***************************************************************************** * 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: St001486 ----------------------------------------------------------------------------- Collection: Integer compositions ----------------------------------------------------------------------------- Description: The number of corners of the ribbon associated with an integer composition. We associate a ribbon shape to a composition \$c=(c_1,\dots,c_n)\$ with \$c_i\$ cells in the \$i\$-th row from bottom to top, such that the cells in two rows overlap in precisely one cell. This statistic records the total number of corners of the ribbon shape. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(c): if c.size() == 1: return 1 p = c.to_skew_partition() return len(p.inner_corners()) + len(p.outer_corners()) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,1] => 2 [2] => 2 [1,1,1] => 2 [1,2] => 3 [2,1] => 3 [3] => 2 [1,1,1,1] => 2 [1,1,2] => 3 [1,2,1] => 4 [1,3] => 3 [2,1,1] => 3 [2,2] => 4 [3,1] => 3 [4] => 2 [1,1,1,1,1] => 2 [1,1,1,2] => 3 [1,1,2,1] => 4 [1,1,3] => 3 [1,2,1,1] => 4 [1,2,2] => 5 [1,3,1] => 4 [1,4] => 3 [2,1,1,1] => 3 [2,1,2] => 4 [2,2,1] => 5 [2,3] => 4 [3,1,1] => 3 [3,2] => 4 [4,1] => 3 [5] => 2 [1,1,1,1,1,1] => 2 [1,1,1,1,2] => 3 [1,1,1,2,1] => 4 [1,1,1,3] => 3 [1,1,2,1,1] => 4 [1,1,2,2] => 5 [1,1,3,1] => 4 [1,1,4] => 3 [1,2,1,1,1] => 4 [1,2,1,2] => 5 [1,2,2,1] => 6 [1,2,3] => 5 [1,3,1,1] => 4 [1,3,2] => 5 [1,4,1] => 4 [1,5] => 3 [2,1,1,1,1] => 3 [2,1,1,2] => 4 [2,1,2,1] => 5 [2,1,3] => 4 [2,2,1,1] => 5 [2,2,2] => 6 [2,3,1] => 5 [2,4] => 4 [3,1,1,1] => 3 [3,1,2] => 4 [3,2,1] => 5 [3,3] => 4 [4,1,1] => 3 [4,2] => 4 [5,1] => 3 [6] => 2 [1,1,1,1,1,1,1] => 2 [1,1,1,1,1,2] => 3 [1,1,1,1,2,1] => 4 [1,1,1,1,3] => 3 [1,1,1,2,1,1] => 4 [1,1,1,2,2] => 5 [1,1,1,3,1] => 4 [1,1,1,4] => 3 [1,1,2,1,1,1] => 4 [1,1,2,1,2] => 5 [1,1,2,2,1] => 6 [1,1,2,3] => 5 [1,1,3,1,1] => 4 [1,1,3,2] => 5 [1,1,4,1] => 4 [1,1,5] => 3 [1,2,1,1,1,1] => 4 [1,2,1,1,2] => 5 [1,2,1,2,1] => 6 [1,2,1,3] => 5 [1,2,2,1,1] => 6 [1,2,2,2] => 7 [1,2,3,1] => 6 [1,2,4] => 5 [1,3,1,1,1] => 4 [1,3,1,2] => 5 [1,3,2,1] => 6 [1,3,3] => 5 [1,4,1,1] => 4 [1,4,2] => 5 [1,5,1] => 4 [1,6] => 3 [2,1,1,1,1,1] => 3 [2,1,1,1,2] => 4 [2,1,1,2,1] => 5 [2,1,1,3] => 4 [2,1,2,1,1] => 5 [2,1,2,2] => 6 [2,1,3,1] => 5 [2,1,4] => 4 [2,2,1,1,1] => 5 [2,2,1,2] => 6 [2,2,2,1] => 7 [2,2,3] => 6 [2,3,1,1] => 5 [2,3,2] => 6 [2,4,1] => 5 [2,5] => 4 [3,1,1,1,1] => 3 [3,1,1,2] => 4 [3,1,2,1] => 5 [3,1,3] => 4 [3,2,1,1] => 5 [3,2,2] => 6 [3,3,1] => 5 [3,4] => 4 [4,1,1,1] => 3 [4,1,2] => 4 [4,2,1] => 5 [4,3] => 4 [5,1,1] => 3 [5,2] => 4 [6,1] => 3 [7] => 2 [1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,2] => 3 [1,1,1,1,1,2,1] => 4 [1,1,1,1,1,3] => 3 [1,1,1,1,2,1,1] => 4 [1,1,1,1,2,2] => 5 [1,1,1,1,3,1] => 4 [1,1,1,1,4] => 3 [1,1,1,2,1,1,1] => 4 [1,1,1,2,1,2] => 5 [1,1,1,2,2,1] => 6 [1,1,1,2,3] => 5 [1,1,1,3,1,1] => 4 [1,1,1,3,2] => 5 [1,1,1,4,1] => 4 [1,1,1,5] => 3 [1,1,2,1,1,1,1] => 4 [1,1,2,1,1,2] => 5 [1,1,2,1,2,1] => 6 [1,1,2,1,3] => 5 [1,1,2,2,1,1] => 6 [1,1,2,2,2] => 7 [1,1,2,3,1] => 6 [1,1,2,4] => 5 [1,1,3,1,1,1] => 4 [1,1,3,1,2] => 5 [1,1,3,2,1] => 6 [1,1,3,3] => 5 [1,1,4,1,1] => 4 [1,1,4,2] => 5 [1,1,5,1] => 4 [1,1,6] => 3 [1,2,1,1,1,1,1] => 4 [1,2,1,1,1,2] => 5 [1,2,1,1,2,1] => 6 [1,2,1,1,3] => 5 [1,2,1,2,1,1] => 6 [1,2,1,2,2] => 7 [1,2,1,3,1] => 6 [1,2,1,4] => 5 [1,2,2,1,1,1] => 6 [1,2,2,1,2] => 7 [1,2,2,2,1] => 8 [1,2,2,3] => 7 [1,2,3,1,1] => 6 [1,2,3,2] => 7 [1,2,4,1] => 6 [1,2,5] => 5 [1,3,1,1,1,1] => 4 [1,3,1,1,2] => 5 [1,3,1,2,1] => 6 [1,3,1,3] => 5 [1,3,2,1,1] => 6 [1,3,2,2] => 7 [1,3,3,1] => 6 [1,3,4] => 5 [1,4,1,1,1] => 4 [1,4,1,2] => 5 [1,4,2,1] => 6 [1,4,3] => 5 [1,5,1,1] => 4 [1,5,2] => 5 [1,6,1] => 4 [1,7] => 3 [2,1,1,1,1,1,1] => 3 [2,1,1,1,1,2] => 4 [2,1,1,1,2,1] => 5 [2,1,1,1,3] => 4 [2,1,1,2,1,1] => 5 [2,1,1,2,2] => 6 [2,1,1,3,1] => 5 [2,1,1,4] => 4 [2,1,2,1,1,1] => 5 [2,1,2,1,2] => 6 [2,1,2,2,1] => 7 [2,1,2,3] => 6 [2,1,3,1,1] => 5 [2,1,3,2] => 6 [2,1,4,1] => 5 [2,1,5] => 4 [2,2,1,1,1,1] => 5 [2,2,1,1,2] => 6 [2,2,1,2,1] => 7 [2,2,1,3] => 6 [2,2,2,1,1] => 7 [2,2,2,2] => 8 [2,2,3,1] => 7 [2,2,4] => 6 [2,3,1,1,1] => 5 [2,3,1,2] => 6 [2,3,2,1] => 7 [2,3,3] => 6 [2,4,1,1] => 5 [2,4,2] => 6 [2,5,1] => 5 [2,6] => 4 [3,1,1,1,1,1] => 3 [3,1,1,1,2] => 4 [3,1,1,2,1] => 5 [3,1,1,3] => 4 [3,1,2,1,1] => 5 [3,1,2,2] => 6 [3,1,3,1] => 5 [3,1,4] => 4 [3,2,1,1,1] => 5 [3,2,1,2] => 6 [3,2,2,1] => 7 [3,2,3] => 6 [3,3,1,1] => 5 [3,3,2] => 6 [3,4,1] => 5 [3,5] => 4 [4,1,1,1,1] => 3 [4,1,1,2] => 4 [4,1,2,1] => 5 [4,1,3] => 4 [4,2,1,1] => 5 [4,2,2] => 6 [4,3,1] => 5 [4,4] => 4 [5,1,1,1] => 3 [5,1,2] => 4 [5,2,1] => 5 [5,3] => 4 [6,1,1] => 3 [6,2] => 4 [7,1] => 3 [8] => 2 [1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,2] => 3 [1,1,1,1,1,1,2,1] => 4 [1,1,1,1,1,1,3] => 3 [1,1,1,1,1,2,1,1] => 4 [1,1,1,1,1,2,2] => 5 [1,1,1,1,1,3,1] => 4 [1,1,1,1,1,4] => 3 [1,1,1,1,2,1,1,1] => 4 [1,1,1,1,2,1,2] => 5 [1,1,1,1,2,2,1] => 6 [1,1,1,1,2,3] => 5 [1,1,1,1,3,1,1] => 4 [1,1,1,1,3,2] => 5 [1,1,1,1,4,1] => 4 [1,1,1,1,5] => 3 [1,1,1,2,1,1,1,1] => 4 [1,1,1,2,1,1,2] => 5 [1,1,1,2,1,2,1] => 6 [1,1,1,2,1,3] => 5 [1,1,1,2,2,1,1] => 6 [1,1,1,2,2,2] => 7 [1,1,1,2,3,1] => 6 [1,1,1,2,4] => 5 [1,1,1,3,1,1,1] => 4 [1,1,1,3,1,2] => 5 [1,1,1,3,2,1] => 6 [1,1,1,3,3] => 5 [1,1,1,4,1,1] => 4 [1,1,1,4,2] => 5 [1,1,1,5,1] => 4 [1,1,1,6] => 3 [1,1,2,1,1,1,1,1] => 4 [1,1,2,1,1,1,2] => 5 [1,1,2,1,1,2,1] => 6 [1,1,2,1,1,3] => 5 [1,1,2,1,2,1,1] => 6 [1,1,2,1,2,2] => 7 [1,1,2,1,3,1] => 6 [1,1,2,1,4] => 5 [1,1,2,2,1,1,1] => 6 [1,1,2,2,1,2] => 7 [1,1,2,2,2,1] => 8 [1,1,2,2,3] => 7 [1,1,2,3,1,1] => 6 [1,1,2,3,2] => 7 [1,1,2,4,1] => 6 [1,1,2,5] => 5 [1,1,3,1,1,1,1] => 4 [1,1,3,1,1,2] => 5 [1,1,3,1,2,1] => 6 [1,1,3,1,3] => 5 [1,1,3,2,1,1] => 6 [1,1,3,2,2] => 7 [1,1,3,3,1] => 6 [1,1,3,4] => 5 [1,1,4,1,1,1] => 4 [1,1,4,1,2] => 5 [1,1,4,2,1] => 6 [1,1,4,3] => 5 [1,1,5,1,1] => 4 [1,1,5,2] => 5 [1,1,6,1] => 4 [1,1,7] => 3 [1,2,1,1,1,1,1,1] => 4 [1,2,1,1,1,1,2] => 5 [1,2,1,1,1,2,1] => 6 [1,2,1,1,1,3] => 5 [1,2,1,1,2,1,1] => 6 [1,2,1,1,2,2] => 7 [1,2,1,1,3,1] => 6 [1,2,1,1,4] => 5 [1,2,1,2,1,1,1] => 6 [1,2,1,2,1,2] => 7 [1,2,1,2,2,1] => 8 [1,2,1,2,3] => 7 [1,2,1,3,1,1] => 6 [1,2,1,3,2] => 7 [1,2,1,4,1] => 6 [1,2,1,5] => 5 [1,2,2,1,1,1,1] => 6 [1,2,2,1,1,2] => 7 [1,2,2,1,2,1] => 8 [1,2,2,1,3] => 7 [1,2,2,2,1,1] => 8 [1,2,2,2,2] => 9 [1,2,2,3,1] => 8 [1,2,2,4] => 7 [1,2,3,1,1,1] => 6 [1,2,3,1,2] => 7 [1,2,3,2,1] => 8 [1,2,3,3] => 7 [1,2,4,1,1] => 6 [1,2,4,2] => 7 [1,2,5,1] => 6 [1,2,6] => 5 [1,3,1,1,1,1,1] => 4 [1,3,1,1,1,2] => 5 [1,3,1,1,2,1] => 6 [1,3,1,1,3] => 5 [1,3,1,2,1,1] => 6 [1,3,1,2,2] => 7 [1,3,1,3,1] => 6 [1,3,1,4] => 5 [1,3,2,1,1,1] => 6 [1,3,2,1,2] => 7 [1,3,2,2,1] => 8 [1,3,2,3] => 7 [1,3,3,1,1] => 6 [1,3,3,2] => 7 [1,3,4,1] => 6 [1,3,5] => 5 [1,4,1,1,1,1] => 4 [1,4,1,1,2] => 5 [1,4,1,2,1] => 6 [1,4,1,3] => 5 [1,4,2,1,1] => 6 [1,4,2,2] => 7 [1,4,3,1] => 6 [1,4,4] => 5 [1,5,1,1,1] => 4 [1,5,1,2] => 5 [1,5,2,1] => 6 [1,5,3] => 5 [1,6,1,1] => 4 [1,6,2] => 5 [1,7,1] => 4 [1,8] => 3 [2,1,1,1,1,1,1,1] => 3 [2,1,1,1,1,1,2] => 4 [2,1,1,1,1,2,1] => 5 [2,1,1,1,1,3] => 4 [2,1,1,1,2,1,1] => 5 [2,1,1,1,2,2] => 6 [2,1,1,1,3,1] => 5 [2,1,1,1,4] => 4 [2,1,1,2,1,1,1] => 5 [2,1,1,2,1,2] => 6 [2,1,1,2,2,1] => 7 [2,1,1,2,3] => 6 [2,1,1,3,1,1] => 5 [2,1,1,3,2] => 6 [2,1,1,4,1] => 5 [2,1,1,5] => 4 [2,1,2,1,1,1,1] => 5 [2,1,2,1,1,2] => 6 [2,1,2,1,2,1] => 7 [2,1,2,1,3] => 6 [2,1,2,2,1,1] => 7 [2,1,2,2,2] => 8 [2,1,2,3,1] => 7 [2,1,2,4] => 6 [2,1,3,1,1,1] => 5 [2,1,3,1,2] => 6 [2,1,3,2,1] => 7 [2,1,3,3] => 6 [2,1,4,1,1] => 5 [2,1,4,2] => 6 [2,1,5,1] => 5 [2,1,6] => 4 [2,2,1,1,1,1,1] => 5 [2,2,1,1,1,2] => 6 [2,2,1,1,2,1] => 7 [2,2,1,1,3] => 6 [2,2,1,2,1,1] => 7 [2,2,1,2,2] => 8 [2,2,1,3,1] => 7 [2,2,1,4] => 6 [2,2,2,1,1,1] => 7 [2,2,2,1,2] => 8 [2,2,2,2,1] => 9 [2,2,2,3] => 8 [2,2,3,1,1] => 7 [2,2,3,2] => 8 [2,2,4,1] => 7 [2,2,5] => 6 [2,3,1,1,1,1] => 5 [2,3,1,1,2] => 6 [2,3,1,2,1] => 7 [2,3,1,3] => 6 [2,3,2,1,1] => 7 [2,3,2,2] => 8 [2,3,3,1] => 7 [2,3,4] => 6 [2,4,1,1,1] => 5 [2,4,1,2] => 6 [2,4,2,1] => 7 [2,4,3] => 6 [2,5,1,1] => 5 [2,5,2] => 6 [2,6,1] => 5 [2,7] => 4 [3,1,1,1,1,1,1] => 3 [3,1,1,1,1,2] => 4 [3,1,1,1,2,1] => 5 [3,1,1,1,3] => 4 [3,1,1,2,1,1] => 5 [3,1,1,2,2] => 6 [3,1,1,3,1] => 5 [3,1,1,4] => 4 [3,1,2,1,1,1] => 5 [3,1,2,1,2] => 6 [3,1,2,2,1] => 7 [3,1,2,3] => 6 [3,1,3,1,1] => 5 [3,1,3,2] => 6 [3,1,4,1] => 5 [3,1,5] => 4 [3,2,1,1,1,1] => 5 [3,2,1,1,2] => 6 [3,2,1,2,1] => 7 [3,2,1,3] => 6 [3,2,2,1,1] => 7 [3,2,2,2] => 8 [3,2,3,1] => 7 [3,2,4] => 6 [3,3,1,1,1] => 5 [3,3,1,2] => 6 [3,3,2,1] => 7 [3,3,3] => 6 [3,4,1,1] => 5 [3,4,2] => 6 [3,5,1] => 5 [3,6] => 4 [4,1,1,1,1,1] => 3 [4,1,1,1,2] => 4 [4,1,1,2,1] => 5 [4,1,1,3] => 4 [4,1,2,1,1] => 5 [4,1,2,2] => 6 [4,1,3,1] => 5 [4,1,4] => 4 [4,2,1,1,1] => 5 [4,2,1,2] => 6 [4,2,2,1] => 7 [4,2,3] => 6 [4,3,1,1] => 5 [4,3,2] => 6 [4,4,1] => 5 [4,5] => 4 [5,1,1,1,1] => 3 [5,1,1,2] => 4 [5,1,2,1] => 5 [5,1,3] => 4 [5,2,1,1] => 5 [5,2,2] => 6 [5,3,1] => 5 [5,4] => 4 [6,1,1,1] => 3 [6,1,2] => 4 [6,2,1] => 5 [6,3] => 4 [7,1,1] => 3 [7,2] => 4 [8,1] => 3 [9] => 2 [1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,2] => 3 [1,1,1,1,1,1,1,2,1] => 4 [1,1,1,1,1,1,1,3] => 3 [1,1,1,1,1,1,2,1,1] => 4 [1,1,1,1,1,1,2,2] => 5 [1,1,1,1,1,1,3,1] => 4 [1,1,1,1,1,1,4] => 3 [1,1,1,1,1,2,1,1,1] => 4 [1,1,1,1,1,2,1,2] => 5 [1,1,1,1,1,2,2,1] => 6 [1,1,1,1,1,2,3] => 5 [1,1,1,1,1,3,1,1] => 4 [1,1,1,1,1,3,2] => 5 [1,1,1,1,1,4,1] => 4 [1,1,1,1,1,5] => 3 [1,1,1,1,2,1,1,1,1] => 4 [1,1,1,1,2,1,1,2] => 5 [1,1,1,1,2,1,2,1] => 6 [1,1,1,1,2,1,3] => 5 [1,1,1,1,2,2,1,1] => 6 [1,1,1,1,2,2,2] => 7 [1,1,1,1,2,3,1] => 6 [1,1,1,1,2,4] => 5 [1,1,1,1,3,1,1,1] => 4 [1,1,1,1,3,1,2] => 5 [1,1,1,1,3,2,1] => 6 [1,1,1,1,3,3] => 5 [1,1,1,1,4,1,1] => 4 [1,1,1,1,4,2] => 5 [1,1,1,1,5,1] => 4 [1,1,1,1,6] => 3 [1,1,1,2,1,1,1,1,1] => 4 [1,1,1,2,1,1,1,2] => 5 [1,1,1,2,1,1,2,1] => 6 [1,1,1,2,1,1,3] => 5 [1,1,1,2,1,2,1,1] => 6 [1,1,1,2,1,2,2] => 7 [1,1,1,2,1,3,1] => 6 [1,1,1,2,1,4] => 5 [1,1,1,2,2,1,1,1] => 6 [1,1,1,2,2,1,2] => 7 [1,1,1,2,2,2,1] => 8 [1,1,1,2,2,3] => 7 [1,1,1,2,3,1,1] => 6 [1,1,1,2,3,2] => 7 [1,1,1,2,4,1] => 6 [1,1,1,2,5] => 5 [1,1,1,3,1,1,1,1] => 4 [1,1,1,3,1,1,2] => 5 [1,1,1,3,1,2,1] => 6 [1,1,1,3,1,3] => 5 [1,1,1,3,2,1,1] => 6 [1,1,1,3,2,2] => 7 [1,1,1,3,3,1] => 6 [1,1,1,3,4] => 5 [1,1,1,4,1,1,1] => 4 [1,1,1,4,1,2] => 5 [1,1,1,4,2,1] => 6 [1,1,1,4,3] => 5 [1,1,1,5,1,1] => 4 [1,1,1,5,2] => 5 [1,1,1,6,1] => 4 [1,1,1,7] => 3 [1,1,2,1,1,1,1,1,1] => 4 [1,1,2,1,1,1,1,2] => 5 [1,1,2,1,1,1,2,1] => 6 [1,1,2,1,1,1,3] => 5 [1,1,2,1,1,2,1,1] => 6 [1,1,2,1,1,2,2] => 7 [1,1,2,1,1,3,1] => 6 [1,1,2,1,1,4] => 5 [1,1,2,1,2,1,1,1] => 6 [1,1,2,1,2,1,2] => 7 [1,1,2,1,2,2,1] => 8 [1,1,2,1,2,3] => 7 [1,1,2,1,3,1,1] => 6 [1,1,2,1,3,2] => 7 [1,1,2,1,4,1] => 6 [1,1,2,1,5] => 5 [1,1,2,2,1,1,1,1] => 6 [1,1,2,2,1,1,2] => 7 [1,1,2,2,1,2,1] => 8 [1,1,2,2,1,3] => 7 [1,1,2,2,2,1,1] => 8 [1,1,2,2,2,2] => 9 [1,1,2,2,3,1] => 8 [1,1,2,2,4] => 7 [1,1,2,3,1,1,1] => 6 [1,1,2,3,1,2] => 7 [1,1,2,3,2,1] => 8 [1,1,2,3,3] => 7 [1,1,2,4,1,1] => 6 [1,1,2,4,2] => 7 [1,1,2,5,1] => 6 [1,1,2,6] => 5 [1,1,3,1,1,1,1,1] => 4 [1,1,3,1,1,1,2] => 5 [1,1,3,1,1,2,1] => 6 [1,1,3,1,1,3] => 5 [1,1,3,1,2,1,1] => 6 [1,1,3,1,2,2] => 7 [1,1,3,1,3,1] => 6 [1,1,3,1,4] => 5 [1,1,3,2,1,1,1] => 6 [1,1,3,2,1,2] => 7 [1,1,3,2,2,1] => 8 [1,1,3,2,3] => 7 [1,1,3,3,1,1] => 6 [1,1,3,3,2] => 7 [1,1,3,4,1] => 6 [1,1,3,5] => 5 [1,1,4,1,1,1,1] => 4 [1,1,4,1,1,2] => 5 [1,1,4,1,2,1] => 6 [1,1,4,1,3] => 5 [1,1,4,2,1,1] => 6 [1,1,4,2,2] => 7 [1,1,4,3,1] => 6 [1,1,4,4] => 5 [1,1,5,1,1,1] => 4 [1,1,5,1,2] => 5 [1,1,5,2,1] => 6 [1,1,5,3] => 5 [1,1,6,1,1] => 4 [1,1,6,2] => 5 [1,1,7,1] => 4 [1,1,8] => 3 [1,2,1,1,1,1,1,1,1] => 4 [1,2,1,1,1,1,1,2] => 5 [1,2,1,1,1,1,2,1] => 6 [1,2,1,1,1,1,3] => 5 [1,2,1,1,1,2,1,1] => 6 [1,2,1,1,1,2,2] => 7 [1,2,1,1,1,3,1] => 6 [1,2,1,1,1,4] => 5 [1,2,1,1,2,1,1,1] => 6 [1,2,1,1,2,1,2] => 7 [1,2,1,1,2,2,1] => 8 [1,2,1,1,2,3] => 7 [1,2,1,1,3,1,1] => 6 [1,2,1,1,3,2] => 7 [1,2,1,1,4,1] => 6 [1,2,1,1,5] => 5 [1,2,1,2,1,1,1,1] => 6 [1,2,1,2,1,1,2] => 7 [1,2,1,2,1,2,1] => 8 [1,2,1,2,1,3] => 7 [1,2,1,2,2,1,1] => 8 [1,2,1,2,2,2] => 9 [1,2,1,2,3,1] => 8 [1,2,1,2,4] => 7 [1,2,1,3,1,1,1] => 6 [1,2,1,3,1,2] => 7 [1,2,1,3,2,1] => 8 [1,2,1,3,3] => 7 [1,2,1,4,1,1] => 6 [1,2,1,4,2] => 7 [1,2,1,5,1] => 6 [1,2,1,6] => 5 [1,2,2,1,1,1,1,1] => 6 [1,2,2,1,1,1,2] => 7 [1,2,2,1,1,2,1] => 8 [1,2,2,1,1,3] => 7 [1,2,2,1,2,1,1] => 8 [1,2,2,1,2,2] => 9 [1,2,2,1,3,1] => 8 [1,2,2,1,4] => 7 [1,2,2,2,1,1,1] => 8 [1,2,2,2,1,2] => 9 [1,2,2,2,2,1] => 10 [1,2,2,2,3] => 9 [1,2,2,3,1,1] => 8 [1,2,2,3,2] => 9 [1,2,2,4,1] => 8 [1,2,2,5] => 7 [1,2,3,1,1,1,1] => 6 [1,2,3,1,1,2] => 7 [1,2,3,1,2,1] => 8 [1,2,3,1,3] => 7 [1,2,3,2,1,1] => 8 [1,2,3,2,2] => 9 [1,2,3,3,1] => 8 [1,2,3,4] => 7 [1,2,4,1,1,1] => 6 [1,2,4,1,2] => 7 [1,2,4,2,1] => 8 [1,2,4,3] => 7 [1,2,5,1,1] => 6 [1,2,5,2] => 7 [1,2,6,1] => 6 [1,2,7] => 5 [1,3,1,1,1,1,1,1] => 4 [1,3,1,1,1,1,2] => 5 [1,3,1,1,1,2,1] => 6 [1,3,1,1,1,3] => 5 [1,3,1,1,2,1,1] => 6 [1,3,1,1,2,2] => 7 [1,3,1,1,3,1] => 6 [1,3,1,1,4] => 5 [1,3,1,2,1,1,1] => 6 [1,3,1,2,1,2] => 7 [1,3,1,2,2,1] => 8 [1,3,1,2,3] => 7 [1,3,1,3,1,1] => 6 [1,3,1,3,2] => 7 [1,3,1,4,1] => 6 [1,3,1,5] => 5 [1,3,2,1,1,1,1] => 6 [1,3,2,1,1,2] => 7 [1,3,2,1,2,1] => 8 [1,3,2,1,3] => 7 [1,3,2,2,1,1] => 8 [1,3,2,2,2] => 9 [1,3,2,3,1] => 8 [1,3,2,4] => 7 [1,3,3,1,1,1] => 6 [1,3,3,1,2] => 7 [1,3,3,2,1] => 8 [1,3,3,3] => 7 [1,3,4,1,1] => 6 [1,3,4,2] => 7 [1,3,5,1] => 6 [1,3,6] => 5 [1,4,1,1,1,1,1] => 4 [1,4,1,1,1,2] => 5 [1,4,1,1,2,1] => 6 [1,4,1,1,3] => 5 [1,4,1,2,1,1] => 6 [1,4,1,2,2] => 7 [1,4,1,3,1] => 6 [1,4,1,4] => 5 [1,4,2,1,1,1] => 6 [1,4,2,1,2] => 7 [1,4,2,2,1] => 8 [1,4,2,3] => 7 [1,4,3,1,1] => 6 [1,4,3,2] => 7 [1,4,4,1] => 6 [1,4,5] => 5 [1,5,1,1,1,1] => 4 [1,5,1,1,2] => 5 [1,5,1,2,1] => 6 [1,5,1,3] => 5 [1,5,2,1,1] => 6 [1,5,2,2] => 7 [1,5,3,1] => 6 [1,5,4] => 5 [1,6,1,1,1] => 4 [1,6,1,2] => 5 [1,6,2,1] => 6 [1,6,3] => 5 [1,7,1,1] => 4 [1,7,2] => 5 [1,8,1] => 4 [1,9] => 3 [2,1,1,1,1,1,1,1,1] => 3 [2,1,1,1,1,1,1,2] => 4 [2,1,1,1,1,1,2,1] => 5 [2,1,1,1,1,1,3] => 4 [2,1,1,1,1,2,1,1] => 5 [2,1,1,1,1,2,2] => 6 [2,1,1,1,1,3,1] => 5 [2,1,1,1,1,4] => 4 [2,1,1,1,2,1,1,1] => 5 [2,1,1,1,2,1,2] => 6 [2,1,1,1,2,2,1] => 7 [2,1,1,1,2,3] => 6 [2,1,1,1,3,1,1] => 5 [2,1,1,1,3,2] => 6 [2,1,1,1,4,1] => 5 [2,1,1,1,5] => 4 [2,1,1,2,1,1,1,1] => 5 [2,1,1,2,1,1,2] => 6 [2,1,1,2,1,2,1] => 7 [2,1,1,2,1,3] => 6 [2,1,1,2,2,1,1] => 7 [2,1,1,2,2,2] => 8 [2,1,1,2,3,1] => 7 [2,1,1,2,4] => 6 [2,1,1,3,1,1,1] => 5 [2,1,1,3,1,2] => 6 [2,1,1,3,2,1] => 7 [2,1,1,3,3] => 6 [2,1,1,4,1,1] => 5 [2,1,1,4,2] => 6 [2,1,1,5,1] => 5 [2,1,1,6] => 4 [2,1,2,1,1,1,1,1] => 5 [2,1,2,1,1,1,2] => 6 [2,1,2,1,1,2,1] => 7 [2,1,2,1,1,3] => 6 [2,1,2,1,2,1,1] => 7 [2,1,2,1,2,2] => 8 [2,1,2,1,3,1] => 7 [2,1,2,1,4] => 6 [2,1,2,2,1,1,1] => 7 [2,1,2,2,1,2] => 8 [2,1,2,2,2,1] => 9 [2,1,2,2,3] => 8 [2,1,2,3,1,1] => 7 [2,1,2,3,2] => 8 [2,1,2,4,1] => 7 [2,1,2,5] => 6 [2,1,3,1,1,1,1] => 5 [2,1,3,1,1,2] => 6 [2,1,3,1,2,1] => 7 [2,1,3,1,3] => 6 [2,1,3,2,1,1] => 7 [2,1,3,2,2] => 8 [2,1,3,3,1] => 7 [2,1,3,4] => 6 [2,1,4,1,1,1] => 5 [2,1,4,1,2] => 6 [2,1,4,2,1] => 7 [2,1,4,3] => 6 [2,1,5,1,1] => 5 [2,1,5,2] => 6 [2,1,6,1] => 5 [2,1,7] => 4 [2,2,1,1,1,1,1,1] => 5 [2,2,1,1,1,1,2] => 6 [2,2,1,1,1,2,1] => 7 [2,2,1,1,1,3] => 6 [2,2,1,1,2,1,1] => 7 [2,2,1,1,2,2] => 8 [2,2,1,1,3,1] => 7 [2,2,1,1,4] => 6 [2,2,1,2,1,1,1] => 7 [2,2,1,2,1,2] => 8 [2,2,1,2,2,1] => 9 [2,2,1,2,3] => 8 [2,2,1,3,1,1] => 7 [2,2,1,3,2] => 8 [2,2,1,4,1] => 7 [2,2,1,5] => 6 [2,2,2,1,1,1,1] => 7 [2,2,2,1,1,2] => 8 [2,2,2,1,2,1] => 9 [2,2,2,1,3] => 8 [2,2,2,2,1,1] => 9 [2,2,2,2,2] => 10 [2,2,2,3,1] => 9 [2,2,2,4] => 8 [2,2,3,1,1,1] => 7 [2,2,3,1,2] => 8 [2,2,3,2,1] => 9 [2,2,3,3] => 8 [2,2,4,1,1] => 7 [2,2,4,2] => 8 [2,2,5,1] => 7 [2,2,6] => 6 [2,3,1,1,1,1,1] => 5 [2,3,1,1,1,2] => 6 [2,3,1,1,2,1] => 7 [2,3,1,1,3] => 6 [2,3,1,2,1,1] => 7 [2,3,1,2,2] => 8 [2,3,1,3,1] => 7 [2,3,1,4] => 6 [2,3,2,1,1,1] => 7 [2,3,2,1,2] => 8 [2,3,2,2,1] => 9 [2,3,2,3] => 8 [2,3,3,1,1] => 7 [2,3,3,2] => 8 [2,3,4,1] => 7 [2,3,5] => 6 [2,4,1,1,1,1] => 5 [2,4,1,1,2] => 6 [2,4,1,2,1] => 7 [2,4,1,3] => 6 [2,4,2,1,1] => 7 [2,4,2,2] => 8 [2,4,3,1] => 7 [2,4,4] => 6 [2,5,1,1,1] => 5 [2,5,1,2] => 6 [2,5,2,1] => 7 [2,5,3] => 6 [2,6,1,1] => 5 [2,6,2] => 6 [2,7,1] => 5 [2,8] => 4 [3,1,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,2] => 4 [3,1,1,1,1,2,1] => 5 [3,1,1,1,1,3] => 4 [3,1,1,1,2,1,1] => 5 [3,1,1,1,2,2] => 6 [3,1,1,1,3,1] => 5 [3,1,1,1,4] => 4 [3,1,1,2,1,1,1] => 5 [3,1,1,2,1,2] => 6 [3,1,1,2,2,1] => 7 [3,1,1,2,3] => 6 [3,1,1,3,1,1] => 5 [3,1,1,3,2] => 6 [3,1,1,4,1] => 5 [3,1,1,5] => 4 [3,1,2,1,1,1,1] => 5 [3,1,2,1,1,2] => 6 [3,1,2,1,2,1] => 7 [3,1,2,1,3] => 6 [3,1,2,2,1,1] => 7 [3,1,2,2,2] => 8 [3,1,2,3,1] => 7 [3,1,2,4] => 6 [3,1,3,1,1,1] => 5 [3,1,3,1,2] => 6 [3,1,3,2,1] => 7 [3,1,3,3] => 6 [3,1,4,1,1] => 5 [3,1,4,2] => 6 [3,1,5,1] => 5 [3,1,6] => 4 [3,2,1,1,1,1,1] => 5 [3,2,1,1,1,2] => 6 [3,2,1,1,2,1] => 7 [3,2,1,1,3] => 6 [3,2,1,2,1,1] => 7 [3,2,1,2,2] => 8 [3,2,1,3,1] => 7 [3,2,1,4] => 6 [3,2,2,1,1,1] => 7 [3,2,2,1,2] => 8 [3,2,2,2,1] => 9 [3,2,2,3] => 8 [3,2,3,1,1] => 7 [3,2,3,2] => 8 [3,2,4,1] => 7 [3,2,5] => 6 [3,3,1,1,1,1] => 5 [3,3,1,1,2] => 6 [3,3,1,2,1] => 7 [3,3,1,3] => 6 [3,3,2,1,1] => 7 [3,3,2,2] => 8 [3,3,3,1] => 7 [3,3,4] => 6 [3,4,1,1,1] => 5 [3,4,1,2] => 6 [3,4,2,1] => 7 [3,4,3] => 6 [3,5,1,1] => 5 [3,5,2] => 6 [3,6,1] => 5 [3,7] => 4 [4,1,1,1,1,1,1] => 3 [4,1,1,1,1,2] => 4 [4,1,1,1,2,1] => 5 [4,1,1,1,3] => 4 [4,1,1,2,1,1] => 5 [4,1,1,2,2] => 6 [4,1,1,3,1] => 5 [4,1,1,4] => 4 [4,1,2,1,1,1] => 5 [4,1,2,1,2] => 6 [4,1,2,2,1] => 7 [4,1,2,3] => 6 [4,1,3,1,1] => 5 [4,1,3,2] => 6 [4,1,4,1] => 5 [4,1,5] => 4 [4,2,1,1,1,1] => 5 [4,2,1,1,2] => 6 [4,2,1,2,1] => 7 [4,2,1,3] => 6 [4,2,2,1,1] => 7 [4,2,2,2] => 8 [4,2,3,1] => 7 [4,2,4] => 6 [4,3,1,1,1] => 5 [4,3,1,2] => 6 [4,3,2,1] => 7 [4,3,3] => 6 [4,4,1,1] => 5 [4,4,2] => 6 [4,5,1] => 5 [4,6] => 4 [5,1,1,1,1,1] => 3 [5,1,1,1,2] => 4 [5,1,1,2,1] => 5 [5,1,1,3] => 4 [5,1,2,1,1] => 5 [5,1,2,2] => 6 [5,1,3,1] => 5 [5,1,4] => 4 [5,2,1,1,1] => 5 [5,2,1,2] => 6 [5,2,2,1] => 7 [5,2,3] => 6 [5,3,1,1] => 5 [5,3,2] => 6 [5,4,1] => 5 [5,5] => 4 [6,1,1,1,1] => 3 [6,1,1,2] => 4 [6,1,2,1] => 5 [6,1,3] => 4 [6,2,1,1] => 5 [6,2,2] => 6 [6,3,1] => 5 [6,4] => 4 [7,1,1,1] => 3 [7,1,2] => 4 [7,2,1] => 5 [7,3] => 4 [8,1,1] => 3 [8,2] => 4 [9,1] => 3 [10] => 2 ----------------------------------------------------------------------------- Created: Oct 28, 2019 at 18:32 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Oct 28, 2019 at 18:32 by Martin Rubey