***************************************************************************** * 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: St000385 ----------------------------------------------------------------------------- Collection: Binary trees ----------------------------------------------------------------------------- Description: The number of vertices with out-degree 1 in a binary tree. See the references for several connections of this statistic. In particular, the number $T(n,k)$ of binary trees with $n$ vertices and $k$ out-degree $1$ vertices is given by $T(n,k) = 0$ for $n-k$ odd and $$T(n,k)=\frac{2^k}{n+1}\binom{n+1}{k}\binom{n+1-k}{(n-k)/2}$$ for $n-k$ is even. ----------------------------------------------------------------------------- References: [1] Triangle read by rows: T(n,k) is the number of binary trees with n edges and having k vertices of outdegree 1 (n>=0, k>=0). A binary tree is a rooted tree in which each vertex has at most two children and each child of a vertex is designated as its left or right child. [[OEIS:A121448]] [2] Copeland, T. Has anyone seen these binary trees (Catalan-type related to the Gegenbauer polynomials and Motzkin paths)? [[MathOverflow:230714]] ----------------------------------------------------------------------------- Code: def statistic(tree): return tree.graph(with_leaves=False).out_degree_sequence().count(1) ----------------------------------------------------------------------------- Statistic values: [.,[.,.]] => 1 [[.,.],.] => 1 [.,[.,[.,.]]] => 2 [.,[[.,.],.]] => 2 [[.,.],[.,.]] => 0 [[.,[.,.]],.] => 2 [[[.,.],.],.] => 2 [.,[.,[.,[.,.]]]] => 3 [.,[.,[[.,.],.]]] => 3 [.,[[.,.],[.,.]]] => 1 [.,[[.,[.,.]],.]] => 3 [.,[[[.,.],.],.]] => 3 [[.,.],[.,[.,.]]] => 1 [[.,.],[[.,.],.]] => 1 [[.,[.,.]],[.,.]] => 1 [[[.,.],.],[.,.]] => 1 [[.,[.,[.,.]]],.] => 3 [[.,[[.,.],.]],.] => 3 [[[.,.],[.,.]],.] => 1 [[[.,[.,.]],.],.] => 3 [[[[.,.],.],.],.] => 3 [.,[.,[.,[.,[.,.]]]]] => 4 [.,[.,[.,[[.,.],.]]]] => 4 [.,[.,[[.,.],[.,.]]]] => 2 [.,[.,[[.,[.,.]],.]]] => 4 [.,[.,[[[.,.],.],.]]] => 4 [.,[[.,.],[.,[.,.]]]] => 2 [.,[[.,.],[[.,.],.]]] => 2 [.,[[.,[.,.]],[.,.]]] => 2 [.,[[[.,.],.],[.,.]]] => 2 [.,[[.,[.,[.,.]]],.]] => 4 [.,[[.,[[.,.],.]],.]] => 4 [.,[[[.,.],[.,.]],.]] => 2 [.,[[[.,[.,.]],.],.]] => 4 [.,[[[[.,.],.],.],.]] => 4 [[.,.],[.,[.,[.,.]]]] => 2 [[.,.],[.,[[.,.],.]]] => 2 [[.,.],[[.,.],[.,.]]] => 0 [[.,.],[[.,[.,.]],.]] => 2 [[.,.],[[[.,.],.],.]] => 2 [[.,[.,.]],[.,[.,.]]] => 2 [[.,[.,.]],[[.,.],.]] => 2 [[[.,.],.],[.,[.,.]]] => 2 [[[.,.],.],[[.,.],.]] => 2 [[.,[.,[.,.]]],[.,.]] => 2 [[.,[[.,.],.]],[.,.]] => 2 [[[.,.],[.,.]],[.,.]] => 0 [[[.,[.,.]],.],[.,.]] => 2 [[[[.,.],.],.],[.,.]] => 2 [[.,[.,[.,[.,.]]]],.] => 4 [[.,[.,[[.,.],.]]],.] => 4 [[.,[[.,.],[.,.]]],.] => 2 [[.,[[.,[.,.]],.]],.] => 4 [[.,[[[.,.],.],.]],.] => 4 [[[.,.],[.,[.,.]]],.] => 2 [[[.,.],[[.,.],.]],.] => 2 [[[.,[.,.]],[.,.]],.] => 2 [[[[.,.],.],[.,.]],.] => 2 [[[.,[.,[.,.]]],.],.] => 4 [[[.,[[.,.],.]],.],.] => 4 [[[[.,.],[.,.]],.],.] => 2 [[[[.,[.,.]],.],.],.] => 4 [[[[[.,.],.],.],.],.] => 4 [.,[.,[.,[.,[.,[.,.]]]]]] => 5 [.,[.,[.,[.,[[.,.],.]]]]] => 5 [.,[.,[.,[[.,.],[.,.]]]]] => 3 [.,[.,[.,[[.,[.,.]],.]]]] => 5 [.,[.,[.,[[[.,.],.],.]]]] => 5 [.,[.,[[.,.],[.,[.,.]]]]] => 3 [.,[.,[[.,.],[[.,.],.]]]] => 3 [.,[.,[[.,[.,.]],[.,.]]]] => 3 [.,[.,[[[.,.],.],[.,.]]]] => 3 [.,[.,[[.,[.,[.,.]]],.]]] => 5 [.,[.,[[.,[[.,.],.]],.]]] => 5 [.,[.,[[[.,.],[.,.]],.]]] => 3 [.,[.,[[[.,[.,.]],.],.]]] => 5 [.,[.,[[[[.,.],.],.],.]]] => 5 [.,[[.,.],[.,[.,[.,.]]]]] => 3 [.,[[.,.],[.,[[.,.],.]]]] => 3 [.,[[.,.],[[.,.],[.,.]]]] => 1 [.,[[.,.],[[.,[.,.]],.]]] => 3 [.,[[.,.],[[[.,.],.],.]]] => 3 [.,[[.,[.,.]],[.,[.,.]]]] => 3 [.,[[.,[.,.]],[[.,.],.]]] => 3 [.,[[[.,.],.],[.,[.,.]]]] => 3 [.,[[[.,.],.],[[.,.],.]]] => 3 [.,[[.,[.,[.,.]]],[.,.]]] => 3 [.,[[.,[[.,.],.]],[.,.]]] => 3 [.,[[[.,.],[.,.]],[.,.]]] => 1 [.,[[[.,[.,.]],.],[.,.]]] => 3 [.,[[[[.,.],.],.],[.,.]]] => 3 [.,[[.,[.,[.,[.,.]]]],.]] => 5 [.,[[.,[.,[[.,.],.]]],.]] => 5 [.,[[.,[[.,.],[.,.]]],.]] => 3 [.,[[.,[[.,[.,.]],.]],.]] => 5 [.,[[.,[[[.,.],.],.]],.]] => 5 [.,[[[.,.],[.,[.,.]]],.]] => 3 [.,[[[.,.],[[.,.],.]],.]] => 3 [.,[[[.,[.,.]],[.,.]],.]] => 3 [.,[[[[.,.],.],[.,.]],.]] => 3 [.,[[[.,[.,[.,.]]],.],.]] => 5 [.,[[[.,[[.,.],.]],.],.]] => 5 [.,[[[[.,.],[.,.]],.],.]] => 3 [.,[[[[.,[.,.]],.],.],.]] => 5 [.,[[[[[.,.],.],.],.],.]] => 5 [[.,.],[.,[.,[.,[.,.]]]]] => 3 [[.,.],[.,[.,[[.,.],.]]]] => 3 [[.,.],[.,[[.,.],[.,.]]]] => 1 [[.,.],[.,[[.,[.,.]],.]]] => 3 [[.,.],[.,[[[.,.],.],.]]] => 3 [[.,.],[[.,.],[.,[.,.]]]] => 1 [[.,.],[[.,.],[[.,.],.]]] => 1 [[.,.],[[.,[.,.]],[.,.]]] => 1 [[.,.],[[[.,.],.],[.,.]]] => 1 [[.,.],[[.,[.,[.,.]]],.]] => 3 [[.,.],[[.,[[.,.],.]],.]] => 3 [[.,.],[[[.,.],[.,.]],.]] => 1 [[.,.],[[[.,[.,.]],.],.]] => 3 [[.,.],[[[[.,.],.],.],.]] => 3 [[.,[.,.]],[.,[.,[.,.]]]] => 3 [[.,[.,.]],[.,[[.,.],.]]] => 3 [[.,[.,.]],[[.,.],[.,.]]] => 1 [[.,[.,.]],[[.,[.,.]],.]] => 3 [[.,[.,.]],[[[.,.],.],.]] => 3 [[[.,.],.],[.,[.,[.,.]]]] => 3 [[[.,.],.],[.,[[.,.],.]]] => 3 [[[.,.],.],[[.,.],[.,.]]] => 1 [[[.,.],.],[[.,[.,.]],.]] => 3 [[[.,.],.],[[[.,.],.],.]] => 3 [[.,[.,[.,.]]],[.,[.,.]]] => 3 [[.,[.,[.,.]]],[[.,.],.]] => 3 [[.,[[.,.],.]],[.,[.,.]]] => 3 [[.,[[.,.],.]],[[.,.],.]] => 3 [[[.,.],[.,.]],[.,[.,.]]] => 1 [[[.,.],[.,.]],[[.,.],.]] => 1 [[[.,[.,.]],.],[.,[.,.]]] => 3 [[[.,[.,.]],.],[[.,.],.]] => 3 [[[[.,.],.],.],[.,[.,.]]] => 3 [[[[.,.],.],.],[[.,.],.]] => 3 [[.,[.,[.,[.,.]]]],[.,.]] => 3 [[.,[.,[[.,.],.]]],[.,.]] => 3 [[.,[[.,.],[.,.]]],[.,.]] => 1 [[.,[[.,[.,.]],.]],[.,.]] => 3 [[.,[[[.,.],.],.]],[.,.]] => 3 [[[.,.],[.,[.,.]]],[.,.]] => 1 [[[.,.],[[.,.],.]],[.,.]] => 1 [[[.,[.,.]],[.,.]],[.,.]] => 1 [[[[.,.],.],[.,.]],[.,.]] => 1 [[[.,[.,[.,.]]],.],[.,.]] => 3 [[[.,[[.,.],.]],.],[.,.]] => 3 [[[[.,.],[.,.]],.],[.,.]] => 1 [[[[.,[.,.]],.],.],[.,.]] => 3 [[[[[.,.],.],.],.],[.,.]] => 3 [[.,[.,[.,[.,[.,.]]]]],.] => 5 [[.,[.,[.,[[.,.],.]]]],.] => 5 [[.,[.,[[.,.],[.,.]]]],.] => 3 [[.,[.,[[.,[.,.]],.]]],.] => 5 [[.,[.,[[[.,.],.],.]]],.] => 5 [[.,[[.,.],[.,[.,.]]]],.] => 3 [[.,[[.,.],[[.,.],.]]],.] => 3 [[.,[[.,[.,.]],[.,.]]],.] => 3 [[.,[[[.,.],.],[.,.]]],.] => 3 [[.,[[.,[.,[.,.]]],.]],.] => 5 [[.,[[.,[[.,.],.]],.]],.] => 5 [[.,[[[.,.],[.,.]],.]],.] => 3 [[.,[[[.,[.,.]],.],.]],.] => 5 [[.,[[[[.,.],.],.],.]],.] => 5 [[[.,.],[.,[.,[.,.]]]],.] => 3 [[[.,.],[.,[[.,.],.]]],.] => 3 [[[.,.],[[.,.],[.,.]]],.] => 1 [[[.,.],[[.,[.,.]],.]],.] => 3 [[[.,.],[[[.,.],.],.]],.] => 3 [[[.,[.,.]],[.,[.,.]]],.] => 3 [[[.,[.,.]],[[.,.],.]],.] => 3 [[[[.,.],.],[.,[.,.]]],.] => 3 [[[[.,.],.],[[.,.],.]],.] => 3 [[[.,[.,[.,.]]],[.,.]],.] => 3 [[[.,[[.,.],.]],[.,.]],.] => 3 [[[[.,.],[.,.]],[.,.]],.] => 1 [[[[.,[.,.]],.],[.,.]],.] => 3 [[[[[.,.],.],.],[.,.]],.] => 3 [[[.,[.,[.,[.,.]]]],.],.] => 5 [[[.,[.,[[.,.],.]]],.],.] => 5 [[[.,[[.,.],[.,.]]],.],.] => 3 [[[.,[[.,[.,.]],.]],.],.] => 5 [[[.,[[[.,.],.],.]],.],.] => 5 [[[[.,.],[.,[.,.]]],.],.] => 3 [[[[.,.],[[.,.],.]],.],.] => 3 [[[[.,[.,.]],[.,.]],.],.] => 3 [[[[[.,.],.],[.,.]],.],.] => 3 [[[[.,[.,[.,.]]],.],.],.] => 5 [[[[.,[[.,.],.]],.],.],.] => 5 [[[[[.,.],[.,.]],.],.],.] => 3 [[[[[.,[.,.]],.],.],.],.] => 5 [[[[[[.,.],.],.],.],.],.] => 5 [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 6 [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6 [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 4 [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 6 [.,[.,[.,[.,[[[.,.],.],.]]]]] => 6 [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 4 [.,[.,[.,[[.,.],[[.,.],.]]]]] => 4 [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 4 [.,[.,[.,[[[.,.],.],[.,.]]]]] => 4 [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 6 [.,[.,[.,[[.,[[.,.],.]],.]]]] => 6 [.,[.,[.,[[[.,.],[.,.]],.]]]] => 4 [.,[.,[.,[[[.,[.,.]],.],.]]]] => 6 [.,[.,[.,[[[[.,.],.],.],.]]]] => 6 [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 4 [.,[.,[[.,.],[.,[[.,.],.]]]]] => 4 [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2 [.,[.,[[.,.],[[.,[.,.]],.]]]] => 4 [.,[.,[[.,.],[[[.,.],.],.]]]] => 4 [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 4 [.,[.,[[.,[.,.]],[[.,.],.]]]] => 4 [.,[.,[[[.,.],.],[.,[.,.]]]]] => 4 [.,[.,[[[.,.],.],[[.,.],.]]]] => 4 [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4 [.,[.,[[.,[[.,.],.]],[.,.]]]] => 4 [.,[.,[[[.,.],[.,.]],[.,.]]]] => 2 [.,[.,[[[.,[.,.]],.],[.,.]]]] => 4 [.,[.,[[[[.,.],.],.],[.,.]]]] => 4 [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 6 [.,[.,[[.,[.,[[.,.],.]]],.]]] => 6 [.,[.,[[.,[[.,.],[.,.]]],.]]] => 4 [.,[.,[[.,[[.,[.,.]],.]],.]]] => 6 [.,[.,[[.,[[[.,.],.],.]],.]]] => 6 [.,[.,[[[.,.],[.,[.,.]]],.]]] => 4 [.,[.,[[[.,.],[[.,.],.]],.]]] => 4 [.,[.,[[[.,[.,.]],[.,.]],.]]] => 4 [.,[.,[[[[.,.],.],[.,.]],.]]] => 4 [.,[.,[[[.,[.,[.,.]]],.],.]]] => 6 [.,[.,[[[.,[[.,.],.]],.],.]]] => 6 [.,[.,[[[[.,.],[.,.]],.],.]]] => 4 [.,[.,[[[[.,[.,.]],.],.],.]]] => 6 [.,[.,[[[[[.,.],.],.],.],.]]] => 6 [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 4 [.,[[.,.],[.,[.,[[.,.],.]]]]] => 4 [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2 [.,[[.,.],[.,[[.,[.,.]],.]]]] => 4 [.,[[.,.],[.,[[[.,.],.],.]]]] => 4 [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2 [.,[[.,.],[[.,.],[[.,.],.]]]] => 2 [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2 [.,[[.,.],[[[.,.],.],[.,.]]]] => 2 [.,[[.,.],[[.,[.,[.,.]]],.]]] => 4 [.,[[.,.],[[.,[[.,.],.]],.]]] => 4 [.,[[.,.],[[[.,.],[.,.]],.]]] => 2 [.,[[.,.],[[[.,[.,.]],.],.]]] => 4 [.,[[.,.],[[[[.,.],.],.],.]]] => 4 [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 4 [.,[[.,[.,.]],[.,[[.,.],.]]]] => 4 [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2 [.,[[.,[.,.]],[[.,[.,.]],.]]] => 4 [.,[[.,[.,.]],[[[.,.],.],.]]] => 4 [.,[[[.,.],.],[.,[.,[.,.]]]]] => 4 [.,[[[.,.],.],[.,[[.,.],.]]]] => 4 [.,[[[.,.],.],[[.,.],[.,.]]]] => 2 [.,[[[.,.],.],[[.,[.,.]],.]]] => 4 [.,[[[.,.],.],[[[.,.],.],.]]] => 4 [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4 [.,[[.,[.,[.,.]]],[[.,.],.]]] => 4 [.,[[.,[[.,.],.]],[.,[.,.]]]] => 4 [.,[[.,[[.,.],.]],[[.,.],.]]] => 4 [.,[[[.,.],[.,.]],[.,[.,.]]]] => 2 [.,[[[.,.],[.,.]],[[.,.],.]]] => 2 [.,[[[.,[.,.]],.],[.,[.,.]]]] => 4 [.,[[[.,[.,.]],.],[[.,.],.]]] => 4 [.,[[[[.,.],.],.],[.,[.,.]]]] => 4 [.,[[[[.,.],.],.],[[.,.],.]]] => 4 [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 4 [.,[[.,[.,[[.,.],.]]],[.,.]]] => 4 [.,[[.,[[.,.],[.,.]]],[.,.]]] => 2 [.,[[.,[[.,[.,.]],.]],[.,.]]] => 4 [.,[[.,[[[.,.],.],.]],[.,.]]] => 4 [.,[[[.,.],[.,[.,.]]],[.,.]]] => 2 [.,[[[.,.],[[.,.],.]],[.,.]]] => 2 [.,[[[.,[.,.]],[.,.]],[.,.]]] => 2 [.,[[[[.,.],.],[.,.]],[.,.]]] => 2 [.,[[[.,[.,[.,.]]],.],[.,.]]] => 4 [.,[[[.,[[.,.],.]],.],[.,.]]] => 4 [.,[[[[.,.],[.,.]],.],[.,.]]] => 2 [.,[[[[.,[.,.]],.],.],[.,.]]] => 4 [.,[[[[[.,.],.],.],.],[.,.]]] => 4 [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 6 [.,[[.,[.,[.,[[.,.],.]]]],.]] => 6 [.,[[.,[.,[[.,.],[.,.]]]],.]] => 4 [.,[[.,[.,[[.,[.,.]],.]]],.]] => 6 [.,[[.,[.,[[[.,.],.],.]]],.]] => 6 [.,[[.,[[.,.],[.,[.,.]]]],.]] => 4 [.,[[.,[[.,.],[[.,.],.]]],.]] => 4 [.,[[.,[[.,[.,.]],[.,.]]],.]] => 4 [.,[[.,[[[.,.],.],[.,.]]],.]] => 4 [.,[[.,[[.,[.,[.,.]]],.]],.]] => 6 [.,[[.,[[.,[[.,.],.]],.]],.]] => 6 [.,[[.,[[[.,.],[.,.]],.]],.]] => 4 [.,[[.,[[[.,[.,.]],.],.]],.]] => 6 [.,[[.,[[[[.,.],.],.],.]],.]] => 6 [.,[[[.,.],[.,[.,[.,.]]]],.]] => 4 [.,[[[.,.],[.,[[.,.],.]]],.]] => 4 [.,[[[.,.],[[.,.],[.,.]]],.]] => 2 [.,[[[.,.],[[.,[.,.]],.]],.]] => 4 [.,[[[.,.],[[[.,.],.],.]],.]] => 4 [.,[[[.,[.,.]],[.,[.,.]]],.]] => 4 [.,[[[.,[.,.]],[[.,.],.]],.]] => 4 [.,[[[[.,.],.],[.,[.,.]]],.]] => 4 [.,[[[[.,.],.],[[.,.],.]],.]] => 4 [.,[[[.,[.,[.,.]]],[.,.]],.]] => 4 [.,[[[.,[[.,.],.]],[.,.]],.]] => 4 [.,[[[[.,.],[.,.]],[.,.]],.]] => 2 [.,[[[[.,[.,.]],.],[.,.]],.]] => 4 [.,[[[[[.,.],.],.],[.,.]],.]] => 4 [.,[[[.,[.,[.,[.,.]]]],.],.]] => 6 [.,[[[.,[.,[[.,.],.]]],.],.]] => 6 [.,[[[.,[[.,.],[.,.]]],.],.]] => 4 [.,[[[.,[[.,[.,.]],.]],.],.]] => 6 [.,[[[.,[[[.,.],.],.]],.],.]] => 6 [.,[[[[.,.],[.,[.,.]]],.],.]] => 4 [.,[[[[.,.],[[.,.],.]],.],.]] => 4 [.,[[[[.,[.,.]],[.,.]],.],.]] => 4 [.,[[[[[.,.],.],[.,.]],.],.]] => 4 [.,[[[[.,[.,[.,.]]],.],.],.]] => 6 [.,[[[[.,[[.,.],.]],.],.],.]] => 6 [.,[[[[[.,.],[.,.]],.],.],.]] => 4 [.,[[[[[.,[.,.]],.],.],.],.]] => 6 [.,[[[[[[.,.],.],.],.],.],.]] => 6 [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 4 [[.,.],[.,[.,[.,[[.,.],.]]]]] => 4 [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2 [[.,.],[.,[.,[[.,[.,.]],.]]]] => 4 [[.,.],[.,[.,[[[.,.],.],.]]]] => 4 [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2 [[.,.],[.,[[.,.],[[.,.],.]]]] => 2 [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2 [[.,.],[.,[[[.,.],.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,[.,.]]],.]]] => 4 [[.,.],[.,[[.,[[.,.],.]],.]]] => 4 [[.,.],[.,[[[.,.],[.,.]],.]]] => 2 [[.,.],[.,[[[.,[.,.]],.],.]]] => 4 [[.,.],[.,[[[[.,.],.],.],.]]] => 4 [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2 [[.,.],[[.,.],[.,[[.,.],.]]]] => 2 [[.,.],[[.,.],[[.,.],[.,.]]]] => 0 [[.,.],[[.,.],[[.,[.,.]],.]]] => 2 [[.,.],[[.,.],[[[.,.],.],.]]] => 2 [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2 [[.,.],[[.,[.,.]],[[.,.],.]]] => 2 [[.,.],[[[.,.],.],[.,[.,.]]]] => 2 [[.,.],[[[.,.],.],[[.,.],.]]] => 2 [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2 [[.,.],[[.,[[.,.],.]],[.,.]]] => 2 [[.,.],[[[.,.],[.,.]],[.,.]]] => 0 [[.,.],[[[.,[.,.]],.],[.,.]]] => 2 [[.,.],[[[[.,.],.],.],[.,.]]] => 2 [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4 [[.,.],[[.,[.,[[.,.],.]]],.]] => 4 [[.,.],[[.,[[.,.],[.,.]]],.]] => 2 [[.,.],[[.,[[.,[.,.]],.]],.]] => 4 [[.,.],[[.,[[[.,.],.],.]],.]] => 4 [[.,.],[[[.,.],[.,[.,.]]],.]] => 2 [[.,.],[[[.,.],[[.,.],.]],.]] => 2 [[.,.],[[[.,[.,.]],[.,.]],.]] => 2 [[.,.],[[[[.,.],.],[.,.]],.]] => 2 [[.,.],[[[.,[.,[.,.]]],.],.]] => 4 [[.,.],[[[.,[[.,.],.]],.],.]] => 4 [[.,.],[[[[.,.],[.,.]],.],.]] => 2 [[.,.],[[[[.,[.,.]],.],.],.]] => 4 [[.,.],[[[[[.,.],.],.],.],.]] => 4 [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 4 [[.,[.,.]],[.,[.,[[.,.],.]]]] => 4 [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2 [[.,[.,.]],[.,[[.,[.,.]],.]]] => 4 [[.,[.,.]],[.,[[[.,.],.],.]]] => 4 [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2 [[.,[.,.]],[[.,.],[[.,.],.]]] => 2 [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2 [[.,[.,.]],[[[.,.],.],[.,.]]] => 2 [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4 [[.,[.,.]],[[.,[[.,.],.]],.]] => 4 [[.,[.,.]],[[[.,.],[.,.]],.]] => 2 [[.,[.,.]],[[[.,[.,.]],.],.]] => 4 [[.,[.,.]],[[[[.,.],.],.],.]] => 4 [[[.,.],.],[.,[.,[.,[.,.]]]]] => 4 [[[.,.],.],[.,[.,[[.,.],.]]]] => 4 [[[.,.],.],[.,[[.,.],[.,.]]]] => 2 [[[.,.],.],[.,[[.,[.,.]],.]]] => 4 [[[.,.],.],[.,[[[.,.],.],.]]] => 4 [[[.,.],.],[[.,.],[.,[.,.]]]] => 2 [[[.,.],.],[[.,.],[[.,.],.]]] => 2 [[[.,.],.],[[.,[.,.]],[.,.]]] => 2 [[[.,.],.],[[[.,.],.],[.,.]]] => 2 [[[.,.],.],[[.,[.,[.,.]]],.]] => 4 [[[.,.],.],[[.,[[.,.],.]],.]] => 4 [[[.,.],.],[[[.,.],[.,.]],.]] => 2 [[[.,.],.],[[[.,[.,.]],.],.]] => 4 [[[.,.],.],[[[[.,.],.],.],.]] => 4 [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 4 [[.,[.,[.,.]]],[.,[[.,.],.]]] => 4 [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2 [[.,[.,[.,.]]],[[.,[.,.]],.]] => 4 [[.,[.,[.,.]]],[[[.,.],.],.]] => 4 [[.,[[.,.],.]],[.,[.,[.,.]]]] => 4 [[.,[[.,.],.]],[.,[[.,.],.]]] => 4 [[.,[[.,.],.]],[[.,.],[.,.]]] => 2 [[.,[[.,.],.]],[[.,[.,.]],.]] => 4 [[.,[[.,.],.]],[[[.,.],.],.]] => 4 [[[.,.],[.,.]],[.,[.,[.,.]]]] => 2 [[[.,.],[.,.]],[.,[[.,.],.]]] => 2 [[[.,.],[.,.]],[[.,.],[.,.]]] => 0 [[[.,.],[.,.]],[[.,[.,.]],.]] => 2 [[[.,.],[.,.]],[[[.,.],.],.]] => 2 [[[.,[.,.]],.],[.,[.,[.,.]]]] => 4 [[[.,[.,.]],.],[.,[[.,.],.]]] => 4 [[[.,[.,.]],.],[[.,.],[.,.]]] => 2 [[[.,[.,.]],.],[[.,[.,.]],.]] => 4 [[[.,[.,.]],.],[[[.,.],.],.]] => 4 [[[[.,.],.],.],[.,[.,[.,.]]]] => 4 [[[[.,.],.],.],[.,[[.,.],.]]] => 4 [[[[.,.],.],.],[[.,.],[.,.]]] => 2 [[[[.,.],.],.],[[.,[.,.]],.]] => 4 [[[[.,.],.],.],[[[.,.],.],.]] => 4 [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 4 [[.,[.,[.,[.,.]]]],[[.,.],.]] => 4 [[.,[.,[[.,.],.]]],[.,[.,.]]] => 4 [[.,[.,[[.,.],.]]],[[.,.],.]] => 4 [[.,[[.,.],[.,.]]],[.,[.,.]]] => 2 [[.,[[.,.],[.,.]]],[[.,.],.]] => 2 [[.,[[.,[.,.]],.]],[.,[.,.]]] => 4 [[.,[[.,[.,.]],.]],[[.,.],.]] => 4 [[.,[[[.,.],.],.]],[.,[.,.]]] => 4 [[.,[[[.,.],.],.]],[[.,.],.]] => 4 [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2 [[[.,.],[.,[.,.]]],[[.,.],.]] => 2 [[[.,.],[[.,.],.]],[.,[.,.]]] => 2 [[[.,.],[[.,.],.]],[[.,.],.]] => 2 [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2 [[[.,[.,.]],[.,.]],[[.,.],.]] => 2 [[[[.,.],.],[.,.]],[.,[.,.]]] => 2 [[[[.,.],.],[.,.]],[[.,.],.]] => 2 [[[.,[.,[.,.]]],.],[.,[.,.]]] => 4 [[[.,[.,[.,.]]],.],[[.,.],.]] => 4 [[[.,[[.,.],.]],.],[.,[.,.]]] => 4 [[[.,[[.,.],.]],.],[[.,.],.]] => 4 [[[[.,.],[.,.]],.],[.,[.,.]]] => 2 [[[[.,.],[.,.]],.],[[.,.],.]] => 2 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[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => 3 [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => 3 [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => 3 [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => 5 [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => 5 [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => 3 [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => 5 [.,[[.,.],[[[[[.,.],.],.],.],.]]] => 5 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 5 [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 5 [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 3 [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 5 [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => 5 [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 3 [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 3 [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 3 [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => 3 [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => 5 [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => 5 [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => 3 [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => 5 [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => 5 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 5 [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => 5 [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => 3 [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => 5 [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => 5 [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => 3 [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => 3 [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => 3 [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => 3 [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => 5 [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => 5 [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => 3 [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => 5 [.,[[[.,.],.],[[[[.,.],.],.],.]]] => 5 [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 5 [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 5 [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 3 [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => 5 [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => 5 [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => 5 [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => 5 [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => 3 [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => 5 [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => 5 [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 3 [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 3 [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 1 [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 3 [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 3 [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => 5 [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => 5 [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => 3 [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => 5 [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => 5 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => 5 [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => 5 [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => 3 [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => 5 [.,[[[[.,.],.],.],[[[.,.],.],.]]] => 5 [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 5 [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => 5 [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => 5 [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => 5 [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => 3 [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => 3 [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => 5 [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => 5 [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => 5 [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => 5 [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => 3 [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => 3 [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => 3 [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => 3 [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => 3 [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => 3 [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => 3 [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 3 [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => 5 [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => 5 [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => 5 [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => 5 [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => 3 [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 3 [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => 5 [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => 5 [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => 5 [.,[[[[[.,.],.],.],.],[[.,.],.]]] => 5 [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 5 [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => 5 [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => 3 [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => 5 [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => 5 [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => 3 [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => 3 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => 3 [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => 3 [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => 5 [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => 5 [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => 3 [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => 5 [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => 5 [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => 3 [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => 3 [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => 1 [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => 3 [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => 3 [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => 3 [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => 3 [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => 3 [.,[[[[.,.],.],[[.,.],.]],[.,.]]] => 3 [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => 3 [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => 3 [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 1 [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => 3 [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => 3 [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => 5 [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => 5 [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 3 [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => 5 [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => 5 [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => 3 [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => 3 [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => 3 [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => 3 [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => 5 [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => 5 [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => 3 [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => 5 [.,[[[[[[.,.],.],.],.],.],[.,.]]] => 5 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => 7 [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => 7 [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => 5 [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => 7 [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => 7 [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => 5 [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => 5 [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => 5 [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => 5 [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => 7 [.,[[.,[.,[[.,[[.,.],.]],.]]],.]] => 7 [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => 5 [.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => 7 [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => 7 [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => 5 [.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => 5 [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => 3 [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => 5 [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => 5 [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => 5 [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => 5 [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => 5 [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => 5 [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => 5 [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => 5 [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 3 [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => 5 [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => 5 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => 7 [.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => 7 [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 5 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 7 [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => 7 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => 5 [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => 5 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 5 [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => 5 [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => 7 [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => 7 [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => 5 [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => 7 [.,[[.,[[[[[.,.],.],.],.],.]],.]] => 7 [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => 5 [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => 5 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[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => 5 [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => 5 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 3 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 1 [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => 3 [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => 3 [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 3 [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3 [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => 3 [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => 3 [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 3 [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => 3 [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => 1 [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => 3 [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => 3 [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => 5 [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => 5 [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => 3 [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => 5 [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => 5 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => 3 [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => 3 [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => 3 [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => 3 [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => 5 [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => 5 [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => 3 [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => 5 [[.,.],[.,[[[[[.,.],.],.],.],.]]] => 5 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 3 [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3 [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 1 [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 3 [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => 3 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 1 [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 1 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 1 [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => 1 [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 3 [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 3 [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => 1 [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => 3 [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 3 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 3 [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3 [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 1 [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 3 [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 3 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => 3 [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => 3 [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => 1 [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => 3 [[.,.],[[[.,.],.],[[[.,.],.],.]]] => 3 [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 3 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3 [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => 3 [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 3 [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => 1 [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => 1 [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => 3 [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => 3 [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => 3 [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 3 [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => 3 [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => 1 [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 3 [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 3 [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 1 [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 1 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 1 [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 1 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 3 [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 3 [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 1 [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 3 [[.,.],[[[[[.,.],.],.],.],[.,.]]] => 3 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 5 [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 5 [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 3 [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 5 [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 5 [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 3 [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 3 [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 3 [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 3 [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 5 [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 5 [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 3 [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 5 [[.,.],[[.,[[[[.,.],.],.],.]],.]] => 5 [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 3 [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 3 [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 1 [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 3 [[.,.],[[[.,.],[[[.,.],.],.]],.]] => 3 [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 3 [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 3 [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 3 [[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3 [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 3 [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 3 [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 1 [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 3 [[.,.],[[[[[.,.],.],.],[.,.]],.]] => 3 [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 5 [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 5 [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 3 [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 5 [[.,.],[[[.,[[[.,.],.],.]],.],.]] => 5 [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 3 [[.,.],[[[[.,.],[[.,.],.]],.],.]] => 3 [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 3 [[.,.],[[[[[.,.],.],[.,.]],.],.]] => 3 [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 5 [[.,.],[[[[.,[[.,.],.]],.],.],.]] => 5 [[.,.],[[[[[.,.],[.,.]],.],.],.]] => 3 [[.,.],[[[[[.,[.,.]],.],.],.],.]] => 5 [[.,.],[[[[[[.,.],.],.],.],.],.]] => 5 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 5 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 5 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 3 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 5 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 5 [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 3 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 3 [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 3 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 5 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 5 [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 3 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 5 [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 5 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 3 ----------------------------------------------------------------------------- Created: Feb 10, 2016 at 09:37 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Feb 10, 2016 at 09:57 by Christian Stump