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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
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