***************************************************************************** * 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: St001767 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. Assign to each cell of the Ferrers diagram an arrow pointing north, east, south or west. Then compute for each cell the number of arrows pointing towards it, and take the minimum of those. This statistic is the maximal minimum that can be obtained by assigning arrows in any way. ----------------------------------------------------------------------------- References: [1] JetfiRex More precise bound for the maximin number of arrows pointing to a square when square grid is filled with arrows [[MathOverflow:414328]] ----------------------------------------------------------------------------- Code: def statistic(la): prog = MixedIntegerLinearProgram(maximization=True) arrow = prog.new_variable(binary=True, indices=[(i, j, v) for v in range(4) for i in range(len(la)) for j in range(la[i])]) pointed_at = prog.new_variable(integer=True, indices=[(i, j) for i in range(len(la)) for j in range(la[i])]) min_value = prog.new_variable(integer=True) prog.set_objective(min_value[0]) # 0 right # 1 left # 2 down # 3 up for i in range(len(la)): for j in range(la[i]): # every cell contains exactly an arrow: prog.add_constraint(prog.sum(arrow[(i, j, v)] for v in range(4)) == 1) # pointed_at contains the number of arrows pointing to (i, j) i_max = max(i1+1 for i1 in range(len(la)) if la[i1] > j) prog.add_constraint(pointed_at[i, j] == sum(arrow[(i, j1, 0)] for j1 in range(j)) + sum(arrow[(i, j1, 1)] for j1 in range(j+1, la[i])) + sum(arrow[(i1, j, 2)] for i1 in range(i)) + sum(arrow[(i1, j, 3)] for i1 in range(i+1, i_max))) # min_value contains the minimal value of all cells prog.add_constraint(min_value[0] <= pointed_at[i, j]) return ZZ(prog.solve()) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [2] => 1 [1,1] => 1 [3] => 1 [2,1] => 0 [1,1,1] => 1 [4] => 2 [3,1] => 1 [2,2] => 1 [2,1,1] => 1 [1,1,1,1] => 2 [5] => 2 [4,1] => 1 [3,2] => 1 [3,1,1] => 1 [2,2,1] => 1 [2,1,1,1] => 1 [1,1,1,1,1] => 2 [6] => 3 [5,1] => 1 [4,2] => 1 [4,1,1] => 1 [3,3] => 1 [3,2,1] => 1 [3,1,1,1] => 1 [2,2,2] => 1 [2,2,1,1] => 1 [2,1,1,1,1] => 1 [1,1,1,1,1,1] => 3 [7] => 3 [6,1] => 1 [5,2] => 1 [5,1,1] => 2 [4,3] => 1 [4,2,1] => 1 [4,1,1,1] => 1 [3,3,1] => 1 [3,2,2] => 1 [3,2,1,1] => 1 [3,1,1,1,1] => 2 [2,2,2,1] => 1 [2,2,1,1,1] => 1 [2,1,1,1,1,1] => 1 [1,1,1,1,1,1,1] => 3 [8] => 4 [7,1] => 1 [6,2] => 2 [6,1,1] => 2 [5,3] => 2 [5,2,1] => 1 [5,1,1,1] => 2 [4,4] => 2 [4,3,1] => 1 [4,2,2] => 1 [4,2,1,1] => 1 [4,1,1,1,1] => 2 [3,3,2] => 1 [3,3,1,1] => 1 [3,2,2,1] => 1 [3,2,1,1,1] => 1 [3,1,1,1,1,1] => 2 [2,2,2,2] => 2 [2,2,2,1,1] => 2 [2,2,1,1,1,1] => 2 [2,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1] => 4 [9] => 4 [8,1] => 1 [7,2] => 2 [7,1,1] => 2 [6,3] => 2 [6,2,1] => 1 [6,1,1,1] => 2 [5,4] => 2 [5,3,1] => 1 [5,2,2] => 1 [5,2,1,1] => 1 [5,1,1,1,1] => 2 [4,4,1] => 1 [4,3,2] => 1 [4,3,1,1] => 1 [4,2,2,1] => 1 [4,2,1,1,1] => 1 [4,1,1,1,1,1] => 2 [3,3,3] => 1 [3,3,2,1] => 1 [3,3,1,1,1] => 1 [3,2,2,2] => 1 [3,2,2,1,1] => 1 [3,2,1,1,1,1] => 1 [3,1,1,1,1,1,1] => 2 [2,2,2,2,1] => 2 [2,2,2,1,1,1] => 2 [2,2,1,1,1,1,1] => 2 [2,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1] => 4 [10] => 5 [9,1] => 1 [8,2] => 2 [8,1,1] => 2 [7,3] => 2 [7,2,1] => 1 [7,1,1,1] => 2 [6,4] => 2 [6,3,1] => 1 [6,2,2] => 2 [6,2,1,1] => 2 [6,1,1,1,1] => 2 [5,5] => 2 [5,4,1] => 1 [5,3,2] => 1 [5,3,1,1] => 2 [5,2,2,1] => 1 [5,2,1,1,1] => 1 [5,1,1,1,1,1] => 2 [4,4,2] => 1 [4,4,1,1] => 2 [4,3,3] => 1 [4,3,2,1] => 1 [4,3,1,1,1] => 1 [4,2,2,2] => 2 [4,2,2,1,1] => 2 [4,2,1,1,1,1] => 2 [4,1,1,1,1,1,1] => 2 [3,3,3,1] => 1 [3,3,2,2] => 1 [3,3,2,1,1] => 1 [3,3,1,1,1,1] => 2 [3,2,2,2,1] => 1 [3,2,2,1,1,1] => 1 [3,2,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1] => 2 [2,2,2,2,2] => 2 [2,2,2,2,1,1] => 2 [2,2,2,1,1,1,1] => 2 [2,2,1,1,1,1,1,1] => 2 [2,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1] => 5 [11] => 5 [10,1] => 1 [9,2] => 2 [9,1,1] => 2 [8,3] => 2 [8,2,1] => 1 [8,1,1,1] => 2 [7,4] => 2 [7,3,1] => 2 [7,2,2] => 2 [7,2,1,1] => 2 [7,1,1,1,1] => 3 [6,5] => 2 [6,4,1] => 2 [6,3,2] => 2 [6,3,1,1] => 2 [6,2,2,1] => 2 [6,2,1,1,1] => 2 [6,1,1,1,1,1] => 2 [5,5,1] => 2 [5,4,2] => 2 [5,4,1,1] => 2 [5,3,3] => 2 [5,3,2,1] => 1 [5,3,1,1,1] => 2 [5,2,2,2] => 2 [5,2,2,1,1] => 2 [5,2,1,1,1,1] => 2 [5,1,1,1,1,1,1] => 3 [4,4,3] => 2 [4,4,2,1] => 1 [4,4,1,1,1] => 2 [4,3,3,1] => 1 [4,3,2,2] => 1 [4,3,2,1,1] => 1 [4,3,1,1,1,1] => 2 [4,2,2,2,1] => 2 [4,2,2,1,1,1] => 2 [4,2,1,1,1,1,1] => 2 [4,1,1,1,1,1,1,1] => 2 [3,3,3,2] => 2 [3,3,3,1,1] => 2 [3,3,2,2,1] => 2 [3,3,2,1,1,1] => 2 [3,3,1,1,1,1,1] => 2 [3,2,2,2,2] => 2 [3,2,2,2,1,1] => 2 [3,2,2,1,1,1,1] => 2 [3,2,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1] => 2 [2,2,2,2,2,1] => 2 [2,2,2,2,1,1,1] => 2 [2,2,2,1,1,1,1,1] => 2 [2,2,1,1,1,1,1,1,1] => 2 [2,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1] => 5 [12] => 6 [11,1] => 1 [10,2] => 2 [10,1,1] => 2 [9,3] => 2 [9,2,1] => 1 [9,1,1,1] => 2 [8,4] => 3 [8,3,1] => 2 [8,2,2] => 2 [8,2,1,1] => 2 [8,1,1,1,1] => 3 [7,5] => 3 [7,4,1] => 2 [7,3,2] => 2 [7,3,1,1] => 2 [7,2,2,1] => 2 [7,2,1,1,1] => 2 [7,1,1,1,1,1] => 3 [6,6] => 3 [6,5,1] => 2 [6,4,2] => 2 [6,4,1,1] => 2 [6,3,3] => 2 [6,3,2,1] => 1 [6,3,1,1,1] => 2 [6,2,2,2] => 2 [6,2,2,1,1] => 2 [6,2,1,1,1,1] => 2 [6,1,1,1,1,1,1] => 3 [5,5,2] => 2 [5,5,1,1] => 2 [5,4,3] => 2 [5,4,2,1] => 1 [5,4,1,1,1] => 2 [5,3,3,1] => 2 [5,3,2,2] => 2 [5,3,2,1,1] => 2 [5,3,1,1,1,1] => 2 [5,2,2,2,1] => 2 [5,2,2,1,1,1] => 2 [5,2,1,1,1,1,1] => 2 [5,1,1,1,1,1,1,1] => 3 [4,4,4] => 2 [4,4,3,1] => 1 [4,4,2,2] => 2 [4,4,2,1,1] => 2 [4,4,1,1,1,1] => 2 [4,3,3,2] => 1 [4,3,3,1,1] => 2 [4,3,2,2,1] => 1 [4,3,2,1,1,1] => 1 [4,3,1,1,1,1,1] => 2 [4,2,2,2,2] => 2 [4,2,2,2,1,1] => 2 [4,2,2,1,1,1,1] => 2 [4,2,1,1,1,1,1,1] => 2 [4,1,1,1,1,1,1,1,1] => 2 [3,3,3,3] => 2 [3,3,3,2,1] => 2 [3,3,3,1,1,1] => 2 [3,3,2,2,2] => 2 [3,3,2,2,1,1] => 2 [3,3,2,1,1,1,1] => 2 [3,3,1,1,1,1,1,1] => 2 [3,2,2,2,2,1] => 2 [3,2,2,2,1,1,1] => 2 [3,2,2,1,1,1,1,1] => 2 [3,2,1,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1,1] => 2 [2,2,2,2,2,2] => 3 [2,2,2,2,2,1,1] => 3 [2,2,2,2,1,1,1,1] => 3 [2,2,2,1,1,1,1,1,1] => 2 [2,2,1,1,1,1,1,1,1,1] => 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] => 6 [13] => 6 [12,1] => 1 [11,2] => 2 [11,1,1] => 2 [10,3] => 2 [10,2,1] => 1 [10,1,1,1] => 2 [9,4] => 3 [9,3,1] => 2 [9,2,2] => 2 [9,2,1,1] => 2 [9,1,1,1,1] => 3 [8,5] => 3 [8,4,1] => 2 [8,3,2] => 2 [8,3,1,1] => 2 [8,2,2,1] => 2 [8,2,1,1,1] => 2 [8,1,1,1,1,1] => 3 [7,6] => 3 [7,5,1] => 2 [7,4,2] => 2 [7,4,1,1] => 2 [7,3,3] => 2 [7,3,2,1] => 2 [7,3,1,1,1] => 2 [7,2,2,2] => 2 [7,2,2,1,1] => 2 [7,2,1,1,1,1] => 2 [7,1,1,1,1,1,1] => 3 [6,6,1] => 2 [6,5,2] => 2 [6,5,1,1] => 2 [6,4,3] => 2 [6,4,2,1] => 2 [6,4,1,1,1] => 2 [6,3,3,1] => 2 [6,3,2,2] => 2 [6,3,2,1,1] => 2 [6,3,1,1,1,1] => 2 [6,2,2,2,1] => 2 [6,2,2,1,1,1] => 2 [6,2,1,1,1,1,1] => 2 [6,1,1,1,1,1,1,1] => 3 [5,5,3] => 2 [5,5,2,1] => 2 [5,5,1,1,1] => 2 [5,4,4] => 2 [5,4,3,1] => 2 [5,4,2,2] => 2 [5,4,2,1,1] => 2 [5,4,1,1,1,1] => 2 [5,3,3,2] => 2 [5,3,3,1,1] => 2 [5,3,2,2,1] => 2 [5,3,2,1,1,1] => 2 [5,3,1,1,1,1,1] => 2 [5,2,2,2,2] => 2 [5,2,2,2,1,1] => 2 [5,2,2,1,1,1,1] => 2 [5,2,1,1,1,1,1,1] => 2 [5,1,1,1,1,1,1,1,1] => 3 [4,4,4,1] => 2 [4,4,3,2] => 1 [4,4,3,1,1] => 2 [4,4,2,2,1] => 2 [4,4,2,1,1,1] => 2 [4,4,1,1,1,1,1] => 2 [4,3,3,3] => 2 [4,3,3,2,1] => 2 [4,3,3,1,1,1] => 2 [4,3,2,2,2] => 2 [4,3,2,2,1,1] => 2 [4,3,2,1,1,1,1] => 2 [4,3,1,1,1,1,1,1] => 2 [4,2,2,2,2,1] => 2 [4,2,2,2,1,1,1] => 2 [4,2,2,1,1,1,1,1] => 2 [4,2,1,1,1,1,1,1,1] => 2 [4,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,1] => 2 [3,3,3,2,2] => 2 [3,3,3,2,1,1] => 2 [3,3,3,1,1,1,1] => 2 [3,3,2,2,2,1] => 2 [3,3,2,2,1,1,1] => 2 [3,3,2,1,1,1,1,1] => 2 [3,3,1,1,1,1,1,1,1] => 2 [3,2,2,2,2,2] => 2 [3,2,2,2,2,1,1] => 2 [3,2,2,2,1,1,1,1] => 2 [3,2,2,1,1,1,1,1,1] => 2 [3,2,1,1,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1,1,1] => 2 [2,2,2,2,2,2,1] => 3 [2,2,2,2,2,1,1,1] => 3 [2,2,2,2,1,1,1,1,1] => 3 [2,2,2,1,1,1,1,1,1,1] => 2 [2,2,1,1,1,1,1,1,1,1,1] => 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] => 6 [14] => 7 [13,1] => 1 [12,2] => 2 [12,1,1] => 2 [11,3] => 2 [11,2,1] => 1 [11,1,1,1] => 2 [10,4] => 3 [10,3,1] => 2 [10,2,2] => 2 [10,2,1,1] => 2 [10,1,1,1,1] => 3 [9,5] => 3 [9,4,1] => 2 [9,3,2] => 2 [9,3,1,1] => 2 [9,2,2,1] => 2 [9,2,1,1,1] => 2 [9,1,1,1,1,1] => 3 [8,6] => 3 [8,5,1] => 2 [8,4,2] => 2 [8,4,1,1] => 2 [8,3,3] => 2 [8,3,2,1] => 2 [8,3,1,1,1] => 2 [8,2,2,2] => 2 [8,2,2,1,1] => 2 [8,2,1,1,1,1] => 2 [8,1,1,1,1,1,1] => 3 [7,7] => 3 [7,6,1] => 2 [7,5,2] => 2 [7,5,1,1] => 2 [7,4,3] => 2 [7,4,2,1] => 2 [7,4,1,1,1] => 2 [7,3,3,1] => 2 [7,3,2,2] => 2 [7,3,2,1,1] => 2 [7,3,1,1,1,1] => 2 [7,2,2,2,1] => 2 [7,2,2,1,1,1] => 2 [7,2,1,1,1,1,1] => 2 [7,1,1,1,1,1,1,1] => 3 [6,6,2] => 2 [6,6,1,1] => 2 [6,5,3] => 2 [6,5,2,1] => 2 [6,5,1,1,1] => 2 [6,4,4] => 2 [6,4,3,1] => 2 [6,4,2,2] => 2 [6,4,2,1,1] => 2 [6,4,1,1,1,1] => 2 [6,3,3,2] => 2 [6,3,3,1,1] => 2 [6,3,2,2,1] => 2 [6,3,2,1,1,1] => 2 [6,3,1,1,1,1,1] => 2 [6,2,2,2,2] => 2 [6,2,2,2,1,1] => 2 [6,2,2,1,1,1,1] => 2 [6,2,1,1,1,1,1,1] => 2 [6,1,1,1,1,1,1,1,1] => 3 [5,5,4] => 2 [5,5,3,1] => 2 [5,5,2,2] => 2 [5,5,2,1,1] => 2 [5,5,1,1,1,1] => 2 [5,4,4,1] => 2 [5,4,3,2] => 2 [5,4,3,1,1] => 2 [5,4,2,2,1] => 2 [5,4,2,1,1,1] => 2 [5,4,1,1,1,1,1] => 2 [5,3,3,3] => 2 [5,3,3,2,1] => 2 [5,3,3,1,1,1] => 2 [5,3,2,2,2] => 2 [5,3,2,2,1,1] => 2 [5,3,2,1,1,1,1] => 2 [5,3,1,1,1,1,1,1] => 2 [5,2,2,2,2,1] => 2 [5,2,2,2,1,1,1] => 2 [5,2,2,1,1,1,1,1] => 2 [5,2,1,1,1,1,1,1,1] => 2 [5,1,1,1,1,1,1,1,1,1] => 3 [4,4,4,2] => 2 [4,4,4,1,1] => 2 [4,4,3,3] => 2 [4,4,3,2,1] => 2 [4,4,3,1,1,1] => 2 [4,4,2,2,2] => 2 [4,4,2,2,1,1] => 2 [4,4,2,1,1,1,1] => 2 [4,4,1,1,1,1,1,1] => 2 [4,3,3,3,1] => 2 [4,3,3,2,2] => 2 [4,3,3,2,1,1] => 2 [4,3,3,1,1,1,1] => 2 [4,3,2,2,2,1] => 2 [4,3,2,2,1,1,1] => 2 [4,3,2,1,1,1,1,1] => 2 [4,3,1,1,1,1,1,1,1] => 2 [4,2,2,2,2,2] => 2 [4,2,2,2,2,1,1] => 2 [4,2,2,2,1,1,1,1] => 2 [4,2,2,1,1,1,1,1,1] => 2 [4,2,1,1,1,1,1,1,1,1] => 2 [4,1,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,2] => 2 [3,3,3,3,1,1] => 2 [3,3,3,2,2,1] => 2 [3,3,3,2,1,1,1] => 2 [3,3,3,1,1,1,1,1] => 2 [3,3,2,2,2,2] => 2 [3,3,2,2,2,1,1] => 2 [3,3,2,2,1,1,1,1] => 2 [3,3,2,1,1,1,1,1,1] => 2 [3,3,1,1,1,1,1,1,1,1] => 2 [3,2,2,2,2,2,1] => 2 [3,2,2,2,2,1,1,1] => 2 [3,2,2,2,1,1,1,1,1] => 2 [3,2,2,1,1,1,1,1,1,1] => 2 [3,2,1,1,1,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1,1,1,1] => 2 [2,2,2,2,2,2,2] => 3 [2,2,2,2,2,2,1,1] => 3 [2,2,2,2,2,1,1,1,1] => 3 [2,2,2,2,1,1,1,1,1,1] => 3 [2,2,2,1,1,1,1,1,1,1,1] => 2 [2,2,1,1,1,1,1,1,1,1,1,1] => 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] => 7 [15] => 7 [14,1] => 1 [13,2] => 2 [13,1,1] => 2 [12,3] => 2 [12,2,1] => 1 [12,1,1,1] => 2 [11,4] => 3 [11,3,1] => 2 [11,2,2] => 2 [11,2,1,1] => 2 [11,1,1,1,1] => 3 [10,5] => 3 [10,4,1] => 2 [10,3,2] => 2 [10,3,1,1] => 2 [10,2,2,1] => 2 [10,2,1,1,1] => 2 [10,1,1,1,1,1] => 3 [9,6] => 3 [9,5,1] => 2 [9,4,2] => 2 [9,4,1,1] => 2 [9,3,3] => 2 [9,3,2,1] => 2 [9,3,1,1,1] => 2 [9,2,2,2] => 2 [9,2,2,1,1] => 2 [9,2,1,1,1,1] => 2 [9,1,1,1,1,1,1] => 4 [8,7] => 3 [8,6,1] => 2 [8,5,2] => 2 [8,5,1,1] => 2 [8,4,3] => 2 [8,4,2,1] => 2 [8,4,1,1,1] => 2 [8,3,3,1] => 2 [8,3,2,2] => 2 [8,3,2,1,1] => 2 [8,3,1,1,1,1] => 2 [8,2,2,2,1] => 2 [8,2,2,1,1,1] => 2 [8,2,1,1,1,1,1] => 2 [8,1,1,1,1,1,1,1] => 3 [7,7,1] => 2 [7,6,2] => 2 [7,6,1,1] => 2 [7,5,3] => 2 [7,5,2,1] => 2 [7,5,1,1,1] => 2 [7,4,4] => 2 [7,4,3,1] => 2 [7,4,2,2] => 2 [7,4,2,1,1] => 2 [7,4,1,1,1,1] => 2 [7,3,3,2] => 2 [7,3,3,1,1] => 2 [7,3,2,2,1] => 2 [7,3,2,1,1,1] => 2 [7,3,1,1,1,1,1] => 2 [7,2,2,2,2] => 2 [7,2,2,2,1,1] => 2 [7,2,2,1,1,1,1] => 2 [7,2,1,1,1,1,1,1] => 2 [7,1,1,1,1,1,1,1,1] => 4 [6,6,3] => 2 [6,6,2,1] => 2 [6,6,1,1,1] => 2 [6,5,4] => 2 [6,5,3,1] => 2 [6,5,2,2] => 2 [6,5,2,1,1] => 2 [6,5,1,1,1,1] => 2 [6,4,4,1] => 2 [6,4,3,2] => 2 [6,4,3,1,1] => 2 [6,4,2,2,1] => 2 [6,4,2,1,1,1] => 2 [6,4,1,1,1,1,1] => 2 [6,3,3,3] => 2 [6,3,3,2,1] => 2 [6,3,3,1,1,1] => 2 [6,3,2,2,2] => 2 [6,3,2,2,1,1] => 2 [6,3,2,1,1,1,1] => 2 [6,3,1,1,1,1,1,1] => 2 [6,2,2,2,2,1] => 2 [6,2,2,2,1,1,1] => 2 [6,2,2,1,1,1,1,1] => 2 [6,2,1,1,1,1,1,1,1] => 2 [6,1,1,1,1,1,1,1,1,1] => 3 [5,5,5] => 2 [5,5,4,1] => 2 [5,5,3,2] => 2 [5,5,3,1,1] => 2 [5,5,2,2,1] => 2 [5,5,2,1,1,1] => 2 [5,5,1,1,1,1,1] => 2 [5,4,4,2] => 2 [5,4,4,1,1] => 2 [5,4,3,3] => 2 [5,4,3,2,1] => 2 [5,4,3,1,1,1] => 2 [5,4,2,2,2] => 2 [5,4,2,2,1,1] => 2 [5,4,2,1,1,1,1] => 2 [5,4,1,1,1,1,1,1] => 2 [5,3,3,3,1] => 2 [5,3,3,2,2] => 2 [5,3,3,2,1,1] => 2 [5,3,3,1,1,1,1] => 2 [5,3,2,2,2,1] => 2 [5,3,2,2,1,1,1] => 2 [5,3,2,1,1,1,1,1] => 2 [5,3,1,1,1,1,1,1,1] => 2 [5,2,2,2,2,2] => 2 [5,2,2,2,2,1,1] => 2 [5,2,2,2,1,1,1,1] => 2 [5,2,2,1,1,1,1,1,1] => 2 [5,2,1,1,1,1,1,1,1,1] => 2 [5,1,1,1,1,1,1,1,1,1,1] => 3 [4,4,4,3] => 2 [4,4,4,2,1] => 2 [4,4,4,1,1,1] => 2 [4,4,3,3,1] => 2 [4,4,3,2,2] => 2 [4,4,3,2,1,1] => 2 [4,4,3,1,1,1,1] => 2 [4,4,2,2,2,1] => 2 [4,4,2,2,1,1,1] => 2 [4,4,2,1,1,1,1,1] => 2 [4,4,1,1,1,1,1,1,1] => 2 [4,3,3,3,2] => 2 [4,3,3,3,1,1] => 2 [4,3,3,2,2,1] => 2 [4,3,3,2,1,1,1] => 2 [4,3,3,1,1,1,1,1] => 2 [4,3,2,2,2,2] => 2 [4,3,2,2,2,1,1] => 2 [4,3,2,2,1,1,1,1] => 2 [4,3,2,1,1,1,1,1,1] => 2 [4,3,1,1,1,1,1,1,1,1] => 2 [4,2,2,2,2,2,1] => 2 [4,2,2,2,2,1,1,1] => 2 [4,2,2,2,1,1,1,1,1] => 2 [4,2,2,1,1,1,1,1,1,1] => 2 [4,2,1,1,1,1,1,1,1,1,1] => 2 [4,1,1,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,3] => 2 [3,3,3,3,2,1] => 2 [3,3,3,3,1,1,1] => 2 [3,3,3,2,2,2] => 2 [3,3,3,2,2,1,1] => 2 [3,3,3,2,1,1,1,1] => 2 [3,3,3,1,1,1,1,1,1] => 2 [3,3,2,2,2,2,1] => 2 [3,3,2,2,2,1,1,1] => 2 [3,3,2,2,1,1,1,1,1] => 2 [3,3,2,1,1,1,1,1,1,1] => 2 [3,3,1,1,1,1,1,1,1,1,1] => 2 [3,2,2,2,2,2,2] => 2 [3,2,2,2,2,2,1,1] => 2 [3,2,2,2,2,1,1,1,1] => 2 [3,2,2,2,1,1,1,1,1,1] => 2 [3,2,2,1,1,1,1,1,1,1,1] => 2 [3,2,1,1,1,1,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [2,2,2,2,2,2,2,1] => 3 [2,2,2,2,2,2,1,1,1] => 3 [2,2,2,2,2,1,1,1,1,1] => 3 [2,2,2,2,1,1,1,1,1,1,1] => 3 [2,2,2,1,1,1,1,1,1,1,1,1] => 2 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 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] => 7 [16] => 8 [15,1] => 1 [14,2] => 2 [14,1,1] => 2 [13,3] => 2 [13,2,1] => 1 [13,1,1,1] => 2 [12,4] => 3 [12,3,1] => 2 [12,2,2] => 2 [12,2,1,1] => 2 [12,1,1,1,1] => 3 [11,5] => 3 [11,4,1] => 2 [11,3,2] => 2 [11,3,1,1] => 2 [11,2,2,1] => 2 [11,2,1,1,1] => 2 [11,1,1,1,1,1] => 3 [10,6] => 4 [10,5,1] => 2 [10,4,2] => 2 [10,4,1,1] => 2 [10,3,3] => 2 [10,3,2,1] => 2 [10,3,1,1,1] => 2 [10,2,2,2] => 2 [10,2,2,1,1] => 2 [10,2,1,1,1,1] => 2 [10,1,1,1,1,1,1] => 4 [9,7] => 4 [9,6,1] => 2 [9,5,2] => 2 [9,5,1,1] => 3 [9,4,3] => 2 [9,4,2,1] => 2 [9,4,1,1,1] => 2 [9,3,3,1] => 2 [9,3,2,2] => 2 [9,3,2,1,1] => 2 [9,3,1,1,1,1] => 3 [9,2,2,2,1] => 2 [9,2,2,1,1,1] => 2 [9,2,1,1,1,1,1] => 2 [9,1,1,1,1,1,1,1] => 4 [8,8] => 4 [8,7,1] => 2 [8,6,2] => 2 [8,6,1,1] => 3 [8,5,3] => 2 [8,5,2,1] => 2 [8,5,1,1,1] => 2 [8,4,4] => 3 [8,4,3,1] => 2 [8,4,2,2] => 2 [8,4,2,1,1] => 2 [8,4,1,1,1,1] => 3 [8,3,3,2] => 2 [8,3,3,1,1] => 2 [8,3,2,2,1] => 2 [8,3,2,1,1,1] => 2 [8,3,1,1,1,1,1] => 2 [8,2,2,2,2] => 3 [8,2,2,2,1,1] => 3 [8,2,2,1,1,1,1] => 3 [8,2,1,1,1,1,1,1] => 2 [8,1,1,1,1,1,1,1,1] => 4 [7,7,2] => 2 [7,7,1,1] => 3 [7,6,3] => 2 [7,6,2,1] => 2 [7,6,1,1,1] => 2 [7,5,4] => 2 [7,5,3,1] => 2 [7,5,2,2] => 2 [7,5,2,1,1] => 2 [7,5,1,1,1,1] => 3 [7,4,4,1] => 2 [7,4,3,2] => 2 [7,4,3,1,1] => 2 [7,4,2,2,1] => 2 [7,4,2,1,1,1] => 2 [7,4,1,1,1,1,1] => 2 [7,3,3,3] => 2 [7,3,3,2,1] => 2 [7,3,3,1,1,1] => 2 [7,3,2,2,2] => 2 [7,3,2,2,1,1] => 2 [7,3,2,1,1,1,1] => 2 [7,3,1,1,1,1,1,1] => 3 [7,2,2,2,2,1] => 2 [7,2,2,2,1,1,1] => 2 [7,2,2,1,1,1,1,1] => 2 [7,2,1,1,1,1,1,1,1] => 2 [7,1,1,1,1,1,1,1,1,1] => 4 [6,6,4] => 2 [6,6,3,1] => 2 [6,6,2,2] => 2 [6,6,2,1,1] => 2 [6,6,1,1,1,1] => 3 [6,5,5] => 2 [6,5,4,1] => 2 [6,5,3,2] => 2 [6,5,3,1,1] => 2 [6,5,2,2,1] => 2 [6,5,2,1,1,1] => 2 [6,5,1,1,1,1,1] => 2 [6,4,4,2] => 2 [6,4,4,1,1] => 2 [6,4,3,3] => 2 [6,4,3,2,1] => 2 [6,4,3,1,1,1] => 2 [6,4,2,2,2] => 2 [6,4,2,2,1,1] => 2 [6,4,2,1,1,1,1] => 2 [6,4,1,1,1,1,1,1] => 3 [6,3,3,3,1] => 2 [6,3,3,2,2] => 2 [6,3,3,2,1,1] => 2 [6,3,3,1,1,1,1] => 2 [6,3,2,2,2,1] => 2 [6,3,2,2,1,1,1] => 2 [6,3,2,1,1,1,1,1] => 2 [6,3,1,1,1,1,1,1,1] => 2 [6,2,2,2,2,2] => 3 [6,2,2,2,2,1,1] => 3 [6,2,2,2,1,1,1,1] => 3 [6,2,2,1,1,1,1,1,1] => 3 [6,2,1,1,1,1,1,1,1,1] => 2 [6,1,1,1,1,1,1,1,1,1,1] => 3 [5,5,5,1] => 2 [5,5,4,2] => 2 [5,5,4,1,1] => 2 [5,5,3,3] => 2 [5,5,3,2,1] => 2 [5,5,3,1,1,1] => 2 [5,5,2,2,2] => 2 [5,5,2,2,1,1] => 2 [5,5,2,1,1,1,1] => 2 [5,5,1,1,1,1,1,1] => 3 [5,4,4,3] => 2 [5,4,4,2,1] => 2 [5,4,4,1,1,1] => 2 [5,4,3,3,1] => 2 [5,4,3,2,2] => 2 [5,4,3,2,1,1] => 2 [5,4,3,1,1,1,1] => 2 [5,4,2,2,2,1] => 2 [5,4,2,2,1,1,1] => 2 [5,4,2,1,1,1,1,1] => 2 [5,4,1,1,1,1,1,1,1] => 2 [5,3,3,3,2] => 2 [5,3,3,3,1,1] => 2 [5,3,3,2,2,1] => 2 [5,3,3,2,1,1,1] => 2 [5,3,3,1,1,1,1,1] => 2 [5,3,2,2,2,2] => 2 [5,3,2,2,2,1,1] => 2 [5,3,2,2,1,1,1,1] => 2 [5,3,2,1,1,1,1,1,1] => 2 [5,3,1,1,1,1,1,1,1,1] => 2 [5,2,2,2,2,2,1] => 2 [5,2,2,2,2,1,1,1] => 2 [5,2,2,2,1,1,1,1,1] => 2 [5,2,2,1,1,1,1,1,1,1] => 2 [5,2,1,1,1,1,1,1,1,1,1] => 2 [5,1,1,1,1,1,1,1,1,1,1,1] => 3 [4,4,4,4] => 2 [4,4,4,3,1] => 2 [4,4,4,2,2] => 2 [4,4,4,2,1,1] => 2 [4,4,4,1,1,1,1] => 2 [4,4,3,3,2] => 2 [4,4,3,3,1,1] => 2 [4,4,3,2,2,1] => 2 [4,4,3,2,1,1,1] => 2 [4,4,3,1,1,1,1,1] => 2 [4,4,2,2,2,2] => 2 [4,4,2,2,2,1,1] => 2 [4,4,2,2,1,1,1,1] => 2 [4,4,2,1,1,1,1,1,1] => 2 [4,4,1,1,1,1,1,1,1,1] => 2 [4,3,3,3,3] => 2 [4,3,3,3,2,1] => 2 [4,3,3,3,1,1,1] => 2 [4,3,3,2,2,2] => 2 [4,3,3,2,2,1,1] => 2 [4,3,3,2,1,1,1,1] => 2 [4,3,3,1,1,1,1,1,1] => 2 [4,3,2,2,2,2,1] => 2 [4,3,2,2,2,1,1,1] => 2 [4,3,2,2,1,1,1,1,1] => 2 [4,3,2,1,1,1,1,1,1,1] => 2 [4,3,1,1,1,1,1,1,1,1,1] => 2 [4,2,2,2,2,2,2] => 3 [4,2,2,2,2,2,1,1] => 3 [4,2,2,2,2,1,1,1,1] => 3 [4,2,2,2,1,1,1,1,1,1] => 2 [4,2,2,1,1,1,1,1,1,1,1] => 2 [4,2,1,1,1,1,1,1,1,1,1,1] => 2 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,3,1] => 2 [3,3,3,3,2,2] => 2 [3,3,3,3,2,1,1] => 2 [3,3,3,3,1,1,1,1] => 3 [3,3,3,2,2,2,1] => 2 [3,3,3,2,2,1,1,1] => 2 [3,3,3,2,1,1,1,1,1] => 2 [3,3,3,1,1,1,1,1,1,1] => 2 [3,3,2,2,2,2,2] => 2 [3,3,2,2,2,2,1,1] => 2 [3,3,2,2,2,1,1,1,1] => 2 [3,3,2,2,1,1,1,1,1,1] => 2 [3,3,2,1,1,1,1,1,1,1,1] => 2 [3,3,1,1,1,1,1,1,1,1,1,1] => 2 [3,2,2,2,2,2,2,1] => 2 [3,2,2,2,2,2,1,1,1] => 2 [3,2,2,2,2,1,1,1,1,1] => 2 [3,2,2,2,1,1,1,1,1,1,1] => 2 [3,2,2,1,1,1,1,1,1,1,1,1] => 2 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [2,2,2,2,2,2,2,2] => 4 [2,2,2,2,2,2,2,1,1] => 4 [2,2,2,2,2,2,1,1,1,1] => 4 [2,2,2,2,2,1,1,1,1,1,1] => 3 [2,2,2,2,1,1,1,1,1,1,1,1] => 3 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 2 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 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] => 8 [17] => 8 [16,1] => 1 [15,2] => 2 [15,1,1] => 2 [14,3] => 2 [14,2,1] => 1 [14,1,1,1] => 2 [13,4] => 3 [13,3,1] => 2 [13,2,2] => 2 [13,2,1,1] => 2 [13,1,1,1,1] => 3 [12,5] => 3 [12,4,1] => 2 [12,3,2] => 2 [12,3,1,1] => 2 [12,2,2,1] => 2 [12,2,1,1,1] => 2 [12,1,1,1,1,1] => 3 [11,6] => 4 [11,5,1] => 2 [11,4,2] => 2 [11,4,1,1] => 2 [11,3,3] => 2 [11,3,2,1] => 2 [11,3,1,1,1] => 2 [11,2,2,2] => 2 [11,2,2,1,1] => 2 [11,2,1,1,1,1] => 2 [11,1,1,1,1,1,1] => 4 [10,7] => 4 [10,6,1] => 2 [10,5,2] => 2 [10,5,1,1] => 3 [10,4,3] => 2 [10,4,2,1] => 2 [10,4,1,1,1] => 2 [10,3,3,1] => 2 [10,3,2,2] => 2 [10,3,2,1,1] => 2 [10,3,1,1,1,1] => 3 [10,2,2,2,1] => 2 [10,2,2,1,1,1] => 2 [10,2,1,1,1,1,1] => 2 [10,1,1,1,1,1,1,1] => 4 [9,8] => 4 [9,7,1] => 2 [9,6,2] => 2 [9,6,1,1] => 3 [9,5,3] => 2 [9,5,2,1] => 2 [9,5,1,1,1] => 3 [9,4,4] => 3 [9,4,3,1] => 2 [9,4,2,2] => 2 [9,4,2,1,1] => 2 [9,4,1,1,1,1] => 3 [9,3,3,2] => 2 [9,3,3,1,1] => 2 [9,3,2,2,1] => 2 [9,3,2,1,1,1] => 2 [9,3,1,1,1,1,1] => 3 [9,2,2,2,2] => 3 [9,2,2,2,1,1] => 3 [9,2,2,1,1,1,1] => 3 [9,2,1,1,1,1,1,1] => 2 [9,1,1,1,1,1,1,1,1] => 4 [8,8,1] => 2 [8,7,2] => 2 [8,7,1,1] => 3 [8,6,3] => 2 [8,6,2,1] => 2 [8,6,1,1,1] => 3 [8,5,4] => 3 [8,5,3,1] => 2 [8,5,2,2] => 2 [8,5,2,1,1] => 2 [8,5,1,1,1,1] => 3 [8,4,4,1] => 2 [8,4,3,2] => 2 [8,4,3,1,1] => 2 [8,4,2,2,1] => 2 [8,4,2,1,1,1] => 2 [8,4,1,1,1,1,1] => 3 [8,3,3,3] => 2 [8,3,3,2,1] => 2 [8,3,3,1,1,1] => 2 [8,3,2,2,2] => 2 [8,3,2,2,1,1] => 2 [8,3,2,1,1,1,1] => 2 [8,3,1,1,1,1,1,1] => 3 [8,2,2,2,2,1] => 3 [8,2,2,2,1,1,1] => 3 [8,2,2,1,1,1,1,1] => 3 [8,2,1,1,1,1,1,1,1] => 2 [8,1,1,1,1,1,1,1,1,1] => 4 [7,7,3] => 2 [7,7,2,1] => 2 [7,7,1,1,1] => 3 [7,6,4] => 3 [7,6,3,1] => 2 [7,6,2,2] => 2 [7,6,2,1,1] => 2 [7,6,1,1,1,1] => 3 [7,5,5] => 3 [7,5,4,1] => 2 [7,5,3,2] => 2 [7,5,3,1,1] => 2 [7,5,2,2,1] => 2 [7,5,2,1,1,1] => 2 [7,5,1,1,1,1,1] => 3 [7,4,4,2] => 2 [7,4,4,1,1] => 2 [7,4,3,3] => 2 [7,4,3,2,1] => 2 [7,4,3,1,1,1] => 2 [7,4,2,2,2] => 2 [7,4,2,2,1,1] => 2 [7,4,2,1,1,1,1] => 2 [7,4,1,1,1,1,1,1] => 3 [7,3,3,3,1] => 2 [7,3,3,2,2] => 2 [7,3,3,2,1,1] => 2 [7,3,3,1,1,1,1] => 2 [7,3,2,2,2,1] => 2 [7,3,2,2,1,1,1] => 2 [7,3,2,1,1,1,1,1] => 2 [7,3,1,1,1,1,1,1,1] => 3 [7,2,2,2,2,2] => 3 [7,2,2,2,2,1,1] => 3 [7,2,2,2,1,1,1,1] => 3 [7,2,2,1,1,1,1,1,1] => 3 [7,2,1,1,1,1,1,1,1,1] => 2 [7,1,1,1,1,1,1,1,1,1,1] => 4 [6,6,5] => 3 [6,6,4,1] => 2 [6,6,3,2] => 2 [6,6,3,1,1] => 2 [6,6,2,2,1] => 2 [6,6,2,1,1,1] => 2 [6,6,1,1,1,1,1] => 3 [6,5,5,1] => 2 [6,5,4,2] => 2 [6,5,4,1,1] => 2 [6,5,3,3] => 2 [6,5,3,2,1] => 2 [6,5,3,1,1,1] => 2 [6,5,2,2,2] => 2 [6,5,2,2,1,1] => 2 [6,5,2,1,1,1,1] => 2 [6,5,1,1,1,1,1,1] => 3 [6,4,4,3] => 2 [6,4,4,2,1] => 2 [6,4,4,1,1,1] => 2 [6,4,3,3,1] => 2 [6,4,3,2,2] => 2 [6,4,3,2,1,1] => 2 [6,4,3,1,1,1,1] => 2 [6,4,2,2,2,1] => 2 [6,4,2,2,1,1,1] => 2 [6,4,2,1,1,1,1,1] => 2 [6,4,1,1,1,1,1,1,1] => 3 [6,3,3,3,2] => 2 [6,3,3,3,1,1] => 2 [6,3,3,2,2,1] => 2 [6,3,3,2,1,1,1] => 2 [6,3,3,1,1,1,1,1] => 2 [6,3,2,2,2,2] => 2 [6,3,2,2,2,1,1] => 2 [6,3,2,2,1,1,1,1] => 2 [6,3,2,1,1,1,1,1,1] => 2 [6,3,1,1,1,1,1,1,1,1] => 2 [6,2,2,2,2,2,1] => 3 [6,2,2,2,2,1,1,1] => 3 [6,2,2,2,1,1,1,1,1] => 3 [6,2,2,1,1,1,1,1,1,1] => 3 [6,2,1,1,1,1,1,1,1,1,1] => 2 [6,1,1,1,1,1,1,1,1,1,1,1] => 3 [5,5,5,2] => 2 [5,5,5,1,1] => 2 [5,5,4,3] => 2 [5,5,4,2,1] => 2 [5,5,4,1,1,1] => 2 [5,5,3,3,1] => 2 [5,5,3,2,2] => 2 [5,5,3,2,1,1] => 2 [5,5,3,1,1,1,1] => 2 [5,5,2,2,2,1] => 2 [5,5,2,2,1,1,1] => 2 [5,5,2,1,1,1,1,1] => 2 [5,5,1,1,1,1,1,1,1] => 3 [5,4,4,4] => 2 [5,4,4,3,1] => 2 [5,4,4,2,2] => 2 [5,4,4,2,1,1] => 2 [5,4,4,1,1,1,1] => 2 [5,4,3,3,2] => 2 [5,4,3,3,1,1] => 2 [5,4,3,2,2,1] => 2 [5,4,3,2,1,1,1] => 2 [5,4,3,1,1,1,1,1] => 2 [5,4,2,2,2,2] => 2 [5,4,2,2,2,1,1] => 2 [5,4,2,2,1,1,1,1] => 2 [5,4,2,1,1,1,1,1,1] => 2 [5,4,1,1,1,1,1,1,1,1] => 2 [5,3,3,3,3] => 2 [5,3,3,3,2,1] => 2 [5,3,3,3,1,1,1] => 2 [5,3,3,2,2,2] => 2 [5,3,3,2,2,1,1] => 2 [5,3,3,2,1,1,1,1] => 2 [5,3,3,1,1,1,1,1,1] => 2 [5,3,2,2,2,2,1] => 2 [5,3,2,2,2,1,1,1] => 2 [5,3,2,2,1,1,1,1,1] => 2 [5,3,2,1,1,1,1,1,1,1] => 2 [5,3,1,1,1,1,1,1,1,1,1] => 2 [5,2,2,2,2,2,2] => 3 [5,2,2,2,2,2,1,1] => 3 [5,2,2,2,2,1,1,1,1] => 3 [5,2,2,2,1,1,1,1,1,1] => 2 [5,2,2,1,1,1,1,1,1,1,1] => 2 [5,2,1,1,1,1,1,1,1,1,1,1] => 2 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 3 [4,4,4,4,1] => 2 [4,4,4,3,2] => 2 [4,4,4,3,1,1] => 2 [4,4,4,2,2,1] => 2 [4,4,4,2,1,1,1] => 2 [4,4,4,1,1,1,1,1] => 2 [4,4,3,3,3] => 2 [4,4,3,3,2,1] => 2 [4,4,3,3,1,1,1] => 2 [4,4,3,2,2,2] => 2 [4,4,3,2,2,1,1] => 2 [4,4,3,2,1,1,1,1] => 2 [4,4,3,1,1,1,1,1,1] => 2 [4,4,2,2,2,2,1] => 2 [4,4,2,2,2,1,1,1] => 2 [4,4,2,2,1,1,1,1,1] => 2 [4,4,2,1,1,1,1,1,1,1] => 2 [4,4,1,1,1,1,1,1,1,1,1] => 2 [4,3,3,3,3,1] => 2 [4,3,3,3,2,2] => 2 [4,3,3,3,2,1,1] => 2 [4,3,3,3,1,1,1,1] => 2 [4,3,3,2,2,2,1] => 2 [4,3,3,2,2,1,1,1] => 2 [4,3,3,2,1,1,1,1,1] => 2 [4,3,3,1,1,1,1,1,1,1] => 2 [4,3,2,2,2,2,2] => 2 [4,3,2,2,2,2,1,1] => 2 [4,3,2,2,2,1,1,1,1] => 2 [4,3,2,2,1,1,1,1,1,1] => 2 [4,3,2,1,1,1,1,1,1,1,1] => 2 [4,3,1,1,1,1,1,1,1,1,1,1] => 2 [4,2,2,2,2,2,2,1] => 3 [4,2,2,2,2,2,1,1,1] => 3 [4,2,2,2,2,1,1,1,1,1] => 3 [4,2,2,2,1,1,1,1,1,1,1] => 2 [4,2,2,1,1,1,1,1,1,1,1,1] => 2 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 2 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,3,2] => 3 [3,3,3,3,3,1,1] => 3 [3,3,3,3,2,2,1] => 3 [3,3,3,3,2,1,1,1] => 3 [3,3,3,3,1,1,1,1,1] => 3 [3,3,3,2,2,2,2] => 2 [3,3,3,2,2,2,1,1] => 2 [3,3,3,2,2,1,1,1,1] => 2 [3,3,3,2,1,1,1,1,1,1] => 2 [3,3,3,1,1,1,1,1,1,1,1] => 2 [3,3,2,2,2,2,2,1] => 2 [3,3,2,2,2,2,1,1,1] => 2 [3,3,2,2,2,1,1,1,1,1] => 2 [3,3,2,2,1,1,1,1,1,1,1] => 2 [3,3,2,1,1,1,1,1,1,1,1,1] => 2 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 2 [3,2,2,2,2,2,2,2] => 2 [3,2,2,2,2,2,2,1,1] => 2 [3,2,2,2,2,2,1,1,1,1] => 2 [3,2,2,2,2,1,1,1,1,1,1] => 2 [3,2,2,2,1,1,1,1,1,1,1,1] => 2 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 2 ----------------------------------------------------------------------------- Created: Jan 24, 2022 at 15:52 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jan 24, 2022 at 15:52 by Martin Rubey