***************************************************************************** * 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: St000919 ----------------------------------------------------------------------------- Collection: Binary trees ----------------------------------------------------------------------------- Description: The number of maximal left branches of a binary tree. A maximal left branch of a binary tree is an inclusion wise maximal path which consists of left edges only. This statistic records the number of distinct maximal left branches in the tree. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(B): return B.twisting_number()[0] ----------------------------------------------------------------------------- Statistic values: [.,[.,.]] => 0 [[.,.],.] => 1 [.,[.,[.,.]]] => 0 [.,[[.,.],.]] => 1 [[.,.],[.,.]] => 1 [[.,[.,.]],.] => 1 [[[.,.],.],.] => 1 [.,[.,[.,[.,.]]]] => 0 [.,[.,[[.,.],.]]] => 1 [.,[[.,.],[.,.]]] => 1 [.,[[.,[.,.]],.]] => 1 [.,[[[.,.],.],.]] => 1 [[.,.],[.,[.,.]]] => 1 [[.,.],[[.,.],.]] => 2 [[.,[.,.]],[.,.]] => 1 [[[.,.],.],[.,.]] => 1 [[.,[.,[.,.]]],.] => 1 [[.,[[.,.],.]],.] => 2 [[[.,.],[.,.]],.] => 1 [[[.,[.,.]],.],.] => 1 [[[[.,.],.],.],.] => 1 [.,[.,[.,[.,[.,.]]]]] => 0 [.,[.,[.,[[.,.],.]]]] => 1 [.,[.,[[.,.],[.,.]]]] => 1 [.,[.,[[.,[.,.]],.]]] => 1 [.,[.,[[[.,.],.],.]]] => 1 [.,[[.,.],[.,[.,.]]]] => 1 [.,[[.,.],[[.,.],.]]] => 2 [.,[[.,[.,.]],[.,.]]] => 1 [.,[[[.,.],.],[.,.]]] => 1 [.,[[.,[.,[.,.]]],.]] => 1 [.,[[.,[[.,.],.]],.]] => 2 [.,[[[.,.],[.,.]],.]] => 1 [.,[[[.,[.,.]],.],.]] => 1 [.,[[[[.,.],.],.],.]] => 1 [[.,.],[.,[.,[.,.]]]] => 1 [[.,.],[.,[[.,.],.]]] => 2 [[.,.],[[.,.],[.,.]]] => 2 [[.,.],[[.,[.,.]],.]] => 2 [[.,.],[[[.,.],.],.]] => 2 [[.,[.,.]],[.,[.,.]]] => 1 [[.,[.,.]],[[.,.],.]] => 2 [[[.,.],.],[.,[.,.]]] => 1 [[[.,.],.],[[.,.],.]] => 2 [[.,[.,[.,.]]],[.,.]] => 1 [[.,[[.,.],.]],[.,.]] => 2 [[[.,.],[.,.]],[.,.]] => 1 [[[.,[.,.]],.],[.,.]] => 1 [[[[.,.],.],.],[.,.]] => 1 [[.,[.,[.,[.,.]]]],.] => 1 [[.,[.,[[.,.],.]]],.] => 2 [[.,[[.,.],[.,.]]],.] => 2 [[.,[[.,[.,.]],.]],.] => 2 [[.,[[[.,.],.],.]],.] => 2 [[[.,.],[.,[.,.]]],.] => 1 [[[.,.],[[.,.],.]],.] => 2 [[[.,[.,.]],[.,.]],.] => 1 [[[[.,.],.],[.,.]],.] => 1 [[[.,[.,[.,.]]],.],.] => 1 [[[.,[[.,.],.]],.],.] => 2 [[[[.,.],[.,.]],.],.] => 1 [[[[.,[.,.]],.],.],.] => 1 [[[[[.,.],.],.],.],.] => 1 [.,[.,[.,[.,[.,[.,.]]]]]] => 0 [.,[.,[.,[.,[[.,.],.]]]]] => 1 [.,[.,[.,[[.,.],[.,.]]]]] => 1 [.,[.,[.,[[.,[.,.]],.]]]] => 1 [.,[.,[.,[[[.,.],.],.]]]] => 1 [.,[.,[[.,.],[.,[.,.]]]]] => 1 [.,[.,[[.,.],[[.,.],.]]]] => 2 [.,[.,[[.,[.,.]],[.,.]]]] => 1 [.,[.,[[[.,.],.],[.,.]]]] => 1 [.,[.,[[.,[.,[.,.]]],.]]] => 1 [.,[.,[[.,[[.,.],.]],.]]] => 2 [.,[.,[[[.,.],[.,.]],.]]] => 1 [.,[.,[[[.,[.,.]],.],.]]] => 1 [.,[.,[[[[.,.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,.]]]]] => 1 [.,[[.,.],[.,[[.,.],.]]]] => 2 [.,[[.,.],[[.,.],[.,.]]]] => 2 [.,[[.,.],[[.,[.,.]],.]]] => 2 [.,[[.,.],[[[.,.],.],.]]] => 2 [.,[[.,[.,.]],[.,[.,.]]]] => 1 [.,[[.,[.,.]],[[.,.],.]]] => 2 [.,[[[.,.],.],[.,[.,.]]]] => 1 [.,[[[.,.],.],[[.,.],.]]] => 2 [.,[[.,[.,[.,.]]],[.,.]]] => 1 [.,[[.,[[.,.],.]],[.,.]]] => 2 [.,[[[.,.],[.,.]],[.,.]]] => 1 [.,[[[.,[.,.]],.],[.,.]]] => 1 [.,[[[[.,.],.],.],[.,.]]] => 1 [.,[[.,[.,[.,[.,.]]]],.]] => 1 [.,[[.,[.,[[.,.],.]]],.]] => 2 [.,[[.,[[.,.],[.,.]]],.]] => 2 [.,[[.,[[.,[.,.]],.]],.]] => 2 [.,[[.,[[[.,.],.],.]],.]] => 2 [.,[[[.,.],[.,[.,.]]],.]] => 1 [.,[[[.,.],[[.,.],.]],.]] => 2 [.,[[[.,[.,.]],[.,.]],.]] => 1 [.,[[[[.,.],.],[.,.]],.]] => 1 [.,[[[.,[.,[.,.]]],.],.]] => 1 [.,[[[.,[[.,.],.]],.],.]] => 2 [.,[[[[.,.],[.,.]],.],.]] => 1 [.,[[[[.,[.,.]],.],.],.]] => 1 [.,[[[[[.,.],.],.],.],.]] => 1 [[.,.],[.,[.,[.,[.,.]]]]] => 1 [[.,.],[.,[.,[[.,.],.]]]] => 2 [[.,.],[.,[[.,.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,.]],.]]] => 2 [[.,.],[.,[[[.,.],.],.]]] => 2 [[.,.],[[.,.],[.,[.,.]]]] => 2 [[.,.],[[.,.],[[.,.],.]]] => 3 [[.,.],[[.,[.,.]],[.,.]]] => 2 [[.,.],[[[.,.],.],[.,.]]] => 2 [[.,.],[[.,[.,[.,.]]],.]] => 2 [[.,.],[[.,[[.,.],.]],.]] => 3 [[.,.],[[[.,.],[.,.]],.]] => 2 [[.,.],[[[.,[.,.]],.],.]] => 2 [[.,.],[[[[.,.],.],.],.]] => 2 [[.,[.,.]],[.,[.,[.,.]]]] => 1 [[.,[.,.]],[.,[[.,.],.]]] => 2 [[.,[.,.]],[[.,.],[.,.]]] => 2 [[.,[.,.]],[[.,[.,.]],.]] => 2 [[.,[.,.]],[[[.,.],.],.]] => 2 [[[.,.],.],[.,[.,[.,.]]]] => 1 [[[.,.],.],[.,[[.,.],.]]] => 2 [[[.,.],.],[[.,.],[.,.]]] => 2 [[[.,.],.],[[.,[.,.]],.]] => 2 [[[.,.],.],[[[.,.],.],.]] => 2 [[.,[.,[.,.]]],[.,[.,.]]] => 1 [[.,[.,[.,.]]],[[.,.],.]] => 2 [[.,[[.,.],.]],[.,[.,.]]] => 2 [[.,[[.,.],.]],[[.,.],.]] => 3 [[[.,.],[.,.]],[.,[.,.]]] => 1 [[[.,.],[.,.]],[[.,.],.]] => 2 [[[.,[.,.]],.],[.,[.,.]]] => 1 [[[.,[.,.]],.],[[.,.],.]] => 2 [[[[.,.],.],.],[.,[.,.]]] => 1 [[[[.,.],.],.],[[.,.],.]] => 2 [[.,[.,[.,[.,.]]]],[.,.]] => 1 [[.,[.,[[.,.],.]]],[.,.]] => 2 [[.,[[.,.],[.,.]]],[.,.]] => 2 [[.,[[.,[.,.]],.]],[.,.]] => 2 [[.,[[[.,.],.],.]],[.,.]] => 2 [[[.,.],[.,[.,.]]],[.,.]] => 1 [[[.,.],[[.,.],.]],[.,.]] => 2 [[[.,[.,.]],[.,.]],[.,.]] => 1 [[[[.,.],.],[.,.]],[.,.]] => 1 [[[.,[.,[.,.]]],.],[.,.]] => 1 [[[.,[[.,.],.]],.],[.,.]] => 2 [[[[.,.],[.,.]],.],[.,.]] => 1 [[[[.,[.,.]],.],.],[.,.]] => 1 [[[[[.,.],.],.],.],[.,.]] => 1 [[.,[.,[.,[.,[.,.]]]]],.] => 1 [[.,[.,[.,[[.,.],.]]]],.] => 2 [[.,[.,[[.,.],[.,.]]]],.] => 2 [[.,[.,[[.,[.,.]],.]]],.] => 2 [[.,[.,[[[.,.],.],.]]],.] => 2 [[.,[[.,.],[.,[.,.]]]],.] => 2 [[.,[[.,.],[[.,.],.]]],.] => 3 [[.,[[.,[.,.]],[.,.]]],.] => 2 [[.,[[[.,.],.],[.,.]]],.] => 2 [[.,[[.,[.,[.,.]]],.]],.] => 2 [[.,[[.,[[.,.],.]],.]],.] => 3 [[.,[[[.,.],[.,.]],.]],.] => 2 [[.,[[[.,[.,.]],.],.]],.] => 2 [[.,[[[[.,.],.],.],.]],.] => 2 [[[.,.],[.,[.,[.,.]]]],.] => 1 [[[.,.],[.,[[.,.],.]]],.] => 2 [[[.,.],[[.,.],[.,.]]],.] => 2 [[[.,.],[[.,[.,.]],.]],.] => 2 [[[.,.],[[[.,.],.],.]],.] => 2 [[[.,[.,.]],[.,[.,.]]],.] => 1 [[[.,[.,.]],[[.,.],.]],.] => 2 [[[[.,.],.],[.,[.,.]]],.] => 1 [[[[.,.],.],[[.,.],.]],.] => 2 [[[.,[.,[.,.]]],[.,.]],.] => 1 [[[.,[[.,.],.]],[.,.]],.] => 2 [[[[.,.],[.,.]],[.,.]],.] => 1 [[[[.,[.,.]],.],[.,.]],.] => 1 [[[[[.,.],.],.],[.,.]],.] => 1 [[[.,[.,[.,[.,.]]]],.],.] => 1 [[[.,[.,[[.,.],.]]],.],.] => 2 [[[.,[[.,.],[.,.]]],.],.] => 2 [[[.,[[.,[.,.]],.]],.],.] => 2 [[[.,[[[.,.],.],.]],.],.] => 2 [[[[.,.],[.,[.,.]]],.],.] => 1 [[[[.,.],[[.,.],.]],.],.] => 2 [[[[.,[.,.]],[.,.]],.],.] => 1 [[[[[.,.],.],[.,.]],.],.] => 1 [[[[.,[.,[.,.]]],.],.],.] => 1 [[[[.,[[.,.],.]],.],.],.] => 2 [[[[[.,.],[.,.]],.],.],.] => 1 [[[[[.,[.,.]],.],.],.],.] => 1 [[[[[[.,.],.],.],.],.],.] => 1 [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0 [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1 [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1 [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1 [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1 [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1 [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2 [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 1 [.,[.,[.,[[[.,.],.],[.,.]]]]] => 1 [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1 [.,[.,[.,[[.,[[.,.],.]],.]]]] => 2 [.,[.,[.,[[[.,.],[.,.]],.]]]] => 1 [.,[.,[.,[[[.,[.,.]],.],.]]]] => 1 [.,[.,[.,[[[[.,.],.],.],.]]]] => 1 [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1 [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2 [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2 [.,[.,[[.,.],[[.,[.,.]],.]]]] => 2 [.,[.,[[.,.],[[[.,.],.],.]]]] => 2 [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1 [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2 [.,[.,[[[.,.],.],[.,[.,.]]]]] => 1 [.,[.,[[[.,.],.],[[.,.],.]]]] => 2 [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1 [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2 [.,[.,[[[.,.],[.,.]],[.,.]]]] => 1 [.,[.,[[[.,[.,.]],.],[.,.]]]] => 1 [.,[.,[[[[.,.],.],.],[.,.]]]] => 1 [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1 [.,[.,[[.,[.,[[.,.],.]]],.]]] => 2 [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2 [.,[.,[[.,[[.,[.,.]],.]],.]]] => 2 [.,[.,[[.,[[[.,.],.],.]],.]]] => 2 [.,[.,[[[.,.],[.,[.,.]]],.]]] => 1 [.,[.,[[[.,.],[[.,.],.]],.]]] => 2 [.,[.,[[[.,[.,.]],[.,.]],.]]] => 1 [.,[.,[[[[.,.],.],[.,.]],.]]] => 1 [.,[.,[[[.,[.,[.,.]]],.],.]]] => 1 [.,[.,[[[.,[[.,.],.]],.],.]]] => 2 [.,[.,[[[[.,.],[.,.]],.],.]]] => 1 [.,[.,[[[[.,[.,.]],.],.],.]]] => 1 [.,[.,[[[[[.,.],.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1 [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2 [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2 [.,[[.,.],[.,[[.,[.,.]],.]]]] => 2 [.,[[.,.],[.,[[[.,.],.],.]]]] => 2 [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2 [.,[[.,.],[[.,.],[[.,.],.]]]] => 3 [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2 [.,[[.,.],[[[.,.],.],[.,.]]]] => 2 [.,[[.,.],[[.,[.,[.,.]]],.]]] => 2 [.,[[.,.],[[.,[[.,.],.]],.]]] => 3 [.,[[.,.],[[[.,.],[.,.]],.]]] => 2 [.,[[.,.],[[[.,[.,.]],.],.]]] => 2 [.,[[.,.],[[[[.,.],.],.],.]]] => 2 [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1 [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2 [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2 [.,[[.,[.,.]],[[.,[.,.]],.]]] => 2 [.,[[.,[.,.]],[[[.,.],.],.]]] => 2 [.,[[[.,.],.],[.,[.,[.,.]]]]] => 1 [.,[[[.,.],.],[.,[[.,.],.]]]] => 2 [.,[[[.,.],.],[[.,.],[.,.]]]] => 2 [.,[[[.,.],.],[[.,[.,.]],.]]] => 2 [.,[[[.,.],.],[[[.,.],.],.]]] => 2 [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1 [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2 [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2 [.,[[.,[[.,.],.]],[[.,.],.]]] => 3 [.,[[[.,.],[.,.]],[.,[.,.]]]] => 1 [.,[[[.,.],[.,.]],[[.,.],.]]] => 2 [.,[[[.,[.,.]],.],[.,[.,.]]]] => 1 [.,[[[.,[.,.]],.],[[.,.],.]]] => 2 [.,[[[[.,.],.],.],[.,[.,.]]]] => 1 [.,[[[[.,.],.],.],[[.,.],.]]] => 2 [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1 [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2 [.,[[.,[[.,.],[.,.]]],[.,.]]] => 2 [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2 [.,[[.,[[[.,.],.],.]],[.,.]]] => 2 [.,[[[.,.],[.,[.,.]]],[.,.]]] => 1 [.,[[[.,.],[[.,.],.]],[.,.]]] => 2 [.,[[[.,[.,.]],[.,.]],[.,.]]] => 1 [.,[[[[.,.],.],[.,.]],[.,.]]] => 1 [.,[[[.,[.,[.,.]]],.],[.,.]]] => 1 [.,[[[.,[[.,.],.]],.],[.,.]]] => 2 [.,[[[[.,.],[.,.]],.],[.,.]]] => 1 [.,[[[[.,[.,.]],.],.],[.,.]]] => 1 [.,[[[[[.,.],.],.],.],[.,.]]] => 1 [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1 [.,[[.,[.,[.,[[.,.],.]]]],.]] => 2 [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2 [.,[[.,[.,[[.,[.,.]],.]]],.]] => 2 [.,[[.,[.,[[[.,.],.],.]]],.]] => 2 [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2 [.,[[.,[[.,.],[[.,.],.]]],.]] => 3 [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2 [.,[[.,[[[.,.],.],[.,.]]],.]] => 2 [.,[[.,[[.,[.,[.,.]]],.]],.]] => 2 [.,[[.,[[.,[[.,.],.]],.]],.]] => 3 [.,[[.,[[[.,.],[.,.]],.]],.]] => 2 [.,[[.,[[[.,[.,.]],.],.]],.]] => 2 [.,[[.,[[[[.,.],.],.],.]],.]] => 2 [.,[[[.,.],[.,[.,[.,.]]]],.]] => 1 [.,[[[.,.],[.,[[.,.],.]]],.]] => 2 [.,[[[.,.],[[.,.],[.,.]]],.]] => 2 [.,[[[.,.],[[.,[.,.]],.]],.]] => 2 [.,[[[.,.],[[[.,.],.],.]],.]] => 2 [.,[[[.,[.,.]],[.,[.,.]]],.]] => 1 [.,[[[.,[.,.]],[[.,.],.]],.]] => 2 [.,[[[[.,.],.],[.,[.,.]]],.]] => 1 [.,[[[[.,.],.],[[.,.],.]],.]] => 2 [.,[[[.,[.,[.,.]]],[.,.]],.]] => 1 [.,[[[.,[[.,.],.]],[.,.]],.]] => 2 [.,[[[[.,.],[.,.]],[.,.]],.]] => 1 [.,[[[[.,[.,.]],.],[.,.]],.]] => 1 [.,[[[[[.,.],.],.],[.,.]],.]] => 1 [.,[[[.,[.,[.,[.,.]]]],.],.]] => 1 [.,[[[.,[.,[[.,.],.]]],.],.]] => 2 [.,[[[.,[[.,.],[.,.]]],.],.]] => 2 [.,[[[.,[[.,[.,.]],.]],.],.]] => 2 [.,[[[.,[[[.,.],.],.]],.],.]] => 2 [.,[[[[.,.],[.,[.,.]]],.],.]] => 1 [.,[[[[.,.],[[.,.],.]],.],.]] => 2 [.,[[[[.,[.,.]],[.,.]],.],.]] => 1 [.,[[[[[.,.],.],[.,.]],.],.]] => 1 [.,[[[[.,[.,[.,.]]],.],.],.]] => 1 [.,[[[[.,[[.,.],.]],.],.],.]] => 2 [.,[[[[[.,.],[.,.]],.],.],.]] => 1 [.,[[[[[.,[.,.]],.],.],.],.]] => 1 [.,[[[[[[.,.],.],.],.],.],.]] => 1 [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1 [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2 [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2 [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2 [[.,.],[.,[.,[[[.,.],.],.]]]] => 2 [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2 [[.,.],[.,[[.,.],[[.,.],.]]]] => 3 [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2 [[.,.],[.,[[[.,.],.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2 [[.,.],[.,[[.,[[.,.],.]],.]]] => 3 [[.,.],[.,[[[.,.],[.,.]],.]]] => 2 [[.,.],[.,[[[.,[.,.]],.],.]]] => 2 [[.,.],[.,[[[[.,.],.],.],.]]] => 2 [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2 [[.,.],[[.,.],[.,[[.,.],.]]]] => 3 [[.,.],[[.,.],[[.,.],[.,.]]]] => 3 [[.,.],[[.,.],[[.,[.,.]],.]]] => 3 [[.,.],[[.,.],[[[.,.],.],.]]] => 3 [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2 [[.,.],[[.,[.,.]],[[.,.],.]]] => 3 [[.,.],[[[.,.],.],[.,[.,.]]]] => 2 [[.,.],[[[.,.],.],[[.,.],.]]] => 3 [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2 [[.,.],[[.,[[.,.],.]],[.,.]]] => 3 [[.,.],[[[.,.],[.,.]],[.,.]]] => 2 [[.,.],[[[.,[.,.]],.],[.,.]]] => 2 [[.,.],[[[[.,.],.],.],[.,.]]] => 2 [[.,.],[[.,[.,[.,[.,.]]]],.]] => 2 [[.,.],[[.,[.,[[.,.],.]]],.]] => 3 [[.,.],[[.,[[.,.],[.,.]]],.]] => 3 [[.,.],[[.,[[.,[.,.]],.]],.]] => 3 [[.,.],[[.,[[[.,.],.],.]],.]] => 3 [[.,.],[[[.,.],[.,[.,.]]],.]] => 2 [[.,.],[[[.,.],[[.,.],.]],.]] => 3 [[.,.],[[[.,[.,.]],[.,.]],.]] => 2 [[.,.],[[[[.,.],.],[.,.]],.]] => 2 [[.,.],[[[.,[.,[.,.]]],.],.]] => 2 [[.,.],[[[.,[[.,.],.]],.],.]] => 3 [[.,.],[[[[.,.],[.,.]],.],.]] => 2 [[.,.],[[[[.,[.,.]],.],.],.]] => 2 [[.,.],[[[[[.,.],.],.],.],.]] => 2 [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1 [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2 [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2 [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2 [[.,[.,.]],[.,[[[.,.],.],.]]] => 2 [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2 [[.,[.,.]],[[.,.],[[.,.],.]]] => 3 [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2 [[.,[.,.]],[[[.,.],.],[.,.]]] => 2 [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2 [[.,[.,.]],[[.,[[.,.],.]],.]] => 3 [[.,[.,.]],[[[.,.],[.,.]],.]] => 2 [[.,[.,.]],[[[.,[.,.]],.],.]] => 2 [[.,[.,.]],[[[[.,.],.],.],.]] => 2 [[[.,.],.],[.,[.,[.,[.,.]]]]] => 1 [[[.,.],.],[.,[.,[[.,.],.]]]] => 2 [[[.,.],.],[.,[[.,.],[.,.]]]] => 2 [[[.,.],.],[.,[[.,[.,.]],.]]] => 2 [[[.,.],.],[.,[[[.,.],.],.]]] => 2 [[[.,.],.],[[.,.],[.,[.,.]]]] => 2 [[[.,.],.],[[.,.],[[.,.],.]]] => 3 [[[.,.],.],[[.,[.,.]],[.,.]]] => 2 [[[.,.],.],[[[.,.],.],[.,.]]] => 2 [[[.,.],.],[[.,[.,[.,.]]],.]] => 2 [[[.,.],.],[[.,[[.,.],.]],.]] => 3 [[[.,.],.],[[[.,.],[.,.]],.]] => 2 [[[.,.],.],[[[.,[.,.]],.],.]] => 2 [[[.,.],.],[[[[.,.],.],.],.]] => 2 [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1 [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2 [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2 [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2 [[.,[.,[.,.]]],[[[.,.],.],.]] => 2 [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2 [[.,[[.,.],.]],[.,[[.,.],.]]] => 3 [[.,[[.,.],.]],[[.,.],[.,.]]] => 3 [[.,[[.,.],.]],[[.,[.,.]],.]] => 3 [[.,[[.,.],.]],[[[.,.],.],.]] => 3 [[[.,.],[.,.]],[.,[.,[.,.]]]] => 1 [[[.,.],[.,.]],[.,[[.,.],.]]] => 2 [[[.,.],[.,.]],[[.,.],[.,.]]] => 2 [[[.,.],[.,.]],[[.,[.,.]],.]] => 2 [[[.,.],[.,.]],[[[.,.],.],.]] => 2 [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1 [[[.,[.,.]],.],[.,[[.,.],.]]] => 2 [[[.,[.,.]],.],[[.,.],[.,.]]] => 2 [[[.,[.,.]],.],[[.,[.,.]],.]] => 2 [[[.,[.,.]],.],[[[.,.],.],.]] => 2 [[[[.,.],.],.],[.,[.,[.,.]]]] => 1 [[[[.,.],.],.],[.,[[.,.],.]]] => 2 [[[[.,.],.],.],[[.,.],[.,.]]] => 2 [[[[.,.],.],.],[[.,[.,.]],.]] => 2 [[[[.,.],.],.],[[[.,.],.],.]] => 2 [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1 [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2 [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2 [[.,[.,[[.,.],.]]],[[.,.],.]] => 3 [[.,[[.,.],[.,.]]],[.,[.,.]]] => 2 [[.,[[.,.],[.,.]]],[[.,.],.]] => 3 [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2 [[.,[[.,[.,.]],.]],[[.,.],.]] => 3 [[.,[[[.,.],.],.]],[.,[.,.]]] => 2 [[.,[[[.,.],.],.]],[[.,.],.]] => 3 [[[.,.],[.,[.,.]]],[.,[.,.]]] => 1 [[[.,.],[.,[.,.]]],[[.,.],.]] => 2 [[[.,.],[[.,.],.]],[.,[.,.]]] => 2 [[[.,.],[[.,.],.]],[[.,.],.]] => 3 [[[.,[.,.]],[.,.]],[.,[.,.]]] => 1 [[[.,[.,.]],[.,.]],[[.,.],.]] => 2 [[[[.,.],.],[.,.]],[.,[.,.]]] => 1 [[[[.,.],.],[.,.]],[[.,.],.]] => 2 [[[.,[.,[.,.]]],.],[.,[.,.]]] => 1 [[[.,[.,[.,.]]],.],[[.,.],.]] => 2 [[[.,[[.,.],.]],.],[.,[.,.]]] => 2 [[[.,[[.,.],.]],.],[[.,.],.]] => 3 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[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => 2 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => 2 [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => 2 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 3 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 3 [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => 3 [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => 3 [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2 [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 3 [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => 2 [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => 3 [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2 [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => 3 [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => 2 [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => 2 [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => 2 [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => 3 [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => 3 [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => 3 [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => 3 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => 2 [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => 3 [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => 2 [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => 2 [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => 2 [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => 3 [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => 2 [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => 2 [[.,.],[.,[[[[[.,.],.],.],.],.]]] => 2 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2 [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3 [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 3 [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 3 [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => 3 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 3 [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 3 [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => 3 [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 3 [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 4 [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => 3 [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => 3 [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 3 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2 [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3 [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 3 [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 3 [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 3 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => 2 [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => 3 [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => 3 [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => 3 [[.,.],[[[.,.],.],[[[.,.],.],.]]] => 3 [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3 [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => 3 [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 4 [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => 2 [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => 3 [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => 2 [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => 3 [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => 2 [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2 [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => 3 [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => 3 [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 3 [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 3 [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 2 [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 3 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 2 [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 2 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 2 [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 3 [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 2 [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 2 [[.,.],[[[[[.,.],.],.],.],[.,.]]] => 2 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 2 [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 3 [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 3 [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 3 [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 3 [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 3 [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 4 [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 3 [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 3 [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 3 [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 4 [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 3 [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 3 [[.,.],[[.,[[[[.,.],.],.],.]],.]] => 3 [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 2 [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 3 [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 3 [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 3 [[.,.],[[[.,.],[[[.,.],.],.]],.]] => 3 [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 2 [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 3 [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 2 [[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3 [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 2 [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 3 [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 2 [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 2 [[.,.],[[[[[.,.],.],.],[.,.]],.]] => 2 [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 2 [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 3 [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 3 [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 3 [[.,.],[[[.,[[[.,.],.],.]],.],.]] => 3 [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 2 [[.,.],[[[[.,.],[[.,.],.]],.],.]] => 3 [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 2 [[.,.],[[[[[.,.],.],[.,.]],.],.]] => 2 [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 2 [[.,.],[[[[.,[[.,.],.]],.],.],.]] => 3 [[.,.],[[[[[.,.],[.,.]],.],.],.]] => 2 [[.,.],[[[[[.,[.,.]],.],.],.],.]] => 2 [[.,.],[[[[[[.,.],.],.],.],.],.]] => 2 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 2 [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2 [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 2 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 3 [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 2 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 2 [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 2 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2 ----------------------------------------------------------------------------- Created: Jul 29, 2017 at 22:17 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 29, 2017 at 22:17 by Martin Rubey