***************************************************************************** * 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: St001454 ----------------------------------------------------------------------------- Collection: Plane partitions ----------------------------------------------------------------------------- Description: The difference between the largest and smallest heights of a plane partition. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(P): heights = [height for row in P for height in row] return max(heights) - min(heights) ----------------------------------------------------------------------------- Statistic values: [[1]] => 0 [[1],[1]] => 0 [[2]] => 0 [[1,1]] => 0 [[1],[1],[1]] => 0 [[2],[1]] => 1 [[1,1],[1]] => 0 [[3]] => 0 [[2,1]] => 1 [[1,1,1]] => 0 [[1],[1],[1],[1]] => 0 [[2],[1],[1]] => 1 [[2],[2]] => 0 [[1,1],[1],[1]] => 0 [[1,1],[1,1]] => 0 [[3],[1]] => 2 [[2,1],[1]] => 1 [[1,1,1],[1]] => 0 [[4]] => 0 [[3,1]] => 2 [[2,2]] => 0 [[2,1,1]] => 1 [[1,1,1,1]] => 0 [[1],[1],[1],[1],[1]] => 0 [[2],[1],[1],[1]] => 1 [[2],[2],[1]] => 1 [[1,1],[1],[1],[1]] => 0 [[1,1],[1,1],[1]] => 0 [[3],[1],[1]] => 2 [[3],[2]] => 1 [[2,1],[1],[1]] => 1 [[2,1],[2]] => 1 [[2,1],[1,1]] => 1 [[1,1,1],[1],[1]] => 0 [[1,1,1],[1,1]] => 0 [[4],[1]] => 3 [[3,1],[1]] => 2 [[2,2],[1]] => 1 [[2,1,1],[1]] => 1 [[1,1,1,1],[1]] => 0 [[5]] => 0 [[4,1]] => 3 [[3,2]] => 1 [[3,1,1]] => 2 [[2,2,1]] => 1 [[2,1,1,1]] => 1 [[1,1,1,1,1]] => 0 [[1],[1],[1],[1],[1],[1]] => 0 [[2],[1],[1],[1],[1]] => 1 [[2],[2],[1],[1]] => 1 [[2],[2],[2]] => 0 [[1,1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1],[1]] => 0 [[1,1],[1,1],[1,1]] => 0 [[3],[1],[1],[1]] => 2 [[3],[2],[1]] => 2 [[3],[3]] => 0 [[2,1],[1],[1],[1]] => 1 [[2,1],[2],[1]] => 1 [[2,1],[1,1],[1]] => 1 [[2,1],[2,1]] => 1 [[1,1,1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1]] => 0 [[1,1,1],[1,1,1]] => 0 [[4],[1],[1]] => 3 [[4],[2]] => 2 [[3,1],[1],[1]] => 2 [[3,1],[2]] => 2 [[3,1],[1,1]] => 2 [[2,2],[1],[1]] => 1 [[2,2],[2]] => 0 [[2,2],[1,1]] => 1 [[2,1,1],[1],[1]] => 1 [[2,1,1],[2]] => 1 [[2,1,1],[1,1]] => 1 [[1,1,1,1],[1],[1]] => 0 [[1,1,1,1],[1,1]] => 0 [[5],[1]] => 4 [[4,1],[1]] => 3 [[3,2],[1]] => 2 [[3,1,1],[1]] => 2 [[2,2,1],[1]] => 1 [[2,1,1,1],[1]] => 1 [[1,1,1,1,1],[1]] => 0 [[6]] => 0 [[5,1]] => 4 [[4,2]] => 2 [[4,1,1]] => 3 [[3,3]] => 0 [[3,2,1]] => 2 [[3,1,1,1]] => 2 [[2,2,2]] => 0 [[2,2,1,1]] => 1 [[2,1,1,1,1]] => 1 [[1,1,1,1,1,1]] => 0 [[1],[1],[1],[1],[1],[1],[1]] => 0 [[2],[1],[1],[1],[1],[1]] => 1 [[2],[2],[1],[1],[1]] => 1 [[2],[2],[2],[1]] => 1 [[1,1],[1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1],[1],[1]] => 0 [[1,1],[1,1],[1,1],[1]] => 0 [[3],[1],[1],[1],[1]] => 2 [[3],[2],[1],[1]] => 2 [[3],[2],[2]] => 1 [[3],[3],[1]] => 2 [[2,1],[1],[1],[1],[1]] => 1 [[2,1],[2],[1],[1]] => 1 [[2,1],[2],[2]] => 1 [[2,1],[1,1],[1],[1]] => 1 [[2,1],[1,1],[1,1]] => 1 [[2,1],[2,1],[1]] => 1 [[1,1,1],[1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1],[1]] => 0 [[1,1,1],[1,1],[1,1]] => 0 [[1,1,1],[1,1,1],[1]] => 0 [[4],[1],[1],[1]] => 3 [[4],[2],[1]] => 3 [[4],[3]] => 1 [[3,1],[1],[1],[1]] => 2 [[3,1],[2],[1]] => 2 [[3,1],[1,1],[1]] => 2 [[3,1],[3]] => 2 [[3,1],[2,1]] => 2 [[2,2],[1],[1],[1]] => 1 [[2,2],[2],[1]] => 1 [[2,2],[1,1],[1]] => 1 [[2,2],[2,1]] => 1 [[2,1,1],[1],[1],[1]] => 1 [[2,1,1],[2],[1]] => 1 [[2,1,1],[1,1],[1]] => 1 [[2,1,1],[2,1]] => 1 [[2,1,1],[1,1,1]] => 1 [[1,1,1,1],[1],[1],[1]] => 0 [[1,1,1,1],[1,1],[1]] => 0 [[1,1,1,1],[1,1,1]] => 0 [[5],[1],[1]] => 4 [[5],[2]] => 3 [[4,1],[1],[1]] => 3 [[4,1],[2]] => 3 [[4,1],[1,1]] => 3 [[3,2],[1],[1]] => 2 [[3,2],[2]] => 1 [[3,2],[1,1]] => 2 [[3,1,1],[1],[1]] => 2 [[3,1,1],[2]] => 2 [[3,1,1],[1,1]] => 2 [[2,2,1],[1],[1]] => 1 [[2,2,1],[2]] => 1 [[2,2,1],[1,1]] => 1 [[2,1,1,1],[1],[1]] => 1 [[2,1,1,1],[2]] => 1 [[2,1,1,1],[1,1]] => 1 [[1,1,1,1,1],[1],[1]] => 0 [[1,1,1,1,1],[1,1]] => 0 [[6],[1]] => 5 [[5,1],[1]] => 4 [[4,2],[1]] => 3 [[4,1,1],[1]] => 3 [[3,3],[1]] => 2 [[3,2,1],[1]] => 2 [[3,1,1,1],[1]] => 2 [[2,2,2],[1]] => 1 [[2,2,1,1],[1]] => 1 [[2,1,1,1,1],[1]] => 1 [[1,1,1,1,1,1],[1]] => 0 [[7]] => 0 [[6,1]] => 5 [[5,2]] => 3 [[5,1,1]] => 4 [[4,3]] => 1 [[4,2,1]] => 3 [[4,1,1,1]] => 3 [[3,3,1]] => 2 [[3,2,2]] => 1 [[3,2,1,1]] => 2 [[3,1,1,1,1]] => 2 [[2,2,2,1]] => 1 [[2,2,1,1,1]] => 1 [[2,1,1,1,1,1]] => 1 [[1,1,1,1,1,1,1]] => 0 [[1],[1],[1],[1],[1],[1],[1],[1]] => 0 [[2],[1],[1],[1],[1],[1],[1]] => 1 [[2],[2],[1],[1],[1],[1]] => 1 [[2],[2],[2],[1],[1]] => 1 [[2],[2],[2],[2]] => 0 [[1,1],[1],[1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1,1],[1],[1]] => 0 [[1,1],[1,1],[1,1],[1,1]] => 0 [[3],[1],[1],[1],[1],[1]] => 2 [[3],[2],[1],[1],[1]] => 2 [[3],[2],[2],[1]] => 2 [[3],[3],[1],[1]] => 2 [[3],[3],[2]] => 1 [[2,1],[1],[1],[1],[1],[1]] => 1 [[2,1],[2],[1],[1],[1]] => 1 [[2,1],[2],[2],[1]] => 1 [[2,1],[1,1],[1],[1],[1]] => 1 [[2,1],[1,1],[1,1],[1]] => 1 [[2,1],[2,1],[1],[1]] => 1 [[2,1],[2,1],[2]] => 1 [[2,1],[2,1],[1,1]] => 1 [[1,1,1],[1],[1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1,1],[1]] => 0 [[1,1,1],[1,1,1],[1],[1]] => 0 [[1,1,1],[1,1,1],[1,1]] => 0 [[4],[1],[1],[1],[1]] => 3 [[4],[2],[1],[1]] => 3 [[4],[2],[2]] => 2 [[4],[3],[1]] => 3 [[4],[4]] => 0 [[3,1],[1],[1],[1],[1]] => 2 [[3,1],[2],[1],[1]] => 2 [[3,1],[2],[2]] => 2 [[3,1],[1,1],[1],[1]] => 2 [[3,1],[1,1],[1,1]] => 2 [[3,1],[3],[1]] => 2 [[3,1],[2,1],[1]] => 2 [[3,1],[3,1]] => 2 [[2,2],[1],[1],[1],[1]] => 1 [[2,2],[2],[1],[1]] => 1 [[2,2],[2],[2]] => 0 [[2,2],[1,1],[1],[1]] => 1 [[2,2],[1,1],[1,1]] => 1 [[2,2],[2,1],[1]] => 1 [[2,2],[2,2]] => 0 [[2,1,1],[1],[1],[1],[1]] => 1 [[2,1,1],[2],[1],[1]] => 1 [[2,1,1],[2],[2]] => 1 [[2,1,1],[1,1],[1],[1]] => 1 [[2,1,1],[1,1],[1,1]] => 1 [[2,1,1],[2,1],[1]] => 1 [[2,1,1],[1,1,1],[1]] => 1 [[2,1,1],[2,1,1]] => 1 [[1,1,1,1],[1],[1],[1],[1]] => 0 [[1,1,1,1],[1,1],[1],[1]] => 0 [[1,1,1,1],[1,1],[1,1]] => 0 [[1,1,1,1],[1,1,1],[1]] => 0 [[1,1,1,1],[1,1,1,1]] => 0 [[5],[1],[1],[1]] => 4 [[5],[2],[1]] => 4 [[5],[3]] => 2 [[4,1],[1],[1],[1]] => 3 [[4,1],[2],[1]] => 3 [[4,1],[1,1],[1]] => 3 [[4,1],[3]] => 3 [[4,1],[2,1]] => 3 [[3,2],[1],[1],[1]] => 2 [[3,2],[2],[1]] => 2 [[3,2],[1,1],[1]] => 2 [[3,2],[3]] => 1 [[3,2],[2,1]] => 2 [[3,1,1],[1],[1],[1]] => 2 [[3,1,1],[2],[1]] => 2 [[3,1,1],[1,1],[1]] => 2 [[3,1,1],[3]] => 2 [[3,1,1],[2,1]] => 2 [[3,1,1],[1,1,1]] => 2 [[2,2,1],[1],[1],[1]] => 1 [[2,2,1],[2],[1]] => 1 [[2,2,1],[1,1],[1]] => 1 [[2,2,1],[2,1]] => 1 [[2,2,1],[1,1,1]] => 1 [[2,1,1,1],[1],[1],[1]] => 1 [[2,1,1,1],[2],[1]] => 1 [[2,1,1,1],[1,1],[1]] => 1 [[2,1,1,1],[2,1]] => 1 [[2,1,1,1],[1,1,1]] => 1 [[1,1,1,1,1],[1],[1],[1]] => 0 [[1,1,1,1,1],[1,1],[1]] => 0 [[1,1,1,1,1],[1,1,1]] => 0 [[6],[1],[1]] => 5 [[6],[2]] => 4 [[5,1],[1],[1]] => 4 [[5,1],[2]] => 4 [[5,1],[1,1]] => 4 [[4,2],[1],[1]] => 3 [[4,2],[2]] => 2 [[4,2],[1,1]] => 3 [[4,1,1],[1],[1]] => 3 [[4,1,1],[2]] => 3 [[4,1,1],[1,1]] => 3 [[3,3],[1],[1]] => 2 [[3,3],[2]] => 1 [[3,3],[1,1]] => 2 [[3,2,1],[1],[1]] => 2 [[3,2,1],[2]] => 2 [[3,2,1],[1,1]] => 2 [[3,1,1,1],[1],[1]] => 2 [[3,1,1,1],[2]] => 2 [[3,1,1,1],[1,1]] => 2 [[2,2,2],[1],[1]] => 1 [[2,2,2],[2]] => 0 [[2,2,2],[1,1]] => 1 [[2,2,1,1],[1],[1]] => 1 [[2,2,1,1],[2]] => 1 [[2,2,1,1],[1,1]] => 1 [[2,1,1,1,1],[1],[1]] => 1 [[2,1,1,1,1],[2]] => 1 [[2,1,1,1,1],[1,1]] => 1 [[1,1,1,1,1,1],[1],[1]] => 0 [[1,1,1,1,1,1],[1,1]] => 0 [[7],[1]] => 6 [[6,1],[1]] => 5 [[5,2],[1]] => 4 [[5,1,1],[1]] => 4 [[4,3],[1]] => 3 [[4,2,1],[1]] => 3 [[4,1,1,1],[1]] => 3 [[3,3,1],[1]] => 2 [[3,2,2],[1]] => 2 [[3,2,1,1],[1]] => 2 [[3,1,1,1,1],[1]] => 2 [[2,2,2,1],[1]] => 1 [[2,2,1,1,1],[1]] => 1 [[2,1,1,1,1,1],[1]] => 1 [[1,1,1,1,1,1,1],[1]] => 0 [[8]] => 0 [[7,1]] => 6 [[6,2]] => 4 [[6,1,1]] => 5 [[5,3]] => 2 [[5,2,1]] => 4 [[5,1,1,1]] => 4 [[4,4]] => 0 [[4,3,1]] => 3 [[4,2,2]] => 2 [[4,2,1,1]] => 3 [[4,1,1,1,1]] => 3 [[3,3,2]] => 1 [[3,3,1,1]] => 2 [[3,2,2,1]] => 2 [[3,2,1,1,1]] => 2 [[3,1,1,1,1,1]] => 2 [[2,2,2,2]] => 0 [[2,2,2,1,1]] => 1 [[2,2,1,1,1,1]] => 1 [[2,1,1,1,1,1,1]] => 1 [[1,1,1,1,1,1,1,1]] => 0 [[1],[1],[1],[1],[1],[1],[1],[1],[1]] => 0 [[2],[1],[1],[1],[1],[1],[1],[1]] => 1 [[2],[2],[1],[1],[1],[1],[1]] => 1 [[2],[2],[2],[1],[1],[1]] => 1 [[2],[2],[2],[2],[1]] => 1 [[1,1],[1],[1],[1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1,1],[1],[1],[1]] => 0 [[1,1],[1,1],[1,1],[1,1],[1]] => 0 [[3],[1],[1],[1],[1],[1],[1]] => 2 [[3],[2],[1],[1],[1],[1]] => 2 [[3],[2],[2],[1],[1]] => 2 [[3],[2],[2],[2]] => 1 [[3],[3],[1],[1],[1]] => 2 [[3],[3],[2],[1]] => 2 [[3],[3],[3]] => 0 [[2,1],[1],[1],[1],[1],[1],[1]] => 1 [[2,1],[2],[1],[1],[1],[1]] => 1 [[2,1],[2],[2],[1],[1]] => 1 [[2,1],[2],[2],[2]] => 1 [[2,1],[1,1],[1],[1],[1],[1]] => 1 [[2,1],[1,1],[1,1],[1],[1]] => 1 [[2,1],[1,1],[1,1],[1,1]] => 1 [[2,1],[2,1],[1],[1],[1]] => 1 [[2,1],[2,1],[2],[1]] => 1 [[2,1],[2,1],[1,1],[1]] => 1 [[2,1],[2,1],[2,1]] => 1 [[1,1,1],[1],[1],[1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1,1],[1],[1]] => 0 [[1,1,1],[1,1],[1,1],[1,1]] => 0 [[1,1,1],[1,1,1],[1],[1],[1]] => 0 [[1,1,1],[1,1,1],[1,1],[1]] => 0 [[1,1,1],[1,1,1],[1,1,1]] => 0 [[4],[1],[1],[1],[1],[1]] => 3 [[4],[2],[1],[1],[1]] => 3 [[4],[2],[2],[1]] => 3 [[4],[3],[1],[1]] => 3 [[4],[3],[2]] => 2 [[4],[4],[1]] => 3 [[3,1],[1],[1],[1],[1],[1]] => 2 [[3,1],[2],[1],[1],[1]] => 2 [[3,1],[2],[2],[1]] => 2 [[3,1],[1,1],[1],[1],[1]] => 2 [[3,1],[1,1],[1,1],[1]] => 2 [[3,1],[3],[1],[1]] => 2 [[3,1],[3],[2]] => 2 [[3,1],[2,1],[1],[1]] => 2 [[3,1],[2,1],[2]] => 2 [[3,1],[2,1],[1,1]] => 2 [[3,1],[3,1],[1]] => 2 [[2,2],[1],[1],[1],[1],[1]] => 1 [[2,2],[2],[1],[1],[1]] => 1 [[2,2],[2],[2],[1]] => 1 [[2,2],[1,1],[1],[1],[1]] => 1 [[2,2],[1,1],[1,1],[1]] => 1 [[2,2],[2,1],[1],[1]] => 1 [[2,2],[2,1],[2]] => 1 [[2,2],[2,1],[1,1]] => 1 [[2,2],[2,2],[1]] => 1 [[2,1,1],[1],[1],[1],[1],[1]] => 1 [[2,1,1],[2],[1],[1],[1]] => 1 [[2,1,1],[2],[2],[1]] => 1 [[2,1,1],[1,1],[1],[1],[1]] => 1 [[2,1,1],[1,1],[1,1],[1]] => 1 [[2,1,1],[2,1],[1],[1]] => 1 [[2,1,1],[2,1],[2]] => 1 [[2,1,1],[2,1],[1,1]] => 1 [[2,1,1],[1,1,1],[1],[1]] => 1 [[2,1,1],[1,1,1],[1,1]] => 1 [[2,1,1],[2,1,1],[1]] => 1 [[1,1,1,1],[1],[1],[1],[1],[1]] => 0 [[1,1,1,1],[1,1],[1],[1],[1]] => 0 [[1,1,1,1],[1,1],[1,1],[1]] => 0 [[1,1,1,1],[1,1,1],[1],[1]] => 0 [[1,1,1,1],[1,1,1],[1,1]] => 0 [[1,1,1,1],[1,1,1,1],[1]] => 0 [[5],[1],[1],[1],[1]] => 4 [[5],[2],[1],[1]] => 4 [[5],[2],[2]] => 3 [[5],[3],[1]] => 4 [[5],[4]] => 1 [[4,1],[1],[1],[1],[1]] => 3 [[4,1],[2],[1],[1]] => 3 [[4,1],[2],[2]] => 3 [[4,1],[1,1],[1],[1]] => 3 [[4,1],[1,1],[1,1]] => 3 [[4,1],[3],[1]] => 3 [[4,1],[2,1],[1]] => 3 [[4,1],[4]] => 3 [[4,1],[3,1]] => 3 [[3,2],[1],[1],[1],[1]] => 2 [[3,2],[2],[1],[1]] => 2 [[3,2],[2],[2]] => 1 [[3,2],[1,1],[1],[1]] => 2 [[3,2],[1,1],[1,1]] => 2 [[3,2],[3],[1]] => 2 [[3,2],[2,1],[1]] => 2 [[3,2],[3,1]] => 2 [[3,2],[2,2]] => 1 [[3,1,1],[1],[1],[1],[1]] => 2 [[3,1,1],[2],[1],[1]] => 2 [[3,1,1],[2],[2]] => 2 [[3,1,1],[1,1],[1],[1]] => 2 [[3,1,1],[1,1],[1,1]] => 2 [[3,1,1],[3],[1]] => 2 [[3,1,1],[2,1],[1]] => 2 [[3,1,1],[1,1,1],[1]] => 2 [[3,1,1],[3,1]] => 2 [[3,1,1],[2,1,1]] => 2 [[2,2,1],[1],[1],[1],[1]] => 1 [[2,2,1],[2],[1],[1]] => 1 [[2,2,1],[2],[2]] => 1 [[2,2,1],[1,1],[1],[1]] => 1 [[2,2,1],[1,1],[1,1]] => 1 [[2,2,1],[2,1],[1]] => 1 [[2,2,1],[1,1,1],[1]] => 1 [[2,2,1],[2,2]] => 1 [[2,2,1],[2,1,1]] => 1 [[2,1,1,1],[1],[1],[1],[1]] => 1 [[2,1,1,1],[2],[1],[1]] => 1 [[2,1,1,1],[2],[2]] => 1 [[2,1,1,1],[1,1],[1],[1]] => 1 [[2,1,1,1],[1,1],[1,1]] => 1 [[2,1,1,1],[2,1],[1]] => 1 [[2,1,1,1],[1,1,1],[1]] => 1 [[2,1,1,1],[2,1,1]] => 1 [[2,1,1,1],[1,1,1,1]] => 1 [[1,1,1,1,1],[1],[1],[1],[1]] => 0 [[1,1,1,1,1],[1,1],[1],[1]] => 0 [[1,1,1,1,1],[1,1],[1,1]] => 0 [[1,1,1,1,1],[1,1,1],[1]] => 0 [[1,1,1,1,1],[1,1,1,1]] => 0 [[6],[1],[1],[1]] => 5 [[6],[2],[1]] => 5 [[6],[3]] => 3 [[5,1],[1],[1],[1]] => 4 [[5,1],[2],[1]] => 4 [[5,1],[1,1],[1]] => 4 [[5,1],[3]] => 4 [[5,1],[2,1]] => 4 [[4,2],[1],[1],[1]] => 3 [[4,2],[2],[1]] => 3 [[4,2],[1,1],[1]] => 3 [[4,2],[3]] => 2 [[4,2],[2,1]] => 3 [[4,1,1],[1],[1],[1]] => 3 [[4,1,1],[2],[1]] => 3 [[4,1,1],[1,1],[1]] => 3 [[4,1,1],[3]] => 3 [[4,1,1],[2,1]] => 3 [[4,1,1],[1,1,1]] => 3 [[3,3],[1],[1],[1]] => 2 [[3,3],[2],[1]] => 2 [[3,3],[1,1],[1]] => 2 [[3,3],[3]] => 0 [[3,3],[2,1]] => 2 [[3,2,1],[1],[1],[1]] => 2 [[3,2,1],[2],[1]] => 2 [[3,2,1],[1,1],[1]] => 2 [[3,2,1],[3]] => 2 [[3,2,1],[2,1]] => 2 [[3,2,1],[1,1,1]] => 2 [[3,1,1,1],[1],[1],[1]] => 2 [[3,1,1,1],[2],[1]] => 2 [[3,1,1,1],[1,1],[1]] => 2 [[3,1,1,1],[3]] => 2 [[3,1,1,1],[2,1]] => 2 [[3,1,1,1],[1,1,1]] => 2 [[2,2,2],[1],[1],[1]] => 1 [[2,2,2],[2],[1]] => 1 [[2,2,2],[1,1],[1]] => 1 [[2,2,2],[2,1]] => 1 [[2,2,2],[1,1,1]] => 1 [[2,2,1,1],[1],[1],[1]] => 1 [[2,2,1,1],[2],[1]] => 1 [[2,2,1,1],[1,1],[1]] => 1 [[2,2,1,1],[2,1]] => 1 [[2,2,1,1],[1,1,1]] => 1 [[2,1,1,1,1],[1],[1],[1]] => 1 [[2,1,1,1,1],[2],[1]] => 1 [[2,1,1,1,1],[1,1],[1]] => 1 [[2,1,1,1,1],[2,1]] => 1 [[2,1,1,1,1],[1,1,1]] => 1 [[1,1,1,1,1,1],[1],[1],[1]] => 0 [[1,1,1,1,1,1],[1,1],[1]] => 0 [[1,1,1,1,1,1],[1,1,1]] => 0 [[7],[1],[1]] => 6 [[7],[2]] => 5 [[6,1],[1],[1]] => 5 [[6,1],[2]] => 5 [[6,1],[1,1]] => 5 [[5,2],[1],[1]] => 4 [[5,2],[2]] => 3 [[5,2],[1,1]] => 4 [[5,1,1],[1],[1]] => 4 [[5,1,1],[2]] => 4 [[5,1,1],[1,1]] => 4 [[4,3],[1],[1]] => 3 [[4,3],[2]] => 2 [[4,3],[1,1]] => 3 [[4,2,1],[1],[1]] => 3 [[4,2,1],[2]] => 3 [[4,2,1],[1,1]] => 3 [[4,1,1,1],[1],[1]] => 3 [[4,1,1,1],[2]] => 3 [[4,1,1,1],[1,1]] => 3 [[3,3,1],[1],[1]] => 2 [[3,3,1],[2]] => 2 [[3,3,1],[1,1]] => 2 [[3,2,2],[1],[1]] => 2 [[3,2,2],[2]] => 1 [[3,2,2],[1,1]] => 2 [[3,2,1,1],[1],[1]] => 2 [[3,2,1,1],[2]] => 2 [[3,2,1,1],[1,1]] => 2 [[3,1,1,1,1],[1],[1]] => 2 [[3,1,1,1,1],[2]] => 2 [[3,1,1,1,1],[1,1]] => 2 [[2,2,2,1],[1],[1]] => 1 [[2,2,2,1],[2]] => 1 [[2,2,2,1],[1,1]] => 1 [[2,2,1,1,1],[1],[1]] => 1 [[2,2,1,1,1],[2]] => 1 [[2,2,1,1,1],[1,1]] => 1 [[2,1,1,1,1,1],[1],[1]] => 1 [[2,1,1,1,1,1],[2]] => 1 [[2,1,1,1,1,1],[1,1]] => 1 [[1,1,1,1,1,1,1],[1],[1]] => 0 [[1,1,1,1,1,1,1],[1,1]] => 0 [[8],[1]] => 7 [[7,1],[1]] => 6 [[6,2],[1]] => 5 [[6,1,1],[1]] => 5 [[5,3],[1]] => 4 [[5,2,1],[1]] => 4 [[5,1,1,1],[1]] => 4 [[4,4],[1]] => 3 [[4,3,1],[1]] => 3 [[4,2,2],[1]] => 3 [[4,2,1,1],[1]] => 3 [[4,1,1,1,1],[1]] => 3 [[3,3,2],[1]] => 2 [[3,3,1,1],[1]] => 2 [[3,2,2,1],[1]] => 2 [[3,2,1,1,1],[1]] => 2 [[3,1,1,1,1,1],[1]] => 2 [[2,2,2,2],[1]] => 1 [[2,2,2,1,1],[1]] => 1 [[2,2,1,1,1,1],[1]] => 1 [[2,1,1,1,1,1,1],[1]] => 1 [[1,1,1,1,1,1,1,1],[1]] => 0 [[9]] => 0 [[8,1]] => 7 [[7,2]] => 5 [[7,1,1]] => 6 [[6,3]] => 3 [[6,2,1]] => 5 [[6,1,1,1]] => 5 [[5,4]] => 1 [[5,3,1]] => 4 [[5,2,2]] => 3 [[5,2,1,1]] => 4 [[5,1,1,1,1]] => 4 [[4,4,1]] => 3 [[4,3,2]] => 2 [[4,3,1,1]] => 3 [[4,2,2,1]] => 3 [[4,2,1,1,1]] => 3 [[4,1,1,1,1,1]] => 3 [[3,3,3]] => 0 [[3,3,2,1]] => 2 [[3,3,1,1,1]] => 2 [[3,2,2,2]] => 1 [[3,2,2,1,1]] => 2 [[3,2,1,1,1,1]] => 2 [[3,1,1,1,1,1,1]] => 2 [[2,2,2,2,1]] => 1 [[2,2,2,1,1,1]] => 1 [[2,2,1,1,1,1,1]] => 1 [[2,1,1,1,1,1,1,1]] => 1 [[1,1,1,1,1,1,1,1,1]] => 0 [[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => 0 [[2],[1],[1],[1],[1],[1],[1],[1],[1]] => 1 [[2],[2],[1],[1],[1],[1],[1],[1]] => 1 [[2],[2],[2],[1],[1],[1],[1]] => 1 [[2],[2],[2],[2],[1],[1]] => 1 [[2],[2],[2],[2],[2]] => 0 [[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1,1],[1],[1],[1],[1]] => 0 [[1,1],[1,1],[1,1],[1,1],[1],[1]] => 0 [[1,1],[1,1],[1,1],[1,1],[1,1]] => 0 [[3],[1],[1],[1],[1],[1],[1],[1]] => 2 [[3],[2],[1],[1],[1],[1],[1]] => 2 [[3],[2],[2],[1],[1],[1]] => 2 [[3],[2],[2],[2],[1]] => 2 [[3],[3],[1],[1],[1],[1]] => 2 [[3],[3],[2],[1],[1]] => 2 [[3],[3],[2],[2]] => 1 [[3],[3],[3],[1]] => 2 [[2,1],[1],[1],[1],[1],[1],[1],[1]] => 1 [[2,1],[2],[1],[1],[1],[1],[1]] => 1 [[2,1],[2],[2],[1],[1],[1]] => 1 [[2,1],[2],[2],[2],[1]] => 1 [[2,1],[1,1],[1],[1],[1],[1],[1]] => 1 [[2,1],[1,1],[1,1],[1],[1],[1]] => 1 [[2,1],[1,1],[1,1],[1,1],[1]] => 1 [[2,1],[2,1],[1],[1],[1],[1]] => 1 [[2,1],[2,1],[2],[1],[1]] => 1 [[2,1],[2,1],[2],[2]] => 1 [[2,1],[2,1],[1,1],[1],[1]] => 1 [[2,1],[2,1],[1,1],[1,1]] => 1 [[2,1],[2,1],[2,1],[1]] => 1 [[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1],[1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1,1],[1],[1],[1]] => 0 [[1,1,1],[1,1],[1,1],[1,1],[1]] => 0 [[1,1,1],[1,1,1],[1],[1],[1],[1]] => 0 [[1,1,1],[1,1,1],[1,1],[1],[1]] => 0 [[1,1,1],[1,1,1],[1,1],[1,1]] => 0 [[1,1,1],[1,1,1],[1,1,1],[1]] => 0 [[4],[1],[1],[1],[1],[1],[1]] => 3 [[4],[2],[1],[1],[1],[1]] => 3 [[4],[2],[2],[1],[1]] => 3 [[4],[2],[2],[2]] => 2 [[4],[3],[1],[1],[1]] => 3 [[4],[3],[2],[1]] => 3 [[4],[3],[3]] => 1 [[4],[4],[1],[1]] => 3 [[4],[4],[2]] => 2 [[3,1],[1],[1],[1],[1],[1],[1]] => 2 [[3,1],[2],[1],[1],[1],[1]] => 2 [[3,1],[2],[2],[1],[1]] => 2 [[3,1],[2],[2],[2]] => 2 [[3,1],[1,1],[1],[1],[1],[1]] => 2 [[3,1],[1,1],[1,1],[1],[1]] => 2 [[3,1],[1,1],[1,1],[1,1]] => 2 [[3,1],[3],[1],[1],[1]] => 2 [[3,1],[3],[2],[1]] => 2 [[3,1],[3],[3]] => 2 [[3,1],[2,1],[1],[1],[1]] => 2 [[3,1],[2,1],[2],[1]] => 2 [[3,1],[2,1],[1,1],[1]] => 2 [[3,1],[2,1],[2,1]] => 2 [[3,1],[3,1],[1],[1]] => 2 [[3,1],[3,1],[2]] => 2 [[3,1],[3,1],[1,1]] => 2 [[2,2],[1],[1],[1],[1],[1],[1]] => 1 [[2,2],[2],[1],[1],[1],[1]] => 1 [[2,2],[2],[2],[1],[1]] => 1 [[2,2],[2],[2],[2]] => 0 [[2,2],[1,1],[1],[1],[1],[1]] => 1 [[2,2],[1,1],[1,1],[1],[1]] => 1 [[2,2],[1,1],[1,1],[1,1]] => 1 [[2,2],[2,1],[1],[1],[1]] => 1 [[2,2],[2,1],[2],[1]] => 1 [[2,2],[2,1],[1,1],[1]] => 1 [[2,2],[2,1],[2,1]] => 1 [[2,2],[2,2],[1],[1]] => 1 [[2,2],[2,2],[2]] => 0 [[2,2],[2,2],[1,1]] => 1 [[2,1,1],[1],[1],[1],[1],[1],[1]] => 1 [[2,1,1],[2],[1],[1],[1],[1]] => 1 [[2,1,1],[2],[2],[1],[1]] => 1 [[2,1,1],[2],[2],[2]] => 1 [[2,1,1],[1,1],[1],[1],[1],[1]] => 1 [[2,1,1],[1,1],[1,1],[1],[1]] => 1 [[2,1,1],[1,1],[1,1],[1,1]] => 1 [[2,1,1],[2,1],[1],[1],[1]] => 1 [[2,1,1],[2,1],[2],[1]] => 1 [[2,1,1],[2,1],[1,1],[1]] => 1 [[2,1,1],[2,1],[2,1]] => 1 [[2,1,1],[1,1,1],[1],[1],[1]] => 1 [[2,1,1],[1,1,1],[1,1],[1]] => 1 [[2,1,1],[1,1,1],[1,1,1]] => 1 [[2,1,1],[2,1,1],[1],[1]] => 1 [[2,1,1],[2,1,1],[2]] => 1 [[2,1,1],[2,1,1],[1,1]] => 1 [[1,1,1,1],[1],[1],[1],[1],[1],[1]] => 0 [[1,1,1,1],[1,1],[1],[1],[1],[1]] => 0 [[1,1,1,1],[1,1],[1,1],[1],[1]] => 0 [[1,1,1,1],[1,1],[1,1],[1,1]] => 0 [[1,1,1,1],[1,1,1],[1],[1],[1]] => 0 [[1,1,1,1],[1,1,1],[1,1],[1]] => 0 [[1,1,1,1],[1,1,1],[1,1,1]] => 0 [[1,1,1,1],[1,1,1,1],[1],[1]] => 0 [[1,1,1,1],[1,1,1,1],[1,1]] => 0 [[5],[1],[1],[1],[1],[1]] => 4 [[5],[2],[1],[1],[1]] => 4 [[5],[2],[2],[1]] => 4 [[5],[3],[1],[1]] => 4 [[5],[3],[2]] => 3 [[5],[4],[1]] => 4 [[5],[5]] => 0 [[4,1],[1],[1],[1],[1],[1]] => 3 [[4,1],[2],[1],[1],[1]] => 3 [[4,1],[2],[2],[1]] => 3 [[4,1],[1,1],[1],[1],[1]] => 3 [[4,1],[1,1],[1,1],[1]] => 3 [[4,1],[3],[1],[1]] => 3 [[4,1],[3],[2]] => 3 [[4,1],[2,1],[1],[1]] => 3 [[4,1],[2,1],[2]] => 3 [[4,1],[2,1],[1,1]] => 3 [[4,1],[4],[1]] => 3 [[4,1],[3,1],[1]] => 3 [[4,1],[4,1]] => 3 [[3,2],[1],[1],[1],[1],[1]] => 2 [[3,2],[2],[1],[1],[1]] => 2 [[3,2],[2],[2],[1]] => 2 [[3,2],[1,1],[1],[1],[1]] => 2 [[3,2],[1,1],[1,1],[1]] => 2 [[3,2],[3],[1],[1]] => 2 [[3,2],[3],[2]] => 1 [[3,2],[2,1],[1],[1]] => 2 [[3,2],[2,1],[2]] => 2 [[3,2],[2,1],[1,1]] => 2 [[3,2],[3,1],[1]] => 2 [[3,2],[2,2],[1]] => 2 [[3,2],[3,2]] => 1 [[3,1,1],[1],[1],[1],[1],[1]] => 2 [[3,1,1],[2],[1],[1],[1]] => 2 [[3,1,1],[2],[2],[1]] => 2 [[3,1,1],[1,1],[1],[1],[1]] => 2 [[3,1,1],[1,1],[1,1],[1]] => 2 [[3,1,1],[3],[1],[1]] => 2 [[3,1,1],[3],[2]] => 2 [[3,1,1],[2,1],[1],[1]] => 2 [[3,1,1],[2,1],[2]] => 2 [[3,1,1],[2,1],[1,1]] => 2 [[3,1,1],[1,1,1],[1],[1]] => 2 [[3,1,1],[1,1,1],[1,1]] => 2 [[3,1,1],[3,1],[1]] => 2 [[3,1,1],[2,1,1],[1]] => 2 [[3,1,1],[3,1,1]] => 2 [[2,2,1],[1],[1],[1],[1],[1]] => 1 [[2,2,1],[2],[1],[1],[1]] => 1 [[2,2,1],[2],[2],[1]] => 1 [[2,2,1],[1,1],[1],[1],[1]] => 1 [[2,2,1],[1,1],[1,1],[1]] => 1 [[2,2,1],[2,1],[1],[1]] => 1 [[2,2,1],[2,1],[2]] => 1 [[2,2,1],[2,1],[1,1]] => 1 [[2,2,1],[1,1,1],[1],[1]] => 1 [[2,2,1],[1,1,1],[1,1]] => 1 [[2,2,1],[2,2],[1]] => 1 [[2,2,1],[2,1,1],[1]] => 1 [[2,2,1],[2,2,1]] => 1 [[2,1,1,1],[1],[1],[1],[1],[1]] => 1 [[2,1,1,1],[2],[1],[1],[1]] => 1 [[2,1,1,1],[2],[2],[1]] => 1 [[2,1,1,1],[1,1],[1],[1],[1]] => 1 [[2,1,1,1],[1,1],[1,1],[1]] => 1 [[2,1,1,1],[2,1],[1],[1]] => 1 [[2,1,1,1],[2,1],[2]] => 1 [[2,1,1,1],[2,1],[1,1]] => 1 [[2,1,1,1],[1,1,1],[1],[1]] => 1 [[2,1,1,1],[1,1,1],[1,1]] => 1 [[2,1,1,1],[2,1,1],[1]] => 1 [[2,1,1,1],[1,1,1,1],[1]] => 1 [[2,1,1,1],[2,1,1,1]] => 1 [[1,1,1,1,1],[1],[1],[1],[1],[1]] => 0 [[1,1,1,1,1],[1,1],[1],[1],[1]] => 0 [[1,1,1,1,1],[1,1],[1,1],[1]] => 0 [[1,1,1,1,1],[1,1,1],[1],[1]] => 0 [[1,1,1,1,1],[1,1,1],[1,1]] => 0 [[1,1,1,1,1],[1,1,1,1],[1]] => 0 [[1,1,1,1,1],[1,1,1,1,1]] => 0 [[6],[1],[1],[1],[1]] => 5 [[6],[2],[1],[1]] => 5 [[6],[2],[2]] => 4 [[6],[3],[1]] => 5 [[6],[4]] => 2 [[5,1],[1],[1],[1],[1]] => 4 [[5,1],[2],[1],[1]] => 4 [[5,1],[2],[2]] => 4 [[5,1],[1,1],[1],[1]] => 4 [[5,1],[1,1],[1,1]] => 4 [[5,1],[3],[1]] => 4 [[5,1],[2,1],[1]] => 4 [[5,1],[4]] => 4 [[5,1],[3,1]] => 4 [[4,2],[1],[1],[1],[1]] => 3 [[4,2],[2],[1],[1]] => 3 [[4,2],[2],[2]] => 2 [[4,2],[1,1],[1],[1]] => 3 [[4,2],[1,1],[1,1]] => 3 [[4,2],[3],[1]] => 3 [[4,2],[2,1],[1]] => 3 [[4,2],[4]] => 2 [[4,2],[3,1]] => 3 [[4,2],[2,2]] => 2 [[4,1,1],[1],[1],[1],[1]] => 3 [[4,1,1],[2],[1],[1]] => 3 [[4,1,1],[2],[2]] => 3 [[4,1,1],[1,1],[1],[1]] => 3 [[4,1,1],[1,1],[1,1]] => 3 [[4,1,1],[3],[1]] => 3 [[4,1,1],[2,1],[1]] => 3 [[4,1,1],[1,1,1],[1]] => 3 [[4,1,1],[4]] => 3 [[4,1,1],[3,1]] => 3 [[4,1,1],[2,1,1]] => 3 [[3,3],[1],[1],[1],[1]] => 2 [[3,3],[2],[1],[1]] => 2 [[3,3],[2],[2]] => 1 [[3,3],[1,1],[1],[1]] => 2 [[3,3],[1,1],[1,1]] => 2 [[3,3],[3],[1]] => 2 [[3,3],[2,1],[1]] => 2 [[3,3],[3,1]] => 2 [[3,3],[2,2]] => 1 [[3,2,1],[1],[1],[1],[1]] => 2 [[3,2,1],[2],[1],[1]] => 2 [[3,2,1],[2],[2]] => 2 [[3,2,1],[1,1],[1],[1]] => 2 [[3,2,1],[1,1],[1,1]] => 2 [[3,2,1],[3],[1]] => 2 [[3,2,1],[2,1],[1]] => 2 [[3,2,1],[1,1,1],[1]] => 2 [[3,2,1],[3,1]] => 2 [[3,2,1],[2,2]] => 2 [[3,2,1],[2,1,1]] => 2 [[3,1,1,1],[1],[1],[1],[1]] => 2 [[3,1,1,1],[2],[1],[1]] => 2 [[3,1,1,1],[2],[2]] => 2 [[3,1,1,1],[1,1],[1],[1]] => 2 [[3,1,1,1],[1,1],[1,1]] => 2 [[3,1,1,1],[3],[1]] => 2 [[3,1,1,1],[2,1],[1]] => 2 [[3,1,1,1],[1,1,1],[1]] => 2 [[3,1,1,1],[3,1]] => 2 [[3,1,1,1],[2,1,1]] => 2 [[3,1,1,1],[1,1,1,1]] => 2 [[2,2,2],[1],[1],[1],[1]] => 1 [[2,2,2],[2],[1],[1]] => 1 [[2,2,2],[2],[2]] => 0 [[2,2,2],[1,1],[1],[1]] => 1 [[2,2,2],[1,1],[1,1]] => 1 [[2,2,2],[2,1],[1]] => 1 [[2,2,2],[1,1,1],[1]] => 1 [[2,2,2],[2,2]] => 0 [[2,2,2],[2,1,1]] => 1 [[2,2,1,1],[1],[1],[1],[1]] => 1 [[2,2,1,1],[2],[1],[1]] => 1 [[2,2,1,1],[2],[2]] => 1 [[2,2,1,1],[1,1],[1],[1]] => 1 [[2,2,1,1],[1,1],[1,1]] => 1 [[2,2,1,1],[2,1],[1]] => 1 [[2,2,1,1],[1,1,1],[1]] => 1 [[2,2,1,1],[2,2]] => 1 [[2,2,1,1],[2,1,1]] => 1 [[2,2,1,1],[1,1,1,1]] => 1 [[2,1,1,1,1],[1],[1],[1],[1]] => 1 [[2,1,1,1,1],[2],[1],[1]] => 1 [[2,1,1,1,1],[2],[2]] => 1 [[2,1,1,1,1],[1,1],[1],[1]] => 1 [[2,1,1,1,1],[1,1],[1,1]] => 1 [[2,1,1,1,1],[2,1],[1]] => 1 [[2,1,1,1,1],[1,1,1],[1]] => 1 [[2,1,1,1,1],[2,1,1]] => 1 [[2,1,1,1,1],[1,1,1,1]] => 1 [[1,1,1,1,1,1],[1],[1],[1],[1]] => 0 [[1,1,1,1,1,1],[1,1],[1],[1]] => 0 [[1,1,1,1,1,1],[1,1],[1,1]] => 0 [[1,1,1,1,1,1],[1,1,1],[1]] => 0 [[1,1,1,1,1,1],[1,1,1,1]] => 0 [[7],[1],[1],[1]] => 6 [[7],[2],[1]] => 6 [[7],[3]] => 4 [[6,1],[1],[1],[1]] => 5 [[6,1],[2],[1]] => 5 [[6,1],[1,1],[1]] => 5 [[6,1],[3]] => 5 [[6,1],[2,1]] => 5 [[5,2],[1],[1],[1]] => 4 [[5,2],[2],[1]] => 4 [[5,2],[1,1],[1]] => 4 [[5,2],[3]] => 3 [[5,2],[2,1]] => 4 [[5,1,1],[1],[1],[1]] => 4 [[5,1,1],[2],[1]] => 4 [[5,1,1],[1,1],[1]] => 4 [[5,1,1],[3]] => 4 [[5,1,1],[2,1]] => 4 [[5,1,1],[1,1,1]] => 4 [[4,3],[1],[1],[1]] => 3 [[4,3],[2],[1]] => 3 [[4,3],[1,1],[1]] => 3 [[4,3],[3]] => 1 [[4,3],[2,1]] => 3 [[4,2,1],[1],[1],[1]] => 3 [[4,2,1],[2],[1]] => 3 [[4,2,1],[1,1],[1]] => 3 [[4,2,1],[3]] => 3 [[4,2,1],[2,1]] => 3 [[4,2,1],[1,1,1]] => 3 [[4,1,1,1],[1],[1],[1]] => 3 [[4,1,1,1],[2],[1]] => 3 [[4,1,1,1],[1,1],[1]] => 3 [[4,1,1,1],[3]] => 3 [[4,1,1,1],[2,1]] => 3 [[4,1,1,1],[1,1,1]] => 3 [[3,3,1],[1],[1],[1]] => 2 [[3,3,1],[2],[1]] => 2 [[3,3,1],[1,1],[1]] => 2 [[3,3,1],[3]] => 2 [[3,3,1],[2,1]] => 2 [[3,3,1],[1,1,1]] => 2 [[3,2,2],[1],[1],[1]] => 2 [[3,2,2],[2],[1]] => 2 [[3,2,2],[1,1],[1]] => 2 [[3,2,2],[3]] => 1 [[3,2,2],[2,1]] => 2 [[3,2,2],[1,1,1]] => 2 [[3,2,1,1],[1],[1],[1]] => 2 [[3,2,1,1],[2],[1]] => 2 [[3,2,1,1],[1,1],[1]] => 2 [[3,2,1,1],[3]] => 2 [[3,2,1,1],[2,1]] => 2 [[3,2,1,1],[1,1,1]] => 2 [[3,1,1,1,1],[1],[1],[1]] => 2 [[3,1,1,1,1],[2],[1]] => 2 [[3,1,1,1,1],[1,1],[1]] => 2 [[3,1,1,1,1],[3]] => 2 [[3,1,1,1,1],[2,1]] => 2 [[3,1,1,1,1],[1,1,1]] => 2 [[2,2,2,1],[1],[1],[1]] => 1 [[2,2,2,1],[2],[1]] => 1 [[2,2,2,1],[1,1],[1]] => 1 [[2,2,2,1],[2,1]] => 1 [[2,2,2,1],[1,1,1]] => 1 [[2,2,1,1,1],[1],[1],[1]] => 1 [[2,2,1,1,1],[2],[1]] => 1 [[2,2,1,1,1],[1,1],[1]] => 1 [[2,2,1,1,1],[2,1]] => 1 [[2,2,1,1,1],[1,1,1]] => 1 [[2,1,1,1,1,1],[1],[1],[1]] => 1 [[2,1,1,1,1,1],[2],[1]] => 1 [[2,1,1,1,1,1],[1,1],[1]] => 1 [[2,1,1,1,1,1],[2,1]] => 1 [[2,1,1,1,1,1],[1,1,1]] => 1 [[1,1,1,1,1,1,1],[1],[1],[1]] => 0 [[1,1,1,1,1,1,1],[1,1],[1]] => 0 [[1,1,1,1,1,1,1],[1,1,1]] => 0 [[8],[1],[1]] => 7 [[8],[2]] => 6 [[7,1],[1],[1]] => 6 [[7,1],[2]] => 6 [[7,1],[1,1]] => 6 [[6,2],[1],[1]] => 5 [[6,2],[2]] => 4 [[6,2],[1,1]] => 5 [[6,1,1],[1],[1]] => 5 [[6,1,1],[2]] => 5 [[6,1,1],[1,1]] => 5 [[5,3],[1],[1]] => 4 [[5,3],[2]] => 3 [[5,3],[1,1]] => 4 [[5,2,1],[1],[1]] => 4 [[5,2,1],[2]] => 4 [[5,2,1],[1,1]] => 4 [[5,1,1,1],[1],[1]] => 4 [[5,1,1,1],[2]] => 4 [[5,1,1,1],[1,1]] => 4 [[4,4],[1],[1]] => 3 [[4,4],[2]] => 2 [[4,4],[1,1]] => 3 [[4,3,1],[1],[1]] => 3 [[4,3,1],[2]] => 3 [[4,3,1],[1,1]] => 3 [[4,2,2],[1],[1]] => 3 [[4,2,2],[2]] => 2 [[4,2,2],[1,1]] => 3 [[4,2,1,1],[1],[1]] => 3 [[4,2,1,1],[2]] => 3 [[4,2,1,1],[1,1]] => 3 [[4,1,1,1,1],[1],[1]] => 3 [[4,1,1,1,1],[2]] => 3 [[4,1,1,1,1],[1,1]] => 3 [[3,3,2],[1],[1]] => 2 [[3,3,2],[2]] => 1 [[3,3,2],[1,1]] => 2 [[3,3,1,1],[1],[1]] => 2 [[3,3,1,1],[2]] => 2 [[3,3,1,1],[1,1]] => 2 [[3,2,2,1],[1],[1]] => 2 [[3,2,2,1],[2]] => 2 [[3,2,2,1],[1,1]] => 2 [[3,2,1,1,1],[1],[1]] => 2 [[3,2,1,1,1],[2]] => 2 [[3,2,1,1,1],[1,1]] => 2 [[3,1,1,1,1,1],[1],[1]] => 2 [[3,1,1,1,1,1],[2]] => 2 [[3,1,1,1,1,1],[1,1]] => 2 [[2,2,2,2],[1],[1]] => 1 [[2,2,2,2],[2]] => 0 [[2,2,2,2],[1,1]] => 1 [[2,2,2,1,1],[1],[1]] => 1 [[2,2,2,1,1],[2]] => 1 [[2,2,2,1,1],[1,1]] => 1 [[2,2,1,1,1,1],[1],[1]] => 1 [[2,2,1,1,1,1],[2]] => 1 [[2,2,1,1,1,1],[1,1]] => 1 [[2,1,1,1,1,1,1],[1],[1]] => 1 [[2,1,1,1,1,1,1],[2]] => 1 [[2,1,1,1,1,1,1],[1,1]] => 1 [[1,1,1,1,1,1,1,1],[1],[1]] => 0 [[1,1,1,1,1,1,1,1],[1,1]] => 0 [[9],[1]] => 8 [[8,1],[1]] => 7 [[7,2],[1]] => 6 [[7,1,1],[1]] => 6 [[6,3],[1]] => 5 [[6,2,1],[1]] => 5 [[6,1,1,1],[1]] => 5 [[5,4],[1]] => 4 [[5,3,1],[1]] => 4 [[5,2,2],[1]] => 4 [[5,2,1,1],[1]] => 4 [[5,1,1,1,1],[1]] => 4 [[4,4,1],[1]] => 3 [[4,3,2],[1]] => 3 [[4,3,1,1],[1]] => 3 [[4,2,2,1],[1]] => 3 [[4,2,1,1,1],[1]] => 3 [[4,1,1,1,1,1],[1]] => 3 [[3,3,3],[1]] => 2 [[3,3,2,1],[1]] => 2 [[3,3,1,1,1],[1]] => 2 [[3,2,2,2],[1]] => 2 [[3,2,2,1,1],[1]] => 2 [[3,2,1,1,1,1],[1]] => 2 [[3,1,1,1,1,1,1],[1]] => 2 [[2,2,2,2,1],[1]] => 1 [[2,2,2,1,1,1],[1]] => 1 [[2,2,1,1,1,1,1],[1]] => 1 [[2,1,1,1,1,1,1,1],[1]] => 1 [[1,1,1,1,1,1,1,1,1],[1]] => 0 [[10]] => 0 [[9,1]] => 8 [[8,2]] => 6 [[8,1,1]] => 7 [[7,3]] => 4 [[7,2,1]] => 6 [[7,1,1,1]] => 6 [[6,4]] => 2 [[6,3,1]] => 5 [[6,2,2]] => 4 [[6,2,1,1]] => 5 [[6,1,1,1,1]] => 5 [[5,5]] => 0 [[5,4,1]] => 4 [[5,3,2]] => 3 [[5,3,1,1]] => 4 [[5,2,2,1]] => 4 [[5,2,1,1,1]] => 4 [[5,1,1,1,1,1]] => 4 [[4,4,2]] => 2 [[4,4,1,1]] => 3 [[4,3,3]] => 1 [[4,3,2,1]] => 3 [[4,3,1,1,1]] => 3 [[4,2,2,2]] => 2 [[4,2,2,1,1]] => 3 [[4,2,1,1,1,1]] => 3 [[4,1,1,1,1,1,1]] => 3 [[3,3,3,1]] => 2 [[3,3,2,2]] => 1 [[3,3,2,1,1]] => 2 [[3,3,1,1,1,1]] => 2 [[3,2,2,2,1]] => 2 [[3,2,2,1,1,1]] => 2 [[3,2,1,1,1,1,1]] => 2 [[3,1,1,1,1,1,1,1]] => 2 [[2,2,2,2,2]] => 0 [[2,2,2,2,1,1]] => 1 [[2,2,2,1,1,1,1]] => 1 [[2,2,1,1,1,1,1,1]] => 1 [[2,1,1,1,1,1,1,1,1]] => 1 [[1,1,1,1,1,1,1,1,1,1]] => 0 ----------------------------------------------------------------------------- Created: Jul 26, 2019 at 17:56 by Joseph Bernstein ----------------------------------------------------------------------------- Last Updated: Jul 27, 2019 at 16:30 by Christian Stump