2,4,7]] => 0 [[2,5,7]] => 0 [[2,6,7]] => 0 [[2,7,7]] => 0 [[3,3,7]] => 0 [[3,4,7]] => 0 [[3,5,7]] => 0 [[3,6,7]] => 0 [[3,7,7]] => 0 [[4,4,7]] => 0 [[4,5,7]] => 0 [[4,6,7]] => 0 [[4,7,7]] => 0 [[5,5,7]] => 0 [[5,6,7]] => 0 [[5,7,7]] => 0 [[6,6,7]] => 0 [[6,7,7]] => 0 [[7,7,7]] => 1 [[1,1],[7]] => 1 [[1,2],[7]] => 1 [[1,7],[2]] => 0 [[1,3],[7]] => 1 [[1,7],[3]] => 0 [[1,4],[7]] => 1 [[1,7],[4]] => 0 [[1,5],[7]] => 1 [[1,7],[5]] => 0 [[1,6],[7]] => 1 [[1,7],[6]] => 0 [[1,7],[7]] => 1 [[2,2],[7]] => 1 [[2,3],[7]] => 1 [[2,7],[3]] => 0 [[2,4],[7]] => 1 [[2,7],[4]] => 0 [[2,5],[7]] => 1 [[2,7],[5]] => 0 [[2,6],[7]] => 1 [[2,7],[6]] => 0 [[2,7],[7]] => 1 [[3,3],[7]] => 1 [[3,4],[7]] => 1 [[3,7],[4]] => 0 [[3,5],[7]] => 1 [[3,7],[5]] => 0 [[3,6],[7]] => 1 [[3,7],[6]] => 0 [[3,7],[7]] => 1 [[4,4],[7]] => 1 [[4,5],[7]] => 1 [[4,7],[5]] => 0 [[4,6],[7]] => 1 [[4,7],[6]] => 0 [[4,7],[7]] => 1 [[5,5],[7]] => 1 [[5,6],[7]] => 1 [[5,7],[6]] => 0 [[5,7],[7]] => 1 [[6,6],[7]] => 1 [[6,7],[7]] => 1 [[1],[2],[7]] => 3 [[1],[3],[7]] => 3 [[1],[4],[7]] => 3 [[1],[5],[7]] => 3 [[1],[6],[7]] => 3 [[2],[3],[7]] => 3 [[2],[4],[7]] => 3 [[2],[5],[7]] => 3 [[2],[6],[7]] => 3 [[3],[4],[7]] => 3 [[3],[5],[7]] => 3 [[3],[6],[7]] => 3 [[4],[5],[7]] => 3 [[4],[6],[7]] => 3 [[5],[6],[7]] => 3 [[1,1,1,2]] => 0 [[1,1,2,2]] => 0 [[1,2,2,2]] => 0 [[2,2,2,2]] => 1 [[1,1,1],[2]] => 1 [[1,1,2],[2]] => 1 [[1,2,2],[2]] => 1 [[1,1],[2,2]] => 2 [[1,1,1,3]] => 0 [[1,1,2,3]] => 0 [[1,1,3,3]] => 0 [[1,2,2,3]] => 0 [[1,2,3,3]] => 0 [[1,3,3,3]] => 0 [[2,2,2,3]] => 0 [[2,2,3,3]] => 0 [[2,3,3,3]] => 0 [[3,3,3,3]] => 1 [[1,1,1],[3]] => 1 [[1,1,2],[3]] => 1 [[1,1,3],[2]] => 0 [[1,1,3],[3]] => 1 [[1,2,2],[3]] => 1 [[1,2,3],[2]] => 0 [[1,2,3],[3]] => 1 [[1,3,3],[2]] => 0 [[1,3,3],[3]] => 1 [[2,2,2],[3]] => 1 [[2,2,3],[3]] => 1 [[2,3,3],[3]] => 1 [[1,1],[2,3]] => 2 [[1,1],[3,3]] => 2 [[1,2],[2,3]] => 1 [[1,2],[3,3]] => 1 [[2,2],[3,3]] => 2 [[1,1],[2],[3]] => 1 [[1,2],[2],[3]] => 1 [[1,3],[2],[3]] => 1 [[1,1,1,4]] => 0 [[1,1,2,4]] => 0 [[1,1,3,4]] => 0 [[1,1,4,4]] => 0 [[1,2,2,4]] => 0 [[1,2,3,4]] => 0 [[1,2,4,4]] => 0 [[1,3,3,4]] => 0 [[1,3,4,4]] => 0 [[1,4,4,4]] => 0 [[2,2,2,4]] => 0 [[2,2,3,4]] => 0 [[2,2,4,4]] => 0 [[2,3,3,4]] => 0 [[2,3,4,4]] => 0 [[2,4,4,4]] => 0 [[3,3,3,4]] => 0 [[3,3,4,4]] => 0 [[3,4,4,4]] => 0 [[4,4,4,4]] => 1 [[1,1,1],[4]] => 1 [[1,1,2],[4]] => 1 [[1,1,4],[2]] => 0 [[1,1,3],[4]] => 1 [[1,1,4],[3]] => 0 [[1,1,4],[4]] => 1 [[1,2,2],[4]] => 1 [[1,2,4],[2]] => 0 [[1,2,3],[4]] => 1 [[1,2,4],[3]] => 0 [[1,3,4],[2]] => 0 [[1,2,4],[4]] => 1 [[1,4,4],[2]] => 0 [[1,3,3],[4]] => 1 [[1,3,4],[3]] => 0 [[1,3,4],[4]] => 1 [[1,4,4],[3]] => 0 [[1,4,4],[4]] => 1 [[2,2,2],[4]] => 1 [[2,2,3],[4]] => 1 [[2,2,4],[3]] => 0 [[2,2,4],[4]] => 1 [[2,3,3],[4]] => 1 [[2,3,4],[3]] => 0 [[2,3,4],[4]] => 1 [[2,4,4],[3]] => 0 [[2,4,4],[4]] => 1 [[3,3,3],[4]] => 1 [[3,3,4],[4]] => 1 [[3,4,4],[4]] => 1 [[1,1],[2,4]] => 2 [[1,1],[3,4]] => 2 [[1,1],[4,4]] => 2 [[1,2],[2,4]] => 1 [[1,2],[3,4]] => 1 [[1,3],[2,4]] => 0 [[1,2],[4,4]] => 1 [[1,3],[3,4]] => 1 [[1,3],[4,4]] => 1 [[2,2],[3,4]] => 2 [[2,2],[4,4]] => 2 [[2,3],[3,4]] => 1 [[2,3],[4,4]] => 1 [[3,3],[4,4]] => 2 [[1,1],[2],[4]] => 1 [[1,1],[3],[4]] => 1 [[1,2],[2],[4]] => 1 [[1,2],[3],[4]] => 1 [[1,3],[2],[4]] => 1 [[1,4],[2],[3]] => 0 [[1,4],[2],[4]] => 1 [[1,3],[3],[4]] => 1 [[1,4],[3],[4]] => 1 [[2,2],[3],[4]] => 1 [[2,3],[3],[4]] => 1 [[2,4],[3],[4]] => 1 [[1],[2],[3],[4]] => 4 [[1,1,1,5]] => 0 [[1,1,2,5]] => 0 [[1,1,3,5]] => 0 [[1,1,4,5]] => 0 [[1,1,5,5]] => 0 [[1,2,2,5]] => 0 [[1,2,3,5]] => 0 [[1,2,4,5]] => 0 [[1,2,5,5]] => 0 [[1,3,3,5]] => 0 [[1,3,4,5]] => 0 [[1,3,5,5]] => 0 [[1,4,4,5]] => 0 [[1,4,5,5]] => 0 [[1,5,5,5]] => 0 [[2,2,2,5]] => 0 [[2,2,3,5]] => 0 [[2,2,4,5]] => 0 [[2,2,5,5]] => 0 [[2,3,3,5]] => 0 [[2,3,4,5]] => 0 [[2,3,5,5]] => 0 [[2,4,4,5]] => 0 [[2,4,5,5]] => 0 [[2,5,5,5]] => 0 [[3,3,3,5]] => 0 [[3,3,4,5]] => 0 [[3,3,5,5]] => 0 [[3,4,4,5]] => 0 [[3,4,5,5]] => 0 [[3,5,5,5]] => 0 [[4,4,4,5]] => 0 [[4,4,5,5]] => 0 [[4,5,5,5]] => 0 [[5,5,5,5]] => 1 [[1,1,1],[5]] => 1 [[1,1,2],[5]] => 1 [[1,1,5],[2]] => 0 [[1,1,3],[5]] => 1 [[1,1,5],[3]] => 0 [[1,1,4],[5]] => 1 [[1,1,5],[4]] => 0 [[1,1,5],[5]] => 1 [[1,2,2],[5]] => 1 [[1,2,5],[2]] => 0 [[1,2,3],[5]] => 1 [[1,2,5],[3]] => 0 [[1,3,5],[2]] => 0 [[1,2,4],[5]] => 1 [[1,2,5],[4]] => 0 [[1,4,5],[2]] => 0 [[1,2,5],[5]] => 1 [[1,5,5],[2]] => 0 [[1,3,3],[5]] => 1 [[1,3,5],[3]] => 0 [[1,3,4],[5]] => 1 [[1,3,5],[4]] => 0 [[1,4,5],[3]] => 0 [[1,3,5],[5]] => 1 [[1,5,5],[3]] => 0 [[1,4,4],[5]] => 1 [[1,4,5],[4]] => 0 [[1,4,5],[5]] => 1 [[1,5,5],[4]] => 0 [[1,5,5],[5]] => 1 [[2,2,2],[5]] => 1 [[2,2,3],[5]] => 1 [[2,2,5],[3]] => 0 [[2,2,4],[5]] => 1 [[2,2,5],[4]] => 0 [[2,2,5],[5]] => 1 [[2,3,3],[5]] => 1 [[2,3,5],[3]] => 0 [[2,3,4],[5]] => 1 [[2,3,5],[4]] => 0 [[2,4,5],[3]] => 0 [[2,3,5],[5]] => 1 [[2,5,5],[3]] => 0 [[2,4,4],[5]] => 1 [[2,4,5],[4]] => 0 [[2,4,5],[5]] => 1 [[2,5,5],[4]] => 0 [[2,5,5],[5]] => 1 [[3,3,3],[5]] => 1 [[3,3,4],[5]] => 1 [[3,3,5],[4]] => 0 [[3,3,5],[5]] => 1 [[3,4,4],[5]] => 1 [[3,4,5],[4]] => 0 [[3,4,5],[5]] => 1 [[3,5,5],[4]] => 0 [[3,5,5],[5]] => 1 [[4,4,4],[5]] => 1 [[4,4,5],[5]] => 1 [[4,5,5],[5]] => 1 [[1,1],[2,5]] => 2 [[1,1],[3,5]] => 2 [[1,1],[4,5]] => 2 [[1,1],[5,5]] => 2 [[1,2],[2,5]] => 1 [[1,2],[3,5]] => 1 [[1,3],[2,5]] => 0 [[1,2],[4,5]] => 1 [[1,4],[2,5]] => 0 [[1,2],[5,5]] => 1 [[1,3],[3,5]] => 1 [[1,3],[4,5]] => 1 [[1,4],[3,5]] => 0 [[1,3],[5,5]] => 1 [[1,4],[4,5]] => 1 [[1,4],[5,5]] => 1 [[2,2],[3,5]] => 2 [[2,2],[4,5]] => 2 [[2,2],[5,5]] => 2 [[2,3],[3,5]] => 1 [[2,3],[4,5]] => 1 [[2,4],[3,5]] => 0 [[2,3],[5,5]] => 1 [[2,4],[4,5]] => 1 [[2,4],[5,5]] => 1 [[3,3],[4,5]] => 2 [[3,3],[5,5]] => 2 [[3,4],[4,5]] => 1 [[3,4],[5,5]] => 1 [[4,4],[5,5]] => 2 [[1,1],[2],[5]] => 1 [[1,1],[3],[5]] => 1 [[1,1],[4],[5]] => 1 [[1,2],[2],[5]] => 1 [[1,2],[3],[5]] => 1 [[1,3],[2],[5]] => 1 [[1,5],[2],[3]] => 0 [[1,2],[4],[5]] => 1 [[1,4],[2],[5]] => 1 [[1,5],[2],[4]] => 0 [[1,5],[2],[5]] => 1 [[1,3],[3],[5]] => 1 [[1,3],[4],[5]] => 1 [[1,4],[3],[5]] => 1 [[1,5],[3],[4]] => 0 [[1,5],[3],[5]] => 1 [[1,4],[4],[5]] => 1 [[1,5],[4],[5]] => 1 [[2,2],[3],[5]] => 1 [[2,2],[4],[5]] => 1 [[2,3],[3],[5]] => 1 [[2,3],[4],[5]] => 1 [[2,4],[3],[5]] => 1 [[2,5],[3],[4]] => 0 [[2,5],[3],[5]] => 1 [[2,4],[4],[5]] => 1 [[2,5],[4],[5]] => 1 [[3,3],[4],[5]] => 1 [[3,4],[4],[5]] => 1 [[3,5],[4],[5]] => 1 [[1],[2],[3],[5]] => 4 [[1],[2],[4],[5]] => 4 [[1],[3],[4],[5]] => 4 [[2],[3],[4],[5]] => 4 [[1,1,1,6]] => 0 [[1,1,2,6]] => 0 [[1,1,3,6]] => 0 [[1,1,4,6]] => 0 [[1,1,5,6]] => 0 [[1,1,6,6]] => 0 [[1,2,2,6]] => 0 [[1,2,3,6]] => 0 [[1,2,4,6]] => 0 [[1,2,5,6]] => 0 [[1,2,6,6]] => 0 [[1,3,3,6]] => 0 [[1,3,4,6]] => 0 [[1,3,5,6]] => 0 [[1,3,6,6]] => 0 [[1,4,4,6]] => 0 [[1,4,5,6]] => 0 [[1,4,6,6]] => 0 [[1,5,5,6]] => 0 [[1,5,6,6]] => 0 [[1,6,6,6]] => 0 [[2,2,2,6]] => 0 [[2,2,3,6]] => 0 [[2,2,4,6]] => 0 [[2,2,5,6]] => 0 [[2,2,6,6]] => 0 [[2,3,3,6]] => 0 [[2,3,4,6]] => 0 [[2,3,5,6]] => 0 [[2,3,6,6]] => 0 [[2,4,4,6]] => 0 [[2,4,5,6]] => 0 [[2,4,6,6]] => 0 [[2,5,5,6]] => 0 [[2,5,6,6]] => 0 [[2,6,6,6]] => 0 [[3,3,3,6]] => 0 [[3,3,4,6]] => 0 [[3,3,5,6]] => 0 [[3,3,6,6]] => 0 [[3,4,4,6]] => 0 [[3,4,5,6]] => 0 [[3,4,6,6]] => 0 [[3,5,5,6]] => 0 [[3,5,6,6]] => 0 [[3,6,6,6]] => 0 [[4,4,4,6]] => 0 [[4,4,5,6]] => 0 [[4,4,6,6]] => 0 [[4,5,5,6]] => 0 [[4,5,6,6]] => 0 [[4,6,6,6]] => 0 [[5,5,5,6]] => 0 [[5,5,6,6]] => 0 [[5,6,6,6]] => 0 [[6,6,6,6]] => 1 [[1,1,1],[6]] => 1 [[1,1,2],[6]] => 1 [[1,1,6],[2]] => 0 [[1,1,3],[6]] => 1 [[1,1,6],[3]] => 0 [[1,1,4],[6]] => 1 [[1,1,6],[4]] => 0 [[1,1,5],[6]] => 1 [[1,1,6],[5]] => 0 [[1,1,6],[6]] => 1 [[1,2,2],[6]] => 1 [[1,2,6],[2]] => 0 [[1,2,3],[6]] => 1 [[1,2,6],[3]] => 0 [[1,3,6],[2]] => 0 [[1,2,4],[6]] => 1 [[1,2,6],[4]] => 0 [[1,4,6],[2]] => 0 [[1,2,5],[6]] => 1 [[1,2,6],[5]] => 0 [[1,5,6],[2]] => 0 [[1,2,6],[6]] => 1 [[1,6,6],[2]] => 0 [[1,3,3],[6]] => 1 [[1,3,6],[3]] => 0 [[1,3,4],[6]] => 1 [[1,3,6],[4]] => 0 [[1,4,6],[3]] => 0 [[1,3,5],[6]] => 1 [[1,3,6],[5]] => 0 [[1,5,6],[3]] => 0 [[1,3,6],[6]] => 1 [[1,6,6],[3]] => 0 [[1,4,4],[6]] => 1 [[1,4,6],[4]] => 0 [[1,4,5],[6]] => 1 [[1,4,6],[5]] => 0 [[1,5,6],[4]] => 0 [[1,4,6],[6]] => 1 [[1,6,6],[4]] => 0 [[1,5,5],[6]] => 1 [[1,5,6],[5]] => 0 [[1,5,6],[6]] => 1 [[1,6,6],[5]] => 0 [[1,6,6],[6]] => 1 [[2,2,2],[6]] => 1 [[2,2,3],[6]] => 1 [[2,2,6],[3]] => 0 [[2,2,4],[6]] => 1 [[2,2,6],[4]] => 0 [[2,2,5],[6]] => 1 [[2,2,6],[5]] => 0 [[2,2,6],[6]] => 1 [[2,3,3],[6]] => 1 [[2,3,6],[3]] => 0 [[2,3,4],[6]] => 1 [[2,3,6],[4]] => 0 [[2,4,6],[3]] => 0 [[2,3,5],[6]] => 1 [[2,3,6],[5]] => 0 [[2,5,6],[3]] => 0 [[2,3,6],[6]] => 1 [[2,6,6],[3]] => 0 [[2,4,4],[6]] => 1 [[2,4,6],[4]] => 0 [[2,4,5],[6]] => 1 [[2,4,6],[5]] => 0 [[2,5,6],[4]] => 0 [[2,4,6],[6]] => 1 [[2,6,6],[4]] => 0 [[2,5,5],[6]] => 1 [[2,5,6],[5]] => 0 [[2,5,6],[6]] => 1 [[2,6,6],[5]] => 0 [[2,6,6],[6]] => 1 [[3,3,3],[6]] => 1 [[3,3,4],[6]] => 1 [[3,3,6],[4]] => 0 [[3,3,5],[6]] => 1 [[3,3,6],[5]] => 0 [[3,3,6],[6]] => 1 [[3,4,4],[6]] => 1 [[3,4,6],[4]] => 0 [[3,4,5],[6]] => 1 [[3,4,6],[5]] => 0 [[3,5,6],[4]] => 0 [[3,4,6],[6]] => 1 [[3,6,6],[4]] => 0 [[3,5,5],[6]] => 1 [[3,5,6],[5]] => 0 [[3,5,6],[6]] => 1 [[3,6,6],[5]] => 0 [[3,6,6],[6]] => 1 [[4,4,4],[6]] => 1 [[4,4,5],[6]] => 1 [[4,4,6],[5]] => 0 [[4,4,6],[6]] => 1 [[4,5,5],[6]] => 1 [[4,5,6],[5]] => 0 [[4,5,6],[6]] => 1 [[4,6,6],[5]] => 0 [[4,6,6],[6]] => 1 [[5,5,5],[6]] => 1 [[5,5,6],[6]] => 1 [[5,6,6],[6]] => 1 [[1,1],[2,6]] => 2 [[1,1],[3,6]] => 2 [[1,1],[4,6]] => 2 [[1,1],[5,6]] => 2 [[1,1],[6,6]] => 2 [[1,2],[2,6]] => 1 [[1,2],[3,6]] => 1 [[1,3],[2,6]] => 0 [[1,2],[4,6]] => 1 [[1,4],[2,6]] => 0 [[1,2],[5,6]] => 1 [[1,5],[2,6]] => 0 [[1,2],[6,6]] => 1 [[1,3],[3,6]] => 1 [[1,3],[4,6]] => 1 [[1,4],[3,6]] => 0 [[1,3],[5,6]] => 1 [[1,5],[3,6]] => 0 [[1,3],[6,6]] => 1 [[1,4],[4,6]] => 1 [[1,4],[5,6]] => 1 [[1,5],[4,6]] => 0 [[1,4],[6,6]] => 1 [[1,5],[5,6]] => 1 [[1,5],[6,6]] => 1 [[2,2],[3,6]] => 2 [[2,2],[4,6]] => 2 [[2,2],[5,6]] => 2 [[2,2],[6,6]] => 2 [[2,3],[3,6]] => 1 [[2,3],[4,6]] => 1 [[2,4],[3,6]] => 0 [[2,3],[5,6]] => 1 [[2,5],[3,6]] => 0 [[2,3],[6,6]] => 1 [[2,4],[4,6]] => 1 [[2,4],[5,6]] => 1 [[2,5],[4,6]] => 0 [[2,4],[6,6]] => 1 [[2,5],[5,6]] => 1 [[2,5],[6,6]] => 1 [[3,3],[4,6]] => 2 [[3,3],[5,6]] => 2 [[3,3],[6,6]] => 2 [[3,4],[4,6]] => 1 [[3,4],[5,6]] => 1 [[3,5],[4,6]] => 0 [[3,4],[6,6]] => 1 [[3,5],[5,6]] => 1 [[3,5],[6,6]] => 1 [[4,4],[5,6]] => 2 [[4,4],[6,6]] => 2 [[4,5],[5,6]] => 1 [[4,5],[6,6]] => 1 [[5,5],[6,6]] => 2 [[1,1],[2],[6]] => 1 [[1,1],[3],[6]] => 1 [[1,1],[4],[6]] => 1 [[1,1],[5],[6]] => 1 [[1,2],[2],[6]] => 1 [[1,2],[3],[6]] => 1 [[1,3],[2],[6]] => 1 [[1,6],[2],[3]] => 0 [[1,2],[4],[6]] => 1 [[1,4],[2],[6]] => 1 [[1,6],[2],[4]] => 0 [[1,2],[5],[6]] => 1 [[1,5],[2],[6]] => 1 [[1,6],[2],[5]] => 0 [[1,6],[2],[6]] => 1 [[1,3],[3],[6]] => 1 [[1,3],[4],[6]] => 1 [[1,4],[3],[6]] => 1 [[1,6],[3],[4]] => 0 [[1,3],[5],[6]] => 1 [[1,5],[3],[6]] => 1 [[1,1,1,1,2]] => 0 [[1,1,1,2,2]] => 0 [[1,1,2,2,2]] => 0 [[1,2,2,2,2]] => 0 [[2,2,2,2,2]] => 1 [[1,1,1,1],[2]] => 1 [[1,1,1,2],[2]] => 1 [[1,1,2,2],[2]] => 1 [[1,2,2,2],[2]] => 1 [[1,1,1],[2,2]] => 1 [[1,1,2],[2,2]] => 1 [[1,1,1,1,3]] => 0 [[1,1,1,2,3]] => 0 [[1,1,1,3,3]] => 0 [[1,1,2,2,3]] => 0 [[1,1,2,3,3]] => 0 [[1,1,3,3,3]] => 0 [[1,2,2,2,3]] => 0 [[1,2,2,3,3]] => 0 [[1,2,3,3,3]] => 0 [[1,3,3,3,3]] => 0 [[2,2,2,2,3]] => 0 [[2,2,2,3,3]] => 0 [[2,2,3,3,3]] => 0 [[2,3,3,3,3]] => 0 [[3,3,3,3,3]] => 1 [[1,1,1,1],[3]] => 1 [[1,1,1,2],[3]] => 1 [[1,1,1,3],[2]] => 0 [[1,1,1,3],[3]] => 1 [[1,1,2,2],[3]] => 1 [[1,1,2,3],[2]] => 0 [[1,1,2,3],[3]] => 1 [[1,1,3,3],[2]] => 0 [[1,1,3,3],[3]] => 1 [[1,2,2,2],[3]] => 1 [[1,2,2,3],[2]] => 0 [[1,2,2,3],[3]] => 1 [[1,2,3,3],[2]] => 0 [[1,2,3,3],[3]] => 1 [[1,3,3,3],[2]] => 0 [[1,3,3,3],[3]] => 1 [[2,2,2,2],[3]] => 1 [[2,2,2,3],[3]] => 1 [[2,2,3,3],[3]] => 1 [[2,3,3,3],[3]] => 1 [[1,1,1],[2,3]] => 1 [[1,1,1],[3,3]] => 1 [[1,1,2],[2,3]] => 1 [[1,1,3],[2,2]] => 0 [[1,1,2],[3,3]] => 1 [[1,1,3],[2,3]] => 0 [[1,1,3],[3,3]] => 1 [[1,2,2],[2,3]] => 1 [[1,2,2],[3,3]] => 1 [[1,2,3],[2,3]] => 0 [[1,2,3],[3,3]] => 1 [[2,2,2],[3,3]] => 1 [[2,2,3],[3,3]] => 1 [[1,1,1],[2],[3]] => 1 [[1,1,2],[2],[3]] => 1 [[1,1,3],[2],[3]] => 1 [[1,2,2],[2],[3]] => 1 [[1,2,3],[2],[3]] => 1 [[1,3,3],[2],[3]] => 1 [[1,1],[2,2],[3]] => 2 [[1,1],[2,3],[3]] => 2 [[1,2],[2,3],[3]] => 2 [[1,1,1,1,4]] => 0 [[1,1,1,2,4]] => 0 [[1,1,1,3,4]] => 0 [[1,1,1,4,4]] => 0 [[1,1,2,2,4]] => 0 [[1,1,2,3,4]] => 0 [[1,1,2,4,4]] => 0 [[1,1,3,3,4]] => 0 [[1,1,3,4,4]] => 0 [[1,1,4,4,4]] => 0 [[1,2,2,2,4]] => 0 [[1,2,2,3,4]] => 0 [[1,2,2,4,4]] => 0 [[1,2,3,3,4]] => 0 [[1,2,3,4,4]] => 0 [[1,2,4,4,4]] => 0 [[1,3,3,3,4]] => 0 [[1,3,3,4,4]] => 0 [[1,3,4,4,4]] => 0 [[1,4,4,4,4]] => 0 [[2,2,2,2,4]] => 0 [[2,2,2,3,4]] => 0 [[2,2,2,4,4]] => 0 [[2,2,3,3,4]] => 0 [[2,2,3,4,4]] => 0 [[2,2,4,4,4]] => 0 [[2,3,3,3,4]] => 0 [[2,3,3,4,4]] => 0 [[2,3,4,4,4]] => 0 [[2,4,4,4,4]] => 0 [[3,3,3,3,4]] => 0 [[3,3,3,4,4]] => 0 [[3,3,4,4,4]] => 0 [[3,4,4,4,4]] => 0 [[4,4,4,4,4]] => 1 [[1,1,1,1],[4]] => 1 [[1,1,1,2],[4]] => 1 [[1,1,1,4],[2]] => 0 [[1,1,1,3],[4]] => 1 [[1,1,1,4],[3]] => 0 [[1,1,1,4],[4]] => 1 [[1,1,2,2],[4]] => 1 [[1,1,2,4],[2]] => 0 [[1,1,2,3],[4]] => 1 [[1,1,2,4],[3]] => 0 [[1,1,3,4],[2]] => 0 [[1,1,2,4],[4]] => 1 [[1,1,4,4],[2]] => 0 [[1,1,3,3],[4]] => 1 [[1,1,3,4],[3]] => 0 [[1,1,3,4],[4]] => 1 [[1,1,4,4],[3]] => 0 [[1,1,4,4],[4]] => 1 [[1,2,2,2],[4]] => 1 [[1,2,2,4],[2]] => 0 [[1,2,2,3],[4]] => 1 [[1,2,2,4],[3]] => 0 [[1,2,3,4],[2]] => 0 [[1,2,2,4],[4]] => 1 [[1,2,4,4],[2]] => 0 [[1,2,3,3],[4]] => 1 [[1,2,3,4],[3]] => 0 [[1,3,3,4],[2]] => 0 [[1,2,3,4],[4]] => 1 [[1,2,4,4],[3]] => 0 [[1,3,4,4],[2]] => 0 [[1,2,4,4],[4]] => 1 [[1,4,4,4],[2]] => 0 [[1,3,3,3],[4]] => 1 [[1,3,3,4],[3]] => 0 [[1,3,3,4],[4]] => 1 [[1,3,4,4],[3]] => 0 [[1,3,4,4],[4]] => 1 [[1,4,4,4],[3]] => 0 [[1,4,4,4],[4]] => 1 [[2,2,2,2],[4]] => 1 [[2,2,2,3],[4]] => 1 [[2,2,2,4],[3]] => 0 [[2,2,2,4],[4]] => 1 [[2,2,3,3],[4]] => 1 [[2,2,3,4],[3]] => 0 [[2,2,3,4],[4]] => 1 [[2,2,4,4],[3]] => 0 [[2,2,4,4],[4]] => 1 [[2,3,3,3],[4]] => 1 [[2,3,3,4],[3]] => 0 [[2,3,3,4],[4]] => 1 [[2,3,4,4],[3]] => 0 [[2,3,4,4],[4]] => 1 [[2,4,4,4],[3]] => 0 [[2,4,4,4],[4]] => 1 [[3,3,3,3],[4]] => 1 [[3,3,3,4],[4]] => 1 [[3,3,4,4],[4]] => 1 [[3,4,4,4],[4]] => 1 [[1,1,1],[2,4]] => 1 [[1,1,1],[3,4]] => 1 [[1,1,1],[4,4]] => 1 [[1,1,2],[2,4]] => 1 [[1,1,4],[2,2]] => 0 [[1,1,2],[3,4]] => 1 [[1,1,3],[2,4]] => 0 [[1,1,4],[2,3]] => 0 [[1,1,2],[4,4]] => 1 [[1,1,4],[2,4]] => 0 [[1,1,3],[3,4]] => 1 [[1,1,4],[3,3]] => 0 [[1,1,3],[4,4]] => 1 [[1,1,4],[3,4]] => 0 [[1,1,4],[4,4]] => 1 [[1,2,2],[2,4]] => 1 [[1,2,2],[3,4]] => 1 [[1,2,3],[2,4]] => 0 [[1,2,4],[2,3]] => 0 [[1,2,2],[4,4]] => 1 [[1,2,4],[2,4]] => 0 [[1,2,3],[3,4]] => 1 [[1,2,4],[3,3]] => 0 [[1,3,3],[2,4]] => 0 [[1,2,3],[4,4]] => 1 [[1,2,4],[3,4]] => 0 [[1,3,4],[2,4]] => 0 [[1,2,4],[4,4]] => 1 [[1,3,3],[3,4]] => 1 [[1,3,3],[4,4]] => 1 [[1,3,4],[3,4]] => 0 [[1,3,4],[4,4]] => 1 [[2,2,2],[3,4]] => 1 [[2,2,2],[4,4]] => 1 [[2,2,3],[3,4]] => 1 [[2,2,4],[3,3]] => 0 [[2,2,3],[4,4]] => 1 [[2,2,4],[3,4]] => 0 [[2,2,4],[4,4]] => 1 [[2,3,3],[3,4]] => 1 [[2,3,3],[4,4]] => 1 [[2,3,4],[3,4]] => 0 [[2,3,4],[4,4]] => 1 [[3,3,3],[4,4]] => 1 [[3,3,4],[4,4]] => 1 [[1,1,1],[2],[4]] => 1 [[1,1,1],[3],[4]] => 1 [[1,1,2],[2],[4]] => 1 [[1,1,2],[3],[4]] => 1 [[1,1,3],[2],[4]] => 1 [[1,1,4],[2],[3]] => 0 [[1,1,4],[2],[4]] => 1 [[1,1,3],[3],[4]] => 1 [[1,1,4],[3],[4]] => 1 [[1,2,2],[2],[4]] => 1 [[1,2,2],[3],[4]] => 1 [[1,2,3],[2],[4]] => 1 [[1,2,4],[2],[3]] => 0 [[1,2,4],[2],[4]] => 1 [[1,2,3],[3],[4]] => 1 [[1,3,3],[2],[4]] => 1 [[1,3,4],[2],[3]] => 0 [[1,2,4],[3],[4]] => 1 [[1,3,4],[2],[4]] => 1 [[1,4,4],[2],[3]] => 0 [[1,4,4],[2],[4]] => 1 [[1,3,3],[3],[4]] => 1 [[1,3,4],[3],[4]] => 1 [[1,4,4],[3],[4]] => 1 [[2,2,2],[3],[4]] => 1 [[2,2,3],[3],[4]] => 1 [[2,2,4],[3],[4]] => 1 [[2,3,3],[3],[4]] => 1 [[2,3,4],[3],[4]] => 1 [[2,4,4],[3],[4]] => 1 [[1,1],[2,2],[4]] => 2 [[1,1],[2,3],[4]] => 2 [[1,1],[2,4],[3]] => 2 [[1,1],[2,4],[4]] => 2 [[1,1],[3,3],[4]] => 2 [[1,1],[3,4],[4]] => 2 [[1,2],[2,3],[4]] => 2 [[1,2],[2,4],[3]] => 2 [[1,2],[2,4],[4]] => 2 [[1,2],[3,3],[4]] => 2 [[1,3],[2,4],[3]] => 1 [[1,2],[3,4],[4]] => 2 [[1,3],[2,4],[4]] => 1 [[1,3],[3,4],[4]] => 2 [[2,2],[3,3],[4]] => 2 [[2,2],[3,4],[4]] => 2 [[2,3],[3,4],[4]] => 2 [[1,1],[2],[3],[4]] => 1 [[1,2],[2],[3],[4]] => 1 [[1,3],[2],[3],[4]] => 1 [[1,4],[2],[3],[4]] => 1 [[1,1,1,1,1,2]] => 0 [[1,1,1,1,2,2]] => 0 [[1,1,1,2,2,2]] => 0 [[1,1,2,2,2,2]] => 0 [[1,2,2,2,2,2]] => 0 [[2,2,2,2,2,2]] => 1 [[1,1,1,1,1],[2]] => 1 [[1,1,1,1,2],[2]] => 1 [[1,1,1,2,2],[2]] => 1 [[1,1,2,2,2],[2]] => 1 [[1,2,2,2,2],[2]] => 1 [[1,1,1,1],[2,2]] => 1 [[1,1,1,2],[2,2]] => 1 [[1,1,2,2],[2,2]] => 1 [[1,1,1],[2,2,2]] => 2 [[1,1,1,1,1,3]] => 0 [[1,1,1,1,2,3]] => 0 [[1,1,1,1,3,3]] => 0 [[1,1,1,2,2,3]] => 0 [[1,1,1,2,3,3]] => 0 [[1,1,1,3,3,3]] => 0 [[1,1,2,2,2,3]] => 0 [[1,1,2,2,3,3]] => 0 [[1,1,2,3,3,3]] => 0 [[1,1,3,3,3,3]] => 0 [[1,2,2,2,2,3]] => 0 [[1,2,2,2,3,3]] => 0 [[1,2,2,3,3,3]] => 0 [[1,2,3,3,3,3]] => 0 [[1,3,3,3,3,3]] => 0 [[2,2,2,2,2,3]] => 0 [[2,2,2,2,3,3]] => 0 [[2,2,2,3,3,3]] => 0 [[2,2,3,3,3,3]] => 0 [[2,3,3,3,3,3]] => 0 [[3,3,3,3,3,3]] => 1 [[1,1,1,1,1],[3]] => 1 [[1,1,1,1,2],[3]] => 1 [[1,1,1,1,3],[2]] => 0 [[1,1,1,1,3],[3]] => 1 [[1,1,1,2,2],[3]] => 1 [[1,1,1,2,3],[2]] => 0 [[1,1,1,2,3],[3]] => 1 [[1,1,1,3,3],[2]] => 0 [[1,1,1,3,3],[3]] => 1 [[1,1,2,2,2],[3]] => 1 [[1,1,2,2,3],[2]] => 0 [[1,1,2,2,3],[3]] => 1 [[1,1,2,3,3],[2]] => 0 [[1,1,2,3,3],[3]] => 1 [[1,1,3,3,3],[2]] => 0 [[1,1,3,3,3],[3]] => 1 [[1,2,2,2,2],[3]] => 1 [[1,2,2,2,3],[2]] => 0 [[1,2,2,2,3],[3]] => 1 [[1,2,2,3,3],[2]] => 0 [[1,2,2,3,3],[3]] => 1 [[1,2,3,3,3],[2]] => 0 [[1,2,3,3,3],[3]] => 1 [[1,3,3,3,3],[2]] => 0 [[1,3,3,3,3],[3]] => 1 [[2,2,2,2,2],[3]] => 1 [[2,2,2,2,3],[3]] => 1 [[2,2,2,3,3],[3]] => 1 [[2,2,3,3,3],[3]] => 1 [[2,3,3,3,3],[3]] => 1 [[1,1,1,1],[2,3]] => 1 [[1,1,1,1],[3,3]] => 1 [[1,1,1,2],[2,3]] => 1 [[1,1,1,3],[2,2]] => 0 [[1,1,1,2],[3,3]] => 1 [[1,1,1,3],[2,3]] => 0 [[1,1,1,3],[3,3]] => 1 [[1,1,2,2],[2,3]] => 1 [[1,1,2,3],[2,2]] => 0 [[1,1,2,2],[3,3]] => 1 [[1,1,2,3],[2,3]] => 0 [[1,1,3,3],[2,2]] => 0 [[1,1,2,3],[3,3]] => 1 [[1,1,3,3],[2,3]] => 0 [[1,1,3,3],[3,3]] => 1 [[1,2,2,2],[2,3]] => 1 [[1,2,2,2],[3,3]] => 1 [[1,2,2,3],[2,3]] => 0 [[1,2,2,3],[3,3]] => 1 [[1,2,3,3],[2,3]] => 0 [[1,2,3,3],[3,3]] => 1 [[2,2,2,2],[3,3]] => 1 [[2,2,2,3],[3,3]] => 1 [[2,2,3,3],[3,3]] => 1 [[1,1,1,1],[2],[3]] => 1 [[1,1,1,2],[2],[3]] => 1 [[1,1,1,3],[2],[3]] => 1 [[1,1,2,2],[2],[3]] => 1 [[1,1,2,3],[2],[3]] => 1 [[1,1,3,3],[2],[3]] => 1 [[1,2,2,2],[2],[3]] => 1 [[1,2,2,3],[2],[3]] => 1 [[1,2,3,3],[2],[3]] => 1 [[1,3,3,3],[2],[3]] => 1 [[1,1,1],[2,2,3]] => 2 [[1,1,1],[2,3,3]] => 2 [[1,1,1],[3,3,3]] => 2 [[1,1,2],[2,2,3]] => 1 [[1,1,2],[2,3,3]] => 1 [[1,1,2],[3,3,3]] => 1 [[1,2,2],[2,3,3]] => 1 [[1,2,2],[3,3,3]] => 1 [[2,2,2],[3,3,3]] => 2 [[1,1,1],[2,2],[3]] => 1 [[1,1,1],[2,3],[3]] => 1 [[1,1,2],[2,2],[3]] => 1 [[1,1,2],[2,3],[3]] => 1 [[1,1,3],[2,2],[3]] => 1 [[1,1,3],[2,3],[3]] => 1 [[1,2,2],[2,3],[3]] => 1 [[1,2,3],[2,3],[3]] => 1 [[1,1],[2,2],[3,3]] => 3 [[1,1,1,1,1,1,2]] => 0 [[1,1,1,1,1,2,2]] => 0 [[1,1,1,1,2,2,2]] => 0 [[1,1,1,2,2,2,2]] => 0 [[1,1,2,2,2,2,2]] => 0 [[1,2,2,2,2,2,2]] => 0 [[2,2,2,2,2,2,2]] => 1 [[1,1,1,1,1,1],[2]] => 1 [[1,1,1,1,1,2],[2]] => 1 [[1,1,1,1,2,2],[2]] => 1 [[1,1,1,2,2,2],[2]] => 1 [[1,1,2,2,2,2],[2]] => 1 [[1,2,2,2,2,2],[2]] => 1 [[1,1,1,1,1],[2,2]] => 1 [[1,1,1,1,2],[2,2]] => 1 [[1,1,1,2,2],[2,2]] => 1 [[1,1,2,2,2],[2,2]] => 1 [[1,1,1,1],[2,2,2]] => 1 [[1,1,1,2],[2,2,2]] => 1 ----------------------------------------------------------------------------- Created: Jun 06, 2022 at 20:05 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 06, 2022 at 20:05 by Martin Rubey