***************************************************************************** * 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: St000396 ----------------------------------------------------------------------------- Collection: Binary trees ----------------------------------------------------------------------------- Description: The register function (or Horton-Strahler number) of a binary tree. This is different from the dimension of the associated poset for the tree $[[[.,.],[.,.]],[[.,.],[.,.]]]$: its register function is 3, whereas the dimension of the associated poset is 2. ----------------------------------------------------------------------------- References: [1] Hackl, B., Heuberger, C., Prodinger, H. The Register Function and Reductions of Binary Trees and Lattice Paths [[arXiv:1602.06200]] ----------------------------------------------------------------------------- Code: def statistic(B): if B.is_empty(): return 0 else: r1 = statistic(B[0]) r2 = statistic(B[1]) if r1 == r2: return r1+1 else: return max(r1, r2) ----------------------------------------------------------------------------- Statistic values: [.,.] => 1 [.,[.,.]] => 1 [[.,.],.] => 1 [.,[.,[.,.]]] => 1 [.,[[.,.],.]] => 1 [[.,.],[.,.]] => 2 [[.,[.,.]],.] => 1 [[[.,.],.],.] => 1 [.,[.,[.,[.,.]]]] => 1 [.,[.,[[.,.],.]]] => 1 [.,[[.,.],[.,.]]] => 2 [.,[[.,[.,.]],.]] => 1 [.,[[[.,.],.],.]] => 1 [[.,.],[.,[.,.]]] => 2 [[.,.],[[.,.],.]] => 2 [[.,[.,.]],[.,.]] => 2 [[[.,.],.],[.,.]] => 2 [[.,[.,[.,.]]],.] => 1 [[.,[[.,.],.]],.] => 1 [[[.,.],[.,.]],.] => 2 [[[.,[.,.]],.],.] => 1 [[[[.,.],.],.],.] => 1 [.,[.,[.,[.,[.,.]]]]] => 1 [.,[.,[.,[[.,.],.]]]] => 1 [.,[.,[[.,.],[.,.]]]] => 2 [.,[.,[[.,[.,.]],.]]] => 1 [.,[.,[[[.,.],.],.]]] => 1 [.,[[.,.],[.,[.,.]]]] => 2 [.,[[.,.],[[.,.],.]]] => 2 [.,[[.,[.,.]],[.,.]]] => 2 [.,[[[.,.],.],[.,.]]] => 2 [.,[[.,[.,[.,.]]],.]] => 1 [.,[[.,[[.,.],.]],.]] => 1 [.,[[[.,.],[.,.]],.]] => 2 [.,[[[.,[.,.]],.],.]] => 1 [.,[[[[.,.],.],.],.]] => 1 [[.,.],[.,[.,[.,.]]]] => 2 [[.,.],[.,[[.,.],.]]] => 2 [[.,.],[[.,.],[.,.]]] => 2 [[.,.],[[.,[.,.]],.]] => 2 [[.,.],[[[.,.],.],.]] => 2 [[.,[.,.]],[.,[.,.]]] => 2 [[.,[.,.]],[[.,.],.]] => 2 [[[.,.],.],[.,[.,.]]] => 2 [[[.,.],.],[[.,.],.]] => 2 [[.,[.,[.,.]]],[.,.]] => 2 [[.,[[.,.],.]],[.,.]] => 2 [[[.,.],[.,.]],[.,.]] => 2 [[[.,[.,.]],.],[.,.]] => 2 [[[[.,.],.],.],[.,.]] => 2 [[.,[.,[.,[.,.]]]],.] => 1 [[.,[.,[[.,.],.]]],.] => 1 [[.,[[.,.],[.,.]]],.] => 2 [[.,[[.,[.,.]],.]],.] => 1 [[.,[[[.,.],.],.]],.] => 1 [[[.,.],[.,[.,.]]],.] => 2 [[[.,.],[[.,.],.]],.] => 2 [[[.,[.,.]],[.,.]],.] => 2 [[[[.,.],.],[.,.]],.] => 2 [[[.,[.,[.,.]]],.],.] => 1 [[[.,[[.,.],.]],.],.] => 1 [[[[.,.],[.,.]],.],.] => 2 [[[[.,[.,.]],.],.],.] => 1 [[[[[.,.],.],.],.],.] => 1 [.,[.,[.,[.,[.,[.,.]]]]]] => 1 [.,[.,[.,[.,[[.,.],.]]]]] => 1 [.,[.,[.,[[.,.],[.,.]]]]] => 2 [.,[.,[.,[[.,[.,.]],.]]]] => 1 [.,[.,[.,[[[.,.],.],.]]]] => 1 [.,[.,[[.,.],[.,[.,.]]]]] => 2 [.,[.,[[.,.],[[.,.],.]]]] => 2 [.,[.,[[.,[.,.]],[.,.]]]] => 2 [.,[.,[[[.,.],.],[.,.]]]] => 2 [.,[.,[[.,[.,[.,.]]],.]]] => 1 [.,[.,[[.,[[.,.],.]],.]]] => 1 [.,[.,[[[.,.],[.,.]],.]]] => 2 [.,[.,[[[.,[.,.]],.],.]]] => 1 [.,[.,[[[[.,.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,.]]]]] => 2 [.,[[.,.],[.,[[.,.],.]]]] => 2 [.,[[.,.],[[.,.],[.,.]]]] => 2 [.,[[.,.],[[.,[.,.]],.]]] => 2 [.,[[.,.],[[[.,.],.],.]]] => 2 [.,[[.,[.,.]],[.,[.,.]]]] => 2 [.,[[.,[.,.]],[[.,.],.]]] => 2 [.,[[[.,.],.],[.,[.,.]]]] => 2 [.,[[[.,.],.],[[.,.],.]]] => 2 [.,[[.,[.,[.,.]]],[.,.]]] => 2 [.,[[.,[[.,.],.]],[.,.]]] => 2 [.,[[[.,.],[.,.]],[.,.]]] => 2 [.,[[[.,[.,.]],.],[.,.]]] => 2 [.,[[[[.,.],.],.],[.,.]]] => 2 [.,[[.,[.,[.,[.,.]]]],.]] => 1 [.,[[.,[.,[[.,.],.]]],.]] => 1 [.,[[.,[[.,.],[.,.]]],.]] => 2 [.,[[.,[[.,[.,.]],.]],.]] => 1 [.,[[.,[[[.,.],.],.]],.]] => 1 [.,[[[.,.],[.,[.,.]]],.]] => 2 [.,[[[.,.],[[.,.],.]],.]] => 2 [.,[[[.,[.,.]],[.,.]],.]] => 2 [.,[[[[.,.],.],[.,.]],.]] => 2 [.,[[[.,[.,[.,.]]],.],.]] => 1 [.,[[[.,[[.,.],.]],.],.]] => 1 [.,[[[[.,.],[.,.]],.],.]] => 2 [.,[[[[.,[.,.]],.],.],.]] => 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 [[.,[.,[[.,.],[.,.]]]],.] => 2 [[.,[.,[[.,[.,.]],.]]],.] => 1 [[.,[.,[[[.,.],.],.]]],.] => 1 [[.,[[.,.],[.,[.,.]]]],.] => 2 [[.,[[.,.],[[.,.],.]]],.] => 2 [[.,[[.,[.,.]],[.,.]]],.] => 2 [[.,[[[.,.],.],[.,.]]],.] => 2 [[.,[[.,[.,[.,.]]],.]],.] => 1 [[.,[[.,[[.,.],.]],.]],.] => 1 [[.,[[[.,.],[.,.]],.]],.] => 2 [[.,[[[.,[.,.]],.],.]],.] => 1 [[.,[[[[.,.],.],.],.]],.] => 1 [[[.,.],[.,[.,[.,.]]]],.] => 2 [[[.,.],[.,[[.,.],.]]],.] => 2 [[[.,.],[[.,.],[.,.]]],.] => 2 [[[.,.],[[.,[.,.]],.]],.] => 2 [[[.,.],[[[.,.],.],.]],.] => 2 [[[.,[.,.]],[.,[.,.]]],.] => 2 [[[.,[.,.]],[[.,.],.]],.] => 2 [[[[.,.],.],[.,[.,.]]],.] => 2 [[[[.,.],.],[[.,.],.]],.] => 2 [[[.,[.,[.,.]]],[.,.]],.] => 2 [[[.,[[.,.],.]],[.,.]],.] => 2 [[[[.,.],[.,.]],[.,.]],.] => 2 [[[[.,[.,.]],.],[.,.]],.] => 2 [[[[[.,.],.],.],[.,.]],.] => 2 [[[.,[.,[.,[.,.]]]],.],.] => 1 [[[.,[.,[[.,.],.]]],.],.] => 1 [[[.,[[.,.],[.,.]]],.],.] => 2 [[[.,[[.,[.,.]],.]],.],.] => 1 [[[.,[[[.,.],.],.]],.],.] => 1 [[[[.,.],[.,[.,.]]],.],.] => 2 [[[[.,.],[[.,.],.]],.],.] => 2 [[[[.,[.,.]],[.,.]],.],.] => 2 [[[[[.,.],.],[.,.]],.],.] => 2 [[[[.,[.,[.,.]]],.],.],.] => 1 [[[[.,[[.,.],.]],.],.],.] => 1 [[[[[.,.],[.,.]],.],.],.] => 2 [[[[[.,[.,.]],.],.],.],.] => 1 [[[[[[.,.],.],.],.],.],.] => 1 [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1 [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1 [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2 [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1 [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1 [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2 [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2 [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2 [.,[.,[.,[[[.,.],.],[.,.]]]]] => 2 [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1 [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1 [.,[.,[.,[[[.,.],[.,.]],.]]]] => 2 [.,[.,[.,[[[.,[.,.]],.],.]]]] => 1 [.,[.,[.,[[[[.,.],.],.],.]]]] => 1 [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2 [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2 [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2 [.,[.,[[.,.],[[.,[.,.]],.]]]] => 2 [.,[.,[[.,.],[[[.,.],.],.]]]] => 2 [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2 [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2 [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2 [.,[.,[[[.,.],.],[[.,.],.]]]] => 2 [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2 [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2 [.,[.,[[[.,.],[.,.]],[.,.]]]] => 2 [.,[.,[[[.,[.,.]],.],[.,.]]]] => 2 [.,[.,[[[[.,.],.],.],[.,.]]]] => 2 [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1 [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1 [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2 [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1 [.,[.,[[.,[[[.,.],.],.]],.]]] => 1 [.,[.,[[[.,.],[.,[.,.]]],.]]] => 2 [.,[.,[[[.,.],[[.,.],.]],.]]] => 2 [.,[.,[[[.,[.,.]],[.,.]],.]]] => 2 [.,[.,[[[[.,.],.],[.,.]],.]]] => 2 [.,[.,[[[.,[.,[.,.]]],.],.]]] => 1 [.,[.,[[[.,[[.,.],.]],.],.]]] => 1 [.,[.,[[[[.,.],[.,.]],.],.]]] => 2 [.,[.,[[[[.,[.,.]],.],.],.]]] => 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 [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2 [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1 [.,[[.,[.,[[[.,.],.],.]]],.]] => 1 [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2 [.,[[.,[[.,.],[[.,.],.]]],.]] => 2 [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2 [.,[[.,[[[.,.],.],[.,.]]],.]] => 2 [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1 [.,[[.,[[.,[[.,.],.]],.]],.]] => 1 [.,[[.,[[[.,.],[.,.]],.]],.]] => 2 [.,[[.,[[[.,[.,.]],.],.]],.]] => 1 [.,[[.,[[[[.,.],.],.],.]],.]] => 1 [.,[[[.,.],[.,[.,[.,.]]]],.]] => 2 [.,[[[.,.],[.,[[.,.],.]]],.]] => 2 [.,[[[.,.],[[.,.],[.,.]]],.]] => 2 [.,[[[.,.],[[.,[.,.]],.]],.]] => 2 [.,[[[.,.],[[[.,.],.],.]],.]] => 2 [.,[[[.,[.,.]],[.,[.,.]]],.]] => 2 [.,[[[.,[.,.]],[[.,.],.]],.]] => 2 [.,[[[[.,.],.],[.,[.,.]]],.]] => 2 [.,[[[[.,.],.],[[.,.],.]],.]] => 2 [.,[[[.,[.,[.,.]]],[.,.]],.]] => 2 [.,[[[.,[[.,.],.]],[.,.]],.]] => 2 [.,[[[[.,.],[.,.]],[.,.]],.]] => 2 [.,[[[[.,[.,.]],.],[.,.]],.]] => 2 [.,[[[[[.,.],.],.],[.,.]],.]] => 2 [.,[[[.,[.,[.,[.,.]]]],.],.]] => 1 [.,[[[.,[.,[[.,.],.]]],.],.]] => 1 [.,[[[.,[[.,.],[.,.]]],.],.]] => 2 [.,[[[.,[[.,[.,.]],.]],.],.]] => 1 [.,[[[.,[[[.,.],.],.]],.],.]] => 1 [.,[[[[.,.],[.,[.,.]]],.],.]] => 2 [.,[[[[.,.],[[.,.],.]],.],.]] => 2 [.,[[[[.,[.,.]],[.,.]],.],.]] => 2 [.,[[[[[.,.],.],[.,.]],.],.]] => 2 [.,[[[[.,[.,[.,.]]],.],.],.]] => 1 [.,[[[[.,[[.,.],.]],.],.],.]] => 1 [.,[[[[[.,.],[.,.]],.],.],.]] => 2 [.,[[[[[.,[.,.]],.],.],.],.]] => 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 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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 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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 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 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 [[.,.],[[[.,[[[.,.],.],.]],.],.]] => 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 22, 2016 at 08:21 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 22, 2016 at 08:57 by Martin Rubey