***************************************************************************** * 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: St000414 ----------------------------------------------------------------------------- Collection: Binary trees ----------------------------------------------------------------------------- Description: The binary logarithm of the number of binary trees with the same underlying unordered tree. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: @cached_function def Binary_to_Rooted(n): return [RootedTree(S) for S in BinaryTrees(n)] def statistic(tree): T = RootedTree(tree) return ZZ(Binary_to_Rooted(tree.node_number()).count(T)).log(2) ----------------------------------------------------------------------------- Statistic values: [.,[.,.]] => 1 [[.,.],.] => 1 [.,[.,[.,.]]] => 2 [.,[[.,.],.]] => 2 [[.,.],[.,.]] => 0 [[.,[.,.]],.] => 2 [[[.,.],.],.] => 2 [.,[.,[.,[.,.]]]] => 3 [.,[.,[[.,.],.]]] => 3 [.,[[.,.],[.,.]]] => 1 [.,[[.,[.,.]],.]] => 3 [.,[[[.,.],.],.]] => 3 [[.,.],[.,[.,.]]] => 2 [[.,.],[[.,.],.]] => 2 [[.,[.,.]],[.,.]] => 2 [[[.,.],.],[.,.]] => 2 [[.,[.,[.,.]]],.] => 3 [[.,[[.,.],.]],.] => 3 [[[.,.],[.,.]],.] => 1 [[[.,[.,.]],.],.] => 3 [[[[.,.],.],.],.] => 3 [.,[.,[.,[.,[.,.]]]]] => 4 [.,[.,[.,[[.,.],.]]]] => 4 [.,[.,[[.,.],[.,.]]]] => 2 [.,[.,[[.,[.,.]],.]]] => 4 [.,[.,[[[.,.],.],.]]] => 4 [.,[[.,.],[.,[.,.]]]] => 3 [.,[[.,.],[[.,.],.]]] => 3 [.,[[.,[.,.]],[.,.]]] => 3 [.,[[[.,.],.],[.,.]]] => 3 [.,[[.,[.,[.,.]]],.]] => 4 [.,[[.,[[.,.],.]],.]] => 4 [.,[[[.,.],[.,.]],.]] => 2 [.,[[[.,[.,.]],.],.]] => 4 [.,[[[[.,.],.],.],.]] => 4 [[.,.],[.,[.,[.,.]]]] => 3 [[.,.],[.,[[.,.],.]]] => 3 [[.,.],[[.,.],[.,.]]] => 1 [[.,.],[[.,[.,.]],.]] => 3 [[.,.],[[[.,.],.],.]] => 3 [[.,[.,.]],[.,[.,.]]] => 2 [[.,[.,.]],[[.,.],.]] => 2 [[[.,.],.],[.,[.,.]]] => 2 [[[.,.],.],[[.,.],.]] => 2 [[.,[.,[.,.]]],[.,.]] => 3 [[.,[[.,.],.]],[.,.]] => 3 [[[.,.],[.,.]],[.,.]] => 1 [[[.,[.,.]],.],[.,.]] => 3 [[[[.,.],.],.],[.,.]] => 3 [[.,[.,[.,[.,.]]]],.] => 4 [[.,[.,[[.,.],.]]],.] => 4 [[.,[[.,.],[.,.]]],.] => 2 [[.,[[.,[.,.]],.]],.] => 4 [[.,[[[.,.],.],.]],.] => 4 [[[.,.],[.,[.,.]]],.] => 3 [[[.,.],[[.,.],.]],.] => 3 [[[.,[.,.]],[.,.]],.] => 3 [[[[.,.],.],[.,.]],.] => 3 [[[.,[.,[.,.]]],.],.] => 4 [[[.,[[.,.],.]],.],.] => 4 [[[[.,.],[.,.]],.],.] => 2 [[[[.,[.,.]],.],.],.] => 4 [[[[[.,.],.],.],.],.] => 4 [.,[.,[.,[.,[.,[.,.]]]]]] => 5 [.,[.,[.,[.,[[.,.],.]]]]] => 5 [.,[.,[.,[[.,.],[.,.]]]]] => 3 [.,[.,[.,[[.,[.,.]],.]]]] => 5 [.,[.,[.,[[[.,.],.],.]]]] => 5 [.,[.,[[.,.],[.,[.,.]]]]] => 4 [.,[.,[[.,.],[[.,.],.]]]] => 4 [.,[.,[[.,[.,.]],[.,.]]]] => 4 [.,[.,[[[.,.],.],[.,.]]]] => 4 [.,[.,[[.,[.,[.,.]]],.]]] => 5 [.,[.,[[.,[[.,.],.]],.]]] => 5 [.,[.,[[[.,.],[.,.]],.]]] => 3 [.,[.,[[[.,[.,.]],.],.]]] => 5 [.,[.,[[[[.,.],.],.],.]]] => 5 [.,[[.,.],[.,[.,[.,.]]]]] => 4 [.,[[.,.],[.,[[.,.],.]]]] => 4 [.,[[.,.],[[.,.],[.,.]]]] => 2 [.,[[.,.],[[.,[.,.]],.]]] => 4 [.,[[.,.],[[[.,.],.],.]]] => 4 [.,[[.,[.,.]],[.,[.,.]]]] => 3 [.,[[.,[.,.]],[[.,.],.]]] => 3 [.,[[[.,.],.],[.,[.,.]]]] => 3 [.,[[[.,.],.],[[.,.],.]]] => 3 [.,[[.,[.,[.,.]]],[.,.]]] => 4 [.,[[.,[[.,.],.]],[.,.]]] => 4 [.,[[[.,.],[.,.]],[.,.]]] => 2 [.,[[[.,[.,.]],.],[.,.]]] => 4 [.,[[[[.,.],.],.],[.,.]]] => 4 [.,[[.,[.,[.,[.,.]]]],.]] => 5 [.,[[.,[.,[[.,.],.]]],.]] => 5 [.,[[.,[[.,.],[.,.]]],.]] => 3 [.,[[.,[[.,[.,.]],.]],.]] => 5 [.,[[.,[[[.,.],.],.]],.]] => 5 [.,[[[.,.],[.,[.,.]]],.]] => 4 [.,[[[.,.],[[.,.],.]],.]] => 4 [.,[[[.,[.,.]],[.,.]],.]] => 4 [.,[[[[.,.],.],[.,.]],.]] => 4 [.,[[[.,[.,[.,.]]],.],.]] => 5 [.,[[[.,[[.,.],.]],.],.]] => 5 [.,[[[[.,.],[.,.]],.],.]] => 3 [.,[[[[.,[.,.]],.],.],.]] => 5 [.,[[[[[.,.],.],.],.],.]] => 5 [[.,.],[.,[.,[.,[.,.]]]]] => 4 [[.,.],[.,[.,[[.,.],.]]]] => 4 [[.,.],[.,[[.,.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,.]],.]]] => 4 [[.,.],[.,[[[.,.],.],.]]] => 4 [[.,.],[[.,.],[.,[.,.]]]] => 3 [[.,.],[[.,.],[[.,.],.]]] => 3 [[.,.],[[.,[.,.]],[.,.]]] => 3 [[.,.],[[[.,.],.],[.,.]]] => 3 [[.,.],[[.,[.,[.,.]]],.]] => 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 [[[.,.],[.,[.,.]]],[.,.]] => 3 [[[.,.],[[.,.],.]],[.,.]] => 3 [[[.,[.,.]],[.,.]],[.,.]] => 3 [[[[.,.],.],[.,.]],[.,.]] => 3 [[[.,[.,[.,.]]],.],[.,.]] => 4 [[[.,[[.,.],.]],.],[.,.]] => 4 [[[[.,.],[.,.]],.],[.,.]] => 2 [[[[.,[.,.]],.],.],[.,.]] => 4 [[[[[.,.],.],.],.],[.,.]] => 4 [[.,[.,[.,[.,[.,.]]]]],.] => 5 [[.,[.,[.,[[.,.],.]]]],.] => 5 [[.,[.,[[.,.],[.,.]]]],.] => 3 [[.,[.,[[.,[.,.]],.]]],.] => 5 [[.,[.,[[[.,.],.],.]]],.] => 5 [[.,[[.,.],[.,[.,.]]]],.] => 4 [[.,[[.,.],[[.,.],.]]],.] => 4 [[.,[[.,[.,.]],[.,.]]],.] => 4 [[.,[[[.,.],.],[.,.]]],.] => 4 [[.,[[.,[.,[.,.]]],.]],.] => 5 [[.,[[.,[[.,.],.]],.]],.] => 5 [[.,[[[.,.],[.,.]],.]],.] => 3 [[.,[[[.,[.,.]],.],.]],.] => 5 [[.,[[[[.,.],.],.],.]],.] => 5 [[[.,.],[.,[.,[.,.]]]],.] => 4 [[[.,.],[.,[[.,.],.]]],.] => 4 [[[.,.],[[.,.],[.,.]]],.] => 2 [[[.,.],[[.,[.,.]],.]],.] => 4 [[[.,.],[[[.,.],.],.]],.] => 4 [[[.,[.,.]],[.,[.,.]]],.] => 3 [[[.,[.,.]],[[.,.],.]],.] => 3 [[[[.,.],.],[.,[.,.]]],.] => 3 [[[[.,.],.],[[.,.],.]],.] => 3 [[[.,[.,[.,.]]],[.,.]],.] => 4 [[[.,[[.,.],.]],[.,.]],.] => 4 [[[[.,.],[.,.]],[.,.]],.] => 2 [[[[.,[.,.]],.],[.,.]],.] => 4 [[[[[.,.],.],.],[.,.]],.] => 4 [[[.,[.,[.,[.,.]]]],.],.] => 5 [[[.,[.,[[.,.],.]]],.],.] => 5 [[[.,[[.,.],[.,.]]],.],.] => 3 [[[.,[[.,[.,.]],.]],.],.] => 5 [[[.,[[[.,.],.],.]],.],.] => 5 [[[[.,.],[.,[.,.]]],.],.] => 4 [[[[.,.],[[.,.],.]],.],.] => 4 [[[[.,[.,.]],[.,.]],.],.] => 4 [[[[[.,.],.],[.,.]],.],.] => 4 [[[[.,[.,[.,.]]],.],.],.] => 5 [[[[.,[[.,.],.]],.],.],.] => 5 [[[[[.,.],[.,.]],.],.],.] => 3 [[[[[.,[.,.]],.],.],.],.] => 5 [[[[[[.,.],.],.],.],.],.] => 5 [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 6 [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6 [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 4 [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 6 [.,[.,[.,[.,[[[.,.],.],.]]]]] => 6 [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 5 [.,[.,[.,[[.,.],[[.,.],.]]]]] => 5 [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5 [.,[.,[.,[[[.,.],.],[.,.]]]]] => 5 [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 6 [.,[.,[.,[[.,[[.,.],.]],.]]]] => 6 [.,[.,[.,[[[.,.],[.,.]],.]]]] => 4 [.,[.,[.,[[[.,[.,.]],.],.]]]] => 6 [.,[.,[.,[[[[.,.],.],.],.]]]] => 6 [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 5 [.,[.,[[.,.],[.,[[.,.],.]]]]] => 5 [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3 [.,[.,[[.,.],[[.,[.,.]],.]]]] => 5 [.,[.,[[.,.],[[[.,.],.],.]]]] => 5 [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 4 [.,[.,[[.,[.,.]],[[.,.],.]]]] => 4 [.,[.,[[[.,.],.],[.,[.,.]]]]] => 4 [.,[.,[[[.,.],.],[[.,.],.]]]] => 4 [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 5 [.,[.,[[.,[[.,.],.]],[.,.]]]] => 5 [.,[.,[[[.,.],[.,.]],[.,.]]]] => 3 [.,[.,[[[.,[.,.]],.],[.,.]]]] => 5 [.,[.,[[[[.,.],.],.],[.,.]]]] => 5 [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 6 [.,[.,[[.,[.,[[.,.],.]]],.]]] => 6 [.,[.,[[.,[[.,.],[.,.]]],.]]] => 4 [.,[.,[[.,[[.,[.,.]],.]],.]]] => 6 [.,[.,[[.,[[[.,.],.],.]],.]]] => 6 [.,[.,[[[.,.],[.,[.,.]]],.]]] => 5 [.,[.,[[[.,.],[[.,.],.]],.]]] => 5 [.,[.,[[[.,[.,.]],[.,.]],.]]] => 5 [.,[.,[[[[.,.],.],[.,.]],.]]] => 5 [.,[.,[[[.,[.,[.,.]]],.],.]]] => 6 [.,[.,[[[.,[[.,.],.]],.],.]]] => 6 [.,[.,[[[[.,.],[.,.]],.],.]]] => 4 [.,[.,[[[[.,[.,.]],.],.],.]]] => 6 [.,[.,[[[[[.,.],.],.],.],.]]] => 6 [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 5 [.,[[.,.],[.,[.,[[.,.],.]]]]] => 5 [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3 [.,[[.,.],[.,[[.,[.,.]],.]]]] => 5 [.,[[.,.],[.,[[[.,.],.],.]]]] => 5 [.,[[.,.],[[.,.],[.,[.,.]]]]] => 4 [.,[[.,.],[[.,.],[[.,.],.]]]] => 4 [.,[[.,.],[[.,[.,.]],[.,.]]]] => 4 [.,[[.,.],[[[.,.],.],[.,.]]]] => 4 [.,[[.,.],[[.,[.,[.,.]]],.]]] => 5 [.,[[.,.],[[.,[[.,.],.]],.]]] => 5 [.,[[.,.],[[[.,.],[.,.]],.]]] => 3 [.,[[.,.],[[[.,[.,.]],.],.]]] => 5 [.,[[.,.],[[[[.,.],.],.],.]]] => 5 [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5 [.,[[.,[.,.]],[.,[[.,.],.]]]] => 5 [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3 [.,[[.,[.,.]],[[.,[.,.]],.]]] => 5 [.,[[.,[.,.]],[[[.,.],.],.]]] => 5 [.,[[[.,.],.],[.,[.,[.,.]]]]] => 5 [.,[[[.,.],.],[.,[[.,.],.]]]] => 5 [.,[[[.,.],.],[[.,.],[.,.]]]] => 3 [.,[[[.,.],.],[[.,[.,.]],.]]] => 5 [.,[[[.,.],.],[[[.,.],.],.]]] => 5 [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 5 [.,[[.,[.,[.,.]]],[[.,.],.]]] => 5 [.,[[.,[[.,.],.]],[.,[.,.]]]] => 5 [.,[[.,[[.,.],.]],[[.,.],.]]] => 5 [.,[[[.,.],[.,.]],[.,[.,.]]]] => 3 [.,[[[.,.],[.,.]],[[.,.],.]]] => 3 [.,[[[.,[.,.]],.],[.,[.,.]]]] => 5 [.,[[[.,[.,.]],.],[[.,.],.]]] => 5 [.,[[[[.,.],.],.],[.,[.,.]]]] => 5 [.,[[[[.,.],.],.],[[.,.],.]]] => 5 [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 5 [.,[[.,[.,[[.,.],.]]],[.,.]]] => 5 [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3 [.,[[.,[[.,[.,.]],.]],[.,.]]] => 5 [.,[[.,[[[.,.],.],.]],[.,.]]] => 5 [.,[[[.,.],[.,[.,.]]],[.,.]]] => 4 [.,[[[.,.],[[.,.],.]],[.,.]]] => 4 [.,[[[.,[.,.]],[.,.]],[.,.]]] => 4 [.,[[[[.,.],.],[.,.]],[.,.]]] => 4 [.,[[[.,[.,[.,.]]],.],[.,.]]] => 5 [.,[[[.,[[.,.],.]],.],[.,.]]] => 5 [.,[[[[.,.],[.,.]],.],[.,.]]] => 3 [.,[[[[.,[.,.]],.],.],[.,.]]] => 5 [.,[[[[[.,.],.],.],.],[.,.]]] => 5 [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 6 [.,[[.,[.,[.,[[.,.],.]]]],.]] => 6 [.,[[.,[.,[[.,.],[.,.]]]],.]] => 4 [.,[[.,[.,[[.,[.,.]],.]]],.]] => 6 [.,[[.,[.,[[[.,.],.],.]]],.]] => 6 [.,[[.,[[.,.],[.,[.,.]]]],.]] => 5 [.,[[.,[[.,.],[[.,.],.]]],.]] => 5 [.,[[.,[[.,[.,.]],[.,.]]],.]] => 5 [.,[[.,[[[.,.],.],[.,.]]],.]] => 5 [.,[[.,[[.,[.,[.,.]]],.]],.]] => 6 [.,[[.,[[.,[[.,.],.]],.]],.]] => 6 [.,[[.,[[[.,.],[.,.]],.]],.]] => 4 [.,[[.,[[[.,[.,.]],.],.]],.]] => 6 [.,[[.,[[[[.,.],.],.],.]],.]] => 6 [.,[[[.,.],[.,[.,[.,.]]]],.]] => 5 [.,[[[.,.],[.,[[.,.],.]]],.]] => 5 [.,[[[.,.],[[.,.],[.,.]]],.]] => 3 [.,[[[.,.],[[.,[.,.]],.]],.]] => 5 [.,[[[.,.],[[[.,.],.],.]],.]] => 5 [.,[[[.,[.,.]],[.,[.,.]]],.]] => 4 [.,[[[.,[.,.]],[[.,.],.]],.]] => 4 [.,[[[[.,.],.],[.,[.,.]]],.]] => 4 [.,[[[[.,.],.],[[.,.],.]],.]] => 4 [.,[[[.,[.,[.,.]]],[.,.]],.]] => 5 [.,[[[.,[[.,.],.]],[.,.]],.]] => 5 [.,[[[[.,.],[.,.]],[.,.]],.]] => 3 [.,[[[[.,[.,.]],.],[.,.]],.]] => 5 [.,[[[[[.,.],.],.],[.,.]],.]] => 5 [.,[[[.,[.,[.,[.,.]]]],.],.]] => 6 [.,[[[.,[.,[[.,.],.]]],.],.]] => 6 [.,[[[.,[[.,.],[.,.]]],.],.]] => 4 [.,[[[.,[[.,[.,.]],.]],.],.]] => 6 [.,[[[.,[[[.,.],.],.]],.],.]] => 6 [.,[[[[.,.],[.,[.,.]]],.],.]] => 5 [.,[[[[.,.],[[.,.],.]],.],.]] => 5 [.,[[[[.,[.,.]],[.,.]],.],.]] => 5 [.,[[[[[.,.],.],[.,.]],.],.]] => 5 [.,[[[[.,[.,[.,.]]],.],.],.]] => 6 [.,[[[[.,[[.,.],.]],.],.],.]] => 6 [.,[[[[[.,.],[.,.]],.],.],.]] => 4 [.,[[[[[.,[.,.]],.],.],.],.]] => 6 [.,[[[[[[.,.],.],.],.],.],.]] => 6 [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 5 [[.,.],[.,[.,[.,[[.,.],.]]]]] => 5 [[.,.],[.,[.,[[.,.],[.,.]]]]] => 3 [[.,.],[.,[.,[[.,[.,.]],.]]]] => 5 [[.,.],[.,[.,[[[.,.],.],.]]]] => 5 [[.,.],[.,[[.,.],[.,[.,.]]]]] => 4 [[.,.],[.,[[.,.],[[.,.],.]]]] => 4 [[.,.],[.,[[.,[.,.]],[.,.]]]] => 4 [[.,.],[.,[[[.,.],.],[.,.]]]] => 4 [[.,.],[.,[[.,[.,[.,.]]],.]]] => 5 [[.,.],[.,[[.,[[.,.],.]],.]]] => 5 [[.,.],[.,[[[.,.],[.,.]],.]]] => 3 [[.,.],[.,[[[.,[.,.]],.],.]]] => 5 [[.,.],[.,[[[[.,.],.],.],.]]] => 5 [[.,.],[[.,.],[.,[.,[.,.]]]]] => 4 [[.,.],[[.,.],[.,[[.,.],.]]]] => 4 [[.,.],[[.,.],[[.,.],[.,.]]]] => 2 [[.,.],[[.,.],[[.,[.,.]],.]]] => 4 [[.,.],[[.,.],[[[.,.],.],.]]] => 4 [[.,.],[[.,[.,.]],[.,[.,.]]]] => 3 [[.,.],[[.,[.,.]],[[.,.],.]]] => 3 [[.,.],[[[.,.],.],[.,[.,.]]]] => 3 [[.,.],[[[.,.],.],[[.,.],.]]] => 3 [[.,.],[[.,[.,[.,.]]],[.,.]]] => 4 [[.,.],[[.,[[.,.],.]],[.,.]]] => 4 [[.,.],[[[.,.],[.,.]],[.,.]]] => 2 [[.,.],[[[.,[.,.]],.],[.,.]]] => 4 [[.,.],[[[[.,.],.],.],[.,.]]] => 4 [[.,.],[[.,[.,[.,[.,.]]]],.]] => 5 [[.,.],[[.,[.,[[.,.],.]]],.]] => 5 [[.,.],[[.,[[.,.],[.,.]]],.]] => 3 [[.,.],[[.,[[.,[.,.]],.]],.]] => 5 [[.,.],[[.,[[[.,.],.],.]],.]] => 5 [[.,.],[[[.,.],[.,[.,.]]],.]] => 4 [[.,.],[[[.,.],[[.,.],.]],.]] => 4 [[.,.],[[[.,[.,.]],[.,.]],.]] => 4 [[.,.],[[[[.,.],.],[.,.]],.]] => 4 [[.,.],[[[.,[.,[.,.]]],.],.]] => 5 [[.,.],[[[.,[[.,.],.]],.],.]] => 5 [[.,.],[[[[.,.],[.,.]],.],.]] => 3 [[.,.],[[[[.,[.,.]],.],.],.]] => 5 [[.,.],[[[[[.,.],.],.],.],.]] => 5 [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 5 [[.,[.,.]],[.,[.,[[.,.],.]]]] => 5 [[.,[.,.]],[.,[[.,.],[.,.]]]] => 3 [[.,[.,.]],[.,[[.,[.,.]],.]]] => 5 [[.,[.,.]],[.,[[[.,.],.],.]]] => 5 [[.,[.,.]],[[.,.],[.,[.,.]]]] => 4 [[.,[.,.]],[[.,.],[[.,.],.]]] => 4 [[.,[.,.]],[[.,[.,.]],[.,.]]] => 4 [[.,[.,.]],[[[.,.],.],[.,.]]] => 4 [[.,[.,.]],[[.,[.,[.,.]]],.]] => 5 [[.,[.,.]],[[.,[[.,.],.]],.]] => 5 [[.,[.,.]],[[[.,.],[.,.]],.]] => 3 [[.,[.,.]],[[[.,[.,.]],.],.]] => 5 [[.,[.,.]],[[[[.,.],.],.],.]] => 5 [[[.,.],.],[.,[.,[.,[.,.]]]]] => 5 [[[.,.],.],[.,[.,[[.,.],.]]]] => 5 [[[.,.],.],[.,[[.,.],[.,.]]]] => 3 [[[.,.],.],[.,[[.,[.,.]],.]]] => 5 [[[.,.],.],[.,[[[.,.],.],.]]] => 5 [[[.,.],.],[[.,.],[.,[.,.]]]] => 4 [[[.,.],.],[[.,.],[[.,.],.]]] => 4 [[[.,.],.],[[.,[.,.]],[.,.]]] => 4 [[[.,.],.],[[[.,.],.],[.,.]]] => 4 [[[.,.],.],[[.,[.,[.,.]]],.]] => 5 [[[.,.],.],[[.,[[.,.],.]],.]] => 5 [[[.,.],.],[[[.,.],[.,.]],.]] => 3 [[[.,.],.],[[[.,[.,.]],.],.]] => 5 [[[.,.],.],[[[[.,.],.],.],.]] => 5 [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 4 [[.,[.,[.,.]]],[.,[[.,.],.]]] => 4 [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3 [[.,[.,[.,.]]],[[.,[.,.]],.]] => 4 [[.,[.,[.,.]]],[[[.,.],.],.]] => 4 [[.,[[.,.],.]],[.,[.,[.,.]]]] => 4 [[.,[[.,.],.]],[.,[[.,.],.]]] => 4 [[.,[[.,.],.]],[[.,.],[.,.]]] => 3 [[.,[[.,.],.]],[[.,[.,.]],.]] => 4 [[.,[[.,.],.]],[[[.,.],.],.]] => 4 [[[.,.],[.,.]],[.,[.,[.,.]]]] => 3 [[[.,.],[.,.]],[.,[[.,.],.]]] => 3 [[[.,.],[.,.]],[[.,.],[.,.]]] => 0 [[[.,.],[.,.]],[[.,[.,.]],.]] => 3 [[[.,.],[.,.]],[[[.,.],.],.]] => 3 [[[.,[.,.]],.],[.,[.,[.,.]]]] => 4 [[[.,[.,.]],.],[.,[[.,.],.]]] => 4 [[[.,[.,.]],.],[[.,.],[.,.]]] => 3 [[[.,[.,.]],.],[[.,[.,.]],.]] => 4 [[[.,[.,.]],.],[[[.,.],.],.]] => 4 [[[[.,.],.],.],[.,[.,[.,.]]]] => 4 [[[[.,.],.],.],[.,[[.,.],.]]] => 4 [[[[.,.],.],.],[[.,.],[.,.]]] => 3 [[[[.,.],.],.],[[.,[.,.]],.]] => 4 [[[[.,.],.],.],[[[.,.],.],.]] => 4 [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 5 [[.,[.,[.,[.,.]]]],[[.,.],.]] => 5 [[.,[.,[[.,.],.]]],[.,[.,.]]] => 5 [[.,[.,[[.,.],.]]],[[.,.],.]] => 5 [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3 [[.,[[.,.],[.,.]]],[[.,.],.]] => 3 [[.,[[.,[.,.]],.]],[.,[.,.]]] => 5 [[.,[[.,[.,.]],.]],[[.,.],.]] => 5 [[.,[[[.,.],.],.]],[.,[.,.]]] => 5 [[.,[[[.,.],.],.]],[[.,.],.]] => 5 [[[.,.],[.,[.,.]]],[.,[.,.]]] => 4 [[[.,.],[.,[.,.]]],[[.,.],.]] => 4 [[[.,.],[[.,.],.]],[.,[.,.]]] => 4 [[[.,.],[[.,.],.]],[[.,.],.]] => 4 [[[.,[.,.]],[.,.]],[.,[.,.]]] => 4 [[[.,[.,.]],[.,.]],[[.,.],.]] => 4 [[[[.,.],.],[.,.]],[.,[.,.]]] => 4 [[[[.,.],.],[.,.]],[[.,.],.]] => 4 [[[.,[.,[.,.]]],.],[.,[.,.]]] => 5 [[[.,[.,[.,.]]],.],[[.,.],.]] => 5 [[[.,[[.,.],.]],.],[.,[.,.]]] => 5 [[[.,[[.,.],.]],.],[[.,.],.]] => 5 [[[[.,.],[.,.]],.],[.,[.,.]]] => 3 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[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => 5 [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => 6 [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => 6 [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => 4 [.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => 6 [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => 6 [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 5 [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 5 [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 3 [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => 5 [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => 5 [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 4 [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => 4 [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => 4 [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => 4 [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => 5 [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => 5 [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => 3 [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => 5 [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => 5 [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => 6 [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => 6 [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => 4 [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => 6 [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => 6 [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => 5 [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => 5 [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => 5 [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => 5 [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => 6 [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => 6 [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => 4 [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => 6 [.,[[.,.],[[[[[.,.],.],.],.],.]]] => 6 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => 6 [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 6 [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => 4 [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 6 [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => 6 [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => 5 [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => 5 [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => 5 [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => 5 [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => 6 [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => 6 [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => 4 [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => 6 [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => 6 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 6 [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => 6 [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => 4 [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => 6 [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => 6 [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => 5 [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => 5 [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => 5 [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => 5 [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => 6 [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => 6 [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => 4 [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => 6 [.,[[[.,.],.],[[[[.,.],.],.],.]]] => 6 [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => 5 [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => 5 [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => 4 [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => 5 [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => 5 [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => 5 [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => 5 [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => 4 [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => 5 [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => 5 [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 4 [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 4 [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 1 [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 4 [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 4 [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => 5 [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => 5 [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => 4 [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => 5 [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => 5 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => 5 [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => 5 [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => 4 [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => 5 [.,[[[[.,.],.],.],[[[.,.],.],.]]] => 5 [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => 6 [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => 6 [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => 6 [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => 6 [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => 4 [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => 4 [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => 6 [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => 6 [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => 6 [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => 6 [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => 5 [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => 5 [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => 5 [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => 5 [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => 5 [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => 5 [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => 5 [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 5 [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => 6 [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => 6 [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => 6 [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => 6 [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => 4 [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 4 [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => 6 [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => 6 [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => 6 [.,[[[[[.,.],.],.],.],[[.,.],.]]] => 6 [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => 6 [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => 6 [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => 4 [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => 6 [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => 6 [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => 5 [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => 5 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => 5 [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => 5 [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => 6 [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => 6 [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => 4 [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => 6 [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => 6 [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => 5 [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => 5 [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => 3 [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => 5 [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => 5 [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => 4 [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => 4 [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => 4 [.,[[[[.,.],.],[[.,.],.]],[.,.]]] => 4 [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => 5 [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => 5 [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 3 [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => 5 [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => 5 [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => 6 [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => 6 [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 4 [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => 6 [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => 6 [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => 5 [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => 5 [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => 5 [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => 5 [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => 6 [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => 6 [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => 4 [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => 6 [.,[[[[[[.,.],.],.],.],.],[.,.]]] => 6 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => 7 [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => 7 [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => 5 [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => 7 [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => 7 [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => 6 [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => 6 [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => 6 [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => 6 [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => 7 [.,[[.,[.,[[.,[[.,.],.]],.]]],.]] => 7 [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => 5 [.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => 7 [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => 7 [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => 6 [.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => 6 [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => 4 [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => 6 [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => 6 [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => 5 [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => 5 [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => 5 [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => 5 [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => 6 [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => 6 [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 4 [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => 6 [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => 6 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => 7 [.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => 7 [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 5 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 7 [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => 7 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => 6 [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => 6 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 6 [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => 6 [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => 7 [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => 7 [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => 5 [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => 7 [.,[[.,[[[[[.,.],.],.],.],.]],.]] => 7 [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => 6 [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => 6 [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => 4 [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => 6 [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => 6 [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => 5 [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => 5 [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => 5 [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => 5 [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => 6 [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => 6 [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => 4 [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => 6 [.,[[[.,.],[[[[.,.],.],.],.]],.]] => 6 [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => 6 [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => 6 [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => 4 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 6 [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => 6 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => 6 [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => 6 [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => 4 [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => 6 [.,[[[[.,.],.],[[[.,.],.],.]],.]] => 6 [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => 6 [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => 6 [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => 6 [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => 6 [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => 4 [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => 4 [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => 6 [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => 6 [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => 6 [.,[[[[[.,.],.],.],[[.,.],.]],.]] => 6 [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => 6 [.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => 6 [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => 4 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 6 [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => 6 [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => 5 [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => 5 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 5 [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => 5 [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => 6 [.,[[[[.,[[.,.],.]],.],[.,.]],.]] => 6 [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => 4 [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => 6 [.,[[[[[[.,.],.],.],.],[.,.]],.]] => 6 [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => 7 [.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => 7 [.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => 5 [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => 7 [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => 7 [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => 6 [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => 6 [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => 6 [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => 6 [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => 7 [.,[[[.,[[.,[[.,.],.]],.]],.],.]] => 7 [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => 5 [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => 7 [.,[[[.,[[[[.,.],.],.],.]],.],.]] => 7 [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => 6 [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => 6 [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => 4 [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => 6 [.,[[[[.,.],[[[.,.],.],.]],.],.]] => 6 [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => 5 [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => 5 [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => 5 [.,[[[[[.,.],.],[[.,.],.]],.],.]] => 5 [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => 6 [.,[[[[.,[[.,.],.]],[.,.]],.],.]] => 6 [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => 4 [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => 6 [.,[[[[[[.,.],.],.],[.,.]],.],.]] => 6 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => 7 [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => 7 [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => 5 [.,[[[[.,[[.,[.,.]],.]],.],.],.]] => 7 [.,[[[[.,[[[.,.],.],.]],.],.],.]] => 7 [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => 6 [.,[[[[[.,.],[[.,.],.]],.],.],.]] => 6 [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => 6 [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 6 [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 7 [.,[[[[[.,[[.,.],.]],.],.],.],.]] => 7 [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 5 [.,[[[[[[.,[.,.]],.],.],.],.],.]] => 7 [.,[[[[[[[.,.],.],.],.],.],.],.]] => 7 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 6 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 6 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 4 [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 6 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 6 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 5 [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 5 [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 5 [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => 5 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 6 [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => 6 [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => 4 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => 6 [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => 6 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 5 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 5 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3 [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => 5 [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => 5 [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 4 [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 4 [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => 4 [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => 4 [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 5 [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => 5 [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => 3 [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => 5 [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => 5 [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => 6 [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => 6 [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => 4 [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => 6 [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => 6 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => 5 [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => 5 [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => 5 [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => 5 [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => 6 [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => 6 [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => 4 [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => 6 [[.,.],[.,[[[[[.,.],.],.],.],.]]] => 6 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 5 [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 5 [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3 [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 5 [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => 5 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 4 [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 4 [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => 4 [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 5 [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 5 [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => 3 [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => 5 [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 5 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 5 [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 5 [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3 [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 5 [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 5 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => 5 [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => 5 [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => 3 [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => 5 [[.,.],[[[.,.],.],[[[.,.],.],.]]] => 5 [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 5 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 5 [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => 5 [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 5 [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => 3 [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => 3 [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => 5 [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => 5 [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => 5 [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 5 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 5 [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => 5 [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => 3 [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 5 [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 5 [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 4 [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 4 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 4 [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 4 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 5 [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 5 [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 3 [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 5 [[.,.],[[[[[.,.],.],.],.],[.,.]]] => 5 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 6 [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 6 [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 4 [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 6 [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 6 [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 5 [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 5 [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 5 [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 5 [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 6 [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 6 [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 4 [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 6 [[.,.],[[.,[[[[.,.],.],.],.]],.]] => 6 [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 5 [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 5 [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 3 [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 5 [[.,.],[[[.,.],[[[.,.],.],.]],.]] => 5 [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 4 [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 4 [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 4 [[.,.],[[[[.,.],.],[[.,.],.]],.]] => 4 [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 5 [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 5 [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 3 [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 5 [[.,.],[[[[[.,.],.],.],[.,.]],.]] => 5 [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 6 [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 6 [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 4 [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 6 [[.,.],[[[.,[[[.,.],.],.]],.],.]] => 6 [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 5 [[.,.],[[[[.,.],[[.,.],.]],.],.]] => 5 [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 5 [[.,.],[[[[[.,.],.],[.,.]],.],.]] => 5 [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 6 [[.,.],[[[[.,[[.,.],.]],.],.],.]] => 6 [[.,.],[[[[[.,.],[.,.]],.],.],.]] => 4 [[.,.],[[[[[.,[.,.]],.],.],.],.]] => 6 [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 6 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 6 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 4 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 6 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 6 [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 5 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 5 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 5 [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 5 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 6 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 6 [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 4 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 6 [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 6 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 5 ----------------------------------------------------------------------------- Created: Feb 25, 2016 at 11:21 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 31, 2019 at 22:32 by Martin Rubey