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Your data matches 12 different statistics following compositions of up to 3 maps.
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Matching statistic: St000815
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000815: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000815: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => ([],3)
=> [1,1,1]
=> [1,1]
=> 1
[1,2,3,4] => ([],4)
=> [1,1,1,1]
=> [1,1,1]
=> 1
[1,2,4,3] => ([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> 1
[1,3,2,4] => ([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> 1
[2,1,3,4] => ([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> 1
[2,1,4,3] => ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 2
[1,2,3,4,5] => ([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,2,3,5,4] => ([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 1
[1,2,4,3,5] => ([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 1
[1,2,4,5,3] => ([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[1,2,5,3,4] => ([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[1,3,2,4,5] => ([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 1
[1,3,2,5,4] => ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 3
[1,3,4,2,5] => ([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[1,4,2,3,5] => ([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[2,1,3,4,5] => ([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 1
[2,1,3,5,4] => ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 3
[2,1,4,3,5] => ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 3
[2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 2
[2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 2
[2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 2
[2,3,1,4,5] => ([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 2
[3,1,2,4,5] => ([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 2
[3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
[3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 2
[1,2,3,4,5,6] => ([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
[1,2,3,4,6,5] => ([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,2,3,5,4,6] => ([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,2,3,5,6,4] => ([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
[1,2,3,6,4,5] => ([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
[1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
[1,2,4,3,5,6] => ([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,2,4,3,6,5] => ([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> 4
[1,2,4,5,3,6] => ([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
[1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,4,6,5,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,5,3,4,6] => ([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
[1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
[1,2,5,4,6,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,5,6,4,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
[1,2,6,4,3,5] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
Description
The number of semistandard Young tableaux of partition weight of given shape.
The weight of a semistandard Young tableaux is the sequence $(m_1, m_2,\dots)$, where $m_i$ is the number of occurrences of the number $i$ in the tableau. This statistic counts those tableaux whose weight is a weakly decreasing sequence.
Alternatively, this is the sum of the entries in the column specified by the partition of the change of basis matrix from Schur functions to monomial symmetric functions.
Matching statistic: St000455
(load all 21 compositions to match this statistic)
(load all 21 compositions to match this statistic)
Mp00130: Permutations —descent tops⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 10% ●values known / values provided: 20%●distinct values known / distinct values provided: 10%
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 10% ●values known / values provided: 20%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => 00 => [3] => ([],3)
=> ? = 1 - 1
[1,2,3,4] => 000 => [4] => ([],4)
=> ? = 1 - 1
[1,2,4,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,3,2,4] => 010 => [2,2] => ([(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,1,3,4] => 100 => [1,3] => ([(2,3)],4)
=> 0 = 1 - 1
[2,1,4,3] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 2 - 1
[1,2,3,4,5] => 0000 => [5] => ([],5)
=> ? = 1 - 1
[1,2,3,5,4] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,2,4,3,5] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,2,4,5,3] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,2,5,3,4] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,2,5,4,3] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,3,2,4,5] => 0100 => [2,3] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,3,2,5,4] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
[1,3,4,2,5] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,4,2,3,5] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,4,3,2,5] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 1 - 1
[2,1,3,4,5] => 1000 => [1,4] => ([(3,4)],5)
=> 0 = 1 - 1
[2,1,3,5,4] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
[2,1,4,3,5] => 1010 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
[2,1,4,5,3] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 - 1
[2,1,5,3,4] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 - 1
[2,1,5,4,3] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 - 1
[2,3,1,4,5] => 0100 => [2,3] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[2,3,1,5,4] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 - 1
[3,1,2,4,5] => 0100 => [2,3] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[3,1,2,5,4] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 - 1
[3,2,1,4,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> 0 = 1 - 1
[3,2,1,5,4] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 - 1
[1,2,3,4,5,6] => 00000 => [6] => ([],6)
=> ? = 1 - 1
[1,2,3,4,6,5] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,3,5,4,6] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,3,5,6,4] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,3,6,4,5] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,3,6,5,4] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,4,3,5,6] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,4,3,6,5] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,2,4,5,3,6] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,4,5,6,3] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,4,6,3,5] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,4,6,5,3] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,5,3,4,6] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,5,3,6,4] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,5,4,3,6] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,5,4,6,3] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,5,6,3,4] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,5,6,4,3] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 1
[1,2,6,3,4,5] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,6,3,5,4] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,6,4,3,5] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 1
[1,2,6,4,5,3] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,6,5,3,4] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,6,5,4,3] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,3,2,4,5,6] => 01000 => [2,4] => ([(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,3,2,4,6,5] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,3,2,5,4,6] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[1,3,2,5,6,4] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,2,6,4,5] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,2,6,5,4] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,4,2,5,6] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,3,4,2,6,5] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,3,4,5,2,6] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,3,5,2,4,6] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,3,5,4,2,6] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,4,2,3,5,6] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,4,2,3,6,5] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,4,2,5,3,6] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,4,3,2,5,6] => 01100 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,4,3,2,6,5] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[1,4,3,5,2,6] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,4,5,2,3,6] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,4,5,3,2,6] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 1
[1,5,2,3,4,6] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,5,2,4,3,6] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,5,3,2,4,6] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 1
[1,5,3,4,2,6] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,5,4,2,3,6] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 1 - 1
[2,1,3,4,6,5] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[2,1,3,5,4,6] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[2,1,3,5,6,4] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[2,1,3,6,4,5] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[2,1,3,6,5,4] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[2,1,4,3,5,6] => 10100 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[2,1,4,3,6,5] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[2,1,4,5,3,6] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[2,1,4,5,6,3] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,4,6,3,5] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,4,6,5,3] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,5,3,4,6] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[2,1,5,3,6,4] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,5,4,3,6] => 10110 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
[2,1,5,4,6,3] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,5,6,3,4] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,5,6,4,3] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,6,3,4,5] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,6,3,5,4] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,6,4,3,5] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,6,4,5,3] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,6,5,3,4] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[2,1,6,5,4,3] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Matching statistic: St001719
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001719: Lattices ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 10%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001719: Lattices ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => [3] => ([],3)
=> ([],1)
=> 1
[1,2,3,4] => [4] => ([],4)
=> ([],1)
=> 1
[1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[2,1,3,4] => [1,3] => ([(2,3)],4)
=> ([(0,1)],2)
=> 1
[2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2
[1,2,3,4,5] => [5] => ([],5)
=> ([],1)
=> 1
[1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3
[1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1
[2,1,3,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 1
[2,1,3,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 3
[2,1,4,3,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3
[2,1,4,5,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2
[2,1,5,3,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2
[2,1,5,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 2
[2,3,1,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[2,3,1,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 2
[3,1,2,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 1
[3,1,2,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2
[3,2,1,4,5] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
[3,2,1,5,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? = 2
[1,2,3,4,5,6] => [6] => ([],6)
=> ([],1)
=> 1
[1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1
[1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1
[1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1
[1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 4
[1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1
[1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1
[1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1
[1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1
[1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1
[1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1
[1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1
[1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,2,6,5,4,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(1,15),(1,26),(1,27),(1,32),(1,33),(1,41),(1,42),(1,91),(1,94),(2,14),(2,23),(2,25),(2,29),(2,31),(2,40),(2,42),(2,90),(2,93),(3,13),(3,22),(3,24),(3,28),(3,30),(3,40),(3,41),(3,89),(3,92),(4,18),(4,24),(4,25),(4,34),(4,35),(4,43),(4,44),(4,86),(4,94),(5,17),(5,22),(5,26),(5,36),(5,38),(5,43),(5,45),(5,87),(5,93),(6,16),(6,23),(6,27),(6,37),(6,39),(6,44),(6,45),(6,88),(6,92),(7,21),(7,30),(7,31),(7,36),(7,37),(7,46),(7,47),(7,86),(7,91),(8,20),(8,28),(8,32),(8,34),(8,39),(8,46),(8,48),(8,87),(8,90),(9,19),(9,29),(9,33),(9,35),(9,38),(9,47),(9,48),(9,88),(9,89),(10,19),(10,20),(10,21),(10,49),(10,92),(10,93),(10,94),(11,16),(11,17),(11,18),(11,49),(11,89),(11,90),(11,91),(12,13),(12,14),(12,15),(12,49),(12,86),(12,87),(12,88),(13,53),(13,54),(13,98),(13,100),(13,134),(14,53),(14,55),(14,99),(14,101),(14,135),(15,54),(15,55),(15,102),(15,103),(15,136),(16,56),(16,58),(16,107),(16,108),(16,134),(17,57),(17,58),(17,106),(17,109),(17,135),(18,56),(18,57),(18,104),(18,105),(18,136),(19,59),(19,61),(19,113),(19,114),(19,134),(20,60),(20,61),(20,112),(20,115),(20,135),(21,59),(21,60),(21,110),(21,111),(21,136),(22,63),(22,65),(22,80),(22,98),(22,106),(22,131),(23,64),(23,66),(23,81),(23,99),(23,107),(23,131),(24,62),(24,65),(24,82),(24,100),(24,104),(24,132),(25,62),(25,66),(25,83),(25,101),(25,105),(25,133),(26,63),(26,67),(26,84),(26,102),(26,109),(26,133),(27,64),(27,67),(27,85),(27,103),(27,108),(27,132),(28,69),(28,74),(28,82),(28,98),(28,112),(28,128),(29,70),(29,75),(29,83),(29,99),(29,113),(29,128),(30,68),(30,74),(30,80),(30,100),(30,110),(30,129),(31,68),(31,75),(31,81),(31,101),(31,111),(31,130),(32,69),(32,76),(32,85),(32,102),(32,115),(32,130),(33,70),(33,76),(33,84),(33,103),(33,114),(33,129),(34,72),(34,79),(34,82),(34,105),(34,115),(34,126),(35,71),(35,79),(35,83),(35,104),(35,114),(35,125),(36,73),(36,77),(36,80),(36,109),(36,111),(36,126),(37,73),(37,78),(37,81),(37,108),(37,110),(37,125),(38,71),(38,77),(38,84),(38,106),(38,113),(38,127),(39,72),(39,78),(39,85),(39,107),(39,112),(39,127),(40,50),(40,53),(40,62),(40,68),(40,128),(40,131),(41,50),(41,54),(41,63),(41,69),(41,129),(41,132),(42,50),(42,55),(42,64),(42,70),(42,130),(42,133),(43,51),(43,57),(43,65),(43,71),(43,126),(43,133),(44,51),(44,56),(44,66),(44,72),(44,125),(44,132),(45,51),(45,58),(45,67),(45,73),(45,127),(45,131),(46,52),(46,60),(46,74),(46,78),(46,126),(46,130),(47,52),(47,59),(47,75),(47,77),(47,125),(47,129),(48,52),(48,61),(48,76),(48,79),(48,127),(48,128),(49,134),(49,135),(49,136),(50,95),(50,147),(50,148),(51,96),(51,146),(51,148),(52,97),(52,146),(52,147),(53,95),(53,118),(53,151),(54,95),(54,116),(54,149),(55,95),(55,117),(55,150),(56,96),(56,120),(56,149),(57,96),(57,119),(57,150),(58,96),(58,121),(58,151),(59,97),(59,123),(59,149),(60,97),(60,122),(60,150),(61,97),(61,124),(61,151),(62,118),(62,142),(62,148),(63,116),(63,140),(63,148),(64,117),(64,141),(64,148),(65,119),(65,137),(65,148),(66,120),(66,138),(66,148),(67,121),(67,139),(67,148),(68,118),(68,143),(68,147),(69,116),(69,144),(69,147),(70,117),(70,145),(70,147),(71,119),(71,145),(71,146),(72,120),(72,144),(72,146),(73,121),(73,143),(73,146),(74,122),(74,137),(74,147),(75,123),(75,138),(75,147),(76,124),(76,139),(76,147),(77,123),(77,140),(77,146),(78,122),(78,141),(78,146),(79,124),(79,142),(79,146),(80,137),(80,140),(80,143),(81,138),(81,141),(81,143),(82,137),(82,142),(82,144),(83,138),(83,142),(83,145),(84,139),(84,140),(84,145),(85,139),(85,141),(85,144),(86,100),(86,101),(86,125),(86,126),(86,136),(87,98),(87,102),(87,126),(87,127),(87,135),(88,99),(88,103),(88,125),(88,127),(88,134),(89,104),(89,106),(89,128),(89,129),(89,134),(90,105),(90,107),(90,128),(90,130),(90,135),(91,108),(91,109),(91,129),(91,130),(91,136),(92,110),(92,112),(92,131),(92,132),(92,134),(93,111),(93,113),(93,131),(93,133),(93,135),(94,114),(94,115),(94,132),(94,133),(94,136),(95,152),(96,152),(97,152),(98,116),(98,137),(98,151),(99,117),(99,138),(99,151),(100,118),(100,137),(100,149),(101,118),(101,138),(101,150),(102,116),(102,139),(102,150),(103,117),(103,139),(103,149),(104,119),(104,142),(104,149),(105,120),(105,142),(105,150),(106,119),(106,140),(106,151),(107,120),(107,141),(107,151),(108,121),(108,141),(108,149),(109,121),(109,140),(109,150),(110,122),(110,143),(110,149),(111,123),(111,143),(111,150),(112,122),(112,144),(112,151),(113,123),(113,145),(113,151),(114,124),(114,145),(114,149),(115,124),(115,144),(115,150),(116,152),(117,152),(118,152),(119,152),(120,152),(121,152),(122,152),(123,152),(124,152),(125,138),(125,146),(125,149),(126,137),(126,146),(126,150),(127,139),(127,146),(127,151),(128,142),(128,147),(128,151),(129,140),(129,147),(129,149),(130,141),(130,147),(130,150),(131,143),(131,148),(131,151),(132,144),(132,148),(132,149),(133,145),(133,148),(133,150),(134,149),(134,151),(135,150),(135,151),(136,149),(136,150),(137,152),(138,152),(139,152),(140,152),(141,152),(142,152),(143,152),(144,152),(145,152),(146,152),(147,152),(148,152),(149,152),(150,152),(151,152)],153)
=> ? = 1
[1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 4
[1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 4
[1,3,2,5,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3
[1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3
[1,3,2,6,5,4] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,16),(1,17),(1,30),(1,31),(1,39),(1,40),(1,41),(1,42),(1,49),(2,14),(2,15),(2,28),(2,29),(2,35),(2,36),(2,37),(2,38),(2,49),(3,19),(3,23),(3,27),(3,34),(3,36),(3,40),(3,74),(3,79),(4,18),(4,22),(4,26),(4,33),(4,35),(4,39),(4,74),(4,78),(5,21),(5,22),(5,24),(5,34),(5,37),(5,41),(5,75),(5,76),(6,20),(6,23),(6,25),(6,33),(6,38),(6,42),(6,75),(6,77),(7,13),(7,20),(7,21),(7,29),(7,31),(7,32),(7,78),(7,79),(8,12),(8,18),(8,19),(8,28),(8,30),(8,32),(8,76),(8,77),(9,14),(9,16),(9,25),(9,26),(9,48),(9,76),(9,79),(10,15),(10,17),(10,24),(10,27),(10,48),(10,77),(10,78),(11,12),(11,13),(11,48),(11,49),(11,74),(11,75),(12,43),(12,84),(12,98),(12,121),(13,43),(13,85),(13,99),(13,122),(14,55),(14,56),(14,86),(14,89),(14,109),(15,54),(15,57),(15,87),(15,88),(15,109),(16,59),(16,60),(16,90),(16,93),(16,109),(17,58),(17,61),(17,91),(17,92),(17,109),(18,62),(18,66),(18,84),(18,94),(18,113),(19,63),(19,67),(19,84),(19,95),(19,114),(20,64),(20,68),(20,85),(20,97),(20,113),(21,65),(21,69),(21,85),(21,96),(21,114),(22,50),(22,52),(22,94),(22,96),(22,110),(23,51),(23,53),(23,95),(23,97),(23,110),(24,54),(24,58),(24,71),(24,96),(24,121),(25,55),(25,59),(25,70),(25,97),(25,121),(26,56),(26,60),(26,70),(26,94),(26,122),(27,57),(27,61),(27,71),(27,95),(27,122),(28,62),(28,63),(28,72),(28,86),(28,87),(28,98),(29,64),(29,65),(29,72),(29,88),(29,89),(29,99),(30,66),(30,67),(30,73),(30,90),(30,91),(30,98),(31,68),(31,69),(31,73),(31,92),(31,93),(31,99),(32,43),(32,72),(32,73),(32,113),(32,114),(33,44),(33,46),(33,70),(33,110),(33,113),(34,45),(34,47),(34,71),(34,110),(34,114),(35,44),(35,50),(35,56),(35,62),(35,88),(35,111),(36,45),(36,51),(36,57),(36,63),(36,89),(36,111),(37,45),(37,50),(37,54),(37,65),(37,86),(37,112),(38,44),(38,51),(38,55),(38,64),(38,87),(38,112),(39,46),(39,52),(39,60),(39,66),(39,92),(39,111),(40,47),(40,53),(40,61),(40,67),(40,93),(40,111),(41,47),(41,52),(41,58),(41,69),(41,90),(41,112),(42,46),(42,53),(42,59),(42,68),(42,91),(42,112),(43,100),(43,126),(44,80),(44,117),(44,123),(45,81),(45,118),(45,123),(46,82),(46,119),(46,123),(47,83),(47,120),(47,123),(48,109),(48,121),(48,122),(49,98),(49,99),(49,109),(49,111),(49,112),(50,101),(50,103),(50,123),(51,102),(51,104),(51,123),(52,105),(52,107),(52,123),(53,106),(53,108),(53,123),(54,81),(54,103),(54,124),(55,80),(55,104),(55,124),(56,80),(56,101),(56,125),(57,81),(57,102),(57,125),(58,83),(58,107),(58,124),(59,82),(59,108),(59,124),(60,82),(60,105),(60,125),(61,83),(61,106),(61,125),(62,101),(62,115),(62,117),(63,102),(63,115),(63,118),(64,104),(64,116),(64,117),(65,103),(65,116),(65,118),(66,105),(66,115),(66,119),(67,106),(67,115),(67,120),(68,108),(68,116),(68,119),(69,107),(69,116),(69,120),(70,80),(70,82),(70,126),(71,81),(71,83),(71,126),(72,100),(72,117),(72,118),(73,100),(73,119),(73,120),(74,84),(74,110),(74,111),(74,122),(75,85),(75,110),(75,112),(75,121),(76,86),(76,90),(76,94),(76,114),(76,121),(77,87),(77,91),(77,95),(77,113),(77,121),(78,88),(78,92),(78,96),(78,113),(78,122),(79,89),(79,93),(79,97),(79,114),(79,122),(80,127),(81,127),(82,127),(83,127),(84,115),(84,126),(85,116),(85,126),(86,101),(86,118),(86,124),(87,102),(87,117),(87,124),(88,103),(88,117),(88,125),(89,104),(89,118),(89,125),(90,105),(90,120),(90,124),(91,106),(91,119),(91,124),(92,107),(92,119),(92,125),(93,108),(93,120),(93,125),(94,101),(94,105),(94,126),(95,102),(95,106),(95,126),(96,103),(96,107),(96,126),(97,104),(97,108),(97,126),(98,100),(98,115),(98,124),(99,100),(99,116),(99,125),(100,127),(101,127),(102,127),(103,127),(104,127),(105,127),(106,127),(107,127),(108,127),(109,124),(109,125),(110,123),(110,126),(111,115),(111,123),(111,125),(112,116),(112,123),(112,124),(113,117),(113,119),(113,126),(114,118),(114,120),(114,126),(115,127),(116,127),(117,127),(118,127),(119,127),(120,127),(121,124),(121,126),(122,125),(122,126),(123,127),(124,127),(125,127),(126,127)],128)
=> ? = 3
[1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,4,2,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 3
[1,3,4,5,2,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,5,4,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3
[1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1
[1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1
[1,4,3,2,6,5] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,17),(1,18),(1,19),(1,29),(1,30),(1,31),(1,32),(1,33),(1,34),(2,15),(2,16),(2,22),(2,28),(2,31),(2,55),(2,56),(3,12),(3,14),(3,21),(3,27),(3,30),(3,54),(3,56),(4,11),(4,13),(4,20),(4,26),(4,29),(4,54),(4,55),(5,13),(5,14),(5,25),(5,28),(5,32),(5,57),(5,58),(6,11),(6,15),(6,23),(6,27),(6,33),(6,57),(6,59),(7,12),(7,16),(7,24),(7,26),(7,34),(7,58),(7,59),(8,17),(8,20),(8,24),(8,41),(8,56),(8,57),(9,18),(9,21),(9,23),(9,41),(9,55),(9,58),(10,19),(10,22),(10,25),(10,41),(10,54),(10,59),(11,35),(11,70),(11,74),(11,82),(12,36),(12,71),(12,75),(12,82),(13,37),(13,70),(13,73),(13,83),(14,38),(14,71),(14,73),(14,84),(15,39),(15,72),(15,74),(15,84),(16,40),(16,72),(16,75),(16,83),(17,45),(17,49),(17,63),(17,66),(17,67),(18,46),(18,48),(18,63),(18,65),(18,68),(19,47),(19,50),(19,63),(19,64),(19,69),(20,45),(20,51),(20,70),(20,89),(21,46),(21,52),(21,71),(21,89),(22,47),(22,53),(22,72),(22,89),(23,48),(23,52),(23,74),(23,88),(24,49),(24,51),(24,75),(24,88),(25,50),(25,53),(25,73),(25,88),(26,42),(26,51),(26,82),(26,83),(27,43),(27,52),(27,82),(27,84),(28,44),(28,53),(28,83),(28,84),(29,35),(29,37),(29,42),(29,45),(29,64),(29,65),(30,36),(30,38),(30,43),(30,46),(30,64),(30,66),(31,39),(31,40),(31,44),(31,47),(31,65),(31,66),(32,37),(32,38),(32,44),(32,50),(32,67),(32,68),(33,35),(33,39),(33,43),(33,48),(33,67),(33,69),(34,36),(34,40),(34,42),(34,49),(34,68),(34,69),(35,76),(35,80),(35,85),(36,77),(36,81),(36,85),(37,76),(37,79),(37,86),(38,77),(38,79),(38,87),(39,78),(39,80),(39,87),(40,78),(40,81),(40,86),(41,63),(41,88),(41,89),(42,60),(42,85),(42,86),(43,61),(43,85),(43,87),(44,62),(44,86),(44,87),(45,60),(45,76),(45,90),(46,61),(46,77),(46,90),(47,62),(47,78),(47,90),(48,61),(48,80),(48,91),(49,60),(49,81),(49,91),(50,62),(50,79),(50,91),(51,60),(51,92),(52,61),(52,92),(53,62),(53,92),(54,64),(54,73),(54,82),(54,89),(55,65),(55,74),(55,83),(55,89),(56,66),(56,75),(56,84),(56,89),(57,67),(57,70),(57,84),(57,88),(58,68),(58,71),(58,83),(58,88),(59,69),(59,72),(59,82),(59,88),(60,93),(61,93),(62,93),(63,90),(63,91),(64,79),(64,85),(64,90),(65,80),(65,86),(65,90),(66,81),(66,87),(66,90),(67,76),(67,87),(67,91),(68,77),(68,86),(68,91),(69,78),(69,85),(69,91),(70,76),(70,92),(71,77),(71,92),(72,78),(72,92),(73,79),(73,92),(74,80),(74,92),(75,81),(75,92),(76,93),(77,93),(78,93),(79,93),(80,93),(81,93),(82,85),(82,92),(83,86),(83,92),(84,87),(84,92),(85,93),(86,93),(87,93),(88,91),(88,92),(89,90),(89,92),(90,93),(91,93),(92,93)],94)
=> ? = 3
[1,4,3,5,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1
[1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,4,5,3,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1
[1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1
[2,1,3,4,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 1
[2,3,1,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[2,3,4,1,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[2,4,1,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[3,1,2,4,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 1
[3,2,1,4,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
[3,4,1,2,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[4,1,2,3,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 1
[4,2,1,3,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
[4,3,1,2,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
[1,2,3,4,5,6,7] => [7] => ([],7)
=> ([],1)
=> 1
[1,2,4,3,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,5,3,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,6,3,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,7,3,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,2,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,2,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,5,2,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,6,2,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,4,2,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,5,2,3,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,4,6,2,3,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,5,2,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,6,2,3,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,6,2,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
The number of shortest chains of small intervals from the bottom to the top in a lattice.
An interval $[a, b]$ in a lattice is small if $b$ is a join of elements covering $a$.
Matching statistic: St001820
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001820: Lattices ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 10%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001820: Lattices ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => [3] => ([],3)
=> ([],1)
=> 1
[1,2,3,4] => [4] => ([],4)
=> ([],1)
=> 1
[1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[2,1,3,4] => [1,3] => ([(2,3)],4)
=> ([(0,1)],2)
=> 1
[2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2
[1,2,3,4,5] => [5] => ([],5)
=> ([],1)
=> 1
[1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3
[1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1
[2,1,3,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 1
[2,1,3,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 3
[2,1,4,3,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3
[2,1,4,5,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2
[2,1,5,3,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2
[2,1,5,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 2
[2,3,1,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[2,3,1,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 2
[3,1,2,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 1
[3,1,2,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2
[3,2,1,4,5] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
[3,2,1,5,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? = 2
[1,2,3,4,5,6] => [6] => ([],6)
=> ([],1)
=> 1
[1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1
[1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1
[1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1
[1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 4
[1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1
[1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1
[1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1
[1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1
[1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1
[1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1
[1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1
[1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,2,6,5,4,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(1,15),(1,26),(1,27),(1,32),(1,33),(1,41),(1,42),(1,91),(1,94),(2,14),(2,23),(2,25),(2,29),(2,31),(2,40),(2,42),(2,90),(2,93),(3,13),(3,22),(3,24),(3,28),(3,30),(3,40),(3,41),(3,89),(3,92),(4,18),(4,24),(4,25),(4,34),(4,35),(4,43),(4,44),(4,86),(4,94),(5,17),(5,22),(5,26),(5,36),(5,38),(5,43),(5,45),(5,87),(5,93),(6,16),(6,23),(6,27),(6,37),(6,39),(6,44),(6,45),(6,88),(6,92),(7,21),(7,30),(7,31),(7,36),(7,37),(7,46),(7,47),(7,86),(7,91),(8,20),(8,28),(8,32),(8,34),(8,39),(8,46),(8,48),(8,87),(8,90),(9,19),(9,29),(9,33),(9,35),(9,38),(9,47),(9,48),(9,88),(9,89),(10,19),(10,20),(10,21),(10,49),(10,92),(10,93),(10,94),(11,16),(11,17),(11,18),(11,49),(11,89),(11,90),(11,91),(12,13),(12,14),(12,15),(12,49),(12,86),(12,87),(12,88),(13,53),(13,54),(13,98),(13,100),(13,134),(14,53),(14,55),(14,99),(14,101),(14,135),(15,54),(15,55),(15,102),(15,103),(15,136),(16,56),(16,58),(16,107),(16,108),(16,134),(17,57),(17,58),(17,106),(17,109),(17,135),(18,56),(18,57),(18,104),(18,105),(18,136),(19,59),(19,61),(19,113),(19,114),(19,134),(20,60),(20,61),(20,112),(20,115),(20,135),(21,59),(21,60),(21,110),(21,111),(21,136),(22,63),(22,65),(22,80),(22,98),(22,106),(22,131),(23,64),(23,66),(23,81),(23,99),(23,107),(23,131),(24,62),(24,65),(24,82),(24,100),(24,104),(24,132),(25,62),(25,66),(25,83),(25,101),(25,105),(25,133),(26,63),(26,67),(26,84),(26,102),(26,109),(26,133),(27,64),(27,67),(27,85),(27,103),(27,108),(27,132),(28,69),(28,74),(28,82),(28,98),(28,112),(28,128),(29,70),(29,75),(29,83),(29,99),(29,113),(29,128),(30,68),(30,74),(30,80),(30,100),(30,110),(30,129),(31,68),(31,75),(31,81),(31,101),(31,111),(31,130),(32,69),(32,76),(32,85),(32,102),(32,115),(32,130),(33,70),(33,76),(33,84),(33,103),(33,114),(33,129),(34,72),(34,79),(34,82),(34,105),(34,115),(34,126),(35,71),(35,79),(35,83),(35,104),(35,114),(35,125),(36,73),(36,77),(36,80),(36,109),(36,111),(36,126),(37,73),(37,78),(37,81),(37,108),(37,110),(37,125),(38,71),(38,77),(38,84),(38,106),(38,113),(38,127),(39,72),(39,78),(39,85),(39,107),(39,112),(39,127),(40,50),(40,53),(40,62),(40,68),(40,128),(40,131),(41,50),(41,54),(41,63),(41,69),(41,129),(41,132),(42,50),(42,55),(42,64),(42,70),(42,130),(42,133),(43,51),(43,57),(43,65),(43,71),(43,126),(43,133),(44,51),(44,56),(44,66),(44,72),(44,125),(44,132),(45,51),(45,58),(45,67),(45,73),(45,127),(45,131),(46,52),(46,60),(46,74),(46,78),(46,126),(46,130),(47,52),(47,59),(47,75),(47,77),(47,125),(47,129),(48,52),(48,61),(48,76),(48,79),(48,127),(48,128),(49,134),(49,135),(49,136),(50,95),(50,147),(50,148),(51,96),(51,146),(51,148),(52,97),(52,146),(52,147),(53,95),(53,118),(53,151),(54,95),(54,116),(54,149),(55,95),(55,117),(55,150),(56,96),(56,120),(56,149),(57,96),(57,119),(57,150),(58,96),(58,121),(58,151),(59,97),(59,123),(59,149),(60,97),(60,122),(60,150),(61,97),(61,124),(61,151),(62,118),(62,142),(62,148),(63,116),(63,140),(63,148),(64,117),(64,141),(64,148),(65,119),(65,137),(65,148),(66,120),(66,138),(66,148),(67,121),(67,139),(67,148),(68,118),(68,143),(68,147),(69,116),(69,144),(69,147),(70,117),(70,145),(70,147),(71,119),(71,145),(71,146),(72,120),(72,144),(72,146),(73,121),(73,143),(73,146),(74,122),(74,137),(74,147),(75,123),(75,138),(75,147),(76,124),(76,139),(76,147),(77,123),(77,140),(77,146),(78,122),(78,141),(78,146),(79,124),(79,142),(79,146),(80,137),(80,140),(80,143),(81,138),(81,141),(81,143),(82,137),(82,142),(82,144),(83,138),(83,142),(83,145),(84,139),(84,140),(84,145),(85,139),(85,141),(85,144),(86,100),(86,101),(86,125),(86,126),(86,136),(87,98),(87,102),(87,126),(87,127),(87,135),(88,99),(88,103),(88,125),(88,127),(88,134),(89,104),(89,106),(89,128),(89,129),(89,134),(90,105),(90,107),(90,128),(90,130),(90,135),(91,108),(91,109),(91,129),(91,130),(91,136),(92,110),(92,112),(92,131),(92,132),(92,134),(93,111),(93,113),(93,131),(93,133),(93,135),(94,114),(94,115),(94,132),(94,133),(94,136),(95,152),(96,152),(97,152),(98,116),(98,137),(98,151),(99,117),(99,138),(99,151),(100,118),(100,137),(100,149),(101,118),(101,138),(101,150),(102,116),(102,139),(102,150),(103,117),(103,139),(103,149),(104,119),(104,142),(104,149),(105,120),(105,142),(105,150),(106,119),(106,140),(106,151),(107,120),(107,141),(107,151),(108,121),(108,141),(108,149),(109,121),(109,140),(109,150),(110,122),(110,143),(110,149),(111,123),(111,143),(111,150),(112,122),(112,144),(112,151),(113,123),(113,145),(113,151),(114,124),(114,145),(114,149),(115,124),(115,144),(115,150),(116,152),(117,152),(118,152),(119,152),(120,152),(121,152),(122,152),(123,152),(124,152),(125,138),(125,146),(125,149),(126,137),(126,146),(126,150),(127,139),(127,146),(127,151),(128,142),(128,147),(128,151),(129,140),(129,147),(129,149),(130,141),(130,147),(130,150),(131,143),(131,148),(131,151),(132,144),(132,148),(132,149),(133,145),(133,148),(133,150),(134,149),(134,151),(135,150),(135,151),(136,149),(136,150),(137,152),(138,152),(139,152),(140,152),(141,152),(142,152),(143,152),(144,152),(145,152),(146,152),(147,152),(148,152),(149,152),(150,152),(151,152)],153)
=> ? = 1
[1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 4
[1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 4
[1,3,2,5,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3
[1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3
[1,3,2,6,5,4] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,16),(1,17),(1,30),(1,31),(1,39),(1,40),(1,41),(1,42),(1,49),(2,14),(2,15),(2,28),(2,29),(2,35),(2,36),(2,37),(2,38),(2,49),(3,19),(3,23),(3,27),(3,34),(3,36),(3,40),(3,74),(3,79),(4,18),(4,22),(4,26),(4,33),(4,35),(4,39),(4,74),(4,78),(5,21),(5,22),(5,24),(5,34),(5,37),(5,41),(5,75),(5,76),(6,20),(6,23),(6,25),(6,33),(6,38),(6,42),(6,75),(6,77),(7,13),(7,20),(7,21),(7,29),(7,31),(7,32),(7,78),(7,79),(8,12),(8,18),(8,19),(8,28),(8,30),(8,32),(8,76),(8,77),(9,14),(9,16),(9,25),(9,26),(9,48),(9,76),(9,79),(10,15),(10,17),(10,24),(10,27),(10,48),(10,77),(10,78),(11,12),(11,13),(11,48),(11,49),(11,74),(11,75),(12,43),(12,84),(12,98),(12,121),(13,43),(13,85),(13,99),(13,122),(14,55),(14,56),(14,86),(14,89),(14,109),(15,54),(15,57),(15,87),(15,88),(15,109),(16,59),(16,60),(16,90),(16,93),(16,109),(17,58),(17,61),(17,91),(17,92),(17,109),(18,62),(18,66),(18,84),(18,94),(18,113),(19,63),(19,67),(19,84),(19,95),(19,114),(20,64),(20,68),(20,85),(20,97),(20,113),(21,65),(21,69),(21,85),(21,96),(21,114),(22,50),(22,52),(22,94),(22,96),(22,110),(23,51),(23,53),(23,95),(23,97),(23,110),(24,54),(24,58),(24,71),(24,96),(24,121),(25,55),(25,59),(25,70),(25,97),(25,121),(26,56),(26,60),(26,70),(26,94),(26,122),(27,57),(27,61),(27,71),(27,95),(27,122),(28,62),(28,63),(28,72),(28,86),(28,87),(28,98),(29,64),(29,65),(29,72),(29,88),(29,89),(29,99),(30,66),(30,67),(30,73),(30,90),(30,91),(30,98),(31,68),(31,69),(31,73),(31,92),(31,93),(31,99),(32,43),(32,72),(32,73),(32,113),(32,114),(33,44),(33,46),(33,70),(33,110),(33,113),(34,45),(34,47),(34,71),(34,110),(34,114),(35,44),(35,50),(35,56),(35,62),(35,88),(35,111),(36,45),(36,51),(36,57),(36,63),(36,89),(36,111),(37,45),(37,50),(37,54),(37,65),(37,86),(37,112),(38,44),(38,51),(38,55),(38,64),(38,87),(38,112),(39,46),(39,52),(39,60),(39,66),(39,92),(39,111),(40,47),(40,53),(40,61),(40,67),(40,93),(40,111),(41,47),(41,52),(41,58),(41,69),(41,90),(41,112),(42,46),(42,53),(42,59),(42,68),(42,91),(42,112),(43,100),(43,126),(44,80),(44,117),(44,123),(45,81),(45,118),(45,123),(46,82),(46,119),(46,123),(47,83),(47,120),(47,123),(48,109),(48,121),(48,122),(49,98),(49,99),(49,109),(49,111),(49,112),(50,101),(50,103),(50,123),(51,102),(51,104),(51,123),(52,105),(52,107),(52,123),(53,106),(53,108),(53,123),(54,81),(54,103),(54,124),(55,80),(55,104),(55,124),(56,80),(56,101),(56,125),(57,81),(57,102),(57,125),(58,83),(58,107),(58,124),(59,82),(59,108),(59,124),(60,82),(60,105),(60,125),(61,83),(61,106),(61,125),(62,101),(62,115),(62,117),(63,102),(63,115),(63,118),(64,104),(64,116),(64,117),(65,103),(65,116),(65,118),(66,105),(66,115),(66,119),(67,106),(67,115),(67,120),(68,108),(68,116),(68,119),(69,107),(69,116),(69,120),(70,80),(70,82),(70,126),(71,81),(71,83),(71,126),(72,100),(72,117),(72,118),(73,100),(73,119),(73,120),(74,84),(74,110),(74,111),(74,122),(75,85),(75,110),(75,112),(75,121),(76,86),(76,90),(76,94),(76,114),(76,121),(77,87),(77,91),(77,95),(77,113),(77,121),(78,88),(78,92),(78,96),(78,113),(78,122),(79,89),(79,93),(79,97),(79,114),(79,122),(80,127),(81,127),(82,127),(83,127),(84,115),(84,126),(85,116),(85,126),(86,101),(86,118),(86,124),(87,102),(87,117),(87,124),(88,103),(88,117),(88,125),(89,104),(89,118),(89,125),(90,105),(90,120),(90,124),(91,106),(91,119),(91,124),(92,107),(92,119),(92,125),(93,108),(93,120),(93,125),(94,101),(94,105),(94,126),(95,102),(95,106),(95,126),(96,103),(96,107),(96,126),(97,104),(97,108),(97,126),(98,100),(98,115),(98,124),(99,100),(99,116),(99,125),(100,127),(101,127),(102,127),(103,127),(104,127),(105,127),(106,127),(107,127),(108,127),(109,124),(109,125),(110,123),(110,126),(111,115),(111,123),(111,125),(112,116),(112,123),(112,124),(113,117),(113,119),(113,126),(114,118),(114,120),(114,126),(115,127),(116,127),(117,127),(118,127),(119,127),(120,127),(121,124),(121,126),(122,125),(122,126),(123,127),(124,127),(125,127),(126,127)],128)
=> ? = 3
[1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,4,2,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 3
[1,3,4,5,2,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1
[1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,5,4,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3
[1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1
[1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1
[1,4,3,2,6,5] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,17),(1,18),(1,19),(1,29),(1,30),(1,31),(1,32),(1,33),(1,34),(2,15),(2,16),(2,22),(2,28),(2,31),(2,55),(2,56),(3,12),(3,14),(3,21),(3,27),(3,30),(3,54),(3,56),(4,11),(4,13),(4,20),(4,26),(4,29),(4,54),(4,55),(5,13),(5,14),(5,25),(5,28),(5,32),(5,57),(5,58),(6,11),(6,15),(6,23),(6,27),(6,33),(6,57),(6,59),(7,12),(7,16),(7,24),(7,26),(7,34),(7,58),(7,59),(8,17),(8,20),(8,24),(8,41),(8,56),(8,57),(9,18),(9,21),(9,23),(9,41),(9,55),(9,58),(10,19),(10,22),(10,25),(10,41),(10,54),(10,59),(11,35),(11,70),(11,74),(11,82),(12,36),(12,71),(12,75),(12,82),(13,37),(13,70),(13,73),(13,83),(14,38),(14,71),(14,73),(14,84),(15,39),(15,72),(15,74),(15,84),(16,40),(16,72),(16,75),(16,83),(17,45),(17,49),(17,63),(17,66),(17,67),(18,46),(18,48),(18,63),(18,65),(18,68),(19,47),(19,50),(19,63),(19,64),(19,69),(20,45),(20,51),(20,70),(20,89),(21,46),(21,52),(21,71),(21,89),(22,47),(22,53),(22,72),(22,89),(23,48),(23,52),(23,74),(23,88),(24,49),(24,51),(24,75),(24,88),(25,50),(25,53),(25,73),(25,88),(26,42),(26,51),(26,82),(26,83),(27,43),(27,52),(27,82),(27,84),(28,44),(28,53),(28,83),(28,84),(29,35),(29,37),(29,42),(29,45),(29,64),(29,65),(30,36),(30,38),(30,43),(30,46),(30,64),(30,66),(31,39),(31,40),(31,44),(31,47),(31,65),(31,66),(32,37),(32,38),(32,44),(32,50),(32,67),(32,68),(33,35),(33,39),(33,43),(33,48),(33,67),(33,69),(34,36),(34,40),(34,42),(34,49),(34,68),(34,69),(35,76),(35,80),(35,85),(36,77),(36,81),(36,85),(37,76),(37,79),(37,86),(38,77),(38,79),(38,87),(39,78),(39,80),(39,87),(40,78),(40,81),(40,86),(41,63),(41,88),(41,89),(42,60),(42,85),(42,86),(43,61),(43,85),(43,87),(44,62),(44,86),(44,87),(45,60),(45,76),(45,90),(46,61),(46,77),(46,90),(47,62),(47,78),(47,90),(48,61),(48,80),(48,91),(49,60),(49,81),(49,91),(50,62),(50,79),(50,91),(51,60),(51,92),(52,61),(52,92),(53,62),(53,92),(54,64),(54,73),(54,82),(54,89),(55,65),(55,74),(55,83),(55,89),(56,66),(56,75),(56,84),(56,89),(57,67),(57,70),(57,84),(57,88),(58,68),(58,71),(58,83),(58,88),(59,69),(59,72),(59,82),(59,88),(60,93),(61,93),(62,93),(63,90),(63,91),(64,79),(64,85),(64,90),(65,80),(65,86),(65,90),(66,81),(66,87),(66,90),(67,76),(67,87),(67,91),(68,77),(68,86),(68,91),(69,78),(69,85),(69,91),(70,76),(70,92),(71,77),(71,92),(72,78),(72,92),(73,79),(73,92),(74,80),(74,92),(75,81),(75,92),(76,93),(77,93),(78,93),(79,93),(80,93),(81,93),(82,85),(82,92),(83,86),(83,92),(84,87),(84,92),(85,93),(86,93),(87,93),(88,91),(88,92),(89,90),(89,92),(90,93),(91,93),(92,93)],94)
=> ? = 3
[1,4,3,5,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1
[1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,4,5,3,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1
[1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1
[1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1
[2,1,3,4,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 1
[2,3,1,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[2,3,4,1,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[2,4,1,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[3,1,2,4,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 1
[3,2,1,4,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
[3,4,1,2,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[4,1,2,3,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 1
[4,2,1,3,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
[4,3,1,2,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
[1,2,3,4,5,6,7] => [7] => ([],7)
=> ([],1)
=> 1
[1,2,4,3,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,5,3,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,6,3,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,2,7,3,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,2,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,2,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,5,2,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,3,6,2,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,4,2,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,5,2,3,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,4,6,2,3,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,5,2,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,6,2,3,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1
[1,6,2,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
The size of the image of the pop stack sorting operator.
The pop stack sorting operator is defined by $Pop_L^\downarrow(x) = x\wedge\bigwedge\{y\in L\mid y\lessdot x\}$. This statistic returns the size of $Pop_L^\downarrow(L)\}$.
Matching statistic: St001846
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001846: Lattices ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 10%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001846: Lattices ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => [3] => ([],3)
=> ([],1)
=> 0 = 1 - 1
[1,2,3,4] => [4] => ([],4)
=> ([],1)
=> 0 = 1 - 1
[1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,1,3,4] => [1,3] => ([(2,3)],4)
=> ([(0,1)],2)
=> 0 = 1 - 1
[2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2 - 1
[1,2,3,4,5] => [5] => ([],5)
=> ([],1)
=> 0 = 1 - 1
[1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 - 1
[1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 - 1
[1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 - 1
[1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3 - 1
[1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1 - 1
[2,1,3,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 0 = 1 - 1
[2,1,3,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 3 - 1
[2,1,4,3,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3 - 1
[2,1,4,5,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2 - 1
[2,1,5,3,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2 - 1
[2,1,5,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 2 - 1
[2,3,1,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,3,1,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 2 - 1
[3,1,2,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 0 = 1 - 1
[3,1,2,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2 - 1
[3,2,1,4,5] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[3,2,1,5,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? = 2 - 1
[1,2,3,4,5,6] => [6] => ([],6)
=> ([],1)
=> 0 = 1 - 1
[1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 - 1
[1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 - 1
[1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 - 1
[1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 - 1
[1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 - 1
[1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 4 - 1
[1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 - 1
[1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 - 1
[1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 - 1
[1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 - 1
[1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 - 1
[1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 - 1
[1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 - 1
[1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 - 1
[1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 - 1
[1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 - 1
[1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 - 1
[1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 - 1
[1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 - 1
[1,2,6,5,4,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(1,15),(1,26),(1,27),(1,32),(1,33),(1,41),(1,42),(1,91),(1,94),(2,14),(2,23),(2,25),(2,29),(2,31),(2,40),(2,42),(2,90),(2,93),(3,13),(3,22),(3,24),(3,28),(3,30),(3,40),(3,41),(3,89),(3,92),(4,18),(4,24),(4,25),(4,34),(4,35),(4,43),(4,44),(4,86),(4,94),(5,17),(5,22),(5,26),(5,36),(5,38),(5,43),(5,45),(5,87),(5,93),(6,16),(6,23),(6,27),(6,37),(6,39),(6,44),(6,45),(6,88),(6,92),(7,21),(7,30),(7,31),(7,36),(7,37),(7,46),(7,47),(7,86),(7,91),(8,20),(8,28),(8,32),(8,34),(8,39),(8,46),(8,48),(8,87),(8,90),(9,19),(9,29),(9,33),(9,35),(9,38),(9,47),(9,48),(9,88),(9,89),(10,19),(10,20),(10,21),(10,49),(10,92),(10,93),(10,94),(11,16),(11,17),(11,18),(11,49),(11,89),(11,90),(11,91),(12,13),(12,14),(12,15),(12,49),(12,86),(12,87),(12,88),(13,53),(13,54),(13,98),(13,100),(13,134),(14,53),(14,55),(14,99),(14,101),(14,135),(15,54),(15,55),(15,102),(15,103),(15,136),(16,56),(16,58),(16,107),(16,108),(16,134),(17,57),(17,58),(17,106),(17,109),(17,135),(18,56),(18,57),(18,104),(18,105),(18,136),(19,59),(19,61),(19,113),(19,114),(19,134),(20,60),(20,61),(20,112),(20,115),(20,135),(21,59),(21,60),(21,110),(21,111),(21,136),(22,63),(22,65),(22,80),(22,98),(22,106),(22,131),(23,64),(23,66),(23,81),(23,99),(23,107),(23,131),(24,62),(24,65),(24,82),(24,100),(24,104),(24,132),(25,62),(25,66),(25,83),(25,101),(25,105),(25,133),(26,63),(26,67),(26,84),(26,102),(26,109),(26,133),(27,64),(27,67),(27,85),(27,103),(27,108),(27,132),(28,69),(28,74),(28,82),(28,98),(28,112),(28,128),(29,70),(29,75),(29,83),(29,99),(29,113),(29,128),(30,68),(30,74),(30,80),(30,100),(30,110),(30,129),(31,68),(31,75),(31,81),(31,101),(31,111),(31,130),(32,69),(32,76),(32,85),(32,102),(32,115),(32,130),(33,70),(33,76),(33,84),(33,103),(33,114),(33,129),(34,72),(34,79),(34,82),(34,105),(34,115),(34,126),(35,71),(35,79),(35,83),(35,104),(35,114),(35,125),(36,73),(36,77),(36,80),(36,109),(36,111),(36,126),(37,73),(37,78),(37,81),(37,108),(37,110),(37,125),(38,71),(38,77),(38,84),(38,106),(38,113),(38,127),(39,72),(39,78),(39,85),(39,107),(39,112),(39,127),(40,50),(40,53),(40,62),(40,68),(40,128),(40,131),(41,50),(41,54),(41,63),(41,69),(41,129),(41,132),(42,50),(42,55),(42,64),(42,70),(42,130),(42,133),(43,51),(43,57),(43,65),(43,71),(43,126),(43,133),(44,51),(44,56),(44,66),(44,72),(44,125),(44,132),(45,51),(45,58),(45,67),(45,73),(45,127),(45,131),(46,52),(46,60),(46,74),(46,78),(46,126),(46,130),(47,52),(47,59),(47,75),(47,77),(47,125),(47,129),(48,52),(48,61),(48,76),(48,79),(48,127),(48,128),(49,134),(49,135),(49,136),(50,95),(50,147),(50,148),(51,96),(51,146),(51,148),(52,97),(52,146),(52,147),(53,95),(53,118),(53,151),(54,95),(54,116),(54,149),(55,95),(55,117),(55,150),(56,96),(56,120),(56,149),(57,96),(57,119),(57,150),(58,96),(58,121),(58,151),(59,97),(59,123),(59,149),(60,97),(60,122),(60,150),(61,97),(61,124),(61,151),(62,118),(62,142),(62,148),(63,116),(63,140),(63,148),(64,117),(64,141),(64,148),(65,119),(65,137),(65,148),(66,120),(66,138),(66,148),(67,121),(67,139),(67,148),(68,118),(68,143),(68,147),(69,116),(69,144),(69,147),(70,117),(70,145),(70,147),(71,119),(71,145),(71,146),(72,120),(72,144),(72,146),(73,121),(73,143),(73,146),(74,122),(74,137),(74,147),(75,123),(75,138),(75,147),(76,124),(76,139),(76,147),(77,123),(77,140),(77,146),(78,122),(78,141),(78,146),(79,124),(79,142),(79,146),(80,137),(80,140),(80,143),(81,138),(81,141),(81,143),(82,137),(82,142),(82,144),(83,138),(83,142),(83,145),(84,139),(84,140),(84,145),(85,139),(85,141),(85,144),(86,100),(86,101),(86,125),(86,126),(86,136),(87,98),(87,102),(87,126),(87,127),(87,135),(88,99),(88,103),(88,125),(88,127),(88,134),(89,104),(89,106),(89,128),(89,129),(89,134),(90,105),(90,107),(90,128),(90,130),(90,135),(91,108),(91,109),(91,129),(91,130),(91,136),(92,110),(92,112),(92,131),(92,132),(92,134),(93,111),(93,113),(93,131),(93,133),(93,135),(94,114),(94,115),(94,132),(94,133),(94,136),(95,152),(96,152),(97,152),(98,116),(98,137),(98,151),(99,117),(99,138),(99,151),(100,118),(100,137),(100,149),(101,118),(101,138),(101,150),(102,116),(102,139),(102,150),(103,117),(103,139),(103,149),(104,119),(104,142),(104,149),(105,120),(105,142),(105,150),(106,119),(106,140),(106,151),(107,120),(107,141),(107,151),(108,121),(108,141),(108,149),(109,121),(109,140),(109,150),(110,122),(110,143),(110,149),(111,123),(111,143),(111,150),(112,122),(112,144),(112,151),(113,123),(113,145),(113,151),(114,124),(114,145),(114,149),(115,124),(115,144),(115,150),(116,152),(117,152),(118,152),(119,152),(120,152),(121,152),(122,152),(123,152),(124,152),(125,138),(125,146),(125,149),(126,137),(126,146),(126,150),(127,139),(127,146),(127,151),(128,142),(128,147),(128,151),(129,140),(129,147),(129,149),(130,141),(130,147),(130,150),(131,143),(131,148),(131,151),(132,144),(132,148),(132,149),(133,145),(133,148),(133,150),(134,149),(134,151),(135,150),(135,151),(136,149),(136,150),(137,152),(138,152),(139,152),(140,152),(141,152),(142,152),(143,152),(144,152),(145,152),(146,152),(147,152),(148,152),(149,152),(150,152),(151,152)],153)
=> ? = 1 - 1
[1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 4 - 1
[1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 4 - 1
[1,3,2,5,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3 - 1
[1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3 - 1
[1,3,2,6,5,4] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,16),(1,17),(1,30),(1,31),(1,39),(1,40),(1,41),(1,42),(1,49),(2,14),(2,15),(2,28),(2,29),(2,35),(2,36),(2,37),(2,38),(2,49),(3,19),(3,23),(3,27),(3,34),(3,36),(3,40),(3,74),(3,79),(4,18),(4,22),(4,26),(4,33),(4,35),(4,39),(4,74),(4,78),(5,21),(5,22),(5,24),(5,34),(5,37),(5,41),(5,75),(5,76),(6,20),(6,23),(6,25),(6,33),(6,38),(6,42),(6,75),(6,77),(7,13),(7,20),(7,21),(7,29),(7,31),(7,32),(7,78),(7,79),(8,12),(8,18),(8,19),(8,28),(8,30),(8,32),(8,76),(8,77),(9,14),(9,16),(9,25),(9,26),(9,48),(9,76),(9,79),(10,15),(10,17),(10,24),(10,27),(10,48),(10,77),(10,78),(11,12),(11,13),(11,48),(11,49),(11,74),(11,75),(12,43),(12,84),(12,98),(12,121),(13,43),(13,85),(13,99),(13,122),(14,55),(14,56),(14,86),(14,89),(14,109),(15,54),(15,57),(15,87),(15,88),(15,109),(16,59),(16,60),(16,90),(16,93),(16,109),(17,58),(17,61),(17,91),(17,92),(17,109),(18,62),(18,66),(18,84),(18,94),(18,113),(19,63),(19,67),(19,84),(19,95),(19,114),(20,64),(20,68),(20,85),(20,97),(20,113),(21,65),(21,69),(21,85),(21,96),(21,114),(22,50),(22,52),(22,94),(22,96),(22,110),(23,51),(23,53),(23,95),(23,97),(23,110),(24,54),(24,58),(24,71),(24,96),(24,121),(25,55),(25,59),(25,70),(25,97),(25,121),(26,56),(26,60),(26,70),(26,94),(26,122),(27,57),(27,61),(27,71),(27,95),(27,122),(28,62),(28,63),(28,72),(28,86),(28,87),(28,98),(29,64),(29,65),(29,72),(29,88),(29,89),(29,99),(30,66),(30,67),(30,73),(30,90),(30,91),(30,98),(31,68),(31,69),(31,73),(31,92),(31,93),(31,99),(32,43),(32,72),(32,73),(32,113),(32,114),(33,44),(33,46),(33,70),(33,110),(33,113),(34,45),(34,47),(34,71),(34,110),(34,114),(35,44),(35,50),(35,56),(35,62),(35,88),(35,111),(36,45),(36,51),(36,57),(36,63),(36,89),(36,111),(37,45),(37,50),(37,54),(37,65),(37,86),(37,112),(38,44),(38,51),(38,55),(38,64),(38,87),(38,112),(39,46),(39,52),(39,60),(39,66),(39,92),(39,111),(40,47),(40,53),(40,61),(40,67),(40,93),(40,111),(41,47),(41,52),(41,58),(41,69),(41,90),(41,112),(42,46),(42,53),(42,59),(42,68),(42,91),(42,112),(43,100),(43,126),(44,80),(44,117),(44,123),(45,81),(45,118),(45,123),(46,82),(46,119),(46,123),(47,83),(47,120),(47,123),(48,109),(48,121),(48,122),(49,98),(49,99),(49,109),(49,111),(49,112),(50,101),(50,103),(50,123),(51,102),(51,104),(51,123),(52,105),(52,107),(52,123),(53,106),(53,108),(53,123),(54,81),(54,103),(54,124),(55,80),(55,104),(55,124),(56,80),(56,101),(56,125),(57,81),(57,102),(57,125),(58,83),(58,107),(58,124),(59,82),(59,108),(59,124),(60,82),(60,105),(60,125),(61,83),(61,106),(61,125),(62,101),(62,115),(62,117),(63,102),(63,115),(63,118),(64,104),(64,116),(64,117),(65,103),(65,116),(65,118),(66,105),(66,115),(66,119),(67,106),(67,115),(67,120),(68,108),(68,116),(68,119),(69,107),(69,116),(69,120),(70,80),(70,82),(70,126),(71,81),(71,83),(71,126),(72,100),(72,117),(72,118),(73,100),(73,119),(73,120),(74,84),(74,110),(74,111),(74,122),(75,85),(75,110),(75,112),(75,121),(76,86),(76,90),(76,94),(76,114),(76,121),(77,87),(77,91),(77,95),(77,113),(77,121),(78,88),(78,92),(78,96),(78,113),(78,122),(79,89),(79,93),(79,97),(79,114),(79,122),(80,127),(81,127),(82,127),(83,127),(84,115),(84,126),(85,116),(85,126),(86,101),(86,118),(86,124),(87,102),(87,117),(87,124),(88,103),(88,117),(88,125),(89,104),(89,118),(89,125),(90,105),(90,120),(90,124),(91,106),(91,119),(91,124),(92,107),(92,119),(92,125),(93,108),(93,120),(93,125),(94,101),(94,105),(94,126),(95,102),(95,106),(95,126),(96,103),(96,107),(96,126),(97,104),(97,108),(97,126),(98,100),(98,115),(98,124),(99,100),(99,116),(99,125),(100,127),(101,127),(102,127),(103,127),(104,127),(105,127),(106,127),(107,127),(108,127),(109,124),(109,125),(110,123),(110,126),(111,115),(111,123),(111,125),(112,116),(112,123),(112,124),(113,117),(113,119),(113,126),(114,118),(114,120),(114,126),(115,127),(116,127),(117,127),(118,127),(119,127),(120,127),(121,124),(121,126),(122,125),(122,126),(123,127),(124,127),(125,127),(126,127)],128)
=> ? = 3 - 1
[1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,3,4,2,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 3 - 1
[1,3,4,5,2,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 - 1
[1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,3,5,4,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 - 1
[1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3 - 1
[1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1 - 1
[1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1 - 1
[1,4,3,2,6,5] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,17),(1,18),(1,19),(1,29),(1,30),(1,31),(1,32),(1,33),(1,34),(2,15),(2,16),(2,22),(2,28),(2,31),(2,55),(2,56),(3,12),(3,14),(3,21),(3,27),(3,30),(3,54),(3,56),(4,11),(4,13),(4,20),(4,26),(4,29),(4,54),(4,55),(5,13),(5,14),(5,25),(5,28),(5,32),(5,57),(5,58),(6,11),(6,15),(6,23),(6,27),(6,33),(6,57),(6,59),(7,12),(7,16),(7,24),(7,26),(7,34),(7,58),(7,59),(8,17),(8,20),(8,24),(8,41),(8,56),(8,57),(9,18),(9,21),(9,23),(9,41),(9,55),(9,58),(10,19),(10,22),(10,25),(10,41),(10,54),(10,59),(11,35),(11,70),(11,74),(11,82),(12,36),(12,71),(12,75),(12,82),(13,37),(13,70),(13,73),(13,83),(14,38),(14,71),(14,73),(14,84),(15,39),(15,72),(15,74),(15,84),(16,40),(16,72),(16,75),(16,83),(17,45),(17,49),(17,63),(17,66),(17,67),(18,46),(18,48),(18,63),(18,65),(18,68),(19,47),(19,50),(19,63),(19,64),(19,69),(20,45),(20,51),(20,70),(20,89),(21,46),(21,52),(21,71),(21,89),(22,47),(22,53),(22,72),(22,89),(23,48),(23,52),(23,74),(23,88),(24,49),(24,51),(24,75),(24,88),(25,50),(25,53),(25,73),(25,88),(26,42),(26,51),(26,82),(26,83),(27,43),(27,52),(27,82),(27,84),(28,44),(28,53),(28,83),(28,84),(29,35),(29,37),(29,42),(29,45),(29,64),(29,65),(30,36),(30,38),(30,43),(30,46),(30,64),(30,66),(31,39),(31,40),(31,44),(31,47),(31,65),(31,66),(32,37),(32,38),(32,44),(32,50),(32,67),(32,68),(33,35),(33,39),(33,43),(33,48),(33,67),(33,69),(34,36),(34,40),(34,42),(34,49),(34,68),(34,69),(35,76),(35,80),(35,85),(36,77),(36,81),(36,85),(37,76),(37,79),(37,86),(38,77),(38,79),(38,87),(39,78),(39,80),(39,87),(40,78),(40,81),(40,86),(41,63),(41,88),(41,89),(42,60),(42,85),(42,86),(43,61),(43,85),(43,87),(44,62),(44,86),(44,87),(45,60),(45,76),(45,90),(46,61),(46,77),(46,90),(47,62),(47,78),(47,90),(48,61),(48,80),(48,91),(49,60),(49,81),(49,91),(50,62),(50,79),(50,91),(51,60),(51,92),(52,61),(52,92),(53,62),(53,92),(54,64),(54,73),(54,82),(54,89),(55,65),(55,74),(55,83),(55,89),(56,66),(56,75),(56,84),(56,89),(57,67),(57,70),(57,84),(57,88),(58,68),(58,71),(58,83),(58,88),(59,69),(59,72),(59,82),(59,88),(60,93),(61,93),(62,93),(63,90),(63,91),(64,79),(64,85),(64,90),(65,80),(65,86),(65,90),(66,81),(66,87),(66,90),(67,76),(67,87),(67,91),(68,77),(68,86),(68,91),(69,78),(69,85),(69,91),(70,76),(70,92),(71,77),(71,92),(72,78),(72,92),(73,79),(73,92),(74,80),(74,92),(75,81),(75,92),(76,93),(77,93),(78,93),(79,93),(80,93),(81,93),(82,85),(82,92),(83,86),(83,92),(84,87),(84,92),(85,93),(86,93),(87,93),(88,91),(88,92),(89,90),(89,92),(90,93),(91,93),(92,93)],94)
=> ? = 3 - 1
[1,4,3,5,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1 - 1
[1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,4,5,3,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 - 1
[1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1 - 1
[1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1 - 1
[2,1,3,4,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 0 = 1 - 1
[2,3,1,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,3,4,1,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[2,4,1,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[3,1,2,4,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 0 = 1 - 1
[3,2,1,4,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[3,4,1,2,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[4,1,2,3,5,6] => [1,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 0 = 1 - 1
[4,2,1,3,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[4,3,1,2,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,2,3,4,5,6,7] => [7] => ([],7)
=> ([],1)
=> 0 = 1 - 1
[1,2,4,3,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,5,3,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,6,3,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,7,3,4,5,6] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,3,2,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,3,4,2,5,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,3,5,2,4,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,3,6,2,4,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,4,2,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,4,5,2,3,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,4,6,2,3,5,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,5,2,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,5,6,2,3,4,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,6,2,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
Description
The number of elements which do not have a complement in the lattice.
A complement of an element $x$ in a lattice is an element $y$ such that the meet of $x$ and $y$ is the bottom element and their join is the top element.
Matching statistic: St001651
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001651: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 20%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001651: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 20%
Values
[1,2,3] => [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,2,3,4] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,2,4,3] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 - 1
[1,3,2,4] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 - 1
[2,1,3,4] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,1,4,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[1,2,3,4,5] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[1,2,3,5,4] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 1 - 1
[1,2,4,3,5] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 1 - 1
[1,2,4,5,3] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1 - 1
[1,2,5,3,4] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1 - 1
[1,2,5,4,3] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? = 1 - 1
[1,3,2,4,5] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 1 - 1
[1,3,2,5,4] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
=> ? = 3 - 1
[1,3,4,2,5] => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1 - 1
[1,4,2,3,5] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1 - 1
[1,4,3,2,5] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? = 1 - 1
[2,1,3,4,5] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[2,1,3,5,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3 - 1
[2,1,4,3,5] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3 - 1
[2,1,4,5,3] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 2 - 1
[2,1,5,3,4] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 2 - 1
[2,1,5,4,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? = 2 - 1
[2,3,1,4,5] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,3,1,5,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[3,1,2,4,5] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[3,1,2,5,4] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2 - 1
[3,2,1,4,5] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[3,2,1,5,4] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2 - 1
[1,2,3,4,5,6] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[1,2,3,4,6,5] => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 1 - 1
[1,2,3,5,4,6] => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 1 - 1
[1,2,3,5,6,4] => [2,3,6,4,5,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 1 - 1
[1,2,3,6,4,5] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 1 - 1
[1,2,3,6,5,4] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,17),(1,24),(1,38),(1,40),(2,10),(2,16),(2,24),(2,37),(2,39),(3,12),(3,18),(3,23),(3,37),(3,40),(4,13),(4,19),(4,23),(4,38),(4,39),(5,15),(5,21),(5,22),(5,39),(5,40),(6,14),(6,20),(6,22),(6,37),(6,38),(7,9),(7,16),(7,17),(7,18),(7,19),(7,20),(7,21),(8,9),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,31),(9,32),(9,33),(9,34),(9,35),(9,36),(10,25),(10,31),(10,41),(10,43),(11,25),(11,32),(11,42),(11,44),(12,26),(12,33),(12,41),(12,44),(13,26),(13,34),(13,42),(13,43),(14,27),(14,35),(14,41),(14,42),(15,27),(15,36),(15,43),(15,44),(16,28),(16,31),(16,45),(16,47),(17,28),(17,32),(17,46),(17,48),(18,29),(18,33),(18,45),(18,48),(19,29),(19,34),(19,46),(19,47),(20,30),(20,35),(20,45),(20,46),(21,30),(21,36),(21,47),(21,48),(22,27),(22,30),(22,56),(23,26),(23,29),(23,56),(24,25),(24,28),(24,56),(25,49),(25,57),(26,50),(26,57),(27,51),(27,57),(28,49),(28,58),(29,50),(29,58),(30,51),(30,58),(31,49),(31,52),(31,54),(32,49),(32,53),(32,55),(33,50),(33,52),(33,55),(34,50),(34,53),(34,54),(35,51),(35,52),(35,53),(36,51),(36,54),(36,55),(37,41),(37,45),(37,56),(38,42),(38,46),(38,56),(39,43),(39,47),(39,56),(40,44),(40,48),(40,56),(41,52),(41,57),(42,53),(42,57),(43,54),(43,57),(44,55),(44,57),(45,52),(45,58),(46,53),(46,58),(47,54),(47,58),(48,55),(48,58),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,59),(56,57),(56,58),(57,59),(58,59)],60)
=> ? = 1 - 1
[1,2,4,3,5,6] => [2,4,3,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 1 - 1
[1,2,4,3,6,5] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
=> ? = 4 - 1
[1,2,4,5,3,6] => [2,5,3,4,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 1 - 1
[1,2,4,5,6,3] => [2,6,3,4,5,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 - 1
[1,2,4,6,3,5] => [2,5,3,6,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(1,13),(1,14),(1,44),(1,46),(2,9),(2,11),(2,12),(2,44),(2,45),(3,15),(3,24),(3,25),(3,26),(3,27),(3,44),(4,12),(4,17),(4,22),(4,23),(4,25),(4,46),(5,11),(5,16),(5,20),(5,21),(5,24),(5,46),(6,14),(6,19),(6,21),(6,23),(6,27),(6,45),(7,13),(7,18),(7,20),(7,22),(7,26),(7,45),(8,9),(8,10),(8,15),(8,16),(8,17),(8,18),(8,19),(9,36),(9,37),(9,47),(9,52),(10,38),(10,39),(10,47),(10,53),(11,36),(11,48),(11,62),(12,37),(12,49),(12,62),(13,38),(13,50),(13,63),(14,39),(14,51),(14,63),(15,32),(15,33),(15,34),(15,35),(15,47),(16,32),(16,36),(16,40),(16,41),(16,53),(17,33),(17,37),(17,42),(17,43),(17,53),(18,34),(18,38),(18,40),(18,42),(18,52),(19,35),(19,39),(19,41),(19,43),(19,52),(20,28),(20,40),(20,48),(20,50),(21,29),(21,41),(21,48),(21,51),(22,30),(22,42),(22,49),(22,50),(23,31),(23,43),(23,49),(23,51),(24,28),(24,29),(24,32),(24,62),(25,30),(25,31),(25,33),(25,62),(26,28),(26,30),(26,34),(26,63),(27,29),(27,31),(27,35),(27,63),(28,54),(28,66),(29,55),(29,66),(30,56),(30,66),(31,57),(31,66),(32,54),(32,55),(32,64),(33,56),(33,57),(33,64),(34,54),(34,56),(34,65),(35,55),(35,57),(35,65),(36,58),(36,64),(37,59),(37,64),(38,60),(38,65),(39,61),(39,65),(40,54),(40,58),(40,60),(41,55),(41,58),(41,61),(42,56),(42,59),(42,60),(43,57),(43,59),(43,61),(44,47),(44,62),(44,63),(45,48),(45,49),(45,52),(45,63),(46,50),(46,51),(46,53),(46,62),(47,64),(47,65),(48,58),(48,66),(49,59),(49,66),(50,60),(50,66),(51,61),(51,66),(52,58),(52,59),(52,65),(53,60),(53,61),(53,64),(54,67),(55,67),(56,67),(57,67),(58,67),(59,67),(60,67),(61,67),(62,64),(62,66),(63,65),(63,66),(64,67),(65,67),(66,67)],68)
=> ? = 1 - 1
[1,2,4,6,5,3] => [2,6,3,5,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,10),(1,22),(1,23),(1,24),(1,25),(1,26),(1,29),(1,30),(2,13),(2,18),(2,19),(2,20),(2,21),(2,30),(2,36),(3,12),(3,14),(3,15),(3,16),(3,17),(3,29),(3,36),(4,11),(4,12),(4,13),(4,26),(4,51),(4,52),(5,15),(5,19),(5,23),(5,28),(5,50),(5,52),(6,14),(6,18),(6,22),(6,28),(6,49),(6,51),(7,17),(7,20),(7,24),(7,27),(7,49),(7,52),(8,16),(8,21),(8,25),(8,27),(8,50),(8,51),(9,10),(9,11),(9,36),(9,49),(9,50),(10,31),(10,58),(10,59),(10,60),(11,31),(11,57),(11,74),(12,32),(12,57),(12,63),(12,64),(13,33),(13,57),(13,65),(13,66),(14,37),(14,45),(14,63),(14,72),(15,38),(15,45),(15,64),(15,73),(16,39),(16,46),(16,63),(16,73),(17,40),(17,46),(17,64),(17,72),(18,41),(18,47),(18,65),(18,72),(19,42),(19,47),(19,66),(19,73),(20,43),(20,48),(20,66),(20,72),(21,44),(21,48),(21,65),(21,73),(22,34),(22,37),(22,41),(22,58),(22,61),(23,34),(23,38),(23,42),(23,59),(23,62),(24,35),(24,40),(24,43),(24,58),(24,62),(25,35),(25,39),(25,44),(25,59),(25,61),(26,31),(26,32),(26,33),(26,61),(26,62),(27,35),(27,46),(27,48),(27,74),(28,34),(28,45),(28,47),(28,74),(29,32),(29,37),(29,38),(29,39),(29,40),(29,60),(30,33),(30,41),(30,42),(30,43),(30,44),(30,60),(31,71),(31,77),(32,67),(32,68),(32,71),(33,69),(33,70),(33,71),(34,53),(34,55),(34,77),(35,54),(35,56),(35,77),(36,57),(36,60),(36,72),(36,73),(37,53),(37,67),(37,75),(38,53),(38,68),(38,76),(39,54),(39,67),(39,76),(40,54),(40,68),(40,75),(41,55),(41,69),(41,75),(42,55),(42,70),(42,76),(43,56),(43,70),(43,75),(44,56),(44,69),(44,76),(45,53),(45,78),(46,54),(46,78),(47,55),(47,78),(48,56),(48,78),(49,58),(49,72),(49,74),(50,59),(50,73),(50,74),(51,61),(51,63),(51,65),(51,74),(52,62),(52,64),(52,66),(52,74),(53,79),(54,79),(55,79),(56,79),(57,71),(57,78),(58,75),(58,77),(59,76),(59,77),(60,71),(60,75),(60,76),(61,67),(61,69),(61,77),(62,68),(62,70),(62,77),(63,67),(63,78),(64,68),(64,78),(65,69),(65,78),(66,70),(66,78),(67,79),(68,79),(69,79),(70,79),(71,79),(72,75),(72,78),(73,76),(73,78),(74,77),(74,78),(75,79),(76,79),(77,79),(78,79)],80)
=> ? = 1 - 1
[1,2,5,3,4,6] => [2,4,5,3,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 1 - 1
[1,2,5,3,6,4] => [2,4,6,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(1,13),(1,14),(1,44),(1,46),(2,9),(2,11),(2,12),(2,44),(2,45),(3,15),(3,24),(3,25),(3,26),(3,27),(3,44),(4,12),(4,17),(4,22),(4,23),(4,25),(4,46),(5,11),(5,16),(5,20),(5,21),(5,24),(5,46),(6,14),(6,19),(6,21),(6,23),(6,27),(6,45),(7,13),(7,18),(7,20),(7,22),(7,26),(7,45),(8,9),(8,10),(8,15),(8,16),(8,17),(8,18),(8,19),(9,36),(9,37),(9,47),(9,52),(10,38),(10,39),(10,47),(10,53),(11,36),(11,48),(11,62),(12,37),(12,49),(12,62),(13,38),(13,50),(13,63),(14,39),(14,51),(14,63),(15,32),(15,33),(15,34),(15,35),(15,47),(16,32),(16,36),(16,40),(16,41),(16,53),(17,33),(17,37),(17,42),(17,43),(17,53),(18,34),(18,38),(18,40),(18,42),(18,52),(19,35),(19,39),(19,41),(19,43),(19,52),(20,28),(20,40),(20,48),(20,50),(21,29),(21,41),(21,48),(21,51),(22,30),(22,42),(22,49),(22,50),(23,31),(23,43),(23,49),(23,51),(24,28),(24,29),(24,32),(24,62),(25,30),(25,31),(25,33),(25,62),(26,28),(26,30),(26,34),(26,63),(27,29),(27,31),(27,35),(27,63),(28,54),(28,66),(29,55),(29,66),(30,56),(30,66),(31,57),(31,66),(32,54),(32,55),(32,64),(33,56),(33,57),(33,64),(34,54),(34,56),(34,65),(35,55),(35,57),(35,65),(36,58),(36,64),(37,59),(37,64),(38,60),(38,65),(39,61),(39,65),(40,54),(40,58),(40,60),(41,55),(41,58),(41,61),(42,56),(42,59),(42,60),(43,57),(43,59),(43,61),(44,47),(44,62),(44,63),(45,48),(45,49),(45,52),(45,63),(46,50),(46,51),(46,53),(46,62),(47,64),(47,65),(48,58),(48,66),(49,59),(49,66),(50,60),(50,66),(51,61),(51,66),(52,58),(52,59),(52,65),(53,60),(53,61),(53,64),(54,67),(55,67),(56,67),(57,67),(58,67),(59,67),(60,67),(61,67),(62,64),(62,66),(63,65),(63,66),(64,67),(65,67),(66,67)],68)
=> ? = 1 - 1
[1,2,5,4,3,6] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,17),(1,24),(1,38),(1,40),(2,10),(2,16),(2,24),(2,37),(2,39),(3,12),(3,18),(3,23),(3,37),(3,40),(4,13),(4,19),(4,23),(4,38),(4,39),(5,15),(5,21),(5,22),(5,39),(5,40),(6,14),(6,20),(6,22),(6,37),(6,38),(7,9),(7,16),(7,17),(7,18),(7,19),(7,20),(7,21),(8,9),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,31),(9,32),(9,33),(9,34),(9,35),(9,36),(10,25),(10,31),(10,41),(10,43),(11,25),(11,32),(11,42),(11,44),(12,26),(12,33),(12,41),(12,44),(13,26),(13,34),(13,42),(13,43),(14,27),(14,35),(14,41),(14,42),(15,27),(15,36),(15,43),(15,44),(16,28),(16,31),(16,45),(16,47),(17,28),(17,32),(17,46),(17,48),(18,29),(18,33),(18,45),(18,48),(19,29),(19,34),(19,46),(19,47),(20,30),(20,35),(20,45),(20,46),(21,30),(21,36),(21,47),(21,48),(22,27),(22,30),(22,56),(23,26),(23,29),(23,56),(24,25),(24,28),(24,56),(25,49),(25,57),(26,50),(26,57),(27,51),(27,57),(28,49),(28,58),(29,50),(29,58),(30,51),(30,58),(31,49),(31,52),(31,54),(32,49),(32,53),(32,55),(33,50),(33,52),(33,55),(34,50),(34,53),(34,54),(35,51),(35,52),(35,53),(36,51),(36,54),(36,55),(37,41),(37,45),(37,56),(38,42),(38,46),(38,56),(39,43),(39,47),(39,56),(40,44),(40,48),(40,56),(41,52),(41,57),(42,53),(42,57),(43,54),(43,57),(44,55),(44,57),(45,52),(45,58),(46,53),(46,58),(47,54),(47,58),(48,55),(48,58),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,59),(56,57),(56,58),(57,59),(58,59)],60)
=> ? = 1 - 1
[1,2,5,4,6,3] => [2,6,4,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,10),(1,22),(1,23),(1,24),(1,25),(1,26),(1,29),(1,30),(2,13),(2,18),(2,19),(2,20),(2,21),(2,30),(2,36),(3,12),(3,14),(3,15),(3,16),(3,17),(3,29),(3,36),(4,11),(4,12),(4,13),(4,26),(4,51),(4,52),(5,15),(5,19),(5,23),(5,28),(5,50),(5,52),(6,14),(6,18),(6,22),(6,28),(6,49),(6,51),(7,17),(7,20),(7,24),(7,27),(7,49),(7,52),(8,16),(8,21),(8,25),(8,27),(8,50),(8,51),(9,10),(9,11),(9,36),(9,49),(9,50),(10,31),(10,58),(10,59),(10,60),(11,31),(11,57),(11,74),(12,32),(12,57),(12,63),(12,64),(13,33),(13,57),(13,65),(13,66),(14,37),(14,45),(14,63),(14,72),(15,38),(15,45),(15,64),(15,73),(16,39),(16,46),(16,63),(16,73),(17,40),(17,46),(17,64),(17,72),(18,41),(18,47),(18,65),(18,72),(19,42),(19,47),(19,66),(19,73),(20,43),(20,48),(20,66),(20,72),(21,44),(21,48),(21,65),(21,73),(22,34),(22,37),(22,41),(22,58),(22,61),(23,34),(23,38),(23,42),(23,59),(23,62),(24,35),(24,40),(24,43),(24,58),(24,62),(25,35),(25,39),(25,44),(25,59),(25,61),(26,31),(26,32),(26,33),(26,61),(26,62),(27,35),(27,46),(27,48),(27,74),(28,34),(28,45),(28,47),(28,74),(29,32),(29,37),(29,38),(29,39),(29,40),(29,60),(30,33),(30,41),(30,42),(30,43),(30,44),(30,60),(31,71),(31,77),(32,67),(32,68),(32,71),(33,69),(33,70),(33,71),(34,53),(34,55),(34,77),(35,54),(35,56),(35,77),(36,57),(36,60),(36,72),(36,73),(37,53),(37,67),(37,75),(38,53),(38,68),(38,76),(39,54),(39,67),(39,76),(40,54),(40,68),(40,75),(41,55),(41,69),(41,75),(42,55),(42,70),(42,76),(43,56),(43,70),(43,75),(44,56),(44,69),(44,76),(45,53),(45,78),(46,54),(46,78),(47,55),(47,78),(48,56),(48,78),(49,58),(49,72),(49,74),(50,59),(50,73),(50,74),(51,61),(51,63),(51,65),(51,74),(52,62),(52,64),(52,66),(52,74),(53,79),(54,79),(55,79),(56,79),(57,71),(57,78),(58,75),(58,77),(59,76),(59,77),(60,71),(60,75),(60,76),(61,67),(61,69),(61,77),(62,68),(62,70),(62,77),(63,67),(63,78),(64,68),(64,78),(65,69),(65,78),(66,70),(66,78),(67,79),(68,79),(69,79),(70,79),(71,79),(72,75),(72,78),(73,76),(73,78),(74,77),(74,78),(75,79),(76,79),(77,79),(78,79)],80)
=> ? = 1 - 1
[1,2,5,6,3,4] => [2,5,6,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,21),(1,25),(1,29),(1,33),(1,55),(1,57),(2,20),(2,24),(2,28),(2,32),(2,55),(2,56),(3,22),(3,26),(3,30),(3,32),(3,54),(3,57),(4,23),(4,27),(4,31),(4,33),(4,54),(4,56),(5,11),(5,14),(5,15),(5,17),(5,22),(5,23),(5,55),(6,11),(6,12),(6,13),(6,16),(6,20),(6,21),(6,54),(7,10),(7,12),(7,14),(7,18),(7,24),(7,27),(7,57),(8,10),(8,13),(8,15),(8,19),(8,25),(8,26),(8,56),(9,16),(9,17),(9,18),(9,19),(9,28),(9,29),(9,30),(9,31),(10,53),(10,60),(10,61),(10,74),(11,52),(11,58),(11,59),(11,74),(12,34),(12,38),(12,74),(12,76),(13,35),(13,39),(13,74),(13,75),(14,37),(14,40),(14,74),(14,77),(15,36),(15,41),(15,74),(15,78),(16,38),(16,39),(16,44),(16,45),(16,52),(16,62),(17,40),(17,41),(17,46),(17,47),(17,52),(17,63),(18,38),(18,40),(18,48),(18,51),(18,53),(18,65),(19,39),(19,41),(19,49),(19,50),(19,53),(19,64),(20,34),(20,44),(20,58),(20,75),(21,35),(21,45),(21,58),(21,76),(22,36),(22,46),(22,59),(22,77),(23,37),(23,47),(23,59),(23,78),(24,34),(24,48),(24,60),(24,77),(25,35),(25,49),(25,61),(25,78),(26,36),(26,50),(26,61),(26,75),(27,37),(27,51),(27,60),(27,76),(28,42),(28,44),(28,48),(28,63),(28,64),(29,43),(29,45),(29,49),(29,63),(29,65),(30,42),(30,46),(30,50),(30,62),(30,65),(31,43),(31,47),(31,51),(31,62),(31,64),(32,42),(32,75),(32,77),(33,43),(33,76),(33,78),(34,66),(34,84),(35,67),(35,84),(36,68),(36,84),(37,69),(37,84),(38,66),(38,80),(38,83),(39,67),(39,79),(39,83),(40,69),(40,81),(40,83),(41,68),(41,82),(41,83),(42,79),(42,81),(43,80),(43,82),(44,66),(44,70),(44,79),(45,67),(45,70),(45,80),(46,68),(46,71),(46,81),(47,69),(47,71),(47,82),(48,66),(48,72),(48,81),(49,67),(49,73),(49,82),(50,68),(50,73),(50,79),(51,69),(51,72),(51,80),(52,70),(52,71),(52,83),(53,72),(53,73),(53,83),(54,59),(54,62),(54,75),(54,76),(55,58),(55,63),(55,77),(55,78),(56,60),(56,64),(56,75),(56,78),(57,61),(57,65),(57,76),(57,77),(58,70),(58,84),(59,71),(59,84),(60,72),(60,84),(61,73),(61,84),(62,71),(62,79),(62,80),(63,70),(63,81),(63,82),(64,72),(64,79),(64,82),(65,73),(65,80),(65,81),(66,85),(67,85),(68,85),(69,85),(70,85),(71,85),(72,85),(73,85),(74,83),(74,84),(75,79),(75,84),(76,80),(76,84),(77,81),(77,84),(78,82),(78,84),(79,85),(80,85),(81,85),(82,85),(83,85),(84,85)],86)
=> ? = 1 - 1
[1,2,5,6,4,3] => [2,6,5,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,17),(1,18),(1,19),(1,29),(1,30),(1,31),(1,32),(1,33),(1,34),(2,15),(2,16),(2,22),(2,28),(2,31),(2,55),(2,56),(3,12),(3,14),(3,21),(3,27),(3,30),(3,54),(3,56),(4,11),(4,13),(4,20),(4,26),(4,29),(4,54),(4,55),(5,13),(5,14),(5,25),(5,28),(5,32),(5,57),(5,58),(6,11),(6,15),(6,23),(6,27),(6,33),(6,57),(6,59),(7,12),(7,16),(7,24),(7,26),(7,34),(7,58),(7,59),(8,17),(8,20),(8,24),(8,41),(8,56),(8,57),(9,18),(9,21),(9,23),(9,41),(9,55),(9,58),(10,19),(10,22),(10,25),(10,41),(10,54),(10,59),(11,35),(11,70),(11,74),(11,82),(12,36),(12,71),(12,75),(12,82),(13,37),(13,70),(13,73),(13,83),(14,38),(14,71),(14,73),(14,84),(15,39),(15,72),(15,74),(15,84),(16,40),(16,72),(16,75),(16,83),(17,45),(17,49),(17,63),(17,66),(17,67),(18,46),(18,48),(18,63),(18,65),(18,68),(19,47),(19,50),(19,63),(19,64),(19,69),(20,45),(20,51),(20,70),(20,89),(21,46),(21,52),(21,71),(21,89),(22,47),(22,53),(22,72),(22,89),(23,48),(23,52),(23,74),(23,88),(24,49),(24,51),(24,75),(24,88),(25,50),(25,53),(25,73),(25,88),(26,42),(26,51),(26,82),(26,83),(27,43),(27,52),(27,82),(27,84),(28,44),(28,53),(28,83),(28,84),(29,35),(29,37),(29,42),(29,45),(29,64),(29,65),(30,36),(30,38),(30,43),(30,46),(30,64),(30,66),(31,39),(31,40),(31,44),(31,47),(31,65),(31,66),(32,37),(32,38),(32,44),(32,50),(32,67),(32,68),(33,35),(33,39),(33,43),(33,48),(33,67),(33,69),(34,36),(34,40),(34,42),(34,49),(34,68),(34,69),(35,76),(35,80),(35,85),(36,77),(36,81),(36,85),(37,76),(37,79),(37,86),(38,77),(38,79),(38,87),(39,78),(39,80),(39,87),(40,78),(40,81),(40,86),(41,63),(41,88),(41,89),(42,60),(42,85),(42,86),(43,61),(43,85),(43,87),(44,62),(44,86),(44,87),(45,60),(45,76),(45,90),(46,61),(46,77),(46,90),(47,62),(47,78),(47,90),(48,61),(48,80),(48,91),(49,60),(49,81),(49,91),(50,62),(50,79),(50,91),(51,60),(51,92),(52,61),(52,92),(53,62),(53,92),(54,64),(54,73),(54,82),(54,89),(55,65),(55,74),(55,83),(55,89),(56,66),(56,75),(56,84),(56,89),(57,67),(57,70),(57,84),(57,88),(58,68),(58,71),(58,83),(58,88),(59,69),(59,72),(59,82),(59,88),(60,93),(61,93),(62,93),(63,90),(63,91),(64,79),(64,85),(64,90),(65,80),(65,86),(65,90),(66,81),(66,87),(66,90),(67,76),(67,87),(67,91),(68,77),(68,86),(68,91),(69,78),(69,85),(69,91),(70,76),(70,92),(71,77),(71,92),(72,78),(72,92),(73,79),(73,92),(74,80),(74,92),(75,81),(75,92),(76,93),(77,93),(78,93),(79,93),(80,93),(81,93),(82,85),(82,92),(83,86),(83,92),(84,87),(84,92),(85,93),(86,93),(87,93),(88,91),(88,92),(89,90),(89,92),(90,93),(91,93),(92,93)],94)
=> ? = 1 - 1
[1,2,6,3,4,5] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 - 1
[1,2,6,3,5,4] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,10),(1,22),(1,23),(1,24),(1,25),(1,26),(1,29),(1,30),(2,13),(2,18),(2,19),(2,20),(2,21),(2,30),(2,36),(3,12),(3,14),(3,15),(3,16),(3,17),(3,29),(3,36),(4,11),(4,12),(4,13),(4,26),(4,51),(4,52),(5,15),(5,19),(5,23),(5,28),(5,50),(5,52),(6,14),(6,18),(6,22),(6,28),(6,49),(6,51),(7,17),(7,20),(7,24),(7,27),(7,49),(7,52),(8,16),(8,21),(8,25),(8,27),(8,50),(8,51),(9,10),(9,11),(9,36),(9,49),(9,50),(10,31),(10,58),(10,59),(10,60),(11,31),(11,57),(11,74),(12,32),(12,57),(12,63),(12,64),(13,33),(13,57),(13,65),(13,66),(14,37),(14,45),(14,63),(14,72),(15,38),(15,45),(15,64),(15,73),(16,39),(16,46),(16,63),(16,73),(17,40),(17,46),(17,64),(17,72),(18,41),(18,47),(18,65),(18,72),(19,42),(19,47),(19,66),(19,73),(20,43),(20,48),(20,66),(20,72),(21,44),(21,48),(21,65),(21,73),(22,34),(22,37),(22,41),(22,58),(22,61),(23,34),(23,38),(23,42),(23,59),(23,62),(24,35),(24,40),(24,43),(24,58),(24,62),(25,35),(25,39),(25,44),(25,59),(25,61),(26,31),(26,32),(26,33),(26,61),(26,62),(27,35),(27,46),(27,48),(27,74),(28,34),(28,45),(28,47),(28,74),(29,32),(29,37),(29,38),(29,39),(29,40),(29,60),(30,33),(30,41),(30,42),(30,43),(30,44),(30,60),(31,71),(31,77),(32,67),(32,68),(32,71),(33,69),(33,70),(33,71),(34,53),(34,55),(34,77),(35,54),(35,56),(35,77),(36,57),(36,60),(36,72),(36,73),(37,53),(37,67),(37,75),(38,53),(38,68),(38,76),(39,54),(39,67),(39,76),(40,54),(40,68),(40,75),(41,55),(41,69),(41,75),(42,55),(42,70),(42,76),(43,56),(43,70),(43,75),(44,56),(44,69),(44,76),(45,53),(45,78),(46,54),(46,78),(47,55),(47,78),(48,56),(48,78),(49,58),(49,72),(49,74),(50,59),(50,73),(50,74),(51,61),(51,63),(51,65),(51,74),(52,62),(52,64),(52,66),(52,74),(53,79),(54,79),(55,79),(56,79),(57,71),(57,78),(58,75),(58,77),(59,76),(59,77),(60,71),(60,75),(60,76),(61,67),(61,69),(61,77),(62,68),(62,70),(62,77),(63,67),(63,78),(64,68),(64,78),(65,69),(65,78),(66,70),(66,78),(67,79),(68,79),(69,79),(70,79),(71,79),(72,75),(72,78),(73,76),(73,78),(74,77),(74,78),(75,79),(76,79),(77,79),(78,79)],80)
=> ? = 1 - 1
[1,2,6,4,3,5] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,10),(1,22),(1,23),(1,24),(1,25),(1,26),(1,29),(1,30),(2,13),(2,18),(2,19),(2,20),(2,21),(2,30),(2,36),(3,12),(3,14),(3,15),(3,16),(3,17),(3,29),(3,36),(4,11),(4,12),(4,13),(4,26),(4,51),(4,52),(5,15),(5,19),(5,23),(5,28),(5,50),(5,52),(6,14),(6,18),(6,22),(6,28),(6,49),(6,51),(7,17),(7,20),(7,24),(7,27),(7,49),(7,52),(8,16),(8,21),(8,25),(8,27),(8,50),(8,51),(9,10),(9,11),(9,36),(9,49),(9,50),(10,31),(10,58),(10,59),(10,60),(11,31),(11,57),(11,74),(12,32),(12,57),(12,63),(12,64),(13,33),(13,57),(13,65),(13,66),(14,37),(14,45),(14,63),(14,72),(15,38),(15,45),(15,64),(15,73),(16,39),(16,46),(16,63),(16,73),(17,40),(17,46),(17,64),(17,72),(18,41),(18,47),(18,65),(18,72),(19,42),(19,47),(19,66),(19,73),(20,43),(20,48),(20,66),(20,72),(21,44),(21,48),(21,65),(21,73),(22,34),(22,37),(22,41),(22,58),(22,61),(23,34),(23,38),(23,42),(23,59),(23,62),(24,35),(24,40),(24,43),(24,58),(24,62),(25,35),(25,39),(25,44),(25,59),(25,61),(26,31),(26,32),(26,33),(26,61),(26,62),(27,35),(27,46),(27,48),(27,74),(28,34),(28,45),(28,47),(28,74),(29,32),(29,37),(29,38),(29,39),(29,40),(29,60),(30,33),(30,41),(30,42),(30,43),(30,44),(30,60),(31,71),(31,77),(32,67),(32,68),(32,71),(33,69),(33,70),(33,71),(34,53),(34,55),(34,77),(35,54),(35,56),(35,77),(36,57),(36,60),(36,72),(36,73),(37,53),(37,67),(37,75),(38,53),(38,68),(38,76),(39,54),(39,67),(39,76),(40,54),(40,68),(40,75),(41,55),(41,69),(41,75),(42,55),(42,70),(42,76),(43,56),(43,70),(43,75),(44,56),(44,69),(44,76),(45,53),(45,78),(46,54),(46,78),(47,55),(47,78),(48,56),(48,78),(49,58),(49,72),(49,74),(50,59),(50,73),(50,74),(51,61),(51,63),(51,65),(51,74),(52,62),(52,64),(52,66),(52,74),(53,79),(54,79),(55,79),(56,79),(57,71),(57,78),(58,75),(58,77),(59,76),(59,77),(60,71),(60,75),(60,76),(61,67),(61,69),(61,77),(62,68),(62,70),(62,77),(63,67),(63,78),(64,68),(64,78),(65,69),(65,78),(66,70),(66,78),(67,79),(68,79),(69,79),(70,79),(71,79),(72,75),(72,78),(73,76),(73,78),(74,77),(74,78),(75,79),(76,79),(77,79),(78,79)],80)
=> ? = 1 - 1
[1,2,6,4,5,3] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,17),(1,18),(1,19),(1,29),(1,30),(1,31),(1,32),(1,33),(1,34),(2,15),(2,16),(2,22),(2,28),(2,31),(2,55),(2,56),(3,12),(3,14),(3,21),(3,27),(3,30),(3,54),(3,56),(4,11),(4,13),(4,20),(4,26),(4,29),(4,54),(4,55),(5,13),(5,14),(5,25),(5,28),(5,32),(5,57),(5,58),(6,11),(6,15),(6,23),(6,27),(6,33),(6,57),(6,59),(7,12),(7,16),(7,24),(7,26),(7,34),(7,58),(7,59),(8,17),(8,20),(8,24),(8,41),(8,56),(8,57),(9,18),(9,21),(9,23),(9,41),(9,55),(9,58),(10,19),(10,22),(10,25),(10,41),(10,54),(10,59),(11,35),(11,70),(11,74),(11,82),(12,36),(12,71),(12,75),(12,82),(13,37),(13,70),(13,73),(13,83),(14,38),(14,71),(14,73),(14,84),(15,39),(15,72),(15,74),(15,84),(16,40),(16,72),(16,75),(16,83),(17,45),(17,49),(17,63),(17,66),(17,67),(18,46),(18,48),(18,63),(18,65),(18,68),(19,47),(19,50),(19,63),(19,64),(19,69),(20,45),(20,51),(20,70),(20,89),(21,46),(21,52),(21,71),(21,89),(22,47),(22,53),(22,72),(22,89),(23,48),(23,52),(23,74),(23,88),(24,49),(24,51),(24,75),(24,88),(25,50),(25,53),(25,73),(25,88),(26,42),(26,51),(26,82),(26,83),(27,43),(27,52),(27,82),(27,84),(28,44),(28,53),(28,83),(28,84),(29,35),(29,37),(29,42),(29,45),(29,64),(29,65),(30,36),(30,38),(30,43),(30,46),(30,64),(30,66),(31,39),(31,40),(31,44),(31,47),(31,65),(31,66),(32,37),(32,38),(32,44),(32,50),(32,67),(32,68),(33,35),(33,39),(33,43),(33,48),(33,67),(33,69),(34,36),(34,40),(34,42),(34,49),(34,68),(34,69),(35,76),(35,80),(35,85),(36,77),(36,81),(36,85),(37,76),(37,79),(37,86),(38,77),(38,79),(38,87),(39,78),(39,80),(39,87),(40,78),(40,81),(40,86),(41,63),(41,88),(41,89),(42,60),(42,85),(42,86),(43,61),(43,85),(43,87),(44,62),(44,86),(44,87),(45,60),(45,76),(45,90),(46,61),(46,77),(46,90),(47,62),(47,78),(47,90),(48,61),(48,80),(48,91),(49,60),(49,81),(49,91),(50,62),(50,79),(50,91),(51,60),(51,92),(52,61),(52,92),(53,62),(53,92),(54,64),(54,73),(54,82),(54,89),(55,65),(55,74),(55,83),(55,89),(56,66),(56,75),(56,84),(56,89),(57,67),(57,70),(57,84),(57,88),(58,68),(58,71),(58,83),(58,88),(59,69),(59,72),(59,82),(59,88),(60,93),(61,93),(62,93),(63,90),(63,91),(64,79),(64,85),(64,90),(65,80),(65,86),(65,90),(66,81),(66,87),(66,90),(67,76),(67,87),(67,91),(68,77),(68,86),(68,91),(69,78),(69,85),(69,91),(70,76),(70,92),(71,77),(71,92),(72,78),(72,92),(73,79),(73,92),(74,80),(74,92),(75,81),(75,92),(76,93),(77,93),(78,93),(79,93),(80,93),(81,93),(82,85),(82,92),(83,86),(83,92),(84,87),(84,92),(85,93),(86,93),(87,93),(88,91),(88,92),(89,90),(89,92),(90,93),(91,93),(92,93)],94)
=> ? = 1 - 1
[1,2,6,5,3,4] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,17),(1,18),(1,19),(1,29),(1,30),(1,31),(1,32),(1,33),(1,34),(2,15),(2,16),(2,22),(2,28),(2,31),(2,55),(2,56),(3,12),(3,14),(3,21),(3,27),(3,30),(3,54),(3,56),(4,11),(4,13),(4,20),(4,26),(4,29),(4,54),(4,55),(5,13),(5,14),(5,25),(5,28),(5,32),(5,57),(5,58),(6,11),(6,15),(6,23),(6,27),(6,33),(6,57),(6,59),(7,12),(7,16),(7,24),(7,26),(7,34),(7,58),(7,59),(8,17),(8,20),(8,24),(8,41),(8,56),(8,57),(9,18),(9,21),(9,23),(9,41),(9,55),(9,58),(10,19),(10,22),(10,25),(10,41),(10,54),(10,59),(11,35),(11,70),(11,74),(11,82),(12,36),(12,71),(12,75),(12,82),(13,37),(13,70),(13,73),(13,83),(14,38),(14,71),(14,73),(14,84),(15,39),(15,72),(15,74),(15,84),(16,40),(16,72),(16,75),(16,83),(17,45),(17,49),(17,63),(17,66),(17,67),(18,46),(18,48),(18,63),(18,65),(18,68),(19,47),(19,50),(19,63),(19,64),(19,69),(20,45),(20,51),(20,70),(20,89),(21,46),(21,52),(21,71),(21,89),(22,47),(22,53),(22,72),(22,89),(23,48),(23,52),(23,74),(23,88),(24,49),(24,51),(24,75),(24,88),(25,50),(25,53),(25,73),(25,88),(26,42),(26,51),(26,82),(26,83),(27,43),(27,52),(27,82),(27,84),(28,44),(28,53),(28,83),(28,84),(29,35),(29,37),(29,42),(29,45),(29,64),(29,65),(30,36),(30,38),(30,43),(30,46),(30,64),(30,66),(31,39),(31,40),(31,44),(31,47),(31,65),(31,66),(32,37),(32,38),(32,44),(32,50),(32,67),(32,68),(33,35),(33,39),(33,43),(33,48),(33,67),(33,69),(34,36),(34,40),(34,42),(34,49),(34,68),(34,69),(35,76),(35,80),(35,85),(36,77),(36,81),(36,85),(37,76),(37,79),(37,86),(38,77),(38,79),(38,87),(39,78),(39,80),(39,87),(40,78),(40,81),(40,86),(41,63),(41,88),(41,89),(42,60),(42,85),(42,86),(43,61),(43,85),(43,87),(44,62),(44,86),(44,87),(45,60),(45,76),(45,90),(46,61),(46,77),(46,90),(47,62),(47,78),(47,90),(48,61),(48,80),(48,91),(49,60),(49,81),(49,91),(50,62),(50,79),(50,91),(51,60),(51,92),(52,61),(52,92),(53,62),(53,92),(54,64),(54,73),(54,82),(54,89),(55,65),(55,74),(55,83),(55,89),(56,66),(56,75),(56,84),(56,89),(57,67),(57,70),(57,84),(57,88),(58,68),(58,71),(58,83),(58,88),(59,69),(59,72),(59,82),(59,88),(60,93),(61,93),(62,93),(63,90),(63,91),(64,79),(64,85),(64,90),(65,80),(65,86),(65,90),(66,81),(66,87),(66,90),(67,76),(67,87),(67,91),(68,77),(68,86),(68,91),(69,78),(69,85),(69,91),(70,76),(70,92),(71,77),(71,92),(72,78),(72,92),(73,79),(73,92),(74,80),(74,92),(75,81),(75,92),(76,93),(77,93),(78,93),(79,93),(80,93),(81,93),(82,85),(82,92),(83,86),(83,92),(84,87),(84,92),(85,93),(86,93),(87,93),(88,91),(88,92),(89,90),(89,92),(90,93),(91,93),(92,93)],94)
=> ? = 1 - 1
[1,2,6,5,4,3] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,13),(1,24),(1,25),(1,31),(1,54),(1,55),(1,57),(2,12),(2,22),(2,23),(2,30),(2,52),(2,53),(2,57),(3,15),(3,27),(3,29),(3,33),(3,53),(3,55),(3,56),(4,14),(4,26),(4,28),(4,32),(4,52),(4,54),(4,56),(5,16),(5,22),(5,26),(5,35),(5,55),(5,58),(5,60),(6,17),(6,23),(6,27),(6,36),(6,54),(6,58),(6,61),(7,18),(7,24),(7,28),(7,36),(7,53),(7,59),(7,60),(8,19),(8,25),(8,29),(8,35),(8,52),(8,59),(8,61),(9,21),(9,32),(9,33),(9,34),(9,57),(9,60),(9,61),(10,20),(10,30),(10,31),(10,34),(10,56),(10,58),(10,59),(11,12),(11,13),(11,14),(11,15),(11,16),(11,17),(11,18),(11,19),(11,20),(11,21),(12,37),(12,38),(12,45),(12,72),(12,73),(12,77),(13,39),(13,40),(13,46),(13,74),(13,75),(13,77),(14,41),(14,43),(14,47),(14,72),(14,74),(14,76),(15,42),(15,44),(15,48),(15,73),(15,75),(15,76),(16,37),(16,41),(16,49),(16,75),(16,78),(16,80),(17,38),(17,42),(17,50),(17,74),(17,78),(17,81),(18,39),(18,43),(18,50),(18,73),(18,79),(18,80),(19,40),(19,44),(19,49),(19,72),(19,79),(19,81),(20,45),(20,46),(20,51),(20,76),(20,78),(20,79),(21,47),(21,48),(21,51),(21,77),(21,80),(21,81),(22,37),(22,62),(22,66),(22,96),(23,38),(23,62),(23,67),(23,95),(24,39),(24,63),(24,68),(24,96),(25,40),(25,63),(25,69),(25,95),(26,41),(26,64),(26,66),(26,94),(27,42),(27,65),(27,67),(27,94),(28,43),(28,64),(28,68),(28,93),(29,44),(29,65),(29,69),(29,93),(30,45),(30,62),(30,70),(30,93),(31,46),(31,63),(31,70),(31,94),(32,47),(32,64),(32,71),(32,95),(33,48),(33,65),(33,71),(33,96),(34,51),(34,70),(34,71),(34,92),(35,49),(35,66),(35,69),(35,92),(36,50),(36,67),(36,68),(36,92),(37,82),(37,86),(37,100),(38,82),(38,87),(38,99),(39,83),(39,88),(39,100),(40,83),(40,89),(40,99),(41,84),(41,86),(41,98),(42,85),(42,87),(42,98),(43,84),(43,88),(43,97),(44,85),(44,89),(44,97),(45,82),(45,90),(45,97),(46,83),(46,90),(46,98),(47,84),(47,91),(47,99),(48,85),(48,91),(48,100),(49,86),(49,89),(49,101),(50,87),(50,88),(50,101),(51,90),(51,91),(51,101),(52,66),(52,72),(52,93),(52,95),(53,67),(53,73),(53,93),(53,96),(54,68),(54,74),(54,94),(54,95),(55,69),(55,75),(55,94),(55,96),(56,71),(56,76),(56,93),(56,94),(57,70),(57,77),(57,95),(57,96),(58,62),(58,78),(58,92),(58,94),(59,63),(59,79),(59,92),(59,93),(60,64),(60,80),(60,92),(60,96),(61,65),(61,81),(61,92),(61,95),(62,82),(62,102),(63,83),(63,102),(64,84),(64,102),(65,85),(65,102),(66,86),(66,102),(67,87),(67,102),(68,88),(68,102),(69,89),(69,102),(70,90),(70,102),(71,91),(71,102),(72,86),(72,97),(72,99),(73,87),(73,97),(73,100),(74,88),(74,98),(74,99),(75,89),(75,98),(75,100),(76,91),(76,97),(76,98),(77,90),(77,99),(77,100),(78,82),(78,98),(78,101),(79,83),(79,97),(79,101),(80,84),(80,100),(80,101),(81,85),(81,99),(81,101),(82,103),(83,103),(84,103),(85,103),(86,103),(87,103),(88,103),(89,103),(90,103),(91,103),(92,101),(92,102),(93,97),(93,102),(94,98),(94,102),(95,99),(95,102),(96,100),(96,102),(97,103),(98,103),(99,103),(100,103),(101,103),(102,103)],104)
=> ? = 1 - 1
[1,3,2,4,5,6] => [3,2,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 1 - 1
[1,3,2,4,6,5] => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
=> ? = 4 - 1
[1,3,2,5,4,6] => [3,2,5,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
=> ? = 4 - 1
[1,3,2,5,6,4] => [3,2,6,4,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
=> ? = 3 - 1
[1,3,2,6,4,5] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
=> ? = 3 - 1
[1,3,2,6,5,4] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,17),(1,23),(1,30),(1,42),(1,44),(2,10),(2,16),(2,22),(2,30),(2,41),(2,43),(3,12),(3,18),(3,24),(3,29),(3,41),(3,44),(4,13),(4,19),(4,25),(4,29),(4,42),(4,43),(5,15),(5,21),(5,27),(5,28),(5,43),(5,44),(6,14),(6,20),(6,26),(6,28),(6,41),(6,42),(7,22),(7,23),(7,24),(7,25),(7,26),(7,27),(7,31),(8,16),(8,17),(8,18),(8,19),(8,20),(8,21),(8,31),(9,10),(9,11),(9,12),(9,13),(9,14),(9,15),(9,31),(10,32),(10,45),(10,47),(10,57),(11,32),(11,46),(11,48),(11,58),(12,33),(12,45),(12,48),(12,59),(13,33),(13,46),(13,47),(13,60),(14,34),(14,45),(14,46),(14,61),(15,34),(15,47),(15,48),(15,62),(16,35),(16,49),(16,51),(16,57),(17,35),(17,50),(17,52),(17,58),(18,36),(18,49),(18,52),(18,59),(19,36),(19,50),(19,51),(19,60),(20,37),(20,49),(20,50),(20,61),(21,37),(21,51),(21,52),(21,62),(22,38),(22,53),(22,55),(22,57),(23,38),(23,54),(23,56),(23,58),(24,39),(24,53),(24,56),(24,59),(25,39),(25,54),(25,55),(25,60),(26,40),(26,53),(26,54),(26,61),(27,40),(27,55),(27,56),(27,62),(28,34),(28,37),(28,40),(28,70),(29,33),(29,36),(29,39),(29,70),(30,32),(30,35),(30,38),(30,70),(31,57),(31,58),(31,59),(31,60),(31,61),(31,62),(32,63),(32,71),(33,64),(33,71),(34,65),(34,71),(35,63),(35,72),(36,64),(36,72),(37,65),(37,72),(38,63),(38,73),(39,64),(39,73),(40,65),(40,73),(41,45),(41,49),(41,53),(41,70),(42,46),(42,50),(42,54),(42,70),(43,47),(43,51),(43,55),(43,70),(44,48),(44,52),(44,56),(44,70),(45,66),(45,71),(46,67),(46,71),(47,68),(47,71),(48,69),(48,71),(49,66),(49,72),(50,67),(50,72),(51,68),(51,72),(52,69),(52,72),(53,66),(53,73),(54,67),(54,73),(55,68),(55,73),(56,69),(56,73),(57,63),(57,66),(57,68),(58,63),(58,67),(58,69),(59,64),(59,66),(59,69),(60,64),(60,67),(60,68),(61,65),(61,66),(61,67),(62,65),(62,68),(62,69),(63,74),(64,74),(65,74),(66,74),(67,74),(68,74),(69,74),(70,71),(70,72),(70,73),(71,74),(72,74),(73,74)],75)
=> ? = 3 - 1
[1,3,4,2,5,6] => [4,2,3,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 1 - 1
[1,3,4,2,6,5] => [4,2,3,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
=> ? = 3 - 1
[2,1,3,4,5,6] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[2,3,1,4,5,6] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[2,3,4,1,5,6] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,3,4,1,6,5] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[2,4,1,3,5,6] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[2,4,3,1,5,6] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[3,1,2,4,5,6] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[3,2,1,4,5,6] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[3,2,4,1,5,6] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[3,4,1,2,5,6] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[3,4,2,1,5,6] => [3,1,2,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[4,2,1,3,5,6] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[4,2,3,1,5,6] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> 0 = 1 - 1
[2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,3,4,5,1,7,6] => [1,2,3,4,7,6,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[2,3,5,1,4,6,7] => [1,2,5,3,6,7,4] => ([(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[2,3,5,4,1,6,7] => [1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[2,4,1,3,5,6,7] => [1,4,2,5,6,7,3] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[2,4,3,1,5,6,7] => [1,3,2,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[2,4,3,5,1,6,7] => [1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[2,4,5,1,3,6,7] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[2,4,5,3,1,6,7] => [1,4,2,3,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[2,5,3,1,4,6,7] => [1,3,5,2,6,7,4] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[2,5,3,4,1,6,7] => [1,3,4,2,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[3,1,2,4,5,6,7] => [3,1,4,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> 0 = 1 - 1
[3,2,1,4,5,6,7] => [2,1,4,5,6,7,3] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[3,2,4,1,5,6,7] => [2,1,3,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[3,2,4,5,1,6,7] => [2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[3,2,5,1,4,6,7] => [2,1,5,3,6,7,4] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[3,2,5,4,1,6,7] => [2,1,4,3,6,7,5] => ([(0,3),(1,2),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[3,4,1,2,5,6,7] => [4,1,2,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> 0 = 1 - 1
[3,4,2,1,5,6,7] => [3,1,2,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
[3,4,2,5,1,6,7] => [3,1,2,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 0 = 1 - 1
[3,4,5,1,2,6,7] => [5,1,2,3,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> 0 = 1 - 1
[3,4,5,2,1,6,7] => [4,1,2,3,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 0 = 1 - 1
Description
The Frankl number of a lattice.
For a lattice $L$ on at least two elements, this is
$$
\max_x(|L|-2|[x, 1]|),
$$
where we maximize over all join irreducible elements and $[x, 1]$ denotes the interval from $x$ to the top element. Frankl's conjecture asserts that this number is non-negative, and zero if and only if $L$ is a Boolean lattice.
Matching statistic: St001330
(load all 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
Mp00069: Permutations —complement⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 10%
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 2 = 1 + 1
[1,2,3,4] => [4,3,2,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,3] => [4,3,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,4] => [4,2,3,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 1 + 1
[2,1,3,4] => [3,4,2,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 1 + 1
[2,1,4,3] => [3,4,1,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 2 + 1
[1,2,3,4,5] => [5,4,3,2,1] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[1,2,3,5,4] => [5,4,3,1,2] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2 = 1 + 1
[1,2,4,3,5] => [5,4,2,3,1] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[1,2,4,5,3] => [5,4,2,1,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2 = 1 + 1
[1,2,5,3,4] => [5,4,1,3,2] => [4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[1,2,5,4,3] => [5,4,1,2,3] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2 = 1 + 1
[1,3,2,4,5] => [5,3,4,2,1] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[1,3,2,5,4] => [5,3,4,1,2] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
[1,3,4,2,5] => [5,3,2,4,1] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[1,4,2,3,5] => [5,2,4,3,1] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 1 + 1
[1,4,3,2,5] => [5,2,3,4,1] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
[2,1,3,4,5] => [4,5,3,2,1] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[2,1,3,5,4] => [4,5,3,1,2] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ? = 3 + 1
[2,1,4,3,5] => [4,5,2,3,1] => [3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 1
[2,1,4,5,3] => [4,5,2,1,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[2,1,5,3,4] => [4,5,1,3,2] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[2,1,5,4,3] => [4,5,1,2,3] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[2,3,1,4,5] => [4,3,5,2,1] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[2,3,1,5,4] => [4,3,5,1,2] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[3,1,2,4,5] => [3,5,4,2,1] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[3,1,2,5,4] => [3,5,4,1,2] => [4,1,3,5,2] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[3,2,1,4,5] => [3,4,5,2,1] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[3,2,1,5,4] => [3,4,5,1,2] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[1,2,3,4,6,5] => [6,5,4,3,1,2] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
[1,2,3,5,4,6] => [6,5,4,2,3,1] => [3,4,2,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,3,5,6,4] => [6,5,4,2,1,3] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 2 = 1 + 1
[1,2,3,6,4,5] => [6,5,4,1,3,2] => [4,3,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,3,6,5,4] => [6,5,4,1,2,3] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [2,4,5,3,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,4,3,6,5] => [6,5,3,4,1,2] => [4,1,5,3,6,2] => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 + 1
[1,2,4,5,3,6] => [6,5,3,2,4,1] => [4,3,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,4,5,6,3] => [6,5,3,2,1,4] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 2 = 1 + 1
[1,2,4,6,3,5] => [6,5,3,1,4,2] => [3,5,4,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,4,6,5,3] => [6,5,3,1,2,4] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 2 = 1 + 1
[1,2,5,3,4,6] => [6,5,2,4,3,1] => [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 1 + 1
[1,2,5,3,6,4] => [6,5,2,4,1,3] => [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,5,4,3,6] => [6,5,2,3,4,1] => [4,5,2,3,6,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,5,4,6,3] => [6,5,2,3,1,4] => [3,5,2,1,6,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,5,6,3,4] => [6,5,2,1,4,3] => [2,5,4,1,6,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 1 + 1
[1,2,5,6,4,3] => [6,5,2,1,3,4] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 2 = 1 + 1
[1,2,6,3,4,5] => [6,5,1,4,3,2] => [5,3,4,1,6,2] => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,6,3,5,4] => [6,5,1,4,2,3] => [5,4,2,1,6,3] => ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,6,4,3,5] => [6,5,1,3,4,2] => [5,4,1,3,6,2] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,6,4,5,3] => [6,5,1,3,2,4] => [5,3,1,2,6,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,6,5,3,4] => [6,5,1,2,4,3] => [5,1,4,2,6,3] => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,2,6,5,4,3] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
[1,3,2,4,5,6] => [6,4,5,3,2,1] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,3,2,4,6,5] => [6,4,5,3,1,2] => [3,1,5,6,4,2] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 4 + 1
[1,3,2,5,4,6] => [6,4,5,2,3,1] => [3,5,2,6,4,1] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 4 + 1
[1,3,2,5,6,4] => [6,4,5,2,1,3] => [2,5,1,6,4,3] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 1
[1,3,2,6,4,5] => [6,4,5,1,3,2] => [5,3,1,6,4,2] => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 1
[1,3,2,6,5,4] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 1
[1,3,4,2,5,6] => [6,4,3,5,2,1] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,3,4,2,6,5] => [6,4,3,5,1,2] => [5,1,4,6,3,2] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 1
[1,3,4,5,2,6] => [6,4,3,2,5,1] => [5,3,4,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,3,5,2,4,6] => [6,4,2,5,3,1] => [3,5,4,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 1 + 1
[1,3,5,4,2,6] => [6,4,2,3,5,1] => [5,4,2,6,3,1] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,4,2,3,5,6] => [6,3,5,4,2,1] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 1 + 1
[1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[1,2,3,4,5,7,6] => [7,6,5,4,3,1,2] => [3,1,4,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> 2 = 1 + 1
[1,2,3,4,6,7,5] => [7,6,5,4,2,1,3] => [2,4,1,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> 2 = 1 + 1
[1,2,3,4,7,6,5] => [7,6,5,4,1,2,3] => [4,1,2,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> 2 = 1 + 1
[1,2,3,5,6,7,4] => [7,6,5,3,2,1,4] => [2,3,5,1,6,7,4] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 2 = 1 + 1
[1,2,3,5,7,6,4] => [7,6,5,3,1,2,4] => [3,1,5,2,6,7,4] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> 2 = 1 + 1
[1,2,3,6,7,5,4] => [7,6,5,2,1,3,4] => [2,5,1,3,6,7,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
=> 2 = 1 + 1
[1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => [5,1,2,3,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> 2 = 1 + 1
[1,2,4,5,6,7,3] => [7,6,4,3,2,1,5] => [2,3,4,6,1,7,5] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> 2 = 1 + 1
[1,2,4,5,7,6,3] => [7,6,4,3,1,2,5] => [3,1,4,6,2,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> 2 = 1 + 1
[1,2,4,6,7,5,3] => [7,6,4,2,1,3,5] => [2,4,1,6,3,7,5] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> 2 = 1 + 1
[1,2,4,7,6,5,3] => [7,6,4,1,2,3,5] => [4,1,2,6,3,7,5] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> 2 = 1 + 1
[1,2,5,6,7,4,3] => [7,6,3,2,1,4,5] => [2,3,6,1,4,7,5] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
=> 2 = 1 + 1
[1,2,5,7,6,4,3] => [7,6,3,1,2,4,5] => [3,1,6,2,4,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> 2 = 1 + 1
[1,2,6,7,5,4,3] => [7,6,2,1,3,4,5] => [2,6,1,3,4,7,5] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> 2 = 1 + 1
[1,2,7,6,5,4,3] => [7,6,1,2,3,4,5] => [6,1,2,3,4,7,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> 2 = 1 + 1
[1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 2 = 1 + 1
[1,2,6,7,8,5,4,3] => [8,7,3,2,1,4,5,6] => [2,3,7,1,4,5,8,6] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
=> 2 = 1 + 1
[1,2,5,6,8,7,4,3] => [8,7,4,3,1,2,5,6] => [3,1,4,7,2,5,8,6] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> 2 = 1 + 1
[1,2,5,6,7,8,4,3] => [8,7,4,3,2,1,5,6] => [2,3,4,7,1,5,8,6] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
=> 2 = 1 + 1
[1,2,4,6,8,7,5,3] => [8,7,5,3,1,2,4,6] => [3,1,5,2,7,4,8,6] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
=> 2 = 1 + 1
[1,2,4,6,7,8,5,3] => [8,7,5,3,2,1,4,6] => [2,3,5,1,7,4,8,6] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
=> 2 = 1 + 1
[1,2,4,5,8,7,6,3] => [8,7,5,4,1,2,3,6] => [4,1,2,5,7,3,8,6] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
=> 2 = 1 + 1
[1,2,4,5,7,8,6,3] => [8,7,5,4,2,1,3,6] => [2,4,1,5,7,3,8,6] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
=> 2 = 1 + 1
[1,2,4,5,6,8,7,3] => [8,7,5,4,3,1,2,6] => [3,1,4,5,7,2,8,6] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
=> 2 = 1 + 1
[1,2,3,5,6,7,8,4] => [8,7,6,4,3,2,1,5] => [2,3,4,6,1,7,8,5] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
=> 2 = 1 + 1
[1,2,3,4,8,7,6,5] => [8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
=> 2 = 1 + 1
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St000068
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000068: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 10%
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000068: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,4,3] => [1,2,4,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1
[1,3,2,4] => [1,3,2,4] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1
[2,1,4,3] => [2,1,4,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 2
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 1
[1,2,4,3,5] => [1,2,4,3,5] => [4,1,2,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[1,2,4,5,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1
[1,2,5,3,4] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1
[1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1
[1,3,2,4,5] => [1,3,2,4,5] => [3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[1,3,2,5,4] => [1,3,2,5,4] => [3,5,1,2,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 3
[1,3,4,2,5] => [1,4,3,2,5] => [4,3,1,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 1
[1,4,2,3,5] => [1,4,3,2,5] => [4,3,1,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 1
[1,4,3,2,5] => [1,4,3,2,5] => [4,3,1,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 1
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 1
[2,1,3,5,4] => [2,1,3,5,4] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 3
[2,1,4,3,5] => [2,1,4,3,5] => [2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 3
[2,1,4,5,3] => [2,1,5,4,3] => [5,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 2
[2,1,5,3,4] => [2,1,5,4,3] => [5,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 2
[2,1,5,4,3] => [2,1,5,4,3] => [5,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 2
[2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 1
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,6,1,2,3,5] => ([(0,2),(0,3),(0,4),(0,6),(1,15),(1,17),(2,7),(2,14),(3,9),(3,14),(4,9),(4,10),(4,14),(5,1),(5,11),(5,12),(5,16),(6,5),(6,7),(6,10),(6,14),(7,11),(7,16),(9,13),(10,12),(10,13),(10,16),(11,15),(11,17),(12,15),(12,17),(13,17),(14,13),(14,16),(15,8),(16,15),(16,17),(17,8)],18)
=> ? = 4
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [4,6,5,1,2,3] => ([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [5,1,6,2,3,4] => ([(0,2),(0,3),(0,4),(0,6),(1,15),(1,17),(2,7),(2,14),(3,9),(3,14),(4,9),(4,10),(4,14),(5,1),(5,11),(5,12),(5,16),(6,5),(6,7),(6,10),(6,14),(7,11),(7,16),(9,13),(10,12),(10,13),(10,16),(11,15),(11,17),(12,15),(12,17),(13,17),(14,13),(14,16),(15,8),(16,15),(16,17),(17,8)],18)
=> ? = 1
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [4,6,5,1,2,3] => ([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [4,6,5,1,2,3] => ([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [4,6,5,1,2,3] => ([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [4,6,5,1,2,3] => ([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,6,1,2,4,5] => ([(0,3),(0,4),(0,5),(0,6),(1,11),(1,18),(2,12),(2,17),(2,18),(3,7),(3,14),(4,1),(4,10),(4,13),(4,14),(5,2),(5,9),(5,13),(5,14),(6,7),(6,9),(6,10),(7,17),(9,15),(9,17),(10,15),(10,17),(10,18),(11,16),(11,19),(12,16),(12,19),(13,11),(13,12),(13,15),(13,18),(14,17),(14,18),(15,16),(15,19),(16,8),(17,19),(18,16),(18,19),(19,8)],20)
=> ? = 4
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
=> ? = 4
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,17),(1,19),(2,8),(2,18),(2,22),(3,10),(3,11),(3,19),(4,12),(4,14),(4,17),(4,19),(5,10),(5,13),(5,14),(5,17),(6,2),(6,11),(6,12),(6,13),(6,19),(7,20),(8,20),(8,21),(10,15),(10,22),(11,15),(11,18),(11,22),(12,16),(12,18),(12,22),(13,8),(13,15),(13,16),(13,22),(14,7),(14,16),(14,22),(15,20),(15,21),(16,20),(16,21),(17,7),(17,22),(18,21),(19,18),(19,22),(20,9),(21,9),(22,20),(22,21)],23)
=> ? = 3
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,17),(1,19),(2,8),(2,18),(2,22),(3,10),(3,11),(3,19),(4,12),(4,14),(4,17),(4,19),(5,10),(5,13),(5,14),(5,17),(6,2),(6,11),(6,12),(6,13),(6,19),(7,20),(8,20),(8,21),(10,15),(10,22),(11,15),(11,18),(11,22),(12,16),(12,18),(12,22),(13,8),(13,15),(13,16),(13,22),(14,7),(14,16),(14,22),(15,20),(15,21),(16,20),(16,21),(17,7),(17,22),(18,21),(19,18),(19,22),(20,9),(21,9),(22,20),(22,21)],23)
=> ? = 3
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,17),(1,19),(2,8),(2,18),(2,22),(3,10),(3,11),(3,19),(4,12),(4,14),(4,17),(4,19),(5,10),(5,13),(5,14),(5,17),(6,2),(6,11),(6,12),(6,13),(6,19),(7,20),(8,20),(8,21),(10,15),(10,22),(11,15),(11,18),(11,22),(12,16),(12,18),(12,22),(13,8),(13,15),(13,16),(13,22),(14,7),(14,16),(14,22),(15,20),(15,21),(16,20),(16,21),(17,7),(17,22),(18,21),(19,18),(19,22),(20,9),(21,9),(22,20),(22,21)],23)
=> ? = 3
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => ([(0,3),(0,4),(0,5),(0,6),(1,9),(1,18),(2,8),(2,19),(3,10),(3,11),(3,13),(4,11),(4,12),(4,14),(5,2),(5,12),(5,13),(5,15),(6,1),(6,10),(6,14),(6,15),(8,20),(8,21),(9,20),(10,17),(10,18),(11,16),(11,18),(12,16),(12,19),(13,16),(13,17),(13,19),(14,9),(14,18),(14,19),(15,8),(15,17),(15,18),(15,19),(16,21),(17,20),(17,21),(18,20),(18,21),(19,20),(19,21),(20,7),(21,7)],22)
=> ? = 3
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [3,5,4,1,2,6] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? = 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [4,1,5,2,3,6] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,20),(1,22),(2,13),(2,14),(2,17),(3,11),(3,12),(3,17),(4,8),(4,9),(4,11),(4,17),(5,1),(5,8),(5,10),(5,14),(5,17),(6,9),(6,10),(6,12),(6,13),(8,15),(8,20),(8,22),(9,15),(9,19),(9,22),(10,15),(10,16),(10,19),(10,20),(11,22),(12,19),(12,22),(13,16),(13,19),(14,16),(14,20),(14,22),(15,18),(15,21),(16,18),(16,21),(17,19),(17,20),(17,22),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,21)],23)
=> ? = 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 1
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => ([(0,3),(0,4),(0,5),(0,6),(1,9),(1,18),(2,8),(2,19),(3,10),(3,11),(3,13),(4,11),(4,12),(4,14),(5,2),(5,12),(5,13),(5,15),(6,1),(6,10),(6,14),(6,15),(8,20),(8,21),(9,20),(10,17),(10,18),(11,16),(11,18),(12,16),(12,19),(13,16),(13,17),(13,19),(14,9),(14,18),(14,19),(15,8),(15,17),(15,18),(15,19),(16,21),(17,20),(17,21),(18,20),(18,21),(19,20),(19,21),(20,7),(21,7)],22)
=> ? = 3
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [3,5,4,1,2,6] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? = 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
=> ? = 1
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => ([(0,3),(0,4),(0,5),(0,6),(1,9),(1,18),(2,8),(2,19),(3,10),(3,11),(3,13),(4,11),(4,12),(4,14),(5,2),(5,12),(5,13),(5,15),(6,1),(6,10),(6,14),(6,15),(8,20),(8,21),(9,20),(10,17),(10,18),(11,16),(11,18),(12,16),(12,19),(13,16),(13,17),(13,19),(14,9),(14,18),(14,19),(15,8),(15,17),(15,18),(15,19),(16,21),(17,20),(17,21),(18,20),(18,21),(19,20),(19,21),(20,7),(21,7)],22)
=> ? = 3
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [3,5,4,1,2,6] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? = 1
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 1
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [3,5,4,1,2,6] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? = 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [3,5,4,1,2,6] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? = 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 1
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[2,4,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[3,4,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[4,2,1,3,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[4,3,1,2,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 1
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 1
Description
The number of minimal elements in a poset.
Matching statistic: St001630
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 10%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => [3] => ([],3)
=> ([],1)
=> ? = 1 + 1
[1,2,3,4] => [4] => ([],4)
=> ([],1)
=> ? = 1 + 1
[1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,1,3,4] => [1,3] => ([(2,3)],4)
=> ([(0,1)],2)
=> ? = 1 + 1
[2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
[1,2,3,4,5] => [5] => ([],5)
=> ([],1)
=> ? = 1 + 1
[1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 + 1
[1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3 + 1
[1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1 + 1
[2,1,3,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> ? = 1 + 1
[2,1,3,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 3 + 1
[2,1,4,3,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3 + 1
[2,1,4,5,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2 + 1
[2,1,5,3,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
[2,1,5,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 2 + 1
[2,3,1,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,3,1,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 2 + 1
[3,1,2,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> ? = 1 + 1
[3,1,2,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2 + 1
[3,2,1,4,5] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[3,2,1,5,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? = 2 + 1
[1,2,3,4,5,6] => [6] => ([],6)
=> ([],1)
=> ? = 1 + 1
[1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 + 1
[1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 + 1
[1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 + 1
[1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 4 + 1
[1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 + 1
[1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 + 1
[1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 + 1
[1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 + 1
[1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 + 1
[1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 + 1
[1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 + 1
[1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 + 1
[1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 + 1
[1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 + 1
[1,2,6,5,4,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(1,15),(1,26),(1,27),(1,32),(1,33),(1,41),(1,42),(1,91),(1,94),(2,14),(2,23),(2,25),(2,29),(2,31),(2,40),(2,42),(2,90),(2,93),(3,13),(3,22),(3,24),(3,28),(3,30),(3,40),(3,41),(3,89),(3,92),(4,18),(4,24),(4,25),(4,34),(4,35),(4,43),(4,44),(4,86),(4,94),(5,17),(5,22),(5,26),(5,36),(5,38),(5,43),(5,45),(5,87),(5,93),(6,16),(6,23),(6,27),(6,37),(6,39),(6,44),(6,45),(6,88),(6,92),(7,21),(7,30),(7,31),(7,36),(7,37),(7,46),(7,47),(7,86),(7,91),(8,20),(8,28),(8,32),(8,34),(8,39),(8,46),(8,48),(8,87),(8,90),(9,19),(9,29),(9,33),(9,35),(9,38),(9,47),(9,48),(9,88),(9,89),(10,19),(10,20),(10,21),(10,49),(10,92),(10,93),(10,94),(11,16),(11,17),(11,18),(11,49),(11,89),(11,90),(11,91),(12,13),(12,14),(12,15),(12,49),(12,86),(12,87),(12,88),(13,53),(13,54),(13,98),(13,100),(13,134),(14,53),(14,55),(14,99),(14,101),(14,135),(15,54),(15,55),(15,102),(15,103),(15,136),(16,56),(16,58),(16,107),(16,108),(16,134),(17,57),(17,58),(17,106),(17,109),(17,135),(18,56),(18,57),(18,104),(18,105),(18,136),(19,59),(19,61),(19,113),(19,114),(19,134),(20,60),(20,61),(20,112),(20,115),(20,135),(21,59),(21,60),(21,110),(21,111),(21,136),(22,63),(22,65),(22,80),(22,98),(22,106),(22,131),(23,64),(23,66),(23,81),(23,99),(23,107),(23,131),(24,62),(24,65),(24,82),(24,100),(24,104),(24,132),(25,62),(25,66),(25,83),(25,101),(25,105),(25,133),(26,63),(26,67),(26,84),(26,102),(26,109),(26,133),(27,64),(27,67),(27,85),(27,103),(27,108),(27,132),(28,69),(28,74),(28,82),(28,98),(28,112),(28,128),(29,70),(29,75),(29,83),(29,99),(29,113),(29,128),(30,68),(30,74),(30,80),(30,100),(30,110),(30,129),(31,68),(31,75),(31,81),(31,101),(31,111),(31,130),(32,69),(32,76),(32,85),(32,102),(32,115),(32,130),(33,70),(33,76),(33,84),(33,103),(33,114),(33,129),(34,72),(34,79),(34,82),(34,105),(34,115),(34,126),(35,71),(35,79),(35,83),(35,104),(35,114),(35,125),(36,73),(36,77),(36,80),(36,109),(36,111),(36,126),(37,73),(37,78),(37,81),(37,108),(37,110),(37,125),(38,71),(38,77),(38,84),(38,106),(38,113),(38,127),(39,72),(39,78),(39,85),(39,107),(39,112),(39,127),(40,50),(40,53),(40,62),(40,68),(40,128),(40,131),(41,50),(41,54),(41,63),(41,69),(41,129),(41,132),(42,50),(42,55),(42,64),(42,70),(42,130),(42,133),(43,51),(43,57),(43,65),(43,71),(43,126),(43,133),(44,51),(44,56),(44,66),(44,72),(44,125),(44,132),(45,51),(45,58),(45,67),(45,73),(45,127),(45,131),(46,52),(46,60),(46,74),(46,78),(46,126),(46,130),(47,52),(47,59),(47,75),(47,77),(47,125),(47,129),(48,52),(48,61),(48,76),(48,79),(48,127),(48,128),(49,134),(49,135),(49,136),(50,95),(50,147),(50,148),(51,96),(51,146),(51,148),(52,97),(52,146),(52,147),(53,95),(53,118),(53,151),(54,95),(54,116),(54,149),(55,95),(55,117),(55,150),(56,96),(56,120),(56,149),(57,96),(57,119),(57,150),(58,96),(58,121),(58,151),(59,97),(59,123),(59,149),(60,97),(60,122),(60,150),(61,97),(61,124),(61,151),(62,118),(62,142),(62,148),(63,116),(63,140),(63,148),(64,117),(64,141),(64,148),(65,119),(65,137),(65,148),(66,120),(66,138),(66,148),(67,121),(67,139),(67,148),(68,118),(68,143),(68,147),(69,116),(69,144),(69,147),(70,117),(70,145),(70,147),(71,119),(71,145),(71,146),(72,120),(72,144),(72,146),(73,121),(73,143),(73,146),(74,122),(74,137),(74,147),(75,123),(75,138),(75,147),(76,124),(76,139),(76,147),(77,123),(77,140),(77,146),(78,122),(78,141),(78,146),(79,124),(79,142),(79,146),(80,137),(80,140),(80,143),(81,138),(81,141),(81,143),(82,137),(82,142),(82,144),(83,138),(83,142),(83,145),(84,139),(84,140),(84,145),(85,139),(85,141),(85,144),(86,100),(86,101),(86,125),(86,126),(86,136),(87,98),(87,102),(87,126),(87,127),(87,135),(88,99),(88,103),(88,125),(88,127),(88,134),(89,104),(89,106),(89,128),(89,129),(89,134),(90,105),(90,107),(90,128),(90,130),(90,135),(91,108),(91,109),(91,129),(91,130),(91,136),(92,110),(92,112),(92,131),(92,132),(92,134),(93,111),(93,113),(93,131),(93,133),(93,135),(94,114),(94,115),(94,132),(94,133),(94,136),(95,152),(96,152),(97,152),(98,116),(98,137),(98,151),(99,117),(99,138),(99,151),(100,118),(100,137),(100,149),(101,118),(101,138),(101,150),(102,116),(102,139),(102,150),(103,117),(103,139),(103,149),(104,119),(104,142),(104,149),(105,120),(105,142),(105,150),(106,119),(106,140),(106,151),(107,120),(107,141),(107,151),(108,121),(108,141),(108,149),(109,121),(109,140),(109,150),(110,122),(110,143),(110,149),(111,123),(111,143),(111,150),(112,122),(112,144),(112,151),(113,123),(113,145),(113,151),(114,124),(114,145),(114,149),(115,124),(115,144),(115,150),(116,152),(117,152),(118,152),(119,152),(120,152),(121,152),(122,152),(123,152),(124,152),(125,138),(125,146),(125,149),(126,137),(126,146),(126,150),(127,139),(127,146),(127,151),(128,142),(128,147),(128,151),(129,140),(129,147),(129,149),(130,141),(130,147),(130,150),(131,143),(131,148),(131,151),(132,144),(132,148),(132,149),(133,145),(133,148),(133,150),(134,149),(134,151),(135,150),(135,151),(136,149),(136,150),(137,152),(138,152),(139,152),(140,152),(141,152),(142,152),(143,152),(144,152),(145,152),(146,152),(147,152),(148,152),(149,152),(150,152),(151,152)],153)
=> ? = 1 + 1
[1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 4 + 1
[1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 4 + 1
[1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,3,1,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,4,1,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[3,2,1,4,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[3,4,1,2,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[4,2,1,3,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[4,3,1,2,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[1,3,2,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,2,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,2,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,6,2,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,3,1,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,4,1,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,5,1,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[3,2,1,4,5,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[3,4,1,2,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[3,5,1,2,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[4,2,1,3,5,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[4,3,1,2,5,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[4,5,1,2,3,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,2,1,3,4,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[5,3,1,2,4,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[5,4,1,2,3,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St001878
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 10%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => [3] => ([],3)
=> ([],1)
=> ? = 1 + 1
[1,2,3,4] => [4] => ([],4)
=> ([],1)
=> ? = 1 + 1
[1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,1,3,4] => [1,3] => ([(2,3)],4)
=> ([(0,1)],2)
=> ? = 1 + 1
[2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
[1,2,3,4,5] => [5] => ([],5)
=> ([],1)
=> ? = 1 + 1
[1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 + 1
[1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3 + 1
[1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 1 + 1
[2,1,3,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> ? = 1 + 1
[2,1,3,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 3 + 1
[2,1,4,3,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3 + 1
[2,1,4,5,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2 + 1
[2,1,5,3,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 2 + 1
[2,1,5,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 2 + 1
[2,3,1,4,5] => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,3,1,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 2 + 1
[3,1,2,4,5] => [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> ? = 1 + 1
[3,1,2,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 2 + 1
[3,2,1,4,5] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[3,2,1,5,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? = 2 + 1
[1,2,3,4,5,6] => [6] => ([],6)
=> ([],1)
=> ? = 1 + 1
[1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 + 1
[1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 + 1
[1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 + 1
[1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 4 + 1
[1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 1 + 1
[1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 + 1
[1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 + 1
[1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 + 1
[1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 + 1
[1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 1 + 1
[1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
[1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 + 1
[1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 + 1
[1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 1 + 1
[1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 1 + 1
[1,2,6,5,4,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(1,15),(1,26),(1,27),(1,32),(1,33),(1,41),(1,42),(1,91),(1,94),(2,14),(2,23),(2,25),(2,29),(2,31),(2,40),(2,42),(2,90),(2,93),(3,13),(3,22),(3,24),(3,28),(3,30),(3,40),(3,41),(3,89),(3,92),(4,18),(4,24),(4,25),(4,34),(4,35),(4,43),(4,44),(4,86),(4,94),(5,17),(5,22),(5,26),(5,36),(5,38),(5,43),(5,45),(5,87),(5,93),(6,16),(6,23),(6,27),(6,37),(6,39),(6,44),(6,45),(6,88),(6,92),(7,21),(7,30),(7,31),(7,36),(7,37),(7,46),(7,47),(7,86),(7,91),(8,20),(8,28),(8,32),(8,34),(8,39),(8,46),(8,48),(8,87),(8,90),(9,19),(9,29),(9,33),(9,35),(9,38),(9,47),(9,48),(9,88),(9,89),(10,19),(10,20),(10,21),(10,49),(10,92),(10,93),(10,94),(11,16),(11,17),(11,18),(11,49),(11,89),(11,90),(11,91),(12,13),(12,14),(12,15),(12,49),(12,86),(12,87),(12,88),(13,53),(13,54),(13,98),(13,100),(13,134),(14,53),(14,55),(14,99),(14,101),(14,135),(15,54),(15,55),(15,102),(15,103),(15,136),(16,56),(16,58),(16,107),(16,108),(16,134),(17,57),(17,58),(17,106),(17,109),(17,135),(18,56),(18,57),(18,104),(18,105),(18,136),(19,59),(19,61),(19,113),(19,114),(19,134),(20,60),(20,61),(20,112),(20,115),(20,135),(21,59),(21,60),(21,110),(21,111),(21,136),(22,63),(22,65),(22,80),(22,98),(22,106),(22,131),(23,64),(23,66),(23,81),(23,99),(23,107),(23,131),(24,62),(24,65),(24,82),(24,100),(24,104),(24,132),(25,62),(25,66),(25,83),(25,101),(25,105),(25,133),(26,63),(26,67),(26,84),(26,102),(26,109),(26,133),(27,64),(27,67),(27,85),(27,103),(27,108),(27,132),(28,69),(28,74),(28,82),(28,98),(28,112),(28,128),(29,70),(29,75),(29,83),(29,99),(29,113),(29,128),(30,68),(30,74),(30,80),(30,100),(30,110),(30,129),(31,68),(31,75),(31,81),(31,101),(31,111),(31,130),(32,69),(32,76),(32,85),(32,102),(32,115),(32,130),(33,70),(33,76),(33,84),(33,103),(33,114),(33,129),(34,72),(34,79),(34,82),(34,105),(34,115),(34,126),(35,71),(35,79),(35,83),(35,104),(35,114),(35,125),(36,73),(36,77),(36,80),(36,109),(36,111),(36,126),(37,73),(37,78),(37,81),(37,108),(37,110),(37,125),(38,71),(38,77),(38,84),(38,106),(38,113),(38,127),(39,72),(39,78),(39,85),(39,107),(39,112),(39,127),(40,50),(40,53),(40,62),(40,68),(40,128),(40,131),(41,50),(41,54),(41,63),(41,69),(41,129),(41,132),(42,50),(42,55),(42,64),(42,70),(42,130),(42,133),(43,51),(43,57),(43,65),(43,71),(43,126),(43,133),(44,51),(44,56),(44,66),(44,72),(44,125),(44,132),(45,51),(45,58),(45,67),(45,73),(45,127),(45,131),(46,52),(46,60),(46,74),(46,78),(46,126),(46,130),(47,52),(47,59),(47,75),(47,77),(47,125),(47,129),(48,52),(48,61),(48,76),(48,79),(48,127),(48,128),(49,134),(49,135),(49,136),(50,95),(50,147),(50,148),(51,96),(51,146),(51,148),(52,97),(52,146),(52,147),(53,95),(53,118),(53,151),(54,95),(54,116),(54,149),(55,95),(55,117),(55,150),(56,96),(56,120),(56,149),(57,96),(57,119),(57,150),(58,96),(58,121),(58,151),(59,97),(59,123),(59,149),(60,97),(60,122),(60,150),(61,97),(61,124),(61,151),(62,118),(62,142),(62,148),(63,116),(63,140),(63,148),(64,117),(64,141),(64,148),(65,119),(65,137),(65,148),(66,120),(66,138),(66,148),(67,121),(67,139),(67,148),(68,118),(68,143),(68,147),(69,116),(69,144),(69,147),(70,117),(70,145),(70,147),(71,119),(71,145),(71,146),(72,120),(72,144),(72,146),(73,121),(73,143),(73,146),(74,122),(74,137),(74,147),(75,123),(75,138),(75,147),(76,124),(76,139),(76,147),(77,123),(77,140),(77,146),(78,122),(78,141),(78,146),(79,124),(79,142),(79,146),(80,137),(80,140),(80,143),(81,138),(81,141),(81,143),(82,137),(82,142),(82,144),(83,138),(83,142),(83,145),(84,139),(84,140),(84,145),(85,139),(85,141),(85,144),(86,100),(86,101),(86,125),(86,126),(86,136),(87,98),(87,102),(87,126),(87,127),(87,135),(88,99),(88,103),(88,125),(88,127),(88,134),(89,104),(89,106),(89,128),(89,129),(89,134),(90,105),(90,107),(90,128),(90,130),(90,135),(91,108),(91,109),(91,129),(91,130),(91,136),(92,110),(92,112),(92,131),(92,132),(92,134),(93,111),(93,113),(93,131),(93,133),(93,135),(94,114),(94,115),(94,132),(94,133),(94,136),(95,152),(96,152),(97,152),(98,116),(98,137),(98,151),(99,117),(99,138),(99,151),(100,118),(100,137),(100,149),(101,118),(101,138),(101,150),(102,116),(102,139),(102,150),(103,117),(103,139),(103,149),(104,119),(104,142),(104,149),(105,120),(105,142),(105,150),(106,119),(106,140),(106,151),(107,120),(107,141),(107,151),(108,121),(108,141),(108,149),(109,121),(109,140),(109,150),(110,122),(110,143),(110,149),(111,123),(111,143),(111,150),(112,122),(112,144),(112,151),(113,123),(113,145),(113,151),(114,124),(114,145),(114,149),(115,124),(115,144),(115,150),(116,152),(117,152),(118,152),(119,152),(120,152),(121,152),(122,152),(123,152),(124,152),(125,138),(125,146),(125,149),(126,137),(126,146),(126,150),(127,139),(127,146),(127,151),(128,142),(128,147),(128,151),(129,140),(129,147),(129,149),(130,141),(130,147),(130,150),(131,143),(131,148),(131,151),(132,144),(132,148),(132,149),(133,145),(133,148),(133,150),(134,149),(134,151),(135,150),(135,151),(136,149),(136,150),(137,152),(138,152),(139,152),(140,152),(141,152),(142,152),(143,152),(144,152),(145,152),(146,152),(147,152),(148,152),(149,152),(150,152),(151,152)],153)
=> ? = 1 + 1
[1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 4 + 1
[1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 4 + 1
[1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,3,1,4,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,4,1,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[3,2,1,4,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[3,4,1,2,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[4,2,1,3,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[4,3,1,2,5,6] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[1,3,2,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,2,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,2,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,6,2,3,4,5,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,3,1,4,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,4,1,3,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,5,1,3,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[3,2,1,4,5,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[3,4,1,2,5,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[3,5,1,2,4,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[4,2,1,3,5,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[4,3,1,2,5,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[4,5,1,2,3,6,7] => [2,5] => ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,2,1,3,4,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[5,3,1,2,4,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
[5,4,1,2,3,6,7] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
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