***************************************************************************** * 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: St001462 ----------------------------------------------------------------------------- Collection: Standard tableaux ----------------------------------------------------------------------------- Description: The number of factors of a standard tableaux under concatenation. The concatenation of two standard Young tableaux $T_1$ and $T_2$ is obtained by adding the largest entry of $T_1$ to each entry of $T_2$, and then appending the rows of the result to $T_1$, see [1, dfn 2.10]. This statistic returns the maximal number of standard tableaux such that their concatenation is the given tableau. ----------------------------------------------------------------------------- References: [1] Jagenteufel, J. A Sundaram type bijection for $\mathrm {SO}(2k+1)$: vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau [[arXiv:1902.03843]] ----------------------------------------------------------------------------- Code: def factor(T): """ Return smallest i such that the entries i+1,...,n form a SYT. """ n = T.size() for i in range(1, n): rows = [tuple([e-i for e in row if e > i]) for row in T] while not rows[-1]: rows = rows[:-1] try: StandardTableau(rows) return (T.restrict(i), StandardTableau(rows)) except ValueError: pass return (T, StandardTableau([])) @cached_function def statistic(T): A, B = factor(T) if B.size() > 0: return 1 + statistic(B) return 1 ----------------------------------------------------------------------------- Statistic values: [[1]] => 1 [[1,2]] => 2 [[1],[2]] => 1 [[1,2,3]] => 3 [[1,3],[2]] => 2 [[1,2],[3]] => 2 [[1],[2],[3]] => 1 [[1,2,3,4]] => 4 [[1,3,4],[2]] => 3 [[1,2,4],[3]] => 3 [[1,2,3],[4]] => 3 [[1,3],[2,4]] => 2 [[1,2],[3,4]] => 1 [[1,4],[2],[3]] => 2 [[1,3],[2],[4]] => 1 [[1,2],[3],[4]] => 2 [[1],[2],[3],[4]] => 1 [[1,2,3,4,5]] => 5 [[1,3,4,5],[2]] => 4 [[1,2,4,5],[3]] => 4 [[1,2,3,5],[4]] => 4 [[1,2,3,4],[5]] => 4 [[1,3,5],[2,4]] => 3 [[1,2,5],[3,4]] => 2 [[1,3,4],[2,5]] => 3 [[1,2,4],[3,5]] => 3 [[1,2,3],[4,5]] => 2 [[1,4,5],[2],[3]] => 3 [[1,3,5],[2],[4]] => 2 [[1,2,5],[3],[4]] => 3 [[1,3,4],[2],[5]] => 1 [[1,2,4],[3],[5]] => 2 [[1,2,3],[4],[5]] => 3 [[1,4],[2,5],[3]] => 2 [[1,3],[2,5],[4]] => 1 [[1,2],[3,5],[4]] => 1 [[1,3],[2,4],[5]] => 2 [[1,2],[3,4],[5]] => 1 [[1,5],[2],[3],[4]] => 2 [[1,4],[2],[3],[5]] => 1 [[1,3],[2],[4],[5]] => 1 [[1,2],[3],[4],[5]] => 2 [[1],[2],[3],[4],[5]] => 1 [[1,2,3,4,5,6]] => 6 [[1,3,4,5,6],[2]] => 5 [[1,2,4,5,6],[3]] => 5 [[1,2,3,5,6],[4]] => 5 [[1,2,3,4,6],[5]] => 5 [[1,2,3,4,5],[6]] => 5 [[1,3,5,6],[2,4]] => 4 [[1,2,5,6],[3,4]] => 3 [[1,3,4,6],[2,5]] => 4 [[1,2,4,6],[3,5]] => 4 [[1,2,3,6],[4,5]] => 3 [[1,3,4,5],[2,6]] => 4 [[1,2,4,5],[3,6]] => 4 [[1,2,3,5],[4,6]] => 4 [[1,2,3,4],[5,6]] => 3 [[1,4,5,6],[2],[3]] => 4 [[1,3,5,6],[2],[4]] => 3 [[1,2,5,6],[3],[4]] => 4 [[1,3,4,6],[2],[5]] => 2 [[1,2,4,6],[3],[5]] => 3 [[1,2,3,6],[4],[5]] => 4 [[1,3,4,5],[2],[6]] => 1 [[1,2,4,5],[3],[6]] => 2 [[1,2,3,5],[4],[6]] => 3 [[1,2,3,4],[5],[6]] => 4 [[1,3,5],[2,4,6]] => 3 [[1,2,5],[3,4,6]] => 2 [[1,3,4],[2,5,6]] => 2 [[1,2,4],[3,5,6]] => 1 [[1,2,3],[4,5,6]] => 1 [[1,4,6],[2,5],[3]] => 3 [[1,3,6],[2,5],[4]] => 2 [[1,2,6],[3,5],[4]] => 2 [[1,3,6],[2,4],[5]] => 3 [[1,2,6],[3,4],[5]] => 2 [[1,4,5],[2,6],[3]] => 3 [[1,3,5],[2,6],[4]] => 2 [[1,2,5],[3,6],[4]] => 3 [[1,3,4],[2,6],[5]] => 1 [[1,2,4],[3,6],[5]] => 2 [[1,2,3],[4,6],[5]] => 2 [[1,3,5],[2,4],[6]] => 2 [[1,2,5],[3,4],[6]] => 1 [[1,3,4],[2,5],[6]] => 3 [[1,2,4],[3,5],[6]] => 3 [[1,2,3],[4,5],[6]] => 2 [[1,5,6],[2],[3],[4]] => 3 [[1,4,6],[2],[3],[5]] => 2 [[1,3,6],[2],[4],[5]] => 2 [[1,2,6],[3],[4],[5]] => 3 [[1,4,5],[2],[3],[6]] => 1 [[1,3,5],[2],[4],[6]] => 1 [[1,2,5],[3],[4],[6]] => 2 [[1,3,4],[2],[5],[6]] => 1 [[1,2,4],[3],[5],[6]] => 2 [[1,2,3],[4],[5],[6]] => 3 [[1,4],[2,5],[3,6]] => 2 [[1,3],[2,5],[4,6]] => 1 [[1,2],[3,5],[4,6]] => 1 [[1,3],[2,4],[5,6]] => 1 [[1,2],[3,4],[5,6]] => 1 [[1,5],[2,6],[3],[4]] => 2 [[1,4],[2,6],[3],[5]] => 1 [[1,3],[2,6],[4],[5]] => 1 [[1,2],[3,6],[4],[5]] => 1 [[1,4],[2,5],[3],[6]] => 1 [[1,3],[2,5],[4],[6]] => 1 [[1,2],[3,5],[4],[6]] => 1 [[1,3],[2,4],[5],[6]] => 2 [[1,2],[3,4],[5],[6]] => 1 [[1,6],[2],[3],[4],[5]] => 2 [[1,5],[2],[3],[4],[6]] => 1 [[1,4],[2],[3],[5],[6]] => 1 [[1,3],[2],[4],[5],[6]] => 1 [[1,2],[3],[4],[5],[6]] => 2 [[1],[2],[3],[4],[5],[6]] => 1 [[1,2,3,4,5,6,7]] => 7 [[1,3,4,5,6,7],[2]] => 6 [[1,2,4,5,6,7],[3]] => 6 [[1,2,3,5,6,7],[4]] => 6 [[1,2,3,4,6,7],[5]] => 6 [[1,2,3,4,5,7],[6]] => 6 [[1,2,3,4,5,6],[7]] => 6 [[1,3,5,6,7],[2,4]] => 5 [[1,2,5,6,7],[3,4]] => 4 [[1,3,4,6,7],[2,5]] => 5 [[1,2,4,6,7],[3,5]] => 5 [[1,2,3,6,7],[4,5]] => 4 [[1,3,4,5,7],[2,6]] => 5 [[1,2,4,5,7],[3,6]] => 5 [[1,2,3,5,7],[4,6]] => 5 [[1,2,3,4,7],[5,6]] => 4 [[1,3,4,5,6],[2,7]] => 5 [[1,2,4,5,6],[3,7]] => 5 [[1,2,3,5,6],[4,7]] => 5 [[1,2,3,4,6],[5,7]] => 5 [[1,2,3,4,5],[6,7]] => 4 [[1,4,5,6,7],[2],[3]] => 5 [[1,3,5,6,7],[2],[4]] => 4 [[1,2,5,6,7],[3],[4]] => 5 [[1,3,4,6,7],[2],[5]] => 3 [[1,2,4,6,7],[3],[5]] => 4 [[1,2,3,6,7],[4],[5]] => 5 [[1,3,4,5,7],[2],[6]] => 2 [[1,2,4,5,7],[3],[6]] => 3 [[1,2,3,5,7],[4],[6]] => 4 [[1,2,3,4,7],[5],[6]] => 5 [[1,3,4,5,6],[2],[7]] => 1 [[1,2,4,5,6],[3],[7]] => 2 [[1,2,3,5,6],[4],[7]] => 3 [[1,2,3,4,6],[5],[7]] => 4 [[1,2,3,4,5],[6],[7]] => 5 [[1,3,5,7],[2,4,6]] => 4 [[1,2,5,7],[3,4,6]] => 3 [[1,3,4,7],[2,5,6]] => 3 [[1,2,4,7],[3,5,6]] => 2 [[1,2,3,7],[4,5,6]] => 2 [[1,3,5,6],[2,4,7]] => 4 [[1,2,5,6],[3,4,7]] => 3 [[1,3,4,6],[2,5,7]] => 4 [[1,2,4,6],[3,5,7]] => 4 [[1,2,3,6],[4,5,7]] => 3 [[1,3,4,5],[2,6,7]] => 3 [[1,2,4,5],[3,6,7]] => 3 [[1,2,3,5],[4,6,7]] => 2 [[1,2,3,4],[5,6,7]] => 2 [[1,4,6,7],[2,5],[3]] => 4 [[1,3,6,7],[2,5],[4]] => 3 [[1,2,6,7],[3,5],[4]] => 3 [[1,3,6,7],[2,4],[5]] => 4 [[1,2,6,7],[3,4],[5]] => 3 [[1,4,5,7],[2,6],[3]] => 4 [[1,3,5,7],[2,6],[4]] => 3 [[1,2,5,7],[3,6],[4]] => 4 [[1,3,4,7],[2,6],[5]] => 2 [[1,2,4,7],[3,6],[5]] => 3 [[1,2,3,7],[4,6],[5]] => 3 [[1,3,5,7],[2,4],[6]] => 3 [[1,2,5,7],[3,4],[6]] => 2 [[1,3,4,7],[2,5],[6]] => 4 [[1,2,4,7],[3,5],[6]] => 4 [[1,2,3,7],[4,5],[6]] => 3 [[1,4,5,6],[2,7],[3]] => 4 [[1,3,5,6],[2,7],[4]] => 3 [[1,2,5,6],[3,7],[4]] => 4 [[1,3,4,6],[2,7],[5]] => 2 [[1,2,4,6],[3,7],[5]] => 3 [[1,2,3,6],[4,7],[5]] => 4 [[1,3,4,5],[2,7],[6]] => 1 [[1,2,4,5],[3,7],[6]] => 2 [[1,2,3,5],[4,7],[6]] => 3 [[1,2,3,4],[5,7],[6]] => 3 [[1,3,5,6],[2,4],[7]] => 2 [[1,2,5,6],[3,4],[7]] => 1 [[1,3,4,6],[2,5],[7]] => 3 [[1,2,4,6],[3,5],[7]] => 3 [[1,2,3,6],[4,5],[7]] => 2 [[1,3,4,5],[2,6],[7]] => 4 [[1,2,4,5],[3,6],[7]] => 4 [[1,2,3,5],[4,6],[7]] => 4 [[1,2,3,4],[5,6],[7]] => 3 [[1,5,6,7],[2],[3],[4]] => 4 [[1,4,6,7],[2],[3],[5]] => 3 [[1,3,6,7],[2],[4],[5]] => 3 [[1,2,6,7],[3],[4],[5]] => 4 [[1,4,5,7],[2],[3],[6]] => 2 [[1,3,5,7],[2],[4],[6]] => 2 [[1,2,5,7],[3],[4],[6]] => 3 [[1,3,4,7],[2],[5],[6]] => 2 [[1,2,4,7],[3],[5],[6]] => 3 [[1,2,3,7],[4],[5],[6]] => 4 [[1,4,5,6],[2],[3],[7]] => 1 [[1,3,5,6],[2],[4],[7]] => 1 [[1,2,5,6],[3],[4],[7]] => 2 [[1,3,4,6],[2],[5],[7]] => 1 [[1,2,4,6],[3],[5],[7]] => 2 [[1,2,3,6],[4],[5],[7]] => 3 [[1,3,4,5],[2],[6],[7]] => 1 [[1,2,4,5],[3],[6],[7]] => 2 [[1,2,3,5],[4],[6],[7]] => 3 [[1,2,3,4],[5],[6],[7]] => 4 [[1,4,6],[2,5,7],[3]] => 3 [[1,3,6],[2,5,7],[4]] => 2 [[1,2,6],[3,5,7],[4]] => 2 [[1,3,6],[2,4,7],[5]] => 3 [[1,2,6],[3,4,7],[5]] => 2 [[1,4,5],[2,6,7],[3]] => 2 [[1,3,5],[2,6,7],[4]] => 1 [[1,2,5],[3,6,7],[4]] => 1 [[1,3,4],[2,6,7],[5]] => 1 [[1,2,4],[3,6,7],[5]] => 1 [[1,2,3],[4,6,7],[5]] => 1 [[1,3,5],[2,4,7],[6]] => 2 [[1,2,5],[3,4,7],[6]] => 1 [[1,3,4],[2,5,7],[6]] => 2 [[1,2,4],[3,5,7],[6]] => 1 [[1,2,3],[4,5,7],[6]] => 1 [[1,3,5],[2,4,6],[7]] => 3 [[1,2,5],[3,4,6],[7]] => 2 [[1,3,4],[2,5,6],[7]] => 2 [[1,2,4],[3,5,6],[7]] => 1 [[1,2,3],[4,5,6],[7]] => 1 [[1,4,7],[2,5],[3,6]] => 3 [[1,3,7],[2,5],[4,6]] => 2 [[1,2,7],[3,5],[4,6]] => 2 [[1,3,7],[2,4],[5,6]] => 2 [[1,2,7],[3,4],[5,6]] => 2 [[1,4,6],[2,5],[3,7]] => 2 [[1,3,6],[2,5],[4,7]] => 1 [[1,2,6],[3,5],[4,7]] => 1 [[1,3,6],[2,4],[5,7]] => 1 [[1,2,6],[3,4],[5,7]] => 1 [[1,4,5],[2,6],[3,7]] => 3 [[1,3,5],[2,6],[4,7]] => 2 [[1,2,5],[3,6],[4,7]] => 3 [[1,3,4],[2,6],[5,7]] => 1 [[1,2,4],[3,6],[5,7]] => 2 [[1,2,3],[4,6],[5,7]] => 2 [[1,3,5],[2,4],[6,7]] => 1 [[1,2,5],[3,4],[6,7]] => 1 [[1,3,4],[2,5],[6,7]] => 1 [[1,2,4],[3,5],[6,7]] => 2 [[1,2,3],[4,5],[6,7]] => 2 [[1,5,7],[2,6],[3],[4]] => 3 [[1,4,7],[2,6],[3],[5]] => 2 [[1,3,7],[2,6],[4],[5]] => 2 [[1,2,7],[3,6],[4],[5]] => 2 [[1,4,7],[2,5],[3],[6]] => 2 [[1,3,7],[2,5],[4],[6]] => 2 [[1,2,7],[3,5],[4],[6]] => 2 [[1,3,7],[2,4],[5],[6]] => 3 [[1,2,7],[3,4],[5],[6]] => 2 [[1,5,6],[2,7],[3],[4]] => 3 [[1,4,6],[2,7],[3],[5]] => 2 [[1,3,6],[2,7],[4],[5]] => 2 [[1,2,6],[3,7],[4],[5]] => 3 [[1,4,5],[2,7],[3],[6]] => 1 [[1,3,5],[2,7],[4],[6]] => 1 [[1,2,5],[3,7],[4],[6]] => 2 [[1,3,4],[2,7],[5],[6]] => 1 [[1,2,4],[3,7],[5],[6]] => 2 [[1,2,3],[4,7],[5],[6]] => 2 [[1,4,6],[2,5],[3],[7]] => 1 [[1,3,6],[2,5],[4],[7]] => 1 [[1,2,6],[3,5],[4],[7]] => 1 [[1,3,6],[2,4],[5],[7]] => 2 [[1,2,6],[3,4],[5],[7]] => 1 [[1,4,5],[2,6],[3],[7]] => 1 [[1,3,5],[2,6],[4],[7]] => 1 [[1,2,5],[3,6],[4],[7]] => 2 [[1,3,4],[2,6],[5],[7]] => 1 [[1,2,4],[3,6],[5],[7]] => 2 [[1,2,3],[4,6],[5],[7]] => 2 [[1,3,5],[2,4],[6],[7]] => 2 [[1,2,5],[3,4],[6],[7]] => 1 [[1,3,4],[2,5],[6],[7]] => 3 [[1,2,4],[3,5],[6],[7]] => 3 [[1,2,3],[4,5],[6],[7]] => 2 [[1,6,7],[2],[3],[4],[5]] => 3 [[1,5,7],[2],[3],[4],[6]] => 2 [[1,4,7],[2],[3],[5],[6]] => 2 [[1,3,7],[2],[4],[5],[6]] => 2 [[1,2,7],[3],[4],[5],[6]] => 3 [[1,5,6],[2],[3],[4],[7]] => 1 [[1,4,6],[2],[3],[5],[7]] => 1 [[1,3,6],[2],[4],[5],[7]] => 1 [[1,2,6],[3],[4],[5],[7]] => 2 [[1,4,5],[2],[3],[6],[7]] => 1 [[1,3,5],[2],[4],[6],[7]] => 1 [[1,2,5],[3],[4],[6],[7]] => 2 [[1,3,4],[2],[5],[6],[7]] => 1 [[1,2,4],[3],[5],[6],[7]] => 2 [[1,2,3],[4],[5],[6],[7]] => 3 [[1,5],[2,6],[3,7],[4]] => 2 [[1,4],[2,6],[3,7],[5]] => 1 [[1,3],[2,6],[4,7],[5]] => 1 [[1,2],[3,6],[4,7],[5]] => 1 [[1,4],[2,5],[3,7],[6]] => 1 [[1,3],[2,5],[4,7],[6]] => 1 [[1,2],[3,5],[4,7],[6]] => 1 [[1,3],[2,4],[5,7],[6]] => 1 [[1,2],[3,4],[5,7],[6]] => 1 [[1,4],[2,5],[3,6],[7]] => 2 [[1,3],[2,5],[4,6],[7]] => 1 [[1,2],[3,5],[4,6],[7]] => 1 [[1,3],[2,4],[5,6],[7]] => 1 [[1,2],[3,4],[5,6],[7]] => 1 [[1,6],[2,7],[3],[4],[5]] => 2 [[1,5],[2,7],[3],[4],[6]] => 1 [[1,4],[2,7],[3],[5],[6]] => 1 [[1,3],[2,7],[4],[5],[6]] => 1 [[1,2],[3,7],[4],[5],[6]] => 1 [[1,5],[2,6],[3],[4],[7]] => 1 [[1,4],[2,6],[3],[5],[7]] => 1 [[1,3],[2,6],[4],[5],[7]] => 1 [[1,2],[3,6],[4],[5],[7]] => 1 [[1,4],[2,5],[3],[6],[7]] => 1 [[1,3],[2,5],[4],[6],[7]] => 1 [[1,2],[3,5],[4],[6],[7]] => 1 [[1,3],[2,4],[5],[6],[7]] => 2 [[1,2],[3,4],[5],[6],[7]] => 1 [[1,7],[2],[3],[4],[5],[6]] => 2 [[1,6],[2],[3],[4],[5],[7]] => 1 [[1,5],[2],[3],[4],[6],[7]] => 1 [[1,4],[2],[3],[5],[6],[7]] => 1 [[1,3],[2],[4],[5],[6],[7]] => 1 [[1,2],[3],[4],[5],[6],[7]] => 2 [[1],[2],[3],[4],[5],[6],[7]] => 1 [[1,2,3,4,5,6,7,8]] => 8 [[1,3,4,5,6,7,8],[2]] => 7 [[1,2,4,5,6,7,8],[3]] => 7 [[1,2,3,5,6,7,8],[4]] => 7 [[1,2,3,4,6,7,8],[5]] => 7 [[1,2,3,4,5,7,8],[6]] => 7 [[1,2,3,4,5,6,8],[7]] => 7 [[1,2,3,4,5,6,7],[8]] => 7 [[1,3,5,6,7,8],[2,4]] => 6 [[1,2,5,6,7,8],[3,4]] => 5 [[1,3,4,6,7,8],[2,5]] => 6 [[1,2,4,6,7,8],[3,5]] => 6 [[1,2,3,6,7,8],[4,5]] => 5 [[1,3,4,5,7,8],[2,6]] => 6 [[1,2,4,5,7,8],[3,6]] => 6 [[1,2,3,5,7,8],[4,6]] => 6 [[1,2,3,4,7,8],[5,6]] => 5 [[1,3,4,5,6,8],[2,7]] => 6 [[1,2,4,5,6,8],[3,7]] => 6 [[1,2,3,5,6,8],[4,7]] => 6 [[1,2,3,4,6,8],[5,7]] => 6 [[1,2,3,4,5,8],[6,7]] => 5 [[1,3,4,5,6,7],[2,8]] => 6 [[1,2,4,5,6,7],[3,8]] => 6 [[1,2,3,5,6,7],[4,8]] => 6 [[1,2,3,4,6,7],[5,8]] => 6 [[1,2,3,4,5,7],[6,8]] => 6 [[1,2,3,4,5,6],[7,8]] => 5 [[1,4,5,6,7,8],[2],[3]] => 6 [[1,3,5,6,7,8],[2],[4]] => 5 [[1,2,5,6,7,8],[3],[4]] => 6 [[1,3,4,6,7,8],[2],[5]] => 4 [[1,2,4,6,7,8],[3],[5]] => 5 [[1,2,3,6,7,8],[4],[5]] => 6 [[1,3,4,5,7,8],[2],[6]] => 3 [[1,2,4,5,7,8],[3],[6]] => 4 [[1,2,3,5,7,8],[4],[6]] => 5 [[1,2,3,4,7,8],[5],[6]] => 6 [[1,3,4,5,6,8],[2],[7]] => 2 [[1,2,4,5,6,8],[3],[7]] => 3 [[1,2,3,5,6,8],[4],[7]] => 4 [[1,2,3,4,6,8],[5],[7]] => 5 [[1,2,3,4,5,8],[6],[7]] => 6 [[1,3,4,5,6,7],[2],[8]] => 1 [[1,2,4,5,6,7],[3],[8]] => 2 [[1,2,3,5,6,7],[4],[8]] => 3 [[1,2,3,4,6,7],[5],[8]] => 4 [[1,2,3,4,5,7],[6],[8]] => 5 [[1,2,3,4,5,6],[7],[8]] => 6 [[1,3,5,7,8],[2,4,6]] => 5 [[1,2,5,7,8],[3,4,6]] => 4 [[1,3,4,7,8],[2,5,6]] => 4 [[1,2,4,7,8],[3,5,6]] => 3 [[1,2,3,7,8],[4,5,6]] => 3 [[1,3,5,6,8],[2,4,7]] => 5 [[1,2,5,6,8],[3,4,7]] => 4 [[1,3,4,6,8],[2,5,7]] => 5 [[1,2,4,6,8],[3,5,7]] => 5 [[1,2,3,6,8],[4,5,7]] => 4 [[1,3,4,5,8],[2,6,7]] => 4 [[1,2,4,5,8],[3,6,7]] => 4 [[1,2,3,5,8],[4,6,7]] => 3 [[1,2,3,4,8],[5,6,7]] => 3 [[1,3,5,6,7],[2,4,8]] => 5 [[1,2,5,6,7],[3,4,8]] => 4 [[1,3,4,6,7],[2,5,8]] => 5 [[1,2,4,6,7],[3,5,8]] => 5 [[1,2,3,6,7],[4,5,8]] => 4 [[1,3,4,5,7],[2,6,8]] => 5 [[1,2,4,5,7],[3,6,8]] => 5 [[1,2,3,5,7],[4,6,8]] => 5 [[1,2,3,4,7],[5,6,8]] => 4 [[1,3,4,5,6],[2,7,8]] => 4 [[1,2,4,5,6],[3,7,8]] => 4 [[1,2,3,5,6],[4,7,8]] => 4 [[1,2,3,4,6],[5,7,8]] => 3 [[1,2,3,4,5],[6,7,8]] => 3 [[1,4,6,7,8],[2,5],[3]] => 5 [[1,3,6,7,8],[2,5],[4]] => 4 [[1,2,6,7,8],[3,5],[4]] => 4 [[1,3,6,7,8],[2,4],[5]] => 5 [[1,2,6,7,8],[3,4],[5]] => 4 [[1,4,5,7,8],[2,6],[3]] => 5 [[1,3,5,7,8],[2,6],[4]] => 4 [[1,2,5,7,8],[3,6],[4]] => 5 [[1,3,4,7,8],[2,6],[5]] => 3 [[1,2,4,7,8],[3,6],[5]] => 4 [[1,2,3,7,8],[4,6],[5]] => 4 [[1,3,5,7,8],[2,4],[6]] => 4 [[1,2,5,7,8],[3,4],[6]] => 3 [[1,3,4,7,8],[2,5],[6]] => 5 [[1,2,4,7,8],[3,5],[6]] => 5 [[1,2,3,7,8],[4,5],[6]] => 4 [[1,4,5,6,8],[2,7],[3]] => 5 [[1,3,5,6,8],[2,7],[4]] => 4 [[1,2,5,6,8],[3,7],[4]] => 5 [[1,3,4,6,8],[2,7],[5]] => 3 [[1,2,4,6,8],[3,7],[5]] => 4 [[1,2,3,6,8],[4,7],[5]] => 5 [[1,3,4,5,8],[2,7],[6]] => 2 [[1,2,4,5,8],[3,7],[6]] => 3 [[1,2,3,5,8],[4,7],[6]] => 4 [[1,2,3,4,8],[5,7],[6]] => 4 [[1,3,5,6,8],[2,4],[7]] => 3 [[1,2,5,6,8],[3,4],[7]] => 2 [[1,3,4,6,8],[2,5],[7]] => 4 [[1,2,4,6,8],[3,5],[7]] => 4 [[1,2,3,6,8],[4,5],[7]] => 3 [[1,3,4,5,8],[2,6],[7]] => 5 [[1,2,4,5,8],[3,6],[7]] => 5 [[1,2,3,5,8],[4,6],[7]] => 5 [[1,2,3,4,8],[5,6],[7]] => 4 [[1,4,5,6,7],[2,8],[3]] => 5 [[1,3,5,6,7],[2,8],[4]] => 4 [[1,2,5,6,7],[3,8],[4]] => 5 [[1,3,4,6,7],[2,8],[5]] => 3 [[1,2,4,6,7],[3,8],[5]] => 4 [[1,2,3,6,7],[4,8],[5]] => 5 [[1,3,4,5,7],[2,8],[6]] => 2 [[1,2,4,5,7],[3,8],[6]] => 3 [[1,2,3,5,7],[4,8],[6]] => 4 [[1,2,3,4,7],[5,8],[6]] => 5 [[1,3,4,5,6],[2,8],[7]] => 1 [[1,2,4,5,6],[3,8],[7]] => 2 [[1,2,3,5,6],[4,8],[7]] => 3 [[1,2,3,4,6],[5,8],[7]] => 4 [[1,2,3,4,5],[6,8],[7]] => 4 [[1,3,5,6,7],[2,4],[8]] => 2 [[1,2,5,6,7],[3,4],[8]] => 1 [[1,3,4,6,7],[2,5],[8]] => 3 [[1,2,4,6,7],[3,5],[8]] => 3 [[1,2,3,6,7],[4,5],[8]] => 2 [[1,3,4,5,7],[2,6],[8]] => 4 [[1,2,4,5,7],[3,6],[8]] => 4 [[1,2,3,5,7],[4,6],[8]] => 4 [[1,2,3,4,7],[5,6],[8]] => 3 [[1,3,4,5,6],[2,7],[8]] => 5 [[1,2,4,5,6],[3,7],[8]] => 5 [[1,2,3,5,6],[4,7],[8]] => 5 [[1,2,3,4,6],[5,7],[8]] => 5 [[1,2,3,4,5],[6,7],[8]] => 4 [[1,5,6,7,8],[2],[3],[4]] => 5 [[1,4,6,7,8],[2],[3],[5]] => 4 [[1,3,6,7,8],[2],[4],[5]] => 4 [[1,2,6,7,8],[3],[4],[5]] => 5 [[1,4,5,7,8],[2],[3],[6]] => 3 [[1,3,5,7,8],[2],[4],[6]] => 3 [[1,2,5,7,8],[3],[4],[6]] => 4 [[1,3,4,7,8],[2],[5],[6]] => 3 [[1,2,4,7,8],[3],[5],[6]] => 4 [[1,2,3,7,8],[4],[5],[6]] => 5 [[1,4,5,6,8],[2],[3],[7]] => 2 [[1,3,5,6,8],[2],[4],[7]] => 2 [[1,2,5,6,8],[3],[4],[7]] => 3 [[1,3,4,6,8],[2],[5],[7]] => 2 [[1,2,4,6,8],[3],[5],[7]] => 3 [[1,2,3,6,8],[4],[5],[7]] => 4 [[1,3,4,5,8],[2],[6],[7]] => 2 [[1,2,4,5,8],[3],[6],[7]] => 3 [[1,2,3,5,8],[4],[6],[7]] => 4 [[1,2,3,4,8],[5],[6],[7]] => 5 [[1,4,5,6,7],[2],[3],[8]] => 1 [[1,3,5,6,7],[2],[4],[8]] => 1 [[1,2,5,6,7],[3],[4],[8]] => 2 [[1,3,4,6,7],[2],[5],[8]] => 1 [[1,2,4,6,7],[3],[5],[8]] => 2 [[1,2,3,6,7],[4],[5],[8]] => 3 [[1,3,4,5,7],[2],[6],[8]] => 1 [[1,2,4,5,7],[3],[6],[8]] => 2 [[1,2,3,5,7],[4],[6],[8]] => 3 [[1,2,3,4,7],[5],[6],[8]] => 4 [[1,3,4,5,6],[2],[7],[8]] => 1 [[1,2,4,5,6],[3],[7],[8]] => 2 [[1,2,3,5,6],[4],[7],[8]] => 3 [[1,2,3,4,6],[5],[7],[8]] => 4 [[1,2,3,4,5],[6],[7],[8]] => 5 [[1,3,5,7],[2,4,6,8]] => 4 [[1,2,5,7],[3,4,6,8]] => 3 [[1,3,4,7],[2,5,6,8]] => 3 [[1,2,4,7],[3,5,6,8]] => 2 [[1,2,3,7],[4,5,6,8]] => 2 [[1,3,5,6],[2,4,7,8]] => 3 [[1,2,5,6],[3,4,7,8]] => 2 [[1,3,4,6],[2,5,7,8]] => 2 [[1,2,4,6],[3,5,7,8]] => 1 [[1,2,3,6],[4,5,7,8]] => 1 [[1,3,4,5],[2,6,7,8]] => 2 [[1,2,4,5],[3,6,7,8]] => 1 [[1,2,3,5],[4,6,7,8]] => 1 [[1,2,3,4],[5,6,7,8]] => 1 [[1,4,6,8],[2,5,7],[3]] => 4 [[1,3,6,8],[2,5,7],[4]] => 3 [[1,2,6,8],[3,5,7],[4]] => 3 [[1,3,6,8],[2,4,7],[5]] => 4 [[1,2,6,8],[3,4,7],[5]] => 3 [[1,4,5,8],[2,6,7],[3]] => 3 [[1,3,5,8],[2,6,7],[4]] => 2 [[1,2,5,8],[3,6,7],[4]] => 2 [[1,3,4,8],[2,6,7],[5]] => 2 [[1,2,4,8],[3,6,7],[5]] => 2 [[1,2,3,8],[4,6,7],[5]] => 2 [[1,3,5,8],[2,4,7],[6]] => 3 [[1,2,5,8],[3,4,7],[6]] => 2 [[1,3,4,8],[2,5,7],[6]] => 3 [[1,2,4,8],[3,5,7],[6]] => 2 [[1,2,3,8],[4,5,7],[6]] => 2 [[1,3,5,8],[2,4,6],[7]] => 4 [[1,2,5,8],[3,4,6],[7]] => 3 [[1,3,4,8],[2,5,6],[7]] => 3 [[1,2,4,8],[3,5,6],[7]] => 2 [[1,2,3,8],[4,5,6],[7]] => 2 [[1,4,6,7],[2,5,8],[3]] => 4 [[1,3,6,7],[2,5,8],[4]] => 3 [[1,2,6,7],[3,5,8],[4]] => 3 [[1,3,6,7],[2,4,8],[5]] => 4 [[1,2,6,7],[3,4,8],[5]] => 3 [[1,4,5,7],[2,6,8],[3]] => 4 [[1,3,5,7],[2,6,8],[4]] => 3 [[1,2,5,7],[3,6,8],[4]] => 4 [[1,3,4,7],[2,6,8],[5]] => 2 [[1,2,4,7],[3,6,8],[5]] => 3 [[1,2,3,7],[4,6,8],[5]] => 3 [[1,3,5,7],[2,4,8],[6]] => 3 [[1,2,5,7],[3,4,8],[6]] => 2 [[1,3,4,7],[2,5,8],[6]] => 4 [[1,2,4,7],[3,5,8],[6]] => 4 [[1,2,3,7],[4,5,8],[6]] => 3 [[1,4,5,6],[2,7,8],[3]] => 3 [[1,3,5,6],[2,7,8],[4]] => 2 [[1,2,5,6],[3,7,8],[4]] => 3 [[1,3,4,6],[2,7,8],[5]] => 1 [[1,2,4,6],[3,7,8],[5]] => 2 [[1,2,3,6],[4,7,8],[5]] => 2 [[1,3,4,5],[2,7,8],[6]] => 1 [[1,2,4,5],[3,7,8],[6]] => 2 [[1,2,3,5],[4,7,8],[6]] => 2 [[1,2,3,4],[5,7,8],[6]] => 2 [[1,3,5,6],[2,4,8],[7]] => 2 [[1,2,5,6],[3,4,8],[7]] => 1 [[1,3,4,6],[2,5,8],[7]] => 3 [[1,2,4,6],[3,5,8],[7]] => 3 [[1,2,3,6],[4,5,8],[7]] => 2 [[1,3,4,5],[2,6,8],[7]] => 3 [[1,2,4,5],[3,6,8],[7]] => 3 [[1,2,3,5],[4,6,8],[7]] => 2 [[1,2,3,4],[5,6,8],[7]] => 2 [[1,3,5,7],[2,4,6],[8]] => 3 [[1,2,5,7],[3,4,6],[8]] => 2 [[1,3,4,7],[2,5,6],[8]] => 2 [[1,2,4,7],[3,5,6],[8]] => 1 [[1,2,3,7],[4,5,6],[8]] => 1 [[1,3,5,6],[2,4,7],[8]] => 4 [[1,2,5,6],[3,4,7],[8]] => 3 [[1,3,4,6],[2,5,7],[8]] => 4 [[1,2,4,6],[3,5,7],[8]] => 4 [[1,2,3,6],[4,5,7],[8]] => 3 [[1,3,4,5],[2,6,7],[8]] => 3 [[1,2,4,5],[3,6,7],[8]] => 3 [[1,2,3,5],[4,6,7],[8]] => 2 [[1,2,3,4],[5,6,7],[8]] => 2 [[1,4,7,8],[2,5],[3,6]] => 4 [[1,3,7,8],[2,5],[4,6]] => 3 [[1,2,7,8],[3,5],[4,6]] => 3 [[1,3,7,8],[2,4],[5,6]] => 3 [[1,2,7,8],[3,4],[5,6]] => 3 [[1,4,6,8],[2,5],[3,7]] => 3 [[1,3,6,8],[2,5],[4,7]] => 2 [[1,2,6,8],[3,5],[4,7]] => 2 [[1,3,6,8],[2,4],[5,7]] => 2 [[1,2,6,8],[3,4],[5,7]] => 2 [[1,4,5,8],[2,6],[3,7]] => 4 [[1,3,5,8],[2,6],[4,7]] => 3 [[1,2,5,8],[3,6],[4,7]] => 4 [[1,3,4,8],[2,6],[5,7]] => 2 [[1,2,4,8],[3,6],[5,7]] => 3 [[1,2,3,8],[4,6],[5,7]] => 3 [[1,3,5,8],[2,4],[6,7]] => 2 [[1,2,5,8],[3,4],[6,7]] => 2 [[1,3,4,8],[2,5],[6,7]] => 2 [[1,2,4,8],[3,5],[6,7]] => 3 [[1,2,3,8],[4,5],[6,7]] => 3 [[1,4,6,7],[2,5],[3,8]] => 2 [[1,3,6,7],[2,5],[4,8]] => 1 [[1,2,6,7],[3,5],[4,8]] => 1 [[1,3,6,7],[2,4],[5,8]] => 1 [[1,2,6,7],[3,4],[5,8]] => 1 [[1,4,5,7],[2,6],[3,8]] => 3 [[1,3,5,7],[2,6],[4,8]] => 2 [[1,2,5,7],[3,6],[4,8]] => 3 [[1,3,4,7],[2,6],[5,8]] => 1 [[1,2,4,7],[3,6],[5,8]] => 2 [[1,2,3,7],[4,6],[5,8]] => 2 [[1,3,5,7],[2,4],[6,8]] => 1 [[1,2,5,7],[3,4],[6,8]] => 1 [[1,3,4,7],[2,5],[6,8]] => 1 [[1,2,4,7],[3,5],[6,8]] => 2 [[1,2,3,7],[4,5],[6,8]] => 2 [[1,4,5,6],[2,7],[3,8]] => 4 [[1,3,5,6],[2,7],[4,8]] => 3 [[1,2,5,6],[3,7],[4,8]] => 4 [[1,3,4,6],[2,7],[5,8]] => 2 [[1,2,4,6],[3,7],[5,8]] => 3 [[1,2,3,6],[4,7],[5,8]] => 4 [[1,3,4,5],[2,7],[6,8]] => 1 [[1,2,4,5],[3,7],[6,8]] => 2 [[1,2,3,5],[4,7],[6,8]] => 3 [[1,2,3,4],[5,7],[6,8]] => 3 [[1,3,5,6],[2,4],[7,8]] => 1 [[1,2,5,6],[3,4],[7,8]] => 1 [[1,3,4,6],[2,5],[7,8]] => 1 [[1,2,4,6],[3,5],[7,8]] => 2 [[1,2,3,6],[4,5],[7,8]] => 2 [[1,3,4,5],[2,6],[7,8]] => 1 [[1,2,4,5],[3,6],[7,8]] => 2 [[1,2,3,5],[4,6],[7,8]] => 3 [[1,2,3,4],[5,6],[7,8]] => 3 [[1,5,7,8],[2,6],[3],[4]] => 4 [[1,4,7,8],[2,6],[3],[5]] => 3 [[1,3,7,8],[2,6],[4],[5]] => 3 [[1,2,7,8],[3,6],[4],[5]] => 3 [[1,4,7,8],[2,5],[3],[6]] => 3 [[1,3,7,8],[2,5],[4],[6]] => 3 [[1,2,7,8],[3,5],[4],[6]] => 3 [[1,3,7,8],[2,4],[5],[6]] => 4 [[1,2,7,8],[3,4],[5],[6]] => 3 [[1,5,6,8],[2,7],[3],[4]] => 4 [[1,4,6,8],[2,7],[3],[5]] => 3 [[1,3,6,8],[2,7],[4],[5]] => 3 [[1,2,6,8],[3,7],[4],[5]] => 4 [[1,4,5,8],[2,7],[3],[6]] => 2 [[1,3,5,8],[2,7],[4],[6]] => 2 [[1,2,5,8],[3,7],[4],[6]] => 3 [[1,3,4,8],[2,7],[5],[6]] => 2 [[1,2,4,8],[3,7],[5],[6]] => 3 [[1,2,3,8],[4,7],[5],[6]] => 3 [[1,4,6,8],[2,5],[3],[7]] => 2 [[1,3,6,8],[2,5],[4],[7]] => 2 [[1,2,6,8],[3,5],[4],[7]] => 2 [[1,3,6,8],[2,4],[5],[7]] => 3 [[1,2,6,8],[3,4],[5],[7]] => 2 [[1,4,5,8],[2,6],[3],[7]] => 2 [[1,3,5,8],[2,6],[4],[7]] => 2 [[1,2,5,8],[3,6],[4],[7]] => 3 [[1,3,4,8],[2,6],[5],[7]] => 2 [[1,2,4,8],[3,6],[5],[7]] => 3 [[1,2,3,8],[4,6],[5],[7]] => 3 [[1,3,5,8],[2,4],[6],[7]] => 3 [[1,2,5,8],[3,4],[6],[7]] => 2 [[1,3,4,8],[2,5],[6],[7]] => 4 [[1,2,4,8],[3,5],[6],[7]] => 4 [[1,2,3,8],[4,5],[6],[7]] => 3 [[1,5,6,7],[2,8],[3],[4]] => 4 [[1,4,6,7],[2,8],[3],[5]] => 3 [[1,3,6,7],[2,8],[4],[5]] => 3 [[1,2,6,7],[3,8],[4],[5]] => 4 [[1,4,5,7],[2,8],[3],[6]] => 2 [[1,3,5,7],[2,8],[4],[6]] => 2 [[1,2,5,7],[3,8],[4],[6]] => 3 [[1,3,4,7],[2,8],[5],[6]] => 2 [[1,2,4,7],[3,8],[5],[6]] => 3 [[1,2,3,7],[4,8],[5],[6]] => 4 [[1,4,5,6],[2,8],[3],[7]] => 1 [[1,3,5,6],[2,8],[4],[7]] => 1 [[1,2,5,6],[3,8],[4],[7]] => 2 [[1,3,4,6],[2,8],[5],[7]] => 1 [[1,2,4,6],[3,8],[5],[7]] => 2 [[1,2,3,6],[4,8],[5],[7]] => 3 [[1,3,4,5],[2,8],[6],[7]] => 1 [[1,2,4,5],[3,8],[6],[7]] => 2 [[1,2,3,5],[4,8],[6],[7]] => 3 [[1,2,3,4],[5,8],[6],[7]] => 3 [[1,4,6,7],[2,5],[3],[8]] => 1 [[1,3,6,7],[2,5],[4],[8]] => 1 [[1,2,6,7],[3,5],[4],[8]] => 1 [[1,3,6,7],[2,4],[5],[8]] => 2 [[1,2,6,7],[3,4],[5],[8]] => 1 [[1,4,5,7],[2,6],[3],[8]] => 1 [[1,3,5,7],[2,6],[4],[8]] => 1 [[1,2,5,7],[3,6],[4],[8]] => 2 [[1,3,4,7],[2,6],[5],[8]] => 1 [[1,2,4,7],[3,6],[5],[8]] => 2 [[1,2,3,7],[4,6],[5],[8]] => 2 [[1,3,5,7],[2,4],[6],[8]] => 2 [[1,2,5,7],[3,4],[6],[8]] => 1 [[1,3,4,7],[2,5],[6],[8]] => 3 [[1,2,4,7],[3,5],[6],[8]] => 3 [[1,2,3,7],[4,5],[6],[8]] => 2 [[1,4,5,6],[2,7],[3],[8]] => 1 [[1,3,5,6],[2,7],[4],[8]] => 1 [[1,2,5,6],[3,7],[4],[8]] => 2 [[1,3,4,6],[2,7],[5],[8]] => 1 [[1,2,4,6],[3,7],[5],[8]] => 2 [[1,2,3,6],[4,7],[5],[8]] => 3 [[1,3,4,5],[2,7],[6],[8]] => 1 [[1,2,4,5],[3,7],[6],[8]] => 2 [[1,2,3,5],[4,7],[6],[8]] => 3 [[1,2,3,4],[5,7],[6],[8]] => 3 [[1,3,5,6],[2,4],[7],[8]] => 2 [[1,2,5,6],[3,4],[7],[8]] => 1 [[1,3,4,6],[2,5],[7],[8]] => 3 [[1,2,4,6],[3,5],[7],[8]] => 3 [[1,2,3,6],[4,5],[7],[8]] => 2 [[1,3,4,5],[2,6],[7],[8]] => 4 [[1,2,4,5],[3,6],[7],[8]] => 4 [[1,2,3,5],[4,6],[7],[8]] => 4 [[1,2,3,4],[5,6],[7],[8]] => 3 [[1,6,7,8],[2],[3],[4],[5]] => 4 [[1,5,7,8],[2],[3],[4],[6]] => 3 [[1,4,7,8],[2],[3],[5],[6]] => 3 [[1,3,7,8],[2],[4],[5],[6]] => 3 [[1,2,7,8],[3],[4],[5],[6]] => 4 [[1,5,6,8],[2],[3],[4],[7]] => 2 [[1,4,6,8],[2],[3],[5],[7]] => 2 [[1,3,6,8],[2],[4],[5],[7]] => 2 [[1,2,6,8],[3],[4],[5],[7]] => 3 [[1,4,5,8],[2],[3],[6],[7]] => 2 [[1,3,5,8],[2],[4],[6],[7]] => 2 [[1,2,5,8],[3],[4],[6],[7]] => 3 [[1,3,4,8],[2],[5],[6],[7]] => 2 [[1,2,4,8],[3],[5],[6],[7]] => 3 [[1,2,3,8],[4],[5],[6],[7]] => 4 [[1,5,6,7],[2],[3],[4],[8]] => 1 [[1,4,6,7],[2],[3],[5],[8]] => 1 [[1,3,6,7],[2],[4],[5],[8]] => 1 [[1,2,6,7],[3],[4],[5],[8]] => 2 [[1,4,5,7],[2],[3],[6],[8]] => 1 [[1,3,5,7],[2],[4],[6],[8]] => 1 [[1,2,5,7],[3],[4],[6],[8]] => 2 [[1,3,4,7],[2],[5],[6],[8]] => 1 [[1,2,4,7],[3],[5],[6],[8]] => 2 [[1,2,3,7],[4],[5],[6],[8]] => 3 [[1,4,5,6],[2],[3],[7],[8]] => 1 [[1,3,5,6],[2],[4],[7],[8]] => 1 [[1,2,5,6],[3],[4],[7],[8]] => 2 [[1,3,4,6],[2],[5],[7],[8]] => 1 [[1,2,4,6],[3],[5],[7],[8]] => 2 [[1,2,3,6],[4],[5],[7],[8]] => 3 [[1,3,4,5],[2],[6],[7],[8]] => 1 [[1,2,4,5],[3],[6],[7],[8]] => 2 [[1,2,3,5],[4],[6],[7],[8]] => 3 [[1,2,3,4],[5],[6],[7],[8]] => 4 [[1,4,7],[2,5,8],[3,6]] => 3 [[1,3,7],[2,5,8],[4,6]] => 2 [[1,2,7],[3,5,8],[4,6]] => 2 [[1,3,7],[2,4,8],[5,6]] => 2 [[1,2,7],[3,4,8],[5,6]] => 2 [[1,4,6],[2,5,8],[3,7]] => 2 [[1,3,6],[2,5,8],[4,7]] => 1 [[1,2,6],[3,5,8],[4,7]] => 1 [[1,3,6],[2,4,8],[5,7]] => 1 [[1,2,6],[3,4,8],[5,7]] => 1 [[1,4,5],[2,6,8],[3,7]] => 2 [[1,3,5],[2,6,8],[4,7]] => 1 [[1,2,5],[3,6,8],[4,7]] => 1 [[1,3,4],[2,6,8],[5,7]] => 1 [[1,2,4],[3,6,8],[5,7]] => 1 [[1,2,3],[4,6,8],[5,7]] => 1 [[1,3,5],[2,4,8],[6,7]] => 1 [[1,2,5],[3,4,8],[6,7]] => 1 [[1,3,4],[2,5,8],[6,7]] => 1 [[1,2,4],[3,5,8],[6,7]] => 1 [[1,2,3],[4,5,8],[6,7]] => 1 [[1,4,6],[2,5,7],[3,8]] => 3 [[1,3,6],[2,5,7],[4,8]] => 2 [[1,2,6],[3,5,7],[4,8]] => 2 [[1,3,6],[2,4,7],[5,8]] => 3 [[1,2,6],[3,4,7],[5,8]] => 2 [[1,4,5],[2,6,7],[3,8]] => 2 [[1,3,5],[2,6,7],[4,8]] => 1 [[1,2,5],[3,6,7],[4,8]] => 1 [[1,3,4],[2,6,7],[5,8]] => 1 [[1,2,4],[3,6,7],[5,8]] => 1 [[1,2,3],[4,6,7],[5,8]] => 1 [[1,3,5],[2,4,7],[6,8]] => 2 [[1,2,5],[3,4,7],[6,8]] => 1 [[1,3,4],[2,5,7],[6,8]] => 2 [[1,2,4],[3,5,7],[6,8]] => 1 [[1,2,3],[4,5,7],[6,8]] => 1 [[1,3,5],[2,4,6],[7,8]] => 2 [[1,2,5],[3,4,6],[7,8]] => 1 [[1,3,4],[2,5,6],[7,8]] => 2 [[1,2,4],[3,5,6],[7,8]] => 1 [[1,2,3],[4,5,6],[7,8]] => 1 [[1,5,7],[2,6,8],[3],[4]] => 3 [[1,4,7],[2,6,8],[3],[5]] => 2 [[1,3,7],[2,6,8],[4],[5]] => 2 [[1,2,7],[3,6,8],[4],[5]] => 2 [[1,4,7],[2,5,8],[3],[6]] => 2 [[1,3,7],[2,5,8],[4],[6]] => 2 [[1,2,7],[3,5,8],[4],[6]] => 2 [[1,3,7],[2,4,8],[5],[6]] => 3 [[1,2,7],[3,4,8],[5],[6]] => 2 [[1,5,6],[2,7,8],[3],[4]] => 2 [[1,4,6],[2,7,8],[3],[5]] => 1 [[1,3,6],[2,7,8],[4],[5]] => 1 [[1,2,6],[3,7,8],[4],[5]] => 1 [[1,4,5],[2,7,8],[3],[6]] => 1 [[1,3,5],[2,7,8],[4],[6]] => 1 [[1,2,5],[3,7,8],[4],[6]] => 1 [[1,3,4],[2,7,8],[5],[6]] => 1 [[1,2,4],[3,7,8],[5],[6]] => 1 [[1,2,3],[4,7,8],[5],[6]] => 1 [[1,4,6],[2,5,8],[3],[7]] => 1 [[1,3,6],[2,5,8],[4],[7]] => 1 [[1,2,6],[3,5,8],[4],[7]] => 1 [[1,3,6],[2,4,8],[5],[7]] => 2 [[1,2,6],[3,4,8],[5],[7]] => 1 [[1,4,5],[2,6,8],[3],[7]] => 1 [[1,3,5],[2,6,8],[4],[7]] => 1 [[1,2,5],[3,6,8],[4],[7]] => 1 [[1,3,4],[2,6,8],[5],[7]] => 1 [[1,2,4],[3,6,8],[5],[7]] => 1 [[1,2,3],[4,6,8],[5],[7]] => 1 [[1,3,5],[2,4,8],[6],[7]] => 2 [[1,2,5],[3,4,8],[6],[7]] => 1 [[1,3,4],[2,5,8],[6],[7]] => 2 [[1,2,4],[3,5,8],[6],[7]] => 1 [[1,2,3],[4,5,8],[6],[7]] => 1 [[1,4,6],[2,5,7],[3],[8]] => 1 [[1,3,6],[2,5,7],[4],[8]] => 1 [[1,2,6],[3,5,7],[4],[8]] => 1 [[1,3,6],[2,4,7],[5],[8]] => 2 [[1,2,6],[3,4,7],[5],[8]] => 1 [[1,4,5],[2,6,7],[3],[8]] => 1 [[1,3,5],[2,6,7],[4],[8]] => 1 [[1,2,5],[3,6,7],[4],[8]] => 1 [[1,3,4],[2,6,7],[5],[8]] => 1 [[1,2,4],[3,6,7],[5],[8]] => 1 [[1,2,3],[4,6,7],[5],[8]] => 1 [[1,3,5],[2,4,7],[6],[8]] => 2 [[1,2,5],[3,4,7],[6],[8]] => 1 [[1,3,4],[2,5,7],[6],[8]] => 2 [[1,2,4],[3,5,7],[6],[8]] => 1 [[1,2,3],[4,5,7],[6],[8]] => 1 [[1,3,5],[2,4,6],[7],[8]] => 3 [[1,2,5],[3,4,6],[7],[8]] => 2 [[1,3,4],[2,5,6],[7],[8]] => 2 [[1,2,4],[3,5,6],[7],[8]] => 1 [[1,2,3],[4,5,6],[7],[8]] => 1 [[1,5,8],[2,6],[3,7],[4]] => 3 [[1,4,8],[2,6],[3,7],[5]] => 2 [[1,3,8],[2,6],[4,7],[5]] => 2 [[1,2,8],[3,6],[4,7],[5]] => 2 [[1,4,8],[2,5],[3,7],[6]] => 2 [[1,3,8],[2,5],[4,7],[6]] => 2 [[1,2,8],[3,5],[4,7],[6]] => 2 [[1,3,8],[2,4],[5,7],[6]] => 2 [[1,2,8],[3,4],[5,7],[6]] => 2 [[1,4,8],[2,5],[3,6],[7]] => 3 [[1,3,8],[2,5],[4,6],[7]] => 2 [[1,2,8],[3,5],[4,6],[7]] => 2 [[1,3,8],[2,4],[5,6],[7]] => 2 [[1,2,8],[3,4],[5,6],[7]] => 2 [[1,5,7],[2,6],[3,8],[4]] => 2 [[1,4,7],[2,6],[3,8],[5]] => 1 [[1,3,7],[2,6],[4,8],[5]] => 1 [[1,2,7],[3,6],[4,8],[5]] => 1 [[1,4,7],[2,5],[3,8],[6]] => 1 [[1,3,7],[2,5],[4,8],[6]] => 1 [[1,2,7],[3,5],[4,8],[6]] => 1 [[1,3,7],[2,4],[5,8],[6]] => 1 [[1,2,7],[3,4],[5,8],[6]] => 1 [[1,5,6],[2,7],[3,8],[4]] => 3 [[1,4,6],[2,7],[3,8],[5]] => 2 [[1,3,6],[2,7],[4,8],[5]] => 2 [[1,2,6],[3,7],[4,8],[5]] => 3 [[1,4,5],[2,7],[3,8],[6]] => 1 [[1,3,5],[2,7],[4,8],[6]] => 1 [[1,2,5],[3,7],[4,8],[6]] => 2 [[1,3,4],[2,7],[5,8],[6]] => 1 [[1,2,4],[3,7],[5,8],[6]] => 2 [[1,2,3],[4,7],[5,8],[6]] => 2 [[1,4,6],[2,5],[3,8],[7]] => 1 [[1,3,6],[2,5],[4,8],[7]] => 1 [[1,2,6],[3,5],[4,8],[7]] => 1 [[1,3,6],[2,4],[5,8],[7]] => 1 [[1,2,6],[3,4],[5,8],[7]] => 1 [[1,4,5],[2,6],[3,8],[7]] => 1 [[1,3,5],[2,6],[4,8],[7]] => 1 [[1,2,5],[3,6],[4,8],[7]] => 2 [[1,3,4],[2,6],[5,8],[7]] => 1 [[1,2,4],[3,6],[5,8],[7]] => 2 [[1,2,3],[4,6],[5,8],[7]] => 2 [[1,3,5],[2,4],[6,8],[7]] => 1 [[1,2,5],[3,4],[6,8],[7]] => 1 [[1,3,4],[2,5],[6,8],[7]] => 1 [[1,2,4],[3,5],[6,8],[7]] => 2 [[1,2,3],[4,5],[6,8],[7]] => 2 [[1,4,7],[2,5],[3,6],[8]] => 2 [[1,3,7],[2,5],[4,6],[8]] => 1 [[1,2,7],[3,5],[4,6],[8]] => 1 [[1,3,7],[2,4],[5,6],[8]] => 1 [[1,2,7],[3,4],[5,6],[8]] => 1 [[1,4,6],[2,5],[3,7],[8]] => 2 [[1,3,6],[2,5],[4,7],[8]] => 1 [[1,2,6],[3,5],[4,7],[8]] => 1 [[1,3,6],[2,4],[5,7],[8]] => 1 [[1,2,6],[3,4],[5,7],[8]] => 1 [[1,4,5],[2,6],[3,7],[8]] => 3 [[1,3,5],[2,6],[4,7],[8]] => 2 [[1,2,5],[3,6],[4,7],[8]] => 3 [[1,3,4],[2,6],[5,7],[8]] => 1 [[1,2,4],[3,6],[5,7],[8]] => 2 [[1,2,3],[4,6],[5,7],[8]] => 2 [[1,3,5],[2,4],[6,7],[8]] => 1 [[1,2,5],[3,4],[6,7],[8]] => 1 [[1,3,4],[2,5],[6,7],[8]] => 1 [[1,2,4],[3,5],[6,7],[8]] => 2 [[1,2,3],[4,5],[6,7],[8]] => 2 [[1,6,8],[2,7],[3],[4],[5]] => 3 [[1,5,8],[2,7],[3],[4],[6]] => 2 [[1,4,8],[2,7],[3],[5],[6]] => 2 [[1,3,8],[2,7],[4],[5],[6]] => 2 [[1,2,8],[3,7],[4],[5],[6]] => 2 [[1,5,8],[2,6],[3],[4],[7]] => 2 [[1,4,8],[2,6],[3],[5],[7]] => 2 [[1,3,8],[2,6],[4],[5],[7]] => 2 [[1,2,8],[3,6],[4],[5],[7]] => 2 [[1,4,8],[2,5],[3],[6],[7]] => 2 [[1,3,8],[2,5],[4],[6],[7]] => 2 [[1,2,8],[3,5],[4],[6],[7]] => 2 [[1,3,8],[2,4],[5],[6],[7]] => 3 [[1,2,8],[3,4],[5],[6],[7]] => 2 [[1,6,7],[2,8],[3],[4],[5]] => 3 [[1,5,7],[2,8],[3],[4],[6]] => 2 [[1,4,7],[2,8],[3],[5],[6]] => 2 [[1,3,7],[2,8],[4],[5],[6]] => 2 [[1,2,7],[3,8],[4],[5],[6]] => 3 [[1,5,6],[2,8],[3],[4],[7]] => 1 [[1,4,6],[2,8],[3],[5],[7]] => 1 [[1,3,6],[2,8],[4],[5],[7]] => 1 [[1,2,6],[3,8],[4],[5],[7]] => 2 [[1,4,5],[2,8],[3],[6],[7]] => 1 [[1,3,5],[2,8],[4],[6],[7]] => 1 [[1,2,5],[3,8],[4],[6],[7]] => 2 [[1,3,4],[2,8],[5],[6],[7]] => 1 [[1,2,4],[3,8],[5],[6],[7]] => 2 [[1,2,3],[4,8],[5],[6],[7]] => 2 [[1,5,7],[2,6],[3],[4],[8]] => 1 [[1,4,7],[2,6],[3],[5],[8]] => 1 [[1,3,7],[2,6],[4],[5],[8]] => 1 [[1,2,7],[3,6],[4],[5],[8]] => 1 [[1,4,7],[2,5],[3],[6],[8]] => 1 [[1,3,7],[2,5],[4],[6],[8]] => 1 [[1,2,7],[3,5],[4],[6],[8]] => 1 [[1,3,7],[2,4],[5],[6],[8]] => 2 [[1,2,7],[3,4],[5],[6],[8]] => 1 [[1,5,6],[2,7],[3],[4],[8]] => 1 [[1,4,6],[2,7],[3],[5],[8]] => 1 [[1,3,6],[2,7],[4],[5],[8]] => 1 [[1,2,6],[3,7],[4],[5],[8]] => 2 [[1,4,5],[2,7],[3],[6],[8]] => 1 [[1,3,5],[2,7],[4],[6],[8]] => 1 [[1,2,5],[3,7],[4],[6],[8]] => 2 [[1,3,4],[2,7],[5],[6],[8]] => 1 [[1,2,4],[3,7],[5],[6],[8]] => 2 [[1,2,3],[4,7],[5],[6],[8]] => 2 [[1,4,6],[2,5],[3],[7],[8]] => 1 [[1,3,6],[2,5],[4],[7],[8]] => 1 [[1,2,6],[3,5],[4],[7],[8]] => 1 [[1,3,6],[2,4],[5],[7],[8]] => 2 [[1,2,6],[3,4],[5],[7],[8]] => 1 [[1,4,5],[2,6],[3],[7],[8]] => 1 [[1,3,5],[2,6],[4],[7],[8]] => 1 [[1,2,5],[3,6],[4],[7],[8]] => 2 [[1,3,4],[2,6],[5],[7],[8]] => 1 [[1,2,4],[3,6],[5],[7],[8]] => 2 [[1,2,3],[4,6],[5],[7],[8]] => 2 [[1,3,5],[2,4],[6],[7],[8]] => 2 [[1,2,5],[3,4],[6],[7],[8]] => 1 [[1,3,4],[2,5],[6],[7],[8]] => 3 [[1,2,4],[3,5],[6],[7],[8]] => 3 [[1,2,3],[4,5],[6],[7],[8]] => 2 [[1,7,8],[2],[3],[4],[5],[6]] => 3 [[1,6,8],[2],[3],[4],[5],[7]] => 2 [[1,5,8],[2],[3],[4],[6],[7]] => 2 [[1,4,8],[2],[3],[5],[6],[7]] => 2 [[1,3,8],[2],[4],[5],[6],[7]] => 2 [[1,2,8],[3],[4],[5],[6],[7]] => 3 [[1,6,7],[2],[3],[4],[5],[8]] => 1 [[1,5,7],[2],[3],[4],[6],[8]] => 1 [[1,4,7],[2],[3],[5],[6],[8]] => 1 [[1,3,7],[2],[4],[5],[6],[8]] => 1 [[1,2,7],[3],[4],[5],[6],[8]] => 2 [[1,5,6],[2],[3],[4],[7],[8]] => 1 [[1,4,6],[2],[3],[5],[7],[8]] => 1 [[1,3,6],[2],[4],[5],[7],[8]] => 1 [[1,2,6],[3],[4],[5],[7],[8]] => 2 [[1,4,5],[2],[3],[6],[7],[8]] => 1 [[1,3,5],[2],[4],[6],[7],[8]] => 1 [[1,2,5],[3],[4],[6],[7],[8]] => 2 [[1,3,4],[2],[5],[6],[7],[8]] => 1 [[1,2,4],[3],[5],[6],[7],[8]] => 2 [[1,2,3],[4],[5],[6],[7],[8]] => 3 [[1,5],[2,6],[3,7],[4,8]] => 2 [[1,4],[2,6],[3,7],[5,8]] => 1 [[1,3],[2,6],[4,7],[5,8]] => 1 [[1,2],[3,6],[4,7],[5,8]] => 1 [[1,4],[2,5],[3,7],[6,8]] => 1 [[1,3],[2,5],[4,7],[6,8]] => 1 [[1,2],[3,5],[4,7],[6,8]] => 1 [[1,3],[2,4],[5,7],[6,8]] => 1 [[1,2],[3,4],[5,7],[6,8]] => 1 [[1,4],[2,5],[3,6],[7,8]] => 1 [[1,3],[2,5],[4,6],[7,8]] => 1 [[1,2],[3,5],[4,6],[7,8]] => 1 [[1,3],[2,4],[5,6],[7,8]] => 1 [[1,2],[3,4],[5,6],[7,8]] => 1 [[1,6],[2,7],[3,8],[4],[5]] => 2 [[1,5],[2,7],[3,8],[4],[6]] => 1 [[1,4],[2,7],[3,8],[5],[6]] => 1 [[1,3],[2,7],[4,8],[5],[6]] => 1 [[1,2],[3,7],[4,8],[5],[6]] => 1 [[1,5],[2,6],[3,8],[4],[7]] => 1 [[1,4],[2,6],[3,8],[5],[7]] => 1 [[1,3],[2,6],[4,8],[5],[7]] => 1 [[1,2],[3,6],[4,8],[5],[7]] => 1 [[1,4],[2,5],[3,8],[6],[7]] => 1 [[1,3],[2,5],[4,8],[6],[7]] => 1 [[1,2],[3,5],[4,8],[6],[7]] => 1 [[1,3],[2,4],[5,8],[6],[7]] => 1 [[1,2],[3,4],[5,8],[6],[7]] => 1 [[1,5],[2,6],[3,7],[4],[8]] => 1 [[1,4],[2,6],[3,7],[5],[8]] => 1 [[1,3],[2,6],[4,7],[5],[8]] => 1 [[1,2],[3,6],[4,7],[5],[8]] => 1 [[1,4],[2,5],[3,7],[6],[8]] => 1 [[1,3],[2,5],[4,7],[6],[8]] => 1 [[1,2],[3,5],[4,7],[6],[8]] => 1 [[1,3],[2,4],[5,7],[6],[8]] => 1 [[1,2],[3,4],[5,7],[6],[8]] => 1 [[1,4],[2,5],[3,6],[7],[8]] => 2 [[1,3],[2,5],[4,6],[7],[8]] => 1 [[1,2],[3,5],[4,6],[7],[8]] => 1 [[1,3],[2,4],[5,6],[7],[8]] => 1 [[1,2],[3,4],[5,6],[7],[8]] => 1 [[1,7],[2,8],[3],[4],[5],[6]] => 2 [[1,6],[2,8],[3],[4],[5],[7]] => 1 [[1,5],[2,8],[3],[4],[6],[7]] => 1 [[1,4],[2,8],[3],[5],[6],[7]] => 1 [[1,3],[2,8],[4],[5],[6],[7]] => 1 [[1,2],[3,8],[4],[5],[6],[7]] => 1 [[1,6],[2,7],[3],[4],[5],[8]] => 1 [[1,5],[2,7],[3],[4],[6],[8]] => 1 [[1,4],[2,7],[3],[5],[6],[8]] => 1 [[1,3],[2,7],[4],[5],[6],[8]] => 1 [[1,2],[3,7],[4],[5],[6],[8]] => 1 [[1,5],[2,6],[3],[4],[7],[8]] => 1 [[1,4],[2,6],[3],[5],[7],[8]] => 1 [[1,3],[2,6],[4],[5],[7],[8]] => 1 [[1,2],[3,6],[4],[5],[7],[8]] => 1 [[1,4],[2,5],[3],[6],[7],[8]] => 1 [[1,3],[2,5],[4],[6],[7],[8]] => 1 [[1,2],[3,5],[4],[6],[7],[8]] => 1 [[1,3],[2,4],[5],[6],[7],[8]] => 2 [[1,2],[3,4],[5],[6],[7],[8]] => 1 [[1,8],[2],[3],[4],[5],[6],[7]] => 2 [[1,7],[2],[3],[4],[5],[6],[8]] => 1 [[1,6],[2],[3],[4],[5],[7],[8]] => 1 [[1,5],[2],[3],[4],[6],[7],[8]] => 1 [[1,4],[2],[3],[5],[6],[7],[8]] => 1 [[1,3],[2],[4],[5],[6],[7],[8]] => 1 [[1,2],[3],[4],[5],[6],[7],[8]] => 2 [[1],[2],[3],[4],[5],[6],[7],[8]] => 1 ----------------------------------------------------------------------------- Created: Aug 11, 2019 at 09:18 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 11, 2019 at 09:18 by Martin Rubey