***************************************************************************** * 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: St000701 ----------------------------------------------------------------------------- Collection: Binary trees ----------------------------------------------------------------------------- Description: The protection number of a binary tree. This is the minimal distance from the root to a leaf. ----------------------------------------------------------------------------- References: [1] Heuberger, C., Prodinger, H. Protection Number in Plane Trees [[arXiv:1702.06816]] ----------------------------------------------------------------------------- Code: def statistic(T): if len(T) == 0: return 0 else: return 1+min(statistic(S) for S in T) ----------------------------------------------------------------------------- Statistic values: [.,.] => 1 [.,[.,.]] => 1 [[.,.],.] => 1 [.,[.,[.,.]]] => 1 [.,[[.,.],.]] => 1 [[.,.],[.,.]] => 2 [[.,[.,.]],.] => 1 [[[.,.],.],.] => 1 [.,[.,[.,[.,.]]]] => 1 [.,[.,[[.,.],.]]] => 1 [.,[[.,.],[.,.]]] => 1 [.,[[.,[.,.]],.]] => 1 [.,[[[.,.],.],.]] => 1 [[.,.],[.,[.,.]]] => 2 [[.,.],[[.,.],.]] => 2 [[.,[.,.]],[.,.]] => 2 [[[.,.],.],[.,.]] => 2 [[.,[.,[.,.]]],.] => 1 [[.,[[.,.],.]],.] => 1 [[[.,.],[.,.]],.] => 1 [[[.,[.,.]],.],.] => 1 [[[[.,.],.],.],.] => 1 [.,[.,[.,[.,[.,.]]]]] => 1 [.,[.,[.,[[.,.],.]]]] => 1 [.,[.,[[.,.],[.,.]]]] => 1 [.,[.,[[.,[.,.]],.]]] => 1 [.,[.,[[[.,.],.],.]]] => 1 [.,[[.,.],[.,[.,.]]]] => 1 [.,[[.,.],[[.,.],.]]] => 1 [.,[[.,[.,.]],[.,.]]] => 1 [.,[[[.,.],.],[.,.]]] => 1 [.,[[.,[.,[.,.]]],.]] => 1 [.,[[.,[[.,.],.]],.]] => 1 [.,[[[.,.],[.,.]],.]] => 1 [.,[[[.,[.,.]],.],.]] => 1 [.,[[[[.,.],.],.],.]] => 1 [[.,.],[.,[.,[.,.]]]] => 2 [[.,.],[.,[[.,.],.]]] => 2 [[.,.],[[.,.],[.,.]]] => 2 [[.,.],[[.,[.,.]],.]] => 2 [[.,.],[[[.,.],.],.]] => 2 [[.,[.,.]],[.,[.,.]]] => 2 [[.,[.,.]],[[.,.],.]] => 2 [[[.,.],.],[.,[.,.]]] => 2 [[[.,.],.],[[.,.],.]] => 2 [[.,[.,[.,.]]],[.,.]] => 2 [[.,[[.,.],.]],[.,.]] => 2 [[[.,.],[.,.]],[.,.]] => 2 [[[.,[.,.]],.],[.,.]] => 2 [[[[.,.],.],.],[.,.]] => 2 [[.,[.,[.,[.,.]]]],.] => 1 [[.,[.,[[.,.],.]]],.] => 1 [[.,[[.,.],[.,.]]],.] => 1 [[.,[[.,[.,.]],.]],.] => 1 [[.,[[[.,.],.],.]],.] => 1 [[[.,.],[.,[.,.]]],.] => 1 [[[.,.],[[.,.],.]],.] => 1 [[[.,[.,.]],[.,.]],.] => 1 [[[[.,.],.],[.,.]],.] => 1 [[[.,[.,[.,.]]],.],.] => 1 [[[.,[[.,.],.]],.],.] => 1 [[[[.,.],[.,.]],.],.] => 1 [[[[.,[.,.]],.],.],.] => 1 [[[[[.,.],.],.],.],.] => 1 [.,[.,[.,[.,[.,[.,.]]]]]] => 1 [.,[.,[.,[.,[[.,.],.]]]]] => 1 [.,[.,[.,[[.,.],[.,.]]]]] => 1 [.,[.,[.,[[.,[.,.]],.]]]] => 1 [.,[.,[.,[[[.,.],.],.]]]] => 1 [.,[.,[[.,.],[.,[.,.]]]]] => 1 [.,[.,[[.,.],[[.,.],.]]]] => 1 [.,[.,[[.,[.,.]],[.,.]]]] => 1 [.,[.,[[[.,.],.],[.,.]]]] => 1 [.,[.,[[.,[.,[.,.]]],.]]] => 1 [.,[.,[[.,[[.,.],.]],.]]] => 1 [.,[.,[[[.,.],[.,.]],.]]] => 1 [.,[.,[[[.,[.,.]],.],.]]] => 1 [.,[.,[[[[.,.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,.]]]]] => 1 [.,[[.,.],[.,[[.,.],.]]]] => 1 [.,[[.,.],[[.,.],[.,.]]]] => 1 [.,[[.,.],[[.,[.,.]],.]]] => 1 [.,[[.,.],[[[.,.],.],.]]] => 1 [.,[[.,[.,.]],[.,[.,.]]]] => 1 [.,[[.,[.,.]],[[.,.],.]]] => 1 [.,[[[.,.],.],[.,[.,.]]]] => 1 [.,[[[.,.],.],[[.,.],.]]] => 1 [.,[[.,[.,[.,.]]],[.,.]]] => 1 [.,[[.,[[.,.],.]],[.,.]]] => 1 [.,[[[.,.],[.,.]],[.,.]]] => 1 [.,[[[.,[.,.]],.],[.,.]]] => 1 [.,[[[[.,.],.],.],[.,.]]] => 1 [.,[[.,[.,[.,[.,.]]]],.]] => 1 [.,[[.,[.,[[.,.],.]]],.]] => 1 [.,[[.,[[.,.],[.,.]]],.]] => 1 [.,[[.,[[.,[.,.]],.]],.]] => 1 [.,[[.,[[[.,.],.],.]],.]] => 1 [.,[[[.,.],[.,[.,.]]],.]] => 1 [.,[[[.,.],[[.,.],.]],.]] => 1 [.,[[[.,[.,.]],[.,.]],.]] => 1 [.,[[[[.,.],.],[.,.]],.]] => 1 [.,[[[.,[.,[.,.]]],.],.]] => 1 [.,[[[.,[[.,.],.]],.],.]] => 1 [.,[[[[.,.],[.,.]],.],.]] => 1 [.,[[[[.,[.,.]],.],.],.]] => 1 [.,[[[[[.,.],.],.],.],.]] => 1 [[.,.],[.,[.,[.,[.,.]]]]] => 2 [[.,.],[.,[.,[[.,.],.]]]] => 2 [[.,.],[.,[[.,.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,.]],.]]] => 2 [[.,.],[.,[[[.,.],.],.]]] => 2 [[.,.],[[.,.],[.,[.,.]]]] => 2 [[.,.],[[.,.],[[.,.],.]]] => 2 [[.,.],[[.,[.,.]],[.,.]]] => 2 [[.,.],[[[.,.],.],[.,.]]] => 2 [[.,.],[[.,[.,[.,.]]],.]] => 2 [[.,.],[[.,[[.,.],.]],.]] => 2 [[.,.],[[[.,.],[.,.]],.]] => 2 [[.,.],[[[.,[.,.]],.],.]] => 2 [[.,.],[[[[.,.],.],.],.]] => 2 [[.,[.,.]],[.,[.,[.,.]]]] => 2 [[.,[.,.]],[.,[[.,.],.]]] => 2 [[.,[.,.]],[[.,.],[.,.]]] => 2 [[.,[.,.]],[[.,[.,.]],.]] => 2 [[.,[.,.]],[[[.,.],.],.]] => 2 [[[.,.],.],[.,[.,[.,.]]]] => 2 [[[.,.],.],[.,[[.,.],.]]] => 2 [[[.,.],.],[[.,.],[.,.]]] => 2 [[[.,.],.],[[.,[.,.]],.]] => 2 [[[.,.],.],[[[.,.],.],.]] => 2 [[.,[.,[.,.]]],[.,[.,.]]] => 2 [[.,[.,[.,.]]],[[.,.],.]] => 2 [[.,[[.,.],.]],[.,[.,.]]] => 2 [[.,[[.,.],.]],[[.,.],.]] => 2 [[[.,.],[.,.]],[.,[.,.]]] => 2 [[[.,.],[.,.]],[[.,.],.]] => 2 [[[.,[.,.]],.],[.,[.,.]]] => 2 [[[.,[.,.]],.],[[.,.],.]] => 2 [[[[.,.],.],.],[.,[.,.]]] => 2 [[[[.,.],.],.],[[.,.],.]] => 2 [[.,[.,[.,[.,.]]]],[.,.]] => 2 [[.,[.,[[.,.],.]]],[.,.]] => 2 [[.,[[.,.],[.,.]]],[.,.]] => 2 [[.,[[.,[.,.]],.]],[.,.]] => 2 [[.,[[[.,.],.],.]],[.,.]] => 2 [[[.,.],[.,[.,.]]],[.,.]] => 2 [[[.,.],[[.,.],.]],[.,.]] => 2 [[[.,[.,.]],[.,.]],[.,.]] => 2 [[[[.,.],.],[.,.]],[.,.]] => 2 [[[.,[.,[.,.]]],.],[.,.]] => 2 [[[.,[[.,.],.]],.],[.,.]] => 2 [[[[.,.],[.,.]],.],[.,.]] => 2 [[[[.,[.,.]],.],.],[.,.]] => 2 [[[[[.,.],.],.],.],[.,.]] => 2 [[.,[.,[.,[.,[.,.]]]]],.] => 1 [[.,[.,[.,[[.,.],.]]]],.] => 1 [[.,[.,[[.,.],[.,.]]]],.] => 1 [[.,[.,[[.,[.,.]],.]]],.] => 1 [[.,[.,[[[.,.],.],.]]],.] => 1 [[.,[[.,.],[.,[.,.]]]],.] => 1 [[.,[[.,.],[[.,.],.]]],.] => 1 [[.,[[.,[.,.]],[.,.]]],.] => 1 [[.,[[[.,.],.],[.,.]]],.] => 1 [[.,[[.,[.,[.,.]]],.]],.] => 1 [[.,[[.,[[.,.],.]],.]],.] => 1 [[.,[[[.,.],[.,.]],.]],.] => 1 [[.,[[[.,[.,.]],.],.]],.] => 1 [[.,[[[[.,.],.],.],.]],.] => 1 [[[.,.],[.,[.,[.,.]]]],.] => 1 [[[.,.],[.,[[.,.],.]]],.] => 1 [[[.,.],[[.,.],[.,.]]],.] => 1 [[[.,.],[[.,[.,.]],.]],.] => 1 [[[.,.],[[[.,.],.],.]],.] => 1 [[[.,[.,.]],[.,[.,.]]],.] => 1 [[[.,[.,.]],[[.,.],.]],.] => 1 [[[[.,.],.],[.,[.,.]]],.] => 1 [[[[.,.],.],[[.,.],.]],.] => 1 [[[.,[.,[.,.]]],[.,.]],.] => 1 [[[.,[[.,.],.]],[.,.]],.] => 1 [[[[.,.],[.,.]],[.,.]],.] => 1 [[[[.,[.,.]],.],[.,.]],.] => 1 [[[[[.,.],.],.],[.,.]],.] => 1 [[[.,[.,[.,[.,.]]]],.],.] => 1 [[[.,[.,[[.,.],.]]],.],.] => 1 [[[.,[[.,.],[.,.]]],.],.] => 1 [[[.,[[.,[.,.]],.]],.],.] => 1 [[[.,[[[.,.],.],.]],.],.] => 1 [[[[.,.],[.,[.,.]]],.],.] => 1 [[[[.,.],[[.,.],.]],.],.] => 1 [[[[.,[.,.]],[.,.]],.],.] => 1 [[[[[.,.],.],[.,.]],.],.] => 1 [[[[.,[.,[.,.]]],.],.],.] => 1 [[[[.,[[.,.],.]],.],.],.] => 1 [[[[[.,.],[.,.]],.],.],.] => 1 [[[[[.,[.,.]],.],.],.],.] => 1 [[[[[[.,.],.],.],.],.],.] => 1 [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1 [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1 [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1 [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1 [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1 [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1 [.,[.,[.,[[.,.],[[.,.],.]]]]] => 1 [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 1 [.,[.,[.,[[[.,.],.],[.,.]]]]] => 1 [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1 [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1 [.,[.,[.,[[[.,.],[.,.]],.]]]] => 1 [.,[.,[.,[[[.,[.,.]],.],.]]]] => 1 [.,[.,[.,[[[[.,.],.],.],.]]]] => 1 [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1 [.,[.,[[.,.],[.,[[.,.],.]]]]] => 1 [.,[.,[[.,.],[[.,.],[.,.]]]]] => 1 [.,[.,[[.,.],[[.,[.,.]],.]]]] => 1 [.,[.,[[.,.],[[[.,.],.],.]]]] => 1 [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1 [.,[.,[[.,[.,.]],[[.,.],.]]]] => 1 [.,[.,[[[.,.],.],[.,[.,.]]]]] => 1 [.,[.,[[[.,.],.],[[.,.],.]]]] => 1 [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1 [.,[.,[[.,[[.,.],.]],[.,.]]]] => 1 [.,[.,[[[.,.],[.,.]],[.,.]]]] => 1 [.,[.,[[[.,[.,.]],.],[.,.]]]] => 1 [.,[.,[[[[.,.],.],.],[.,.]]]] => 1 [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1 [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1 [.,[.,[[.,[[.,.],[.,.]]],.]]] => 1 [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1 [.,[.,[[.,[[[.,.],.],.]],.]]] => 1 [.,[.,[[[.,.],[.,[.,.]]],.]]] => 1 [.,[.,[[[.,.],[[.,.],.]],.]]] => 1 [.,[.,[[[.,[.,.]],[.,.]],.]]] => 1 [.,[.,[[[[.,.],.],[.,.]],.]]] => 1 [.,[.,[[[.,[.,[.,.]]],.],.]]] => 1 [.,[.,[[[.,[[.,.],.]],.],.]]] => 1 [.,[.,[[[[.,.],[.,.]],.],.]]] => 1 [.,[.,[[[[.,[.,.]],.],.],.]]] => 1 [.,[.,[[[[[.,.],.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1 [.,[[.,.],[.,[.,[[.,.],.]]]]] => 1 [.,[[.,.],[.,[[.,.],[.,.]]]]] => 1 [.,[[.,.],[.,[[.,[.,.]],.]]]] => 1 [.,[[.,.],[.,[[[.,.],.],.]]]] => 1 [.,[[.,.],[[.,.],[.,[.,.]]]]] => 1 [.,[[.,.],[[.,.],[[.,.],.]]]] => 1 [.,[[.,.],[[.,[.,.]],[.,.]]]] => 1 [.,[[.,.],[[[.,.],.],[.,.]]]] => 1 [.,[[.,.],[[.,[.,[.,.]]],.]]] => 1 [.,[[.,.],[[.,[[.,.],.]],.]]] => 1 [.,[[.,.],[[[.,.],[.,.]],.]]] => 1 [.,[[.,.],[[[.,[.,.]],.],.]]] => 1 [.,[[.,.],[[[[.,.],.],.],.]]] => 1 [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1 [.,[[.,[.,.]],[.,[[.,.],.]]]] => 1 [.,[[.,[.,.]],[[.,.],[.,.]]]] => 1 [.,[[.,[.,.]],[[.,[.,.]],.]]] => 1 [.,[[.,[.,.]],[[[.,.],.],.]]] => 1 [.,[[[.,.],.],[.,[.,[.,.]]]]] => 1 [.,[[[.,.],.],[.,[[.,.],.]]]] => 1 [.,[[[.,.],.],[[.,.],[.,.]]]] => 1 [.,[[[.,.],.],[[.,[.,.]],.]]] => 1 [.,[[[.,.],.],[[[.,.],.],.]]] => 1 [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1 [.,[[.,[.,[.,.]]],[[.,.],.]]] => 1 [.,[[.,[[.,.],.]],[.,[.,.]]]] => 1 [.,[[.,[[.,.],.]],[[.,.],.]]] => 1 [.,[[[.,.],[.,.]],[.,[.,.]]]] => 1 [.,[[[.,.],[.,.]],[[.,.],.]]] => 1 [.,[[[.,[.,.]],.],[.,[.,.]]]] => 1 [.,[[[.,[.,.]],.],[[.,.],.]]] => 1 [.,[[[[.,.],.],.],[.,[.,.]]]] => 1 [.,[[[[.,.],.],.],[[.,.],.]]] => 1 [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1 [.,[[.,[.,[[.,.],.]]],[.,.]]] => 1 [.,[[.,[[.,.],[.,.]]],[.,.]]] => 1 [.,[[.,[[.,[.,.]],.]],[.,.]]] => 1 [.,[[.,[[[.,.],.],.]],[.,.]]] => 1 [.,[[[.,.],[.,[.,.]]],[.,.]]] => 1 [.,[[[.,.],[[.,.],.]],[.,.]]] => 1 [.,[[[.,[.,.]],[.,.]],[.,.]]] => 1 [.,[[[[.,.],.],[.,.]],[.,.]]] => 1 [.,[[[.,[.,[.,.]]],.],[.,.]]] => 1 [.,[[[.,[[.,.],.]],.],[.,.]]] => 1 [.,[[[[.,.],[.,.]],.],[.,.]]] => 1 [.,[[[[.,[.,.]],.],.],[.,.]]] => 1 [.,[[[[[.,.],.],.],.],[.,.]]] => 1 [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1 [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1 [.,[[.,[.,[[.,.],[.,.]]]],.]] => 1 [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1 [.,[[.,[.,[[[.,.],.],.]]],.]] => 1 [.,[[.,[[.,.],[.,[.,.]]]],.]] => 1 [.,[[.,[[.,.],[[.,.],.]]],.]] => 1 [.,[[.,[[.,[.,.]],[.,.]]],.]] => 1 [.,[[.,[[[.,.],.],[.,.]]],.]] => 1 [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1 [.,[[.,[[.,[[.,.],.]],.]],.]] => 1 [.,[[.,[[[.,.],[.,.]],.]],.]] => 1 [.,[[.,[[[.,[.,.]],.],.]],.]] => 1 [.,[[.,[[[[.,.],.],.],.]],.]] => 1 [.,[[[.,.],[.,[.,[.,.]]]],.]] => 1 [.,[[[.,.],[.,[[.,.],.]]],.]] => 1 [.,[[[.,.],[[.,.],[.,.]]],.]] => 1 [.,[[[.,.],[[.,[.,.]],.]],.]] => 1 [.,[[[.,.],[[[.,.],.],.]],.]] => 1 [.,[[[.,[.,.]],[.,[.,.]]],.]] => 1 [.,[[[.,[.,.]],[[.,.],.]],.]] => 1 [.,[[[[.,.],.],[.,[.,.]]],.]] => 1 [.,[[[[.,.],.],[[.,.],.]],.]] => 1 [.,[[[.,[.,[.,.]]],[.,.]],.]] => 1 [.,[[[.,[[.,.],.]],[.,.]],.]] => 1 [.,[[[[.,.],[.,.]],[.,.]],.]] => 1 [.,[[[[.,[.,.]],.],[.,.]],.]] => 1 [.,[[[[[.,.],.],.],[.,.]],.]] => 1 [.,[[[.,[.,[.,[.,.]]]],.],.]] => 1 [.,[[[.,[.,[[.,.],.]]],.],.]] => 1 [.,[[[.,[[.,.],[.,.]]],.],.]] => 1 [.,[[[.,[[.,[.,.]],.]],.],.]] => 1 [.,[[[.,[[[.,.],.],.]],.],.]] => 1 [.,[[[[.,.],[.,[.,.]]],.],.]] => 1 [.,[[[[.,.],[[.,.],.]],.],.]] => 1 [.,[[[[.,[.,.]],[.,.]],.],.]] => 1 [.,[[[[[.,.],.],[.,.]],.],.]] => 1 [.,[[[[.,[.,[.,.]]],.],.],.]] => 1 [.,[[[[.,[[.,.],.]],.],.],.]] => 1 [.,[[[[[.,.],[.,.]],.],.],.]] => 1 [.,[[[[[.,[.,.]],.],.],.],.]] => 1 [.,[[[[[[.,.],.],.],.],.],.]] => 1 [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2 [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2 [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2 [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2 [[.,.],[.,[.,[[[.,.],.],.]]]] => 2 [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2 [[.,.],[.,[[.,.],[[.,.],.]]]] => 2 [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2 [[.,.],[.,[[[.,.],.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2 [[.,.],[.,[[.,[[.,.],.]],.]]] => 2 [[.,.],[.,[[[.,.],[.,.]],.]]] => 2 [[.,.],[.,[[[.,[.,.]],.],.]]] => 2 [[.,.],[.,[[[[.,.],.],.],.]]] => 2 [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2 [[.,.],[[.,.],[.,[[.,.],.]]]] => 2 [[.,.],[[.,.],[[.,.],[.,.]]]] => 2 [[.,.],[[.,.],[[.,[.,.]],.]]] => 2 [[.,.],[[.,.],[[[.,.],.],.]]] => 2 [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2 [[.,.],[[.,[.,.]],[[.,.],.]]] => 2 [[.,.],[[[.,.],.],[.,[.,.]]]] => 2 [[.,.],[[[.,.],.],[[.,.],.]]] => 2 [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2 [[.,.],[[.,[[.,.],.]],[.,.]]] => 2 [[.,.],[[[.,.],[.,.]],[.,.]]] => 2 [[.,.],[[[.,[.,.]],.],[.,.]]] => 2 [[.,.],[[[[.,.],.],.],[.,.]]] => 2 [[.,.],[[.,[.,[.,[.,.]]]],.]] => 2 [[.,.],[[.,[.,[[.,.],.]]],.]] => 2 [[.,.],[[.,[[.,.],[.,.]]],.]] => 2 [[.,.],[[.,[[.,[.,.]],.]],.]] => 2 [[.,.],[[.,[[[.,.],.],.]],.]] => 2 [[.,.],[[[.,.],[.,[.,.]]],.]] => 2 [[.,.],[[[.,.],[[.,.],.]],.]] => 2 [[.,.],[[[.,[.,.]],[.,.]],.]] => 2 [[.,.],[[[[.,.],.],[.,.]],.]] => 2 [[.,.],[[[.,[.,[.,.]]],.],.]] => 2 [[.,.],[[[.,[[.,.],.]],.],.]] => 2 [[.,.],[[[[.,.],[.,.]],.],.]] => 2 [[.,.],[[[[.,[.,.]],.],.],.]] => 2 [[.,.],[[[[[.,.],.],.],.],.]] => 2 [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2 [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2 [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2 [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2 [[.,[.,.]],[.,[[[.,.],.],.]]] => 2 [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2 [[.,[.,.]],[[.,.],[[.,.],.]]] => 2 [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2 [[.,[.,.]],[[[.,.],.],[.,.]]] => 2 [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2 [[.,[.,.]],[[.,[[.,.],.]],.]] => 2 [[.,[.,.]],[[[.,.],[.,.]],.]] => 2 [[.,[.,.]],[[[.,[.,.]],.],.]] => 2 [[.,[.,.]],[[[[.,.],.],.],.]] => 2 [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2 [[[.,.],.],[.,[.,[[.,.],.]]]] => 2 [[[.,.],.],[.,[[.,.],[.,.]]]] => 2 [[[.,.],.],[.,[[.,[.,.]],.]]] => 2 [[[.,.],.],[.,[[[.,.],.],.]]] => 2 [[[.,.],.],[[.,.],[.,[.,.]]]] => 2 [[[.,.],.],[[.,.],[[.,.],.]]] => 2 [[[.,.],.],[[.,[.,.]],[.,.]]] => 2 [[[.,.],.],[[[.,.],.],[.,.]]] => 2 [[[.,.],.],[[.,[.,[.,.]]],.]] => 2 [[[.,.],.],[[.,[[.,.],.]],.]] => 2 [[[.,.],.],[[[.,.],[.,.]],.]] => 2 [[[.,.],.],[[[.,[.,.]],.],.]] => 2 [[[.,.],.],[[[[.,.],.],.],.]] => 2 [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2 [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2 [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2 [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2 [[.,[.,[.,.]]],[[[.,.],.],.]] => 2 [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2 [[.,[[.,.],.]],[.,[[.,.],.]]] => 2 [[.,[[.,.],.]],[[.,.],[.,.]]] => 2 [[.,[[.,.],.]],[[.,[.,.]],.]] => 2 [[.,[[.,.],.]],[[[.,.],.],.]] => 2 [[[.,.],[.,.]],[.,[.,[.,.]]]] => 2 [[[.,.],[.,.]],[.,[[.,.],.]]] => 2 [[[.,.],[.,.]],[[.,.],[.,.]]] => 3 [[[.,.],[.,.]],[[.,[.,.]],.]] => 2 [[[.,.],[.,.]],[[[.,.],.],.]] => 2 [[[.,[.,.]],.],[.,[.,[.,.]]]] => 2 [[[.,[.,.]],.],[.,[[.,.],.]]] => 2 [[[.,[.,.]],.],[[.,.],[.,.]]] => 2 [[[.,[.,.]],.],[[.,[.,.]],.]] => 2 [[[.,[.,.]],.],[[[.,.],.],.]] => 2 [[[[.,.],.],.],[.,[.,[.,.]]]] => 2 [[[[.,.],.],.],[.,[[.,.],.]]] => 2 [[[[.,.],.],.],[[.,.],[.,.]]] => 2 [[[[.,.],.],.],[[.,[.,.]],.]] => 2 [[[[.,.],.],.],[[[.,.],.],.]] => 2 [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2 [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2 [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2 [[.,[.,[[.,.],.]]],[[.,.],.]] => 2 [[.,[[.,.],[.,.]]],[.,[.,.]]] => 2 [[.,[[.,.],[.,.]]],[[.,.],.]] => 2 [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2 [[.,[[.,[.,.]],.]],[[.,.],.]] => 2 [[.,[[[.,.],.],.]],[.,[.,.]]] => 2 [[.,[[[.,.],.],.]],[[.,.],.]] => 2 [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2 [[[.,.],[.,[.,.]]],[[.,.],.]] => 2 [[[.,.],[[.,.],.]],[.,[.,.]]] => 2 [[[.,.],[[.,.],.]],[[.,.],.]] => 2 [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2 [[[.,[.,.]],[.,.]],[[.,.],.]] => 2 [[[[.,.],.],[.,.]],[.,[.,.]]] => 2 [[[[.,.],.],[.,.]],[[.,.],.]] => 2 [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2 [[[.,[.,[.,.]]],.],[[.,.],.]] => 2 [[[.,[[.,.],.]],.],[.,[.,.]]] => 2 [[[.,[[.,.],.]],.],[[.,.],.]] => 2 [[[[.,.],[.,.]],.],[.,[.,.]]] => 2 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[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => 2 [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2 [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 2 [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => 2 [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 2 [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => 2 [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => 2 [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 2 [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => 2 [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => 2 [[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2 [[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 2 [[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 2 [[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 2 [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 2 [[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 2 [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 2 [[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 2 [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 2 [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => 2 [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 2 [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 2 [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 2 [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 2 [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => 2 [[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => 2 [[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 2 [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => 2 [[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => 2 [[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 2 [[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 2 [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 2 [[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 2 [[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => 2 [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => 2 [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 2 [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => 2 ----------------------------------------------------------------------------- Created: Feb 23, 2017 at 20:19 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 23, 2019 at 08:47 by Martin Rubey