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Your data matches 77 different statistics following compositions of up to 3 maps.
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Matching statistic: St000755
Mapping
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000755: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => [1,1,1]
 => [1,1]
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => [1,1,1]
 => [1,1]
 => 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [2,2,2]
 => [2,2]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6,1]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [9]
 => [1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1]
 => 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [10]
 => [1,1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1,1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => [1,1,1]
 => [1,1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [4,1,1]
 => [1,1]
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [4,1,1]
 => [1,1]
 => 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,1]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7,1]
 => [2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1]
 => 1
Description
The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. Consider the recurrence f(n)=∑p∈λf(n−p). This statistic returns the number of distinct real roots of the associated characteristic polynomial. For example, the partition (2,1) corresponds to the recurrence f(n)=f(n−1)+f(n−2) with associated characteristic polynomial x2−x−1, which has two real roots.
Matching statistic: St001092
Mapping
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001092: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [2,2,2]
 => [2,2]
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6,1]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [9]
 => [1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [10]
 => [1,1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [4,1,1]
 => [1,1]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [3,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [4,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [3,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,1]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7,1]
 => [2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1]
 => 0 = 1 - 1
Description
The number of distinct even parts of a partition. See Section 3.3.1 of [1].
Matching statistic: St001587
Mapping
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001587: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [2,2,2]
 => [2,2]
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6,1]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [9]
 => [1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [10]
 => [1,1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [4,1,1]
 => [1,1]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [3,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [4,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [3,1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,1]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7,1]
 => [2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1]
 => 0 = 1 - 1
Description
Half of the largest even part of an integer partition. The largest even part is recorded by [[St000995]].
Matching statistic: St000661
(load all 2 compositions to match this statistic)
Mapping
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000661: Dyck paths ⟶ ℤResult quality: 35% ●values known / values provided: 35%●distinct values known / distinct values provided: 100%
Values
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,0,1,0,1,0]
 => 0 = 1 - 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => [1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => [1,0,1,0,1,0]
 => 0 = 1 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => [1,0,1,0,1,0]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 0 = 1 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 - 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 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)
 => [11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 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)
 => [12]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [12]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 - 1
([(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)
 => [12]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 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)
 => [13]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 1
Description
The number of rises of length 3 of a Dyck path.
Matching statistic: St001712
(load all 2 compositions to match this statistic)
Mapping
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St001712: Standard tableaux ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 100%
Values
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [[1,2,3]]
 => [[1],[2],[3]]
 => 0 = 1 - 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => [[1,2,3]]
 => [[1],[2],[3]]
 => 0 = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => [[1,2,3,4,5]]
 => [[1],[2],[3],[4],[5]]
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => [[1,2,3,4,5,6]]
 => [[1],[2],[3],[4],[5],[6]]
 => 0 = 1 - 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => [[1,2,3]]
 => [[1],[2],[3]]
 => 0 = 1 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => [[1,2],[3],[4],[5]]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [[1,2,3,4,5]]
 => [[1],[2],[3],[4],[5]]
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => [[1,2],[3],[4],[5],[6]]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => [[1,2,3,4,5,6]]
 => [[1],[2],[3],[4],[5],[6]]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [[1,2,3,4,5,6,7]]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 0 = 1 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => [[1,4],[2,5],[3,6]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [[1,2,3,4,5]]
 => [[1],[2],[3],[4],[5]]
 => 0 = 1 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => [[1,2,3,4,5,6]]
 => [[1],[2],[3],[4],[5],[6]]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [[1,2,3,4,5,6,7]]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => [[1,2],[3],[4],[5],[6]]
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => [[1,2,3,4,5,6]]
 => [[1],[2],[3],[4],[5],[6]]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6,1]
 => [[1,3,4,5,6,7],[2]]
 => [[1,2],[3],[4],[5],[6],[7]]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => [[1,2,3,4,5,6,7,8]]
 => [[1],[2],[3],[4],[5],[6],[7],[8]]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => [[1,2,3,4,5,6,7]]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [8]
 => [[1,2,3,4,5,6,7,8]]
 => [[1],[2],[3],[4],[5],[6],[7],[8]]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => [[1,2,3]]
 => [[1],[2],[3]]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [[1,5,6],[2],[3],[4]]
 => [[1,2,3,4],[5],[6]]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4]
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1]
 => [[1,3,4,5],[2]]
 => [[1,2],[3],[4],[5]]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => [[1,2,3,4,5]]
 => [[1],[2],[3],[4],[5]]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [[1,4,5,6],[2],[3]]
 => [[1,2,3],[4],[5],[6]]
 => 0 = 1 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => [[1,2],[3],[4],[5],[6]]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [[1,5,6],[2],[3],[4]]
 => [[1,2,3,4],[5],[6]]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [[1,4,5,6,7],[2],[3]]
 => [[1,2,3],[4],[5],[6],[7]]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [[1,2,3,4,5,6]]
 => [[1],[2],[3],[4],[5],[6]]
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [[1,4,5,6],[2],[3]]
 => [[1,2,3],[4],[5],[6]]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,1]
 => [[1,3,4,5,6,7],[2]]
 => [[1,2],[3],[4],[5],[6],[7]]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7]
 => [[1,2,3,4,5,6,7]]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [[1,4,5,6,7],[2],[3]]
 => [[1,2,3],[4],[5],[6],[7]]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7,1]
 => [[1,3,4,5,6,7,8],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8]]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [8]
 => [[1,2,3,4,5,6,7,8]]
 => [[1],[2],[3],[4],[5],[6],[7],[8]]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 0 = 1 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [8,1]
 => [[1,3,4,5,6,7,8,9],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [8,1]
 => [[1,3,4,5,6,7,8,9],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [8,1]
 => [[1,3,4,5,6,7,8,9],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [8,1]
 => [[1,3,4,5,6,7,8,9],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9,1]
 => [[1,3,4,5,6,7,8,9,10],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 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)
 => [11]
 => [[1,2,3,4,5,6,7,8,9,10,11]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [11]
 => [[1,2,3,4,5,6,7,8,9,10,11]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
 => ? = 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)
 => [12]
 => [[1,2,3,4,5,6,7,8,9,10,11,12]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
 => ? = 1 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,3]
 => [[1,2,3,7,8,9],[4,5,6]]
 => [[1,4],[2,5],[3,6],[7],[8],[9]]
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [8,1]
 => [[1,3,4,5,6,7,8,9],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [11]
 => [[1,2,3,4,5,6,7,8,9,10,11]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
 => ? = 1 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [11]
 => [[1,2,3,4,5,6,7,8,9,10,11]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [12]
 => [[1,2,3,4,5,6,7,8,9,10,11,12]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
 => ? = 1 - 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [11]
 => [[1,2,3,4,5,6,7,8,9,10,11]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
 => ? = 1 - 1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9,1]
 => [[1,3,4,5,6,7,8,9,10],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10]
 => [[1,2,3,4,5,6,7,8,9,10]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
 => ? = 1 - 1
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [10,1]
 => [[1,3,4,5,6,7,8,9,10,11],[2]]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
 => ? = 1 - 1
([(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)
 => [12]
 => [[1,2,3,4,5,6,7,8,9,10,11,12]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
 => ? = 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)
 => [13]
 => [[1,2,3,4,5,6,7,8,9,10,11,12,13]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13]]
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [11]
 => [[1,2,3,4,5,6,7,8,9,10,11]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [11]
 => [[1,2,3,4,5,6,7,8,9,10,11]]
 => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
 => ? = 1 - 1
Description
The number of natural descents of a standard Young tableau. A natural descent of a standard tableau T is an entry i such that i+1 appears in a higher row than i in English notation.
Matching statistic: St001568
(load all 2 compositions to match this statistic)
Mapping
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 100%
Values
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => []
 => ? = 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => []
 => ? = 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => []
 => ? = 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => []
 => ? = 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => []
 => ? = 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? = 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [1]
 => [1]
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => []
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => []
 => ? = 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [1]
 => [1]
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6,1]
 => [1]
 => [1]
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => []
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => []
 => ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [8]
 => []
 => []
 => ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [9]
 => []
 => []
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [10]
 => []
 => []
 => ? = 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => []
 => ? = 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4]
 => []
 => []
 => ? = 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? = 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => []
 => ? = 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? = 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => []
 => ? = 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,1]
 => [1]
 => [1]
 => ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [7,1]
 => [1]
 => [1]
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [8]
 => []
 => []
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [9]
 => []
 => []
 => ? = 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,3,1]
 => [3,1]
 => [2,1,1]
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5]
 => []
 => []
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? = 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? = 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => [1]
 => ? = 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [7,1]
 => [1]
 => [1]
 => ? = 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,3]
 => [3]
 => [1,1,1]
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,1]
 => [3,1]
 => [2,1,1]
 => 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,3]
 => [3]
 => [1,1,1]
 => 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => [1]
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1,1]
 => [1,1]
 => [2]
 => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1,1]
 => [1,1]
 => [2]
 => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => [5,1,1]
 => [1,1]
 => [2]
 => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [3,3,1]
 => [3,1]
 => [2,1,1]
 => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,3]
 => [3]
 => [1,1,1]
 => 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1,1]
 => [1,1]
 => [2]
 => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,3]
 => [3]
 => [1,1,1]
 => 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [4,1,1]
 => [1,1]
 => [2]
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1,1]
 => [1,1,1]
 => [3]
 => 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1,1]
 => [1,1]
 => [2]
 => 1
Description
The smallest positive integer that does not appear twice in the partition.
Matching statistic: St001719
(load all 10 compositions to match this statistic)
Mapping
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001719: Lattices ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 50%
Values
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(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
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(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
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(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
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,15),(1,20),(1,21),(2,9),(2,10),(2,14),(2,18),(2,19),(3,8),(3,13),(3,17),(3,19),(3,21),(4,8),(4,12),(4,16),(4,18),(4,20),(5,7),(5,14),(5,15),(5,16),(5,17),(6,7),(6,10),(6,11),(6,12),(6,13),(7,31),(7,32),(8,30),(8,32),(9,30),(9,31),(10,22),(10,23),(10,31),(11,24),(11,25),(11,31),(12,22),(12,24),(12,32),(13,23),(13,25),(13,32),(14,26),(14,27),(14,31),(15,28),(15,29),(15,31),(16,26),(16,28),(16,32),(17,27),(17,29),(17,32),(18,22),(18,26),(18,30),(19,23),(19,27),(19,30),(20,24),(20,28),(20,30),(21,25),(21,29),(21,30),(22,33),(23,33),(24,33),(25,33),(26,33),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,15),(2,7),(2,8),(2,11),(2,14),(3,6),(3,8),(3,10),(3,13),(4,6),(4,7),(4,9),(4,12),(5,12),(5,13),(5,14),(5,15),(6,18),(6,22),(7,16),(7,22),(8,17),(8,22),(9,19),(9,22),(10,20),(10,22),(11,21),(11,22),(12,16),(12,18),(12,19),(13,17),(13,18),(13,20),(14,16),(14,17),(14,21),(15,19),(15,20),(15,21),(16,23),(17,23),(18,23),(19,23),(20,23),(21,23),(22,23)],24)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],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),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(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),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
 => ? = 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,2),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,1),(0,2),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(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
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,12),(1,15),(1,28),(1,31),(1,34),(2,11),(2,14),(2,28),(2,30),(2,33),(3,10),(3,13),(3,28),(3,29),(3,32),(4,10),(4,16),(4,19),(4,21),(4,30),(4,31),(5,11),(5,17),(5,20),(5,22),(5,29),(5,31),(6,12),(6,18),(6,23),(6,24),(6,29),(6,30),(7,13),(7,16),(7,20),(7,23),(7,33),(7,34),(8,14),(8,17),(8,19),(8,24),(8,32),(8,34),(9,15),(9,18),(9,21),(9,22),(9,32),(9,33),(10,25),(10,35),(10,45),(11,26),(11,36),(11,45),(12,27),(12,37),(12,45),(13,25),(13,38),(13,44),(14,26),(14,39),(14,44),(15,27),(15,40),(15,44),(16,25),(16,42),(16,43),(17,26),(17,41),(17,43),(18,27),(18,41),(18,42),(19,35),(19,39),(19,43),(20,36),(20,38),(20,43),(21,35),(21,40),(21,42),(22,36),(22,40),(22,41),(23,37),(23,38),(23,42),(24,37),(24,39),(24,41),(25,46),(26,46),(27,46),(28,44),(28,45),(29,38),(29,41),(29,45),(30,39),(30,42),(30,45),(31,40),(31,43),(31,45),(32,35),(32,41),(32,44),(33,36),(33,42),(33,44),(34,37),(34,43),(34,44),(35,46),(36,46),(37,46),(38,46),(39,46),(40,46),(41,46),(42,46),(43,46),(44,46),(45,46)],47)
 => ? = 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(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),(1,14),(1,18),(1,22),(1,28),(1,30),(1,36),(1,37),(1,66),(2,13),(2,17),(2,21),(2,27),(2,29),(2,34),(2,35),(2,66),(3,12),(3,20),(3,24),(3,26),(3,32),(3,35),(3,37),(3,67),(4,11),(4,19),(4,23),(4,25),(4,31),(4,34),(4,36),(4,67),(5,16),(5,19),(5,20),(5,27),(5,28),(5,39),(5,40),(6,15),(6,17),(6,18),(6,25),(6,26),(6,38),(6,40),(7,29),(7,30),(7,31),(7,32),(7,33),(7,40),(7,41),(8,21),(8,22),(8,23),(8,24),(8,33),(8,38),(8,39),(9,11),(9,12),(9,15),(9,39),(9,41),(9,66),(10,13),(10,14),(10,16),(10,38),(10,41),(10,67),(11,42),(11,74),(11,80),(11,94),(12,43),(12,75),(12,81),(12,94),(13,44),(13,76),(13,78),(13,95),(14,45),(14,77),(14,79),(14,95),(15,42),(15,43),(15,72),(15,98),(16,44),(16,45),(16,73),(16,98),(17,46),(17,47),(17,72),(17,78),(17,82),(18,48),(18,49),(18,72),(18,79),(18,83),(19,50),(19,52),(19,73),(19,80),(19,84),(20,51),(20,53),(20,73),(20,81),(20,85),(21,54),(21,55),(21,64),(21,78),(21,97),(22,56),(22,57),(22,65),(22,79),(22,97),(23,54),(23,56),(23,62),(23,80),(23,96),(24,55),(24,57),(24,63),(24,81),(24,96),(25,42),(25,46),(25,48),(25,84),(25,96),(26,43),(26,47),(26,49),(26,85),(26,96),(27,44),(27,50),(27,51),(27,82),(27,97),(28,45),(28,52),(28,53),(28,83),(28,97),(29,58),(29,59),(29,64),(29,82),(29,95),(30,60),(30,61),(30,65),(30,83),(30,95),(31,58),(31,60),(31,62),(31,84),(31,94),(32,59),(32,61),(32,63),(32,85),(32,94),(33,62),(33,63),(33,64),(33,65),(33,98),(34,46),(34,50),(34,54),(34,58),(34,74),(34,76),(35,47),(35,51),(35,55),(35,59),(35,75),(35,76),(36,48),(36,52),(36,56),(36,60),(36,74),(36,77),(37,49),(37,53),(37,57),(37,61),(37,75),(37,77),(38,78),(38,79),(38,96),(38,98),(39,80),(39,81),(39,97),(39,98),(40,82),(40,83),(40,84),(40,85),(40,98),(41,94),(41,95),(41,98),(42,90),(42,104),(43,91),(43,104),(44,92),(44,105),(45,93),(45,105),(46,86),(46,90),(46,99),(47,87),(47,91),(47,99),(48,88),(48,90),(48,100),(49,89),(49,91),(49,100),(50,86),(50,92),(50,101),(51,87),(51,92),(51,102),(52,88),(52,93),(52,101),(53,89),(53,93),(53,102),(54,68),(54,99),(54,101),(55,69),(55,99),(55,102),(56,70),(56,100),(56,101),(57,71),(57,100),(57,102),(58,68),(58,86),(58,103),(59,69),(59,87),(59,103),(60,70),(60,88),(60,103),(61,71),(61,89),(61,103),(62,68),(62,70),(62,104),(63,69),(63,71),(63,104),(64,68),(64,69),(64,105),(65,70),(65,71),(65,105),(66,72),(66,74),(66,75),(66,95),(66,97),(67,73),(67,76),(67,77),(67,94),(67,96),(68,106),(69,106),(70,106),(71,106),(72,90),(72,91),(72,105),(73,92),(73,93),(73,104),(74,90),(74,101),(74,103),(75,91),(75,102),(75,103),(76,92),(76,99),(76,103),(77,93),(77,100),(77,103),(78,99),(78,105),(79,100),(79,105),(80,101),(80,104),(81,102),(81,104),(82,86),(82,87),(82,105),(83,88),(83,89),(83,105),(84,86),(84,88),(84,104),(85,87),(85,89),(85,104),(86,106),(87,106),(88,106),(89,106),(90,106),(91,106),(92,106),(93,106),(94,103),(94,104),(95,103),(95,105),(96,99),(96,100),(96,104),(97,101),(97,102),(97,105),(98,104),(98,105),(99,106),(100,106),(101,106),(102,106),(103,106),(104,106),(105,106)],107)
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(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
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(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
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(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
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(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),(0,10),(0,11),(1,15),(1,21),(1,29),(1,30),(1,35),(1,36),(1,44),(1,45),(1,93),(2,14),(2,20),(2,26),(2,28),(2,32),(2,34),(2,43),(2,45),(2,92),(3,13),(3,19),(3,25),(3,27),(3,31),(3,33),(3,43),(3,44),(3,91),(4,16),(4,19),(4,28),(4,29),(4,37),(4,39),(4,46),(4,48),(4,90),(5,17),(5,20),(5,27),(5,30),(5,38),(5,40),(5,47),(5,48),(5,89),(6,18),(6,21),(6,25),(6,26),(6,41),(6,42),(6,46),(6,47),(6,88),(7,22),(7,23),(7,33),(7,34),(7,37),(7,38),(7,88),(7,93),(8,22),(8,24),(8,31),(8,35),(8,39),(8,41),(8,89),(8,92),(9,23),(9,24),(9,32),(9,36),(9,40),(9,42),(9,90),(9,91),(10,12),(10,16),(10,17),(10,18),(10,91),(10,92),(10,93),(11,12),(11,13),(11,14),(11,15),(11,88),(11,89),(11,90),(12,120),(12,121),(12,122),(13,52),(13,53),(13,99),(13,101),(13,120),(14,52),(14,54),(14,100),(14,102),(14,121),(15,53),(15,54),(15,103),(15,104),(15,122),(16,55),(16,57),(16,108),(16,109),(16,120),(17,56),(17,57),(17,107),(17,110),(17,121),(18,55),(18,56),(18,105),(18,106),(18,122),(19,64),(19,66),(19,117),(19,118),(19,120),(20,65),(20,67),(20,117),(20,119),(20,121),(21,68),(21,69),(21,118),(21,119),(21,122),(22,51),(22,70),(22,73),(22,124),(22,128),(23,51),(23,71),(23,74),(23,123),(23,127),(24,51),(24,72),(24,75),(24,125),(24,126),(25,58),(25,61),(25,76),(25,101),(25,105),(25,118),(26,58),(26,62),(26,77),(26,102),(26,106),(26,119),(27,59),(27,61),(27,78),(27,99),(27,107),(27,117),(28,60),(28,62),(28,79),(28,100),(28,108),(28,117),(29,60),(29,63),(29,80),(29,104),(29,109),(29,118),(30,59),(30,63),(30,81),(30,103),(30,110),(30,119),(31,66),(31,70),(31,76),(31,83),(31,99),(31,126),(32,67),(32,71),(32,77),(32,84),(32,100),(32,126),(33,64),(33,70),(33,78),(33,82),(33,101),(33,127),(34,65),(34,71),(34,79),(34,82),(34,102),(34,128),(35,69),(35,72),(35,80),(35,83),(35,103),(35,128),(36,68),(36,72),(36,81),(36,84),(36,104),(36,127),(37,64),(37,73),(37,79),(37,87),(37,109),(37,123),(38,65),(38,74),(38,78),(38,87),(38,110),(38,124),(39,66),(39,73),(39,80),(39,85),(39,108),(39,125),(40,67),(40,74),(40,81),(40,86),(40,107),(40,125),(41,69),(41,75),(41,76),(41,85),(41,106),(41,124),(42,68),(42,75),(42,77),(42,86),(42,105),(42,123),(43,49),(43,52),(43,58),(43,82),(43,117),(43,126),(44,49),(44,53),(44,59),(44,83),(44,118),(44,127),(45,49),(45,54),(45,60),(45,84),(45,119),(45,128),(46,50),(46,55),(46,62),(46,85),(46,118),(46,123),(47,50),(47,56),(47,61),(47,86),(47,119),(47,124),(48,50),(48,57),(48,63),(48,87),(48,117),(48,125),(49,97),(49,139),(49,140),(50,98),(50,138),(50,140),(51,138),(51,139),(52,97),(52,113),(52,143),(53,97),(53,111),(53,141),(54,97),(54,112),(54,142),(55,98),(55,115),(55,141),(56,98),(56,114),(56,142),(57,98),(57,116),(57,143),(58,113),(58,137),(58,140),(59,111),(59,135),(59,140),(60,112),(60,136),(60,140),(61,114),(61,132),(61,140),(62,115),(62,133),(62,140),(63,116),(63,134),(63,140),(64,94),(64,129),(64,141),(65,95),(65,129),(65,142),(66,94),(66,130),(66,143),(67,95),(67,131),(67,143),(68,96),(68,131),(68,141),(69,96),(69,130),(69,142),(70,94),(70,132),(70,139),(71,95),(71,133),(71,139),(72,96),(72,134),(72,139),(73,94),(73,136),(73,138),(74,95),(74,135),(74,138),(75,96),(75,137),(75,138),(76,130),(76,132),(76,137),(77,131),(77,133),(77,137),(78,129),(78,132),(78,135),(79,129),(79,133),(79,136),(80,130),(80,134),(80,136),(81,131),(81,134),(81,135),(82,113),(82,129),(82,139),(83,111),(83,130),(83,139),(84,112),(84,131),(84,139),(85,115),(85,130),(85,138),(86,114),(86,131),(86,138),(87,116),(87,129),(87,138),(88,101),(88,102),(88,122),(88,123),(88,124),(89,99),(89,103),(89,121),(89,124),(89,125),(90,100),(90,104),(90,120),(90,123),(90,125),(91,105),(91,107),(91,120),(91,126),(91,127),(92,106),(92,108),(92,121),(92,126),(92,128),(93,109),(93,110),(93,122),(93,127),(93,128),(94,144),(95,144),(96,144),(97,144),(98,144),(99,111),(99,132),(99,143),(100,112),(100,133),(100,143),(101,113),(101,132),(101,141),(102,113),(102,133),(102,142),(103,111),(103,134),(103,142),(104,112),(104,134),(104,141),(105,114),(105,137),(105,141),(106,115),(106,137),(106,142),(107,114),(107,135),(107,143),(108,115),(108,136),(108,143),(109,116),(109,136),(109,141),(110,116),(110,135),(110,142),(111,144),(112,144),(113,144),(114,144),(115,144),(116,144),(117,129),(117,140),(117,143),(118,130),(118,140),(118,141),(119,131),(119,140),(119,142),(120,141),(120,143),(121,142),(121,143),(122,141),(122,142),(123,133),(123,138),(123,141),(124,132),(124,138),(124,142),(125,134),(125,138),(125,143),(126,137),(126,139),(126,143),(127,135),(127,139),(127,141),(128,136),(128,139),(128,142),(129,144),(130,144),(131,144),(132,144),(133,144),(134,144),(135,144),(136,144),(137,144),(138,144),(139,144),(140,144),(141,144),(142,144),(143,144)],145)
 => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(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),(0,10),(1,13),(1,18),(1,28),(1,30),(1,32),(1,35),(1,36),(1,72),(2,12),(2,17),(2,27),(2,29),(2,32),(2,33),(2,34),(2,71),(3,17),(3,20),(3,21),(3,30),(3,31),(3,37),(3,38),(3,73),(4,18),(4,19),(4,22),(4,29),(4,31),(4,39),(4,40),(4,74),(5,16),(5,24),(5,26),(5,34),(5,36),(5,38),(5,40),(5,75),(6,15),(6,23),(6,25),(6,33),(6,35),(6,37),(6,39),(6,75),(7,11),(7,15),(7,16),(7,19),(7,20),(7,71),(7,72),(8,14),(8,22),(8,23),(8,24),(8,27),(8,72),(8,73),(9,14),(9,21),(9,25),(9,26),(9,28),(9,71),(9,74),(10,11),(10,12),(10,13),(10,73),(10,74),(10,75),(11,84),(11,99),(11,100),(12,41),(12,82),(12,85),(12,99),(13,41),(13,83),(13,86),(13,100),(14,58),(14,59),(14,101),(14,102),(15,54),(15,56),(15,84),(15,87),(15,89),(16,55),(16,57),(16,84),(16,88),(16,90),(17,44),(17,45),(17,85),(17,91),(17,98),(18,46),(18,47),(18,86),(18,92),(18,98),(19,54),(19,55),(19,68),(19,92),(19,99),(20,56),(20,57),(20,68),(20,91),(20,100),(21,64),(21,65),(21,70),(21,91),(21,102),(22,66),(22,67),(22,69),(22,92),(22,102),(23,58),(23,60),(23,66),(23,89),(23,103),(24,59),(24,61),(24,67),(24,90),(24,103),(25,58),(25,62),(25,64),(25,87),(25,104),(26,59),(26,63),(26,65),(26,88),(26,104),(27,60),(27,61),(27,69),(27,85),(27,101),(28,62),(28,63),(28,70),(28,86),(28,101),(29,50),(29,51),(29,69),(29,98),(29,99),(30,52),(30,53),(30,70),(30,98),(30,100),(31,48),(31,49),(31,68),(31,98),(31,102),(32,41),(32,42),(32,43),(32,98),(32,101),(33,42),(33,44),(33,50),(33,60),(33,82),(33,87),(34,43),(34,45),(34,51),(34,61),(34,82),(34,88),(35,42),(35,46),(35,52),(35,62),(35,83),(35,89),(36,43),(36,47),(36,53),(36,63),(36,83),(36,90),(37,44),(37,48),(37,52),(37,56),(37,64),(37,103),(38,45),(38,49),(38,53),(38,57),(38,65),(38,103),(39,46),(39,48),(39,50),(39,54),(39,66),(39,104),(40,47),(40,49),(40,51),(40,55),(40,67),(40,104),(41,97),(41,114),(42,97),(42,105),(42,107),(43,97),(43,106),(43,108),(44,93),(44,105),(44,109),(45,94),(45,106),(45,109),(46,95),(46,105),(46,110),(47,96),(47,106),(47,110),(48,80),(48,105),(48,113),(49,81),(49,106),(49,113),(50,76),(50,105),(50,111),(51,77),(51,106),(51,111),(52,78),(52,105),(52,112),(53,79),(53,106),(53,112),(54,80),(54,95),(54,111),(55,81),(55,96),(55,111),(56,80),(56,93),(56,112),(57,81),(57,94),(57,112),(58,107),(58,113),(59,108),(59,113),(60,76),(60,107),(60,109),(61,77),(61,108),(61,109),(62,78),(62,107),(62,110),(63,79),(63,108),(63,110),(64,78),(64,93),(64,113),(65,79),(65,94),(65,113),(66,76),(66,95),(66,113),(67,77),(67,96),(67,113),(68,80),(68,81),(68,114),(69,76),(69,77),(69,114),(70,78),(70,79),(70,114),(71,87),(71,88),(71,91),(71,99),(71,101),(72,89),(72,90),(72,92),(72,100),(72,101),(73,85),(73,100),(73,102),(73,103),(74,86),(74,99),(74,102),(74,104),(75,82),(75,83),(75,84),(75,103),(75,104),(76,115),(77,115),(78,115),(79,115),(80,115),(81,115),(82,97),(82,109),(82,111),(83,97),(83,110),(83,112),(84,111),(84,112),(85,109),(85,114),(86,110),(86,114),(87,93),(87,107),(87,111),(88,94),(88,108),(88,111),(89,95),(89,107),(89,112),(90,96),(90,108),(90,112),(91,93),(91,94),(91,114),(92,95),(92,96),(92,114),(93,115),(94,115),(95,115),(96,115),(97,115),(98,105),(98,106),(98,114),(99,111),(99,114),(100,112),(100,114),(101,107),(101,108),(101,114),(102,113),(102,114),(103,109),(103,112),(103,113),(104,110),(104,111),(104,113),(105,115),(106,115),(107,115),(108,115),(109,115),(110,115),(111,115),(112,115),(113,115),(114,115)],116)
 => ? = 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,16),(1,17),(1,18),(1,34),(1,35),(1,40),(1,41),(1,42),(1,43),(2,14),(2,15),(2,18),(2,32),(2,33),(2,36),(2,37),(2,38),(2,39),(3,12),(3,21),(3,23),(3,27),(3,31),(3,37),(3,41),(3,79),(4,12),(4,20),(4,22),(4,26),(4,30),(4,36),(4,40),(4,78),(5,13),(5,20),(5,24),(5,28),(5,31),(5,38),(5,42),(5,76),(6,13),(6,21),(6,25),(6,29),(6,30),(6,39),(6,43),(6,77),(7,19),(7,28),(7,29),(7,33),(7,35),(7,78),(7,79),(8,19),(8,26),(8,27),(8,32),(8,34),(8,76),(8,77),(9,11),(9,14),(9,16),(9,22),(9,25),(9,76),(9,79),(10,11),(10,15),(10,17),(10,23),(10,24),(10,77),(10,78),(11,105),(11,106),(11,107),(12,44),(12,106),(12,108),(12,111),(13,45),(13,105),(13,108),(13,112),(14,60),(14,63),(14,89),(14,92),(14,107),(15,61),(15,62),(15,90),(15,91),(15,107),(16,64),(16,67),(16,93),(16,96),(16,107),(17,65),(17,66),(17,94),(17,95),(17,107),(18,46),(18,47),(18,107),(18,111),(18,112),(19,48),(19,49),(19,109),(19,110),(20,68),(20,70),(20,85),(20,87),(20,108),(21,69),(21,71),(21,86),(21,88),(21,108),(22,50),(22,60),(22,64),(22,85),(22,106),(23,51),(23,61),(23,65),(23,86),(23,106),(24,51),(24,62),(24,66),(24,87),(24,105),(25,50),(25,63),(25,67),(25,88),(25,105),(26,44),(26,52),(26,56),(26,85),(26,109),(27,44),(27,53),(27,57),(27,86),(27,110),(28,45),(28,54),(28,58),(28,87),(28,110),(29,45),(29,55),(29,59),(29,88),(29,109),(30,50),(30,72),(30,74),(30,108),(30,109),(31,51),(31,73),(31,75),(31,108),(31,110),(32,46),(32,48),(32,52),(32,53),(32,89),(32,90),(33,47),(33,48),(33,54),(33,55),(33,91),(33,92),(34,46),(34,49),(34,56),(34,57),(34,93),(34,94),(35,47),(35,49),(35,58),(35,59),(35,95),(35,96),(36,52),(36,60),(36,68),(36,72),(36,91),(36,111),(37,53),(37,61),(37,69),(37,73),(37,92),(37,111),(38,54),(38,62),(38,68),(38,73),(38,89),(38,112),(39,55),(39,63),(39,69),(39,72),(39,90),(39,112),(40,56),(40,64),(40,70),(40,74),(40,95),(40,111),(41,57),(41,65),(41,71),(41,75),(41,96),(41,111),(42,58),(42,66),(42,70),(42,75),(42,93),(42,112),(43,59),(43,67),(43,71),(43,74),(43,94),(43,112),(44,113),(44,122),(45,114),(45,122),(46,84),(46,113),(46,120),(47,84),(47,114),(47,121),(48,84),(48,115),(48,116),(49,84),(49,117),(49,118),(50,80),(50,82),(50,122),(51,81),(51,83),(51,122),(52,97),(52,113),(52,115),(53,98),(53,113),(53,116),(54,99),(54,114),(54,116),(55,100),(55,114),(55,115),(56,101),(56,113),(56,117),(57,102),(57,113),(57,118),(58,103),(58,114),(58,118),(59,104),(59,114),(59,117),(60,80),(60,97),(60,121),(61,81),(61,98),(61,121),(62,81),(62,99),(62,120),(63,80),(63,100),(63,120),(64,82),(64,101),(64,121),(65,83),(65,102),(65,121),(66,83),(66,103),(66,120),(67,82),(67,104),(67,120),(68,97),(68,99),(68,119),(69,98),(69,100),(69,119),(70,101),(70,103),(70,119),(71,102),(71,104),(71,119),(72,80),(72,115),(72,119),(73,81),(73,116),(73,119),(74,82),(74,117),(74,119),(75,83),(75,118),(75,119),(76,85),(76,89),(76,93),(76,105),(76,110),(77,86),(77,90),(77,94),(77,105),(77,109),(78,87),(78,91),(78,95),(78,106),(78,109),(79,88),(79,92),(79,96),(79,106),(79,110),(80,123),(81,123),(82,123),(83,123),(84,123),(85,97),(85,101),(85,122),(86,98),(86,102),(86,122),(87,99),(87,103),(87,122),(88,100),(88,104),(88,122),(89,97),(89,116),(89,120),(90,98),(90,115),(90,120),(91,99),(91,115),(91,121),(92,100),(92,116),(92,121),(93,101),(93,118),(93,120),(94,102),(94,117),(94,120),(95,103),(95,117),(95,121),(96,104),(96,118),(96,121),(97,123),(98,123),(99,123),(100,123),(101,123),(102,123),(103,123),(104,123),(105,120),(105,122),(106,121),(106,122),(107,120),(107,121),(108,119),(108,122),(109,115),(109,117),(109,122),(110,116),(110,118),(110,122),(111,113),(111,119),(111,121),(112,114),(112,119),(112,120),(113,123),(114,123),(115,123),(116,123),(117,123),(118,123),(119,123),(120,123),(121,123),(122,123)],124)
 => ? = 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(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),(1,21),(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
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(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)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(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),(1,16),(1,20),(1,24),(1,30),(1,32),(2,15),(2,19),(2,23),(2,30),(2,31),(3,17),(3,21),(3,23),(3,29),(3,32),(4,18),(4,22),(4,24),(4,29),(4,31),(5,10),(5,13),(5,14),(5,17),(5,18),(5,30),(6,10),(6,11),(6,12),(6,15),(6,16),(6,29),(7,9),(7,11),(7,13),(7,19),(7,22),(7,32),(8,9),(8,12),(8,14),(8,20),(8,21),(8,31),(9,35),(9,36),(9,41),(10,33),(10,34),(10,41),(11,25),(11,38),(11,41),(12,26),(12,37),(12,41),(13,28),(13,39),(13,41),(14,27),(14,40),(14,41),(15,25),(15,33),(15,37),(16,26),(16,33),(16,38),(17,27),(17,34),(17,39),(18,28),(18,34),(18,40),(19,25),(19,35),(19,39),(20,26),(20,36),(20,40),(21,27),(21,36),(21,37),(22,28),(22,35),(22,38),(23,37),(23,39),(24,38),(24,40),(25,42),(26,42),(27,42),(28,42),(29,34),(29,37),(29,38),(30,33),(30,39),(30,40),(31,35),(31,37),(31,40),(32,36),(32,38),(32,39),(33,42),(34,42),(35,42),(36,42),(37,42),(38,42),(39,42),(40,42),(41,42)],43)
 => ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(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),(0,8),(0,9),(0,10),(1,20),(1,29),(1,30),(1,34),(1,35),(1,39),(1,40),(1,75),(2,19),(2,24),(2,28),(2,31),(2,33),(2,37),(2,40),(2,72),(3,18),(3,23),(3,27),(3,31),(3,32),(3,36),(3,39),(3,71),(4,17),(4,21),(4,26),(4,32),(4,34),(4,37),(4,38),(4,73),(5,16),(5,22),(5,25),(5,33),(5,35),(5,36),(5,38),(5,74),(6,12),(6,14),(6,16),(6,21),(6,23),(6,72),(6,75),(7,11),(7,15),(7,17),(7,22),(7,24),(7,71),(7,75),(8,11),(8,13),(8,18),(8,25),(8,29),(8,72),(8,73),(9,12),(9,13),(9,19),(9,26),(9,30),(9,71),(9,74),(10,14),(10,15),(10,20),(10,27),(10,28),(10,73),(10,74),(11,61),(11,81),(11,83),(11,105),(12,62),(12,82),(12,84),(12,104),(13,65),(13,81),(13,82),(13,101),(14,63),(14,84),(14,85),(14,103),(15,64),(15,83),(15,85),(15,102),(16,52),(16,55),(16,84),(16,87),(16,92),(17,51),(17,56),(17,83),(17,86),(17,93),(18,53),(18,57),(18,81),(18,88),(18,90),(19,54),(19,58),(19,82),(19,89),(19,91),(20,59),(20,60),(20,85),(20,94),(20,95),(21,52),(21,62),(21,66),(21,93),(21,103),(22,51),(22,61),(22,67),(22,92),(22,102),(23,55),(23,63),(23,66),(23,88),(23,104),(24,56),(24,64),(24,67),(24,89),(24,105),(25,53),(25,61),(25,69),(25,87),(25,101),(26,54),(26,62),(26,70),(26,86),(26,101),(27,59),(27,63),(27,68),(27,90),(27,102),(28,60),(28,64),(28,68),(28,91),(28,103),(29,57),(29,65),(29,69),(29,94),(29,105),(30,58),(30,65),(30,70),(30,95),(30,104),(31,41),(31,42),(31,48),(31,68),(31,88),(31,89),(32,41),(32,43),(32,46),(32,66),(32,86),(32,90),(33,42),(33,44),(33,47),(33,67),(33,87),(33,91),(34,43),(34,45),(34,50),(34,70),(34,93),(34,94),(35,44),(35,45),(35,49),(35,69),(35,92),(35,95),(36,42),(36,46),(36,49),(36,53),(36,55),(36,102),(37,41),(37,47),(37,50),(37,54),(37,56),(37,103),(38,45),(38,46),(38,47),(38,51),(38,52),(38,101),(39,43),(39,48),(39,49),(39,57),(39,59),(39,104),(40,44),(40,48),(40,50),(40,58),(40,60),(40,105),(41,97),(41,106),(41,111),(42,96),(42,107),(42,111),(43,99),(43,108),(43,111),(44,100),(44,109),(44,111),(45,98),(45,110),(45,111),(46,76),(46,111),(46,112),(47,77),(47,111),(47,113),(48,80),(48,111),(48,114),(49,78),(49,111),(49,115),(50,79),(50,111),(50,116),(51,77),(51,98),(51,112),(52,76),(52,98),(52,113),(53,78),(53,96),(53,112),(54,79),(54,97),(54,113),(55,76),(55,96),(55,115),(56,77),(56,97),(56,116),(57,78),(57,99),(57,114),(58,79),(58,100),(58,114),(59,80),(59,99),(59,115),(60,80),(60,100),(60,116),(61,109),(61,112),(62,108),(62,113),(63,106),(63,115),(64,107),(64,116),(65,110),(65,114),(66,76),(66,106),(66,108),(67,77),(67,107),(67,109),(68,80),(68,106),(68,107),(69,78),(69,109),(69,110),(70,79),(70,108),(70,110),(71,81),(71,86),(71,89),(71,102),(71,104),(72,82),(72,87),(72,88),(72,103),(72,105),(73,83),(73,90),(73,94),(73,101),(73,103),(74,84),(74,91),(74,95),(74,101),(74,102),(75,85),(75,92),(75,93),(75,104),(75,105),(76,117),(77,117),(78,117),(79,117),(80,117),(81,112),(81,114),(82,113),(82,114),(83,112),(83,116),(84,113),(84,115),(85,115),(85,116),(86,97),(86,108),(86,112),(87,96),(87,109),(87,113),(88,96),(88,106),(88,114),(89,97),(89,107),(89,114),(90,99),(90,106),(90,112),(91,100),(91,107),(91,113),(92,98),(92,109),(92,115),(93,98),(93,108),(93,116),(94,99),(94,110),(94,116),(95,100),(95,110),(95,115),(96,117),(97,117),(98,117),(99,117),(100,117),(101,110),(101,112),(101,113),(102,107),(102,112),(102,115),(103,106),(103,113),(103,116),(104,108),(104,114),(104,115),(105,109),(105,114),(105,116),(106,117),(107,117),(108,117),(109,117),(110,117),(111,117),(112,117),(113,117),(114,117),(115,117),(116,117)],118)
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(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),(1,15),(1,16),(1,17),(1,18),(1,54),(1,55),(2,10),(2,13),(2,14),(2,20),(2,55),(2,57),(3,10),(3,11),(3,12),(3,19),(3,54),(3,56),(4,12),(4,16),(4,23),(4,24),(4,26),(4,30),(4,57),(5,11),(5,15),(5,21),(5,22),(5,25),(5,29),(5,57),(6,14),(6,18),(6,22),(6,24),(6,28),(6,32),(6,56),(7,13),(7,17),(7,21),(7,23),(7,27),(7,31),(7,56),(8,19),(8,27),(8,28),(8,29),(8,30),(8,33),(8,55),(9,20),(9,25),(9,26),(9,31),(9,32),(9,33),(9,54),(10,58),(10,59),(10,78),(11,42),(11,58),(11,60),(11,64),(12,43),(12,58),(12,61),(12,65),(13,44),(13,59),(13,62),(13,66),(14,45),(14,59),(14,63),(14,67),(15,38),(15,39),(15,60),(15,80),(16,40),(16,41),(16,61),(16,80),(17,38),(17,40),(17,62),(17,79),(18,39),(18,41),(18,63),(18,79),(19,42),(19,43),(19,68),(19,78),(20,44),(20,45),(20,69),(20,78),(21,38),(21,46),(21,50),(21,64),(21,66),(22,39),(22,47),(22,51),(22,64),(22,67),(23,40),(23,48),(23,52),(23,65),(23,66),(24,41),(24,49),(24,53),(24,65),(24,67),(25,34),(25,50),(25,51),(25,60),(25,69),(26,35),(26,52),(26,53),(26,61),(26,69),(27,36),(27,46),(27,48),(27,62),(27,68),(28,37),(28,47),(28,49),(28,63),(28,68),(29,34),(29,42),(29,46),(29,47),(29,80),(30,35),(30,43),(30,48),(30,49),(30,80),(31,36),(31,44),(31,50),(31,52),(31,79),(32,37),(32,45),(32,51),(32,53),(32,79),(33,34),(33,35),(33,36),(33,37),(33,78),(34,70),(34,71),(34,86),(35,72),(35,73),(35,86),(36,70),(36,72),(36,87),(37,71),(37,73),(37,87),(38,82),(38,84),(39,82),(39,85),(40,83),(40,84),(41,83),(41,85),(42,74),(42,86),(43,75),(43,86),(44,76),(44,87),(45,77),(45,87),(46,70),(46,74),(46,84),(47,71),(47,74),(47,85),(48,72),(48,75),(48,84),(49,73),(49,75),(49,85),(50,70),(50,76),(50,82),(51,71),(51,77),(51,82),(52,72),(52,76),(52,83),(53,73),(53,77),(53,83),(54,60),(54,61),(54,78),(54,79),(55,62),(55,63),(55,78),(55,80),(56,59),(56,64),(56,65),(56,68),(56,79),(57,58),(57,66),(57,67),(57,69),(57,80),(58,81),(58,86),(59,81),(59,87),(60,82),(60,86),(61,83),(61,86),(62,84),(62,87),(63,85),(63,87),(64,74),(64,81),(64,82),(65,75),(65,81),(65,83),(66,76),(66,81),(66,84),(67,77),(67,81),(67,85),(68,74),(68,75),(68,87),(69,76),(69,77),(69,86),(70,88),(71,88),(72,88),(73,88),(74,88),(75,88),(76,88),(77,88),(78,86),(78,87),(79,82),(79,83),(79,87),(80,84),(80,85),(80,86),(81,88),(82,88),(83,88),(84,88),(85,88),(86,88),(87,88)],89)
 => ? = 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(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),(0,8),(0,9),(1,17),(1,18),(1,21),(1,22),(1,30),(1,32),(1,35),(1,36),(2,15),(2,16),(2,19),(2,20),(2,30),(2,31),(2,33),(2,34),(3,26),(3,27),(3,28),(3,29),(3,31),(3,32),(3,68),(4,12),(4,23),(4,25),(4,29),(4,34),(4,36),(4,70),(5,11),(5,23),(5,24),(5,28),(5,33),(5,35),(5,69),(6,10),(6,14),(6,19),(6,21),(6,24),(6,27),(6,70),(7,10),(7,13),(7,20),(7,22),(7,25),(7,26),(7,69),(8,11),(8,13),(8,15),(8,17),(8,68),(8,70),(9,12),(9,14),(9,16),(9,18),(9,68),(9,69),(10,39),(10,77),(10,78),(10,92),(11,62),(11,64),(11,79),(11,93),(12,63),(12,65),(12,80),(12,94),(13,58),(13,60),(13,78),(13,93),(14,59),(14,61),(14,77),(14,94),(15,58),(15,62),(15,66),(15,82),(15,85),(16,59),(16,63),(16,67),(16,81),(16,85),(17,60),(17,64),(17,66),(17,84),(17,86),(18,61),(18,65),(18,67),(18,83),(18,86),(19,49),(19,52),(19,59),(19,82),(19,92),(20,48),(20,53),(20,58),(20,81),(20,92),(21,51),(21,54),(21,61),(21,84),(21,92),(22,50),(22,55),(22,60),(22,83),(22,92),(23,37),(23,40),(23,41),(23,79),(23,80),(24,52),(24,54),(24,56),(24,77),(24,79),(25,53),(25,55),(25,57),(25,78),(25,80),(26,39),(26,48),(26,50),(26,57),(26,93),(27,39),(27,49),(27,51),(27,56),(27,94),(28,37),(28,44),(28,46),(28,56),(28,93),(29,37),(29,45),(29,47),(29,57),(29,94),(30,38),(30,42),(30,43),(30,66),(30,67),(30,92),(31,38),(31,44),(31,45),(31,48),(31,49),(31,85),(32,38),(32,46),(32,47),(32,50),(32,51),(32,86),(33,40),(33,42),(33,44),(33,52),(33,62),(33,81),(34,40),(34,43),(34,45),(34,53),(34,63),(34,82),(35,41),(35,42),(35,46),(35,54),(35,64),(35,83),(36,41),(36,43),(36,47),(36,55),(36,65),(36,84),(37,100),(37,103),(38,87),(38,95),(38,100),(39,95),(39,103),(40,88),(40,89),(40,100),(41,90),(41,91),(41,100),(42,75),(42,100),(42,101),(43,76),(43,100),(43,102),(44,71),(44,96),(44,100),(45,72),(45,97),(45,100),(46,73),(46,98),(46,100),(47,74),(47,99),(47,100),(48,72),(48,95),(48,96),(49,71),(49,95),(49,97),(50,74),(50,95),(50,98),(51,73),(51,95),(51,99),(52,71),(52,88),(52,101),(53,72),(53,89),(53,102),(54,73),(54,90),(54,101),(55,74),(55,91),(55,102),(56,71),(56,73),(56,103),(57,72),(57,74),(57,103),(58,96),(58,102),(59,97),(59,101),(60,98),(60,102),(61,99),(61,101),(62,75),(62,88),(62,96),(63,76),(63,89),(63,97),(64,75),(64,90),(64,98),(65,76),(65,91),(65,99),(66,75),(66,87),(66,102),(67,76),(67,87),(67,101),(68,85),(68,86),(68,93),(68,94),(69,77),(69,80),(69,81),(69,83),(69,93),(70,78),(70,79),(70,82),(70,84),(70,94),(71,104),(72,104),(73,104),(74,104),(75,104),(76,104),(77,101),(77,103),(78,102),(78,103),(79,88),(79,90),(79,103),(80,89),(80,91),(80,103),(81,89),(81,96),(81,101),(82,88),(82,97),(82,102),(83,91),(83,98),(83,101),(84,90),(84,99),(84,102),(85,87),(85,96),(85,97),(86,87),(86,98),(86,99),(87,104),(88,104),(89,104),(90,104),(91,104),(92,95),(92,101),(92,102),(93,96),(93,98),(93,103),(94,97),(94,99),(94,103),(95,104),(96,104),(97,104),(98,104),(99,104),(100,104),(101,104),(102,104),(103,104)],105)
 => ? = 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(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),(1,18),(1,19),(1,20),(1,21),(1,34),(1,57),(2,12),(2,13),(2,16),(2,17),(2,34),(2,56),(3,10),(3,11),(3,14),(3,15),(3,34),(3,55),(4,15),(4,17),(4,24),(4,25),(4,28),(4,29),(4,57),(5,14),(5,16),(5,22),(5,23),(5,26),(5,27),(5,57),(6,11),(6,19),(6,23),(6,25),(6,32),(6,33),(6,56),(7,10),(7,18),(7,22),(7,24),(7,30),(7,31),(7,56),(8,13),(8,21),(8,27),(8,29),(8,31),(8,33),(8,55),(9,12),(9,20),(9,26),(9,28),(9,30),(9,32),(9,55),(10,35),(10,37),(10,62),(10,83),(11,36),(11,38),(11,63),(11,83),(12,39),(12,41),(12,64),(12,84),(13,40),(13,42),(13,65),(13,84),(14,35),(14,36),(14,58),(14,82),(15,37),(15,38),(15,59),(15,82),(16,39),(16,40),(16,60),(16,82),(17,41),(17,42),(17,61),(17,82),(18,43),(18,44),(18,66),(18,83),(19,45),(19,46),(19,67),(19,83),(20,43),(20,45),(20,68),(20,84),(21,44),(21,46),(21,69),(21,84),(22,35),(22,47),(22,48),(22,60),(22,66),(23,36),(23,49),(23,50),(23,60),(23,67),(24,37),(24,51),(24,52),(24,61),(24,66),(25,38),(25,53),(25,54),(25,61),(25,67),(26,39),(26,47),(26,49),(26,58),(26,68),(27,40),(27,48),(27,50),(27,58),(27,69),(28,41),(28,51),(28,53),(28,59),(28,68),(29,42),(29,52),(29,54),(29,59),(29,69),(30,43),(30,47),(30,51),(30,62),(30,64),(31,44),(31,48),(31,52),(31,62),(31,65),(32,45),(32,49),(32,53),(32,63),(32,64),(33,46),(33,50),(33,54),(33,63),(33,65),(34,82),(34,83),(34,84),(35,70),(35,85),(36,71),(36,85),(37,72),(37,85),(38,73),(38,85),(39,74),(39,86),(40,75),(40,86),(41,76),(41,86),(42,77),(42,86),(43,78),(43,87),(44,79),(44,87),(45,80),(45,87),(46,81),(46,87),(47,70),(47,74),(47,78),(48,70),(48,75),(48,79),(49,71),(49,74),(49,80),(50,71),(50,75),(50,81),(51,72),(51,76),(51,78),(52,72),(52,77),(52,79),(53,73),(53,76),(53,80),(54,73),(54,77),(54,81),(55,58),(55,59),(55,62),(55,63),(55,84),(56,60),(56,61),(56,64),(56,65),(56,83),(57,66),(57,67),(57,68),(57,69),(57,82),(58,70),(58,71),(58,86),(59,72),(59,73),(59,86),(60,74),(60,75),(60,85),(61,76),(61,77),(61,85),(62,70),(62,72),(62,87),(63,71),(63,73),(63,87),(64,74),(64,76),(64,87),(65,75),(65,77),(65,87),(66,78),(66,79),(66,85),(67,80),(67,81),(67,85),(68,78),(68,80),(68,86),(69,79),(69,81),(69,86),(70,88),(71,88),(72,88),(73,88),(74,88),(75,88),(76,88),(77,88),(78,88),(79,88),(80,88),(81,88),(82,85),(82,86),(83,85),(83,87),(84,86),(84,87),(85,88),(86,88),(87,88)],89)
 => ? = 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(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
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,14),(1,18),(1,23),(1,24),(1,26),(1,32),(2,12),(2,13),(2,17),(2,21),(2,22),(2,25),(2,31),(3,11),(3,16),(3,20),(3,22),(3,24),(3,28),(3,34),(4,11),(4,15),(4,19),(4,21),(4,23),(4,27),(4,33),(5,10),(5,17),(5,18),(5,19),(5,20),(5,30),(5,36),(6,10),(6,13),(6,14),(6,15),(6,16),(6,29),(6,35),(7,9),(7,31),(7,32),(7,33),(7,34),(7,35),(7,36),(8,9),(8,25),(8,26),(8,27),(8,28),(8,29),(8,30),(9,88),(9,89),(9,90),(10,86),(10,87),(10,90),(11,85),(11,87),(11,89),(12,85),(12,86),(12,88),(13,37),(13,49),(13,61),(13,62),(13,86),(14,38),(14,50),(14,63),(14,64),(14,86),(15,39),(15,51),(15,61),(15,63),(15,87),(16,40),(16,52),(16,62),(16,64),(16,87),(17,41),(17,53),(17,65),(17,66),(17,86),(18,42),(18,54),(18,67),(18,68),(18,86),(19,43),(19,55),(19,65),(19,67),(19,87),(20,44),(20,56),(20,66),(20,68),(20,87),(21,45),(21,57),(21,61),(21,65),(21,85),(22,46),(22,58),(22,62),(22,66),(22,85),(23,47),(23,59),(23,63),(23,67),(23,85),(24,48),(24,60),(24,64),(24,68),(24,85),(25,37),(25,41),(25,45),(25,46),(25,88),(26,38),(26,42),(26,47),(26,48),(26,88),(27,39),(27,43),(27,45),(27,47),(27,89),(28,40),(28,44),(28,46),(28,48),(28,89),(29,37),(29,38),(29,39),(29,40),(29,90),(30,41),(30,42),(30,43),(30,44),(30,90),(31,49),(31,53),(31,57),(31,58),(31,88),(32,50),(32,54),(32,59),(32,60),(32,88),(33,51),(33,55),(33,57),(33,59),(33,89),(34,52),(34,56),(34,58),(34,60),(34,89),(35,49),(35,50),(35,51),(35,52),(35,90),(36,53),(36,54),(36,55),(36,56),(36,90),(37,69),(37,70),(37,92),(38,71),(38,72),(38,92),(39,69),(39,71),(39,93),(40,70),(40,72),(40,93),(41,73),(41,74),(41,92),(42,75),(42,76),(42,92),(43,73),(43,75),(43,93),(44,74),(44,76),(44,93),(45,69),(45,73),(45,94),(46,70),(46,74),(46,94),(47,71),(47,75),(47,94),(48,72),(48,76),(48,94),(49,77),(49,78),(49,92),(50,79),(50,80),(50,92),(51,77),(51,79),(51,93),(52,78),(52,80),(52,93),(53,81),(53,82),(53,92),(54,83),(54,84),(54,92),(55,81),(55,83),(55,93),(56,82),(56,84),(56,93),(57,77),(57,81),(57,94),(58,78),(58,82),(58,94),(59,79),(59,83),(59,94),(60,80),(60,84),(60,94),(61,69),(61,77),(61,91),(62,70),(62,78),(62,91),(63,71),(63,79),(63,91),(64,72),(64,80),(64,91),(65,73),(65,81),(65,91),(66,74),(66,82),(66,91),(67,75),(67,83),(67,91),(68,76),(68,84),(68,91),(69,95),(70,95),(71,95),(72,95),(73,95),(74,95),(75,95),(76,95),(77,95),(78,95),(79,95),(80,95),(81,95),(82,95),(83,95),(84,95),(85,91),(85,94),(86,91),(86,92),(87,91),(87,93),(88,92),(88,94),(89,93),(89,94),(90,92),(90,93),(91,95),(92,95),(93,95),(94,95)],96)
 => ? = 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,5),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,4),(0,5),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,2),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 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 8 compositions to match this statistic)
Mapping
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001820: Lattices ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 50%
Values
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(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
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(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
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(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
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,15),(1,20),(1,21),(2,9),(2,10),(2,14),(2,18),(2,19),(3,8),(3,13),(3,17),(3,19),(3,21),(4,8),(4,12),(4,16),(4,18),(4,20),(5,7),(5,14),(5,15),(5,16),(5,17),(6,7),(6,10),(6,11),(6,12),(6,13),(7,31),(7,32),(8,30),(8,32),(9,30),(9,31),(10,22),(10,23),(10,31),(11,24),(11,25),(11,31),(12,22),(12,24),(12,32),(13,23),(13,25),(13,32),(14,26),(14,27),(14,31),(15,28),(15,29),(15,31),(16,26),(16,28),(16,32),(17,27),(17,29),(17,32),(18,22),(18,26),(18,30),(19,23),(19,27),(19,30),(20,24),(20,28),(20,30),(21,25),(21,29),(21,30),(22,33),(23,33),(24,33),(25,33),(26,33),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,15),(2,7),(2,8),(2,11),(2,14),(3,6),(3,8),(3,10),(3,13),(4,6),(4,7),(4,9),(4,12),(5,12),(5,13),(5,14),(5,15),(6,18),(6,22),(7,16),(7,22),(8,17),(8,22),(9,19),(9,22),(10,20),(10,22),(11,21),(11,22),(12,16),(12,18),(12,19),(13,17),(13,18),(13,20),(14,16),(14,17),(14,21),(15,19),(15,20),(15,21),(16,23),(17,23),(18,23),(19,23),(20,23),(21,23),(22,23)],24)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],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),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(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),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
 => ? = 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,2),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(0,1),(0,2),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(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
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,12),(1,15),(1,28),(1,31),(1,34),(2,11),(2,14),(2,28),(2,30),(2,33),(3,10),(3,13),(3,28),(3,29),(3,32),(4,10),(4,16),(4,19),(4,21),(4,30),(4,31),(5,11),(5,17),(5,20),(5,22),(5,29),(5,31),(6,12),(6,18),(6,23),(6,24),(6,29),(6,30),(7,13),(7,16),(7,20),(7,23),(7,33),(7,34),(8,14),(8,17),(8,19),(8,24),(8,32),(8,34),(9,15),(9,18),(9,21),(9,22),(9,32),(9,33),(10,25),(10,35),(10,45),(11,26),(11,36),(11,45),(12,27),(12,37),(12,45),(13,25),(13,38),(13,44),(14,26),(14,39),(14,44),(15,27),(15,40),(15,44),(16,25),(16,42),(16,43),(17,26),(17,41),(17,43),(18,27),(18,41),(18,42),(19,35),(19,39),(19,43),(20,36),(20,38),(20,43),(21,35),(21,40),(21,42),(22,36),(22,40),(22,41),(23,37),(23,38),(23,42),(24,37),(24,39),(24,41),(25,46),(26,46),(27,46),(28,44),(28,45),(29,38),(29,41),(29,45),(30,39),(30,42),(30,45),(31,40),(31,43),(31,45),(32,35),(32,41),(32,44),(33,36),(33,42),(33,44),(34,37),(34,43),(34,44),(35,46),(36,46),(37,46),(38,46),(39,46),(40,46),(41,46),(42,46),(43,46),(44,46),(45,46)],47)
 => ? = 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(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),(1,14),(1,18),(1,22),(1,28),(1,30),(1,36),(1,37),(1,66),(2,13),(2,17),(2,21),(2,27),(2,29),(2,34),(2,35),(2,66),(3,12),(3,20),(3,24),(3,26),(3,32),(3,35),(3,37),(3,67),(4,11),(4,19),(4,23),(4,25),(4,31),(4,34),(4,36),(4,67),(5,16),(5,19),(5,20),(5,27),(5,28),(5,39),(5,40),(6,15),(6,17),(6,18),(6,25),(6,26),(6,38),(6,40),(7,29),(7,30),(7,31),(7,32),(7,33),(7,40),(7,41),(8,21),(8,22),(8,23),(8,24),(8,33),(8,38),(8,39),(9,11),(9,12),(9,15),(9,39),(9,41),(9,66),(10,13),(10,14),(10,16),(10,38),(10,41),(10,67),(11,42),(11,74),(11,80),(11,94),(12,43),(12,75),(12,81),(12,94),(13,44),(13,76),(13,78),(13,95),(14,45),(14,77),(14,79),(14,95),(15,42),(15,43),(15,72),(15,98),(16,44),(16,45),(16,73),(16,98),(17,46),(17,47),(17,72),(17,78),(17,82),(18,48),(18,49),(18,72),(18,79),(18,83),(19,50),(19,52),(19,73),(19,80),(19,84),(20,51),(20,53),(20,73),(20,81),(20,85),(21,54),(21,55),(21,64),(21,78),(21,97),(22,56),(22,57),(22,65),(22,79),(22,97),(23,54),(23,56),(23,62),(23,80),(23,96),(24,55),(24,57),(24,63),(24,81),(24,96),(25,42),(25,46),(25,48),(25,84),(25,96),(26,43),(26,47),(26,49),(26,85),(26,96),(27,44),(27,50),(27,51),(27,82),(27,97),(28,45),(28,52),(28,53),(28,83),(28,97),(29,58),(29,59),(29,64),(29,82),(29,95),(30,60),(30,61),(30,65),(30,83),(30,95),(31,58),(31,60),(31,62),(31,84),(31,94),(32,59),(32,61),(32,63),(32,85),(32,94),(33,62),(33,63),(33,64),(33,65),(33,98),(34,46),(34,50),(34,54),(34,58),(34,74),(34,76),(35,47),(35,51),(35,55),(35,59),(35,75),(35,76),(36,48),(36,52),(36,56),(36,60),(36,74),(36,77),(37,49),(37,53),(37,57),(37,61),(37,75),(37,77),(38,78),(38,79),(38,96),(38,98),(39,80),(39,81),(39,97),(39,98),(40,82),(40,83),(40,84),(40,85),(40,98),(41,94),(41,95),(41,98),(42,90),(42,104),(43,91),(43,104),(44,92),(44,105),(45,93),(45,105),(46,86),(46,90),(46,99),(47,87),(47,91),(47,99),(48,88),(48,90),(48,100),(49,89),(49,91),(49,100),(50,86),(50,92),(50,101),(51,87),(51,92),(51,102),(52,88),(52,93),(52,101),(53,89),(53,93),(53,102),(54,68),(54,99),(54,101),(55,69),(55,99),(55,102),(56,70),(56,100),(56,101),(57,71),(57,100),(57,102),(58,68),(58,86),(58,103),(59,69),(59,87),(59,103),(60,70),(60,88),(60,103),(61,71),(61,89),(61,103),(62,68),(62,70),(62,104),(63,69),(63,71),(63,104),(64,68),(64,69),(64,105),(65,70),(65,71),(65,105),(66,72),(66,74),(66,75),(66,95),(66,97),(67,73),(67,76),(67,77),(67,94),(67,96),(68,106),(69,106),(70,106),(71,106),(72,90),(72,91),(72,105),(73,92),(73,93),(73,104),(74,90),(74,101),(74,103),(75,91),(75,102),(75,103),(76,92),(76,99),(76,103),(77,93),(77,100),(77,103),(78,99),(78,105),(79,100),(79,105),(80,101),(80,104),(81,102),(81,104),(82,86),(82,87),(82,105),(83,88),(83,89),(83,105),(84,86),(84,88),(84,104),(85,87),(85,89),(85,104),(86,106),(87,106),(88,106),(89,106),(90,106),(91,106),(92,106),(93,106),(94,103),(94,104),(95,103),(95,105),(96,99),(96,100),(96,104),(97,101),(97,102),(97,105),(98,104),(98,105),(99,106),(100,106),(101,106),(102,106),(103,106),(104,106),(105,106)],107)
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(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
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(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
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(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
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(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),(0,10),(0,11),(1,15),(1,21),(1,29),(1,30),(1,35),(1,36),(1,44),(1,45),(1,93),(2,14),(2,20),(2,26),(2,28),(2,32),(2,34),(2,43),(2,45),(2,92),(3,13),(3,19),(3,25),(3,27),(3,31),(3,33),(3,43),(3,44),(3,91),(4,16),(4,19),(4,28),(4,29),(4,37),(4,39),(4,46),(4,48),(4,90),(5,17),(5,20),(5,27),(5,30),(5,38),(5,40),(5,47),(5,48),(5,89),(6,18),(6,21),(6,25),(6,26),(6,41),(6,42),(6,46),(6,47),(6,88),(7,22),(7,23),(7,33),(7,34),(7,37),(7,38),(7,88),(7,93),(8,22),(8,24),(8,31),(8,35),(8,39),(8,41),(8,89),(8,92),(9,23),(9,24),(9,32),(9,36),(9,40),(9,42),(9,90),(9,91),(10,12),(10,16),(10,17),(10,18),(10,91),(10,92),(10,93),(11,12),(11,13),(11,14),(11,15),(11,88),(11,89),(11,90),(12,120),(12,121),(12,122),(13,52),(13,53),(13,99),(13,101),(13,120),(14,52),(14,54),(14,100),(14,102),(14,121),(15,53),(15,54),(15,103),(15,104),(15,122),(16,55),(16,57),(16,108),(16,109),(16,120),(17,56),(17,57),(17,107),(17,110),(17,121),(18,55),(18,56),(18,105),(18,106),(18,122),(19,64),(19,66),(19,117),(19,118),(19,120),(20,65),(20,67),(20,117),(20,119),(20,121),(21,68),(21,69),(21,118),(21,119),(21,122),(22,51),(22,70),(22,73),(22,124),(22,128),(23,51),(23,71),(23,74),(23,123),(23,127),(24,51),(24,72),(24,75),(24,125),(24,126),(25,58),(25,61),(25,76),(25,101),(25,105),(25,118),(26,58),(26,62),(26,77),(26,102),(26,106),(26,119),(27,59),(27,61),(27,78),(27,99),(27,107),(27,117),(28,60),(28,62),(28,79),(28,100),(28,108),(28,117),(29,60),(29,63),(29,80),(29,104),(29,109),(29,118),(30,59),(30,63),(30,81),(30,103),(30,110),(30,119),(31,66),(31,70),(31,76),(31,83),(31,99),(31,126),(32,67),(32,71),(32,77),(32,84),(32,100),(32,126),(33,64),(33,70),(33,78),(33,82),(33,101),(33,127),(34,65),(34,71),(34,79),(34,82),(34,102),(34,128),(35,69),(35,72),(35,80),(35,83),(35,103),(35,128),(36,68),(36,72),(36,81),(36,84),(36,104),(36,127),(37,64),(37,73),(37,79),(37,87),(37,109),(37,123),(38,65),(38,74),(38,78),(38,87),(38,110),(38,124),(39,66),(39,73),(39,80),(39,85),(39,108),(39,125),(40,67),(40,74),(40,81),(40,86),(40,107),(40,125),(41,69),(41,75),(41,76),(41,85),(41,106),(41,124),(42,68),(42,75),(42,77),(42,86),(42,105),(42,123),(43,49),(43,52),(43,58),(43,82),(43,117),(43,126),(44,49),(44,53),(44,59),(44,83),(44,118),(44,127),(45,49),(45,54),(45,60),(45,84),(45,119),(45,128),(46,50),(46,55),(46,62),(46,85),(46,118),(46,123),(47,50),(47,56),(47,61),(47,86),(47,119),(47,124),(48,50),(48,57),(48,63),(48,87),(48,117),(48,125),(49,97),(49,139),(49,140),(50,98),(50,138),(50,140),(51,138),(51,139),(52,97),(52,113),(52,143),(53,97),(53,111),(53,141),(54,97),(54,112),(54,142),(55,98),(55,115),(55,141),(56,98),(56,114),(56,142),(57,98),(57,116),(57,143),(58,113),(58,137),(58,140),(59,111),(59,135),(59,140),(60,112),(60,136),(60,140),(61,114),(61,132),(61,140),(62,115),(62,133),(62,140),(63,116),(63,134),(63,140),(64,94),(64,129),(64,141),(65,95),(65,129),(65,142),(66,94),(66,130),(66,143),(67,95),(67,131),(67,143),(68,96),(68,131),(68,141),(69,96),(69,130),(69,142),(70,94),(70,132),(70,139),(71,95),(71,133),(71,139),(72,96),(72,134),(72,139),(73,94),(73,136),(73,138),(74,95),(74,135),(74,138),(75,96),(75,137),(75,138),(76,130),(76,132),(76,137),(77,131),(77,133),(77,137),(78,129),(78,132),(78,135),(79,129),(79,133),(79,136),(80,130),(80,134),(80,136),(81,131),(81,134),(81,135),(82,113),(82,129),(82,139),(83,111),(83,130),(83,139),(84,112),(84,131),(84,139),(85,115),(85,130),(85,138),(86,114),(86,131),(86,138),(87,116),(87,129),(87,138),(88,101),(88,102),(88,122),(88,123),(88,124),(89,99),(89,103),(89,121),(89,124),(89,125),(90,100),(90,104),(90,120),(90,123),(90,125),(91,105),(91,107),(91,120),(91,126),(91,127),(92,106),(92,108),(92,121),(92,126),(92,128),(93,109),(93,110),(93,122),(93,127),(93,128),(94,144),(95,144),(96,144),(97,144),(98,144),(99,111),(99,132),(99,143),(100,112),(100,133),(100,143),(101,113),(101,132),(101,141),(102,113),(102,133),(102,142),(103,111),(103,134),(103,142),(104,112),(104,134),(104,141),(105,114),(105,137),(105,141),(106,115),(106,137),(106,142),(107,114),(107,135),(107,143),(108,115),(108,136),(108,143),(109,116),(109,136),(109,141),(110,116),(110,135),(110,142),(111,144),(112,144),(113,144),(114,144),(115,144),(116,144),(117,129),(117,140),(117,143),(118,130),(118,140),(118,141),(119,131),(119,140),(119,142),(120,141),(120,143),(121,142),(121,143),(122,141),(122,142),(123,133),(123,138),(123,141),(124,132),(124,138),(124,142),(125,134),(125,138),(125,143),(126,137),(126,139),(126,143),(127,135),(127,139),(127,141),(128,136),(128,139),(128,142),(129,144),(130,144),(131,144),(132,144),(133,144),(134,144),(135,144),(136,144),(137,144),(138,144),(139,144),(140,144),(141,144),(142,144),(143,144)],145)
 => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(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),(0,10),(1,13),(1,18),(1,28),(1,30),(1,32),(1,35),(1,36),(1,72),(2,12),(2,17),(2,27),(2,29),(2,32),(2,33),(2,34),(2,71),(3,17),(3,20),(3,21),(3,30),(3,31),(3,37),(3,38),(3,73),(4,18),(4,19),(4,22),(4,29),(4,31),(4,39),(4,40),(4,74),(5,16),(5,24),(5,26),(5,34),(5,36),(5,38),(5,40),(5,75),(6,15),(6,23),(6,25),(6,33),(6,35),(6,37),(6,39),(6,75),(7,11),(7,15),(7,16),(7,19),(7,20),(7,71),(7,72),(8,14),(8,22),(8,23),(8,24),(8,27),(8,72),(8,73),(9,14),(9,21),(9,25),(9,26),(9,28),(9,71),(9,74),(10,11),(10,12),(10,13),(10,73),(10,74),(10,75),(11,84),(11,99),(11,100),(12,41),(12,82),(12,85),(12,99),(13,41),(13,83),(13,86),(13,100),(14,58),(14,59),(14,101),(14,102),(15,54),(15,56),(15,84),(15,87),(15,89),(16,55),(16,57),(16,84),(16,88),(16,90),(17,44),(17,45),(17,85),(17,91),(17,98),(18,46),(18,47),(18,86),(18,92),(18,98),(19,54),(19,55),(19,68),(19,92),(19,99),(20,56),(20,57),(20,68),(20,91),(20,100),(21,64),(21,65),(21,70),(21,91),(21,102),(22,66),(22,67),(22,69),(22,92),(22,102),(23,58),(23,60),(23,66),(23,89),(23,103),(24,59),(24,61),(24,67),(24,90),(24,103),(25,58),(25,62),(25,64),(25,87),(25,104),(26,59),(26,63),(26,65),(26,88),(26,104),(27,60),(27,61),(27,69),(27,85),(27,101),(28,62),(28,63),(28,70),(28,86),(28,101),(29,50),(29,51),(29,69),(29,98),(29,99),(30,52),(30,53),(30,70),(30,98),(30,100),(31,48),(31,49),(31,68),(31,98),(31,102),(32,41),(32,42),(32,43),(32,98),(32,101),(33,42),(33,44),(33,50),(33,60),(33,82),(33,87),(34,43),(34,45),(34,51),(34,61),(34,82),(34,88),(35,42),(35,46),(35,52),(35,62),(35,83),(35,89),(36,43),(36,47),(36,53),(36,63),(36,83),(36,90),(37,44),(37,48),(37,52),(37,56),(37,64),(37,103),(38,45),(38,49),(38,53),(38,57),(38,65),(38,103),(39,46),(39,48),(39,50),(39,54),(39,66),(39,104),(40,47),(40,49),(40,51),(40,55),(40,67),(40,104),(41,97),(41,114),(42,97),(42,105),(42,107),(43,97),(43,106),(43,108),(44,93),(44,105),(44,109),(45,94),(45,106),(45,109),(46,95),(46,105),(46,110),(47,96),(47,106),(47,110),(48,80),(48,105),(48,113),(49,81),(49,106),(49,113),(50,76),(50,105),(50,111),(51,77),(51,106),(51,111),(52,78),(52,105),(52,112),(53,79),(53,106),(53,112),(54,80),(54,95),(54,111),(55,81),(55,96),(55,111),(56,80),(56,93),(56,112),(57,81),(57,94),(57,112),(58,107),(58,113),(59,108),(59,113),(60,76),(60,107),(60,109),(61,77),(61,108),(61,109),(62,78),(62,107),(62,110),(63,79),(63,108),(63,110),(64,78),(64,93),(64,113),(65,79),(65,94),(65,113),(66,76),(66,95),(66,113),(67,77),(67,96),(67,113),(68,80),(68,81),(68,114),(69,76),(69,77),(69,114),(70,78),(70,79),(70,114),(71,87),(71,88),(71,91),(71,99),(71,101),(72,89),(72,90),(72,92),(72,100),(72,101),(73,85),(73,100),(73,102),(73,103),(74,86),(74,99),(74,102),(74,104),(75,82),(75,83),(75,84),(75,103),(75,104),(76,115),(77,115),(78,115),(79,115),(80,115),(81,115),(82,97),(82,109),(82,111),(83,97),(83,110),(83,112),(84,111),(84,112),(85,109),(85,114),(86,110),(86,114),(87,93),(87,107),(87,111),(88,94),(88,108),(88,111),(89,95),(89,107),(89,112),(90,96),(90,108),(90,112),(91,93),(91,94),(91,114),(92,95),(92,96),(92,114),(93,115),(94,115),(95,115),(96,115),(97,115),(98,105),(98,106),(98,114),(99,111),(99,114),(100,112),(100,114),(101,107),(101,108),(101,114),(102,113),(102,114),(103,109),(103,112),(103,113),(104,110),(104,111),(104,113),(105,115),(106,115),(107,115),(108,115),(109,115),(110,115),(111,115),(112,115),(113,115),(114,115)],116)
 => ? = 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,16),(1,17),(1,18),(1,34),(1,35),(1,40),(1,41),(1,42),(1,43),(2,14),(2,15),(2,18),(2,32),(2,33),(2,36),(2,37),(2,38),(2,39),(3,12),(3,21),(3,23),(3,27),(3,31),(3,37),(3,41),(3,79),(4,12),(4,20),(4,22),(4,26),(4,30),(4,36),(4,40),(4,78),(5,13),(5,20),(5,24),(5,28),(5,31),(5,38),(5,42),(5,76),(6,13),(6,21),(6,25),(6,29),(6,30),(6,39),(6,43),(6,77),(7,19),(7,28),(7,29),(7,33),(7,35),(7,78),(7,79),(8,19),(8,26),(8,27),(8,32),(8,34),(8,76),(8,77),(9,11),(9,14),(9,16),(9,22),(9,25),(9,76),(9,79),(10,11),(10,15),(10,17),(10,23),(10,24),(10,77),(10,78),(11,105),(11,106),(11,107),(12,44),(12,106),(12,108),(12,111),(13,45),(13,105),(13,108),(13,112),(14,60),(14,63),(14,89),(14,92),(14,107),(15,61),(15,62),(15,90),(15,91),(15,107),(16,64),(16,67),(16,93),(16,96),(16,107),(17,65),(17,66),(17,94),(17,95),(17,107),(18,46),(18,47),(18,107),(18,111),(18,112),(19,48),(19,49),(19,109),(19,110),(20,68),(20,70),(20,85),(20,87),(20,108),(21,69),(21,71),(21,86),(21,88),(21,108),(22,50),(22,60),(22,64),(22,85),(22,106),(23,51),(23,61),(23,65),(23,86),(23,106),(24,51),(24,62),(24,66),(24,87),(24,105),(25,50),(25,63),(25,67),(25,88),(25,105),(26,44),(26,52),(26,56),(26,85),(26,109),(27,44),(27,53),(27,57),(27,86),(27,110),(28,45),(28,54),(28,58),(28,87),(28,110),(29,45),(29,55),(29,59),(29,88),(29,109),(30,50),(30,72),(30,74),(30,108),(30,109),(31,51),(31,73),(31,75),(31,108),(31,110),(32,46),(32,48),(32,52),(32,53),(32,89),(32,90),(33,47),(33,48),(33,54),(33,55),(33,91),(33,92),(34,46),(34,49),(34,56),(34,57),(34,93),(34,94),(35,47),(35,49),(35,58),(35,59),(35,95),(35,96),(36,52),(36,60),(36,68),(36,72),(36,91),(36,111),(37,53),(37,61),(37,69),(37,73),(37,92),(37,111),(38,54),(38,62),(38,68),(38,73),(38,89),(38,112),(39,55),(39,63),(39,69),(39,72),(39,90),(39,112),(40,56),(40,64),(40,70),(40,74),(40,95),(40,111),(41,57),(41,65),(41,71),(41,75),(41,96),(41,111),(42,58),(42,66),(42,70),(42,75),(42,93),(42,112),(43,59),(43,67),(43,71),(43,74),(43,94),(43,112),(44,113),(44,122),(45,114),(45,122),(46,84),(46,113),(46,120),(47,84),(47,114),(47,121),(48,84),(48,115),(48,116),(49,84),(49,117),(49,118),(50,80),(50,82),(50,122),(51,81),(51,83),(51,122),(52,97),(52,113),(52,115),(53,98),(53,113),(53,116),(54,99),(54,114),(54,116),(55,100),(55,114),(55,115),(56,101),(56,113),(56,117),(57,102),(57,113),(57,118),(58,103),(58,114),(58,118),(59,104),(59,114),(59,117),(60,80),(60,97),(60,121),(61,81),(61,98),(61,121),(62,81),(62,99),(62,120),(63,80),(63,100),(63,120),(64,82),(64,101),(64,121),(65,83),(65,102),(65,121),(66,83),(66,103),(66,120),(67,82),(67,104),(67,120),(68,97),(68,99),(68,119),(69,98),(69,100),(69,119),(70,101),(70,103),(70,119),(71,102),(71,104),(71,119),(72,80),(72,115),(72,119),(73,81),(73,116),(73,119),(74,82),(74,117),(74,119),(75,83),(75,118),(75,119),(76,85),(76,89),(76,93),(76,105),(76,110),(77,86),(77,90),(77,94),(77,105),(77,109),(78,87),(78,91),(78,95),(78,106),(78,109),(79,88),(79,92),(79,96),(79,106),(79,110),(80,123),(81,123),(82,123),(83,123),(84,123),(85,97),(85,101),(85,122),(86,98),(86,102),(86,122),(87,99),(87,103),(87,122),(88,100),(88,104),(88,122),(89,97),(89,116),(89,120),(90,98),(90,115),(90,120),(91,99),(91,115),(91,121),(92,100),(92,116),(92,121),(93,101),(93,118),(93,120),(94,102),(94,117),(94,120),(95,103),(95,117),(95,121),(96,104),(96,118),(96,121),(97,123),(98,123),(99,123),(100,123),(101,123),(102,123),(103,123),(104,123),(105,120),(105,122),(106,121),(106,122),(107,120),(107,121),(108,119),(108,122),(109,115),(109,117),(109,122),(110,116),(110,118),(110,122),(111,113),(111,119),(111,121),(112,114),(112,119),(112,120),(113,123),(114,123),(115,123),(116,123),(117,123),(118,123),(119,123),(120,123),(121,123),(122,123)],124)
 => ? = 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(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),(1,21),(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
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(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)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(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),(1,16),(1,20),(1,24),(1,30),(1,32),(2,15),(2,19),(2,23),(2,30),(2,31),(3,17),(3,21),(3,23),(3,29),(3,32),(4,18),(4,22),(4,24),(4,29),(4,31),(5,10),(5,13),(5,14),(5,17),(5,18),(5,30),(6,10),(6,11),(6,12),(6,15),(6,16),(6,29),(7,9),(7,11),(7,13),(7,19),(7,22),(7,32),(8,9),(8,12),(8,14),(8,20),(8,21),(8,31),(9,35),(9,36),(9,41),(10,33),(10,34),(10,41),(11,25),(11,38),(11,41),(12,26),(12,37),(12,41),(13,28),(13,39),(13,41),(14,27),(14,40),(14,41),(15,25),(15,33),(15,37),(16,26),(16,33),(16,38),(17,27),(17,34),(17,39),(18,28),(18,34),(18,40),(19,25),(19,35),(19,39),(20,26),(20,36),(20,40),(21,27),(21,36),(21,37),(22,28),(22,35),(22,38),(23,37),(23,39),(24,38),(24,40),(25,42),(26,42),(27,42),(28,42),(29,34),(29,37),(29,38),(30,33),(30,39),(30,40),(31,35),(31,37),(31,40),(32,36),(32,38),(32,39),(33,42),(34,42),(35,42),(36,42),(37,42),(38,42),(39,42),(40,42),(41,42)],43)
 => ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(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),(0,8),(0,9),(0,10),(1,20),(1,29),(1,30),(1,34),(1,35),(1,39),(1,40),(1,75),(2,19),(2,24),(2,28),(2,31),(2,33),(2,37),(2,40),(2,72),(3,18),(3,23),(3,27),(3,31),(3,32),(3,36),(3,39),(3,71),(4,17),(4,21),(4,26),(4,32),(4,34),(4,37),(4,38),(4,73),(5,16),(5,22),(5,25),(5,33),(5,35),(5,36),(5,38),(5,74),(6,12),(6,14),(6,16),(6,21),(6,23),(6,72),(6,75),(7,11),(7,15),(7,17),(7,22),(7,24),(7,71),(7,75),(8,11),(8,13),(8,18),(8,25),(8,29),(8,72),(8,73),(9,12),(9,13),(9,19),(9,26),(9,30),(9,71),(9,74),(10,14),(10,15),(10,20),(10,27),(10,28),(10,73),(10,74),(11,61),(11,81),(11,83),(11,105),(12,62),(12,82),(12,84),(12,104),(13,65),(13,81),(13,82),(13,101),(14,63),(14,84),(14,85),(14,103),(15,64),(15,83),(15,85),(15,102),(16,52),(16,55),(16,84),(16,87),(16,92),(17,51),(17,56),(17,83),(17,86),(17,93),(18,53),(18,57),(18,81),(18,88),(18,90),(19,54),(19,58),(19,82),(19,89),(19,91),(20,59),(20,60),(20,85),(20,94),(20,95),(21,52),(21,62),(21,66),(21,93),(21,103),(22,51),(22,61),(22,67),(22,92),(22,102),(23,55),(23,63),(23,66),(23,88),(23,104),(24,56),(24,64),(24,67),(24,89),(24,105),(25,53),(25,61),(25,69),(25,87),(25,101),(26,54),(26,62),(26,70),(26,86),(26,101),(27,59),(27,63),(27,68),(27,90),(27,102),(28,60),(28,64),(28,68),(28,91),(28,103),(29,57),(29,65),(29,69),(29,94),(29,105),(30,58),(30,65),(30,70),(30,95),(30,104),(31,41),(31,42),(31,48),(31,68),(31,88),(31,89),(32,41),(32,43),(32,46),(32,66),(32,86),(32,90),(33,42),(33,44),(33,47),(33,67),(33,87),(33,91),(34,43),(34,45),(34,50),(34,70),(34,93),(34,94),(35,44),(35,45),(35,49),(35,69),(35,92),(35,95),(36,42),(36,46),(36,49),(36,53),(36,55),(36,102),(37,41),(37,47),(37,50),(37,54),(37,56),(37,103),(38,45),(38,46),(38,47),(38,51),(38,52),(38,101),(39,43),(39,48),(39,49),(39,57),(39,59),(39,104),(40,44),(40,48),(40,50),(40,58),(40,60),(40,105),(41,97),(41,106),(41,111),(42,96),(42,107),(42,111),(43,99),(43,108),(43,111),(44,100),(44,109),(44,111),(45,98),(45,110),(45,111),(46,76),(46,111),(46,112),(47,77),(47,111),(47,113),(48,80),(48,111),(48,114),(49,78),(49,111),(49,115),(50,79),(50,111),(50,116),(51,77),(51,98),(51,112),(52,76),(52,98),(52,113),(53,78),(53,96),(53,112),(54,79),(54,97),(54,113),(55,76),(55,96),(55,115),(56,77),(56,97),(56,116),(57,78),(57,99),(57,114),(58,79),(58,100),(58,114),(59,80),(59,99),(59,115),(60,80),(60,100),(60,116),(61,109),(61,112),(62,108),(62,113),(63,106),(63,115),(64,107),(64,116),(65,110),(65,114),(66,76),(66,106),(66,108),(67,77),(67,107),(67,109),(68,80),(68,106),(68,107),(69,78),(69,109),(69,110),(70,79),(70,108),(70,110),(71,81),(71,86),(71,89),(71,102),(71,104),(72,82),(72,87),(72,88),(72,103),(72,105),(73,83),(73,90),(73,94),(73,101),(73,103),(74,84),(74,91),(74,95),(74,101),(74,102),(75,85),(75,92),(75,93),(75,104),(75,105),(76,117),(77,117),(78,117),(79,117),(80,117),(81,112),(81,114),(82,113),(82,114),(83,112),(83,116),(84,113),(84,115),(85,115),(85,116),(86,97),(86,108),(86,112),(87,96),(87,109),(87,113),(88,96),(88,106),(88,114),(89,97),(89,107),(89,114),(90,99),(90,106),(90,112),(91,100),(91,107),(91,113),(92,98),(92,109),(92,115),(93,98),(93,108),(93,116),(94,99),(94,110),(94,116),(95,100),(95,110),(95,115),(96,117),(97,117),(98,117),(99,117),(100,117),(101,110),(101,112),(101,113),(102,107),(102,112),(102,115),(103,106),(103,113),(103,116),(104,108),(104,114),(104,115),(105,109),(105,114),(105,116),(106,117),(107,117),(108,117),(109,117),(110,117),(111,117),(112,117),(113,117),(114,117),(115,117),(116,117)],118)
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(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),(1,15),(1,16),(1,17),(1,18),(1,54),(1,55),(2,10),(2,13),(2,14),(2,20),(2,55),(2,57),(3,10),(3,11),(3,12),(3,19),(3,54),(3,56),(4,12),(4,16),(4,23),(4,24),(4,26),(4,30),(4,57),(5,11),(5,15),(5,21),(5,22),(5,25),(5,29),(5,57),(6,14),(6,18),(6,22),(6,24),(6,28),(6,32),(6,56),(7,13),(7,17),(7,21),(7,23),(7,27),(7,31),(7,56),(8,19),(8,27),(8,28),(8,29),(8,30),(8,33),(8,55),(9,20),(9,25),(9,26),(9,31),(9,32),(9,33),(9,54),(10,58),(10,59),(10,78),(11,42),(11,58),(11,60),(11,64),(12,43),(12,58),(12,61),(12,65),(13,44),(13,59),(13,62),(13,66),(14,45),(14,59),(14,63),(14,67),(15,38),(15,39),(15,60),(15,80),(16,40),(16,41),(16,61),(16,80),(17,38),(17,40),(17,62),(17,79),(18,39),(18,41),(18,63),(18,79),(19,42),(19,43),(19,68),(19,78),(20,44),(20,45),(20,69),(20,78),(21,38),(21,46),(21,50),(21,64),(21,66),(22,39),(22,47),(22,51),(22,64),(22,67),(23,40),(23,48),(23,52),(23,65),(23,66),(24,41),(24,49),(24,53),(24,65),(24,67),(25,34),(25,50),(25,51),(25,60),(25,69),(26,35),(26,52),(26,53),(26,61),(26,69),(27,36),(27,46),(27,48),(27,62),(27,68),(28,37),(28,47),(28,49),(28,63),(28,68),(29,34),(29,42),(29,46),(29,47),(29,80),(30,35),(30,43),(30,48),(30,49),(30,80),(31,36),(31,44),(31,50),(31,52),(31,79),(32,37),(32,45),(32,51),(32,53),(32,79),(33,34),(33,35),(33,36),(33,37),(33,78),(34,70),(34,71),(34,86),(35,72),(35,73),(35,86),(36,70),(36,72),(36,87),(37,71),(37,73),(37,87),(38,82),(38,84),(39,82),(39,85),(40,83),(40,84),(41,83),(41,85),(42,74),(42,86),(43,75),(43,86),(44,76),(44,87),(45,77),(45,87),(46,70),(46,74),(46,84),(47,71),(47,74),(47,85),(48,72),(48,75),(48,84),(49,73),(49,75),(49,85),(50,70),(50,76),(50,82),(51,71),(51,77),(51,82),(52,72),(52,76),(52,83),(53,73),(53,77),(53,83),(54,60),(54,61),(54,78),(54,79),(55,62),(55,63),(55,78),(55,80),(56,59),(56,64),(56,65),(56,68),(56,79),(57,58),(57,66),(57,67),(57,69),(57,80),(58,81),(58,86),(59,81),(59,87),(60,82),(60,86),(61,83),(61,86),(62,84),(62,87),(63,85),(63,87),(64,74),(64,81),(64,82),(65,75),(65,81),(65,83),(66,76),(66,81),(66,84),(67,77),(67,81),(67,85),(68,74),(68,75),(68,87),(69,76),(69,77),(69,86),(70,88),(71,88),(72,88),(73,88),(74,88),(75,88),(76,88),(77,88),(78,86),(78,87),(79,82),(79,83),(79,87),(80,84),(80,85),(80,86),(81,88),(82,88),(83,88),(84,88),(85,88),(86,88),(87,88)],89)
 => ? = 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(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),(0,8),(0,9),(1,17),(1,18),(1,21),(1,22),(1,30),(1,32),(1,35),(1,36),(2,15),(2,16),(2,19),(2,20),(2,30),(2,31),(2,33),(2,34),(3,26),(3,27),(3,28),(3,29),(3,31),(3,32),(3,68),(4,12),(4,23),(4,25),(4,29),(4,34),(4,36),(4,70),(5,11),(5,23),(5,24),(5,28),(5,33),(5,35),(5,69),(6,10),(6,14),(6,19),(6,21),(6,24),(6,27),(6,70),(7,10),(7,13),(7,20),(7,22),(7,25),(7,26),(7,69),(8,11),(8,13),(8,15),(8,17),(8,68),(8,70),(9,12),(9,14),(9,16),(9,18),(9,68),(9,69),(10,39),(10,77),(10,78),(10,92),(11,62),(11,64),(11,79),(11,93),(12,63),(12,65),(12,80),(12,94),(13,58),(13,60),(13,78),(13,93),(14,59),(14,61),(14,77),(14,94),(15,58),(15,62),(15,66),(15,82),(15,85),(16,59),(16,63),(16,67),(16,81),(16,85),(17,60),(17,64),(17,66),(17,84),(17,86),(18,61),(18,65),(18,67),(18,83),(18,86),(19,49),(19,52),(19,59),(19,82),(19,92),(20,48),(20,53),(20,58),(20,81),(20,92),(21,51),(21,54),(21,61),(21,84),(21,92),(22,50),(22,55),(22,60),(22,83),(22,92),(23,37),(23,40),(23,41),(23,79),(23,80),(24,52),(24,54),(24,56),(24,77),(24,79),(25,53),(25,55),(25,57),(25,78),(25,80),(26,39),(26,48),(26,50),(26,57),(26,93),(27,39),(27,49),(27,51),(27,56),(27,94),(28,37),(28,44),(28,46),(28,56),(28,93),(29,37),(29,45),(29,47),(29,57),(29,94),(30,38),(30,42),(30,43),(30,66),(30,67),(30,92),(31,38),(31,44),(31,45),(31,48),(31,49),(31,85),(32,38),(32,46),(32,47),(32,50),(32,51),(32,86),(33,40),(33,42),(33,44),(33,52),(33,62),(33,81),(34,40),(34,43),(34,45),(34,53),(34,63),(34,82),(35,41),(35,42),(35,46),(35,54),(35,64),(35,83),(36,41),(36,43),(36,47),(36,55),(36,65),(36,84),(37,100),(37,103),(38,87),(38,95),(38,100),(39,95),(39,103),(40,88),(40,89),(40,100),(41,90),(41,91),(41,100),(42,75),(42,100),(42,101),(43,76),(43,100),(43,102),(44,71),(44,96),(44,100),(45,72),(45,97),(45,100),(46,73),(46,98),(46,100),(47,74),(47,99),(47,100),(48,72),(48,95),(48,96),(49,71),(49,95),(49,97),(50,74),(50,95),(50,98),(51,73),(51,95),(51,99),(52,71),(52,88),(52,101),(53,72),(53,89),(53,102),(54,73),(54,90),(54,101),(55,74),(55,91),(55,102),(56,71),(56,73),(56,103),(57,72),(57,74),(57,103),(58,96),(58,102),(59,97),(59,101),(60,98),(60,102),(61,99),(61,101),(62,75),(62,88),(62,96),(63,76),(63,89),(63,97),(64,75),(64,90),(64,98),(65,76),(65,91),(65,99),(66,75),(66,87),(66,102),(67,76),(67,87),(67,101),(68,85),(68,86),(68,93),(68,94),(69,77),(69,80),(69,81),(69,83),(69,93),(70,78),(70,79),(70,82),(70,84),(70,94),(71,104),(72,104),(73,104),(74,104),(75,104),(76,104),(77,101),(77,103),(78,102),(78,103),(79,88),(79,90),(79,103),(80,89),(80,91),(80,103),(81,89),(81,96),(81,101),(82,88),(82,97),(82,102),(83,91),(83,98),(83,101),(84,90),(84,99),(84,102),(85,87),(85,96),(85,97),(86,87),(86,98),(86,99),(87,104),(88,104),(89,104),(90,104),(91,104),(92,95),(92,101),(92,102),(93,96),(93,98),(93,103),(94,97),(94,99),(94,103),(95,104),(96,104),(97,104),(98,104),(99,104),(100,104),(101,104),(102,104),(103,104)],105)
 => ? = 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(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),(1,18),(1,19),(1,20),(1,21),(1,34),(1,57),(2,12),(2,13),(2,16),(2,17),(2,34),(2,56),(3,10),(3,11),(3,14),(3,15),(3,34),(3,55),(4,15),(4,17),(4,24),(4,25),(4,28),(4,29),(4,57),(5,14),(5,16),(5,22),(5,23),(5,26),(5,27),(5,57),(6,11),(6,19),(6,23),(6,25),(6,32),(6,33),(6,56),(7,10),(7,18),(7,22),(7,24),(7,30),(7,31),(7,56),(8,13),(8,21),(8,27),(8,29),(8,31),(8,33),(8,55),(9,12),(9,20),(9,26),(9,28),(9,30),(9,32),(9,55),(10,35),(10,37),(10,62),(10,83),(11,36),(11,38),(11,63),(11,83),(12,39),(12,41),(12,64),(12,84),(13,40),(13,42),(13,65),(13,84),(14,35),(14,36),(14,58),(14,82),(15,37),(15,38),(15,59),(15,82),(16,39),(16,40),(16,60),(16,82),(17,41),(17,42),(17,61),(17,82),(18,43),(18,44),(18,66),(18,83),(19,45),(19,46),(19,67),(19,83),(20,43),(20,45),(20,68),(20,84),(21,44),(21,46),(21,69),(21,84),(22,35),(22,47),(22,48),(22,60),(22,66),(23,36),(23,49),(23,50),(23,60),(23,67),(24,37),(24,51),(24,52),(24,61),(24,66),(25,38),(25,53),(25,54),(25,61),(25,67),(26,39),(26,47),(26,49),(26,58),(26,68),(27,40),(27,48),(27,50),(27,58),(27,69),(28,41),(28,51),(28,53),(28,59),(28,68),(29,42),(29,52),(29,54),(29,59),(29,69),(30,43),(30,47),(30,51),(30,62),(30,64),(31,44),(31,48),(31,52),(31,62),(31,65),(32,45),(32,49),(32,53),(32,63),(32,64),(33,46),(33,50),(33,54),(33,63),(33,65),(34,82),(34,83),(34,84),(35,70),(35,85),(36,71),(36,85),(37,72),(37,85),(38,73),(38,85),(39,74),(39,86),(40,75),(40,86),(41,76),(41,86),(42,77),(42,86),(43,78),(43,87),(44,79),(44,87),(45,80),(45,87),(46,81),(46,87),(47,70),(47,74),(47,78),(48,70),(48,75),(48,79),(49,71),(49,74),(49,80),(50,71),(50,75),(50,81),(51,72),(51,76),(51,78),(52,72),(52,77),(52,79),(53,73),(53,76),(53,80),(54,73),(54,77),(54,81),(55,58),(55,59),(55,62),(55,63),(55,84),(56,60),(56,61),(56,64),(56,65),(56,83),(57,66),(57,67),(57,68),(57,69),(57,82),(58,70),(58,71),(58,86),(59,72),(59,73),(59,86),(60,74),(60,75),(60,85),(61,76),(61,77),(61,85),(62,70),(62,72),(62,87),(63,71),(63,73),(63,87),(64,74),(64,76),(64,87),(65,75),(65,77),(65,87),(66,78),(66,79),(66,85),(67,80),(67,81),(67,85),(68,78),(68,80),(68,86),(69,79),(69,81),(69,86),(70,88),(71,88),(72,88),(73,88),(74,88),(75,88),(76,88),(77,88),(78,88),(79,88),(80,88),(81,88),(82,85),(82,86),(83,85),(83,87),(84,86),(84,87),(85,88),(86,88),(87,88)],89)
 => ? = 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(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
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,14),(1,18),(1,23),(1,24),(1,26),(1,32),(2,12),(2,13),(2,17),(2,21),(2,22),(2,25),(2,31),(3,11),(3,16),(3,20),(3,22),(3,24),(3,28),(3,34),(4,11),(4,15),(4,19),(4,21),(4,23),(4,27),(4,33),(5,10),(5,17),(5,18),(5,19),(5,20),(5,30),(5,36),(6,10),(6,13),(6,14),(6,15),(6,16),(6,29),(6,35),(7,9),(7,31),(7,32),(7,33),(7,34),(7,35),(7,36),(8,9),(8,25),(8,26),(8,27),(8,28),(8,29),(8,30),(9,88),(9,89),(9,90),(10,86),(10,87),(10,90),(11,85),(11,87),(11,89),(12,85),(12,86),(12,88),(13,37),(13,49),(13,61),(13,62),(13,86),(14,38),(14,50),(14,63),(14,64),(14,86),(15,39),(15,51),(15,61),(15,63),(15,87),(16,40),(16,52),(16,62),(16,64),(16,87),(17,41),(17,53),(17,65),(17,66),(17,86),(18,42),(18,54),(18,67),(18,68),(18,86),(19,43),(19,55),(19,65),(19,67),(19,87),(20,44),(20,56),(20,66),(20,68),(20,87),(21,45),(21,57),(21,61),(21,65),(21,85),(22,46),(22,58),(22,62),(22,66),(22,85),(23,47),(23,59),(23,63),(23,67),(23,85),(24,48),(24,60),(24,64),(24,68),(24,85),(25,37),(25,41),(25,45),(25,46),(25,88),(26,38),(26,42),(26,47),(26,48),(26,88),(27,39),(27,43),(27,45),(27,47),(27,89),(28,40),(28,44),(28,46),(28,48),(28,89),(29,37),(29,38),(29,39),(29,40),(29,90),(30,41),(30,42),(30,43),(30,44),(30,90),(31,49),(31,53),(31,57),(31,58),(31,88),(32,50),(32,54),(32,59),(32,60),(32,88),(33,51),(33,55),(33,57),(33,59),(33,89),(34,52),(34,56),(34,58),(34,60),(34,89),(35,49),(35,50),(35,51),(35,52),(35,90),(36,53),(36,54),(36,55),(36,56),(36,90),(37,69),(37,70),(37,92),(38,71),(38,72),(38,92),(39,69),(39,71),(39,93),(40,70),(40,72),(40,93),(41,73),(41,74),(41,92),(42,75),(42,76),(42,92),(43,73),(43,75),(43,93),(44,74),(44,76),(44,93),(45,69),(45,73),(45,94),(46,70),(46,74),(46,94),(47,71),(47,75),(47,94),(48,72),(48,76),(48,94),(49,77),(49,78),(49,92),(50,79),(50,80),(50,92),(51,77),(51,79),(51,93),(52,78),(52,80),(52,93),(53,81),(53,82),(53,92),(54,83),(54,84),(54,92),(55,81),(55,83),(55,93),(56,82),(56,84),(56,93),(57,77),(57,81),(57,94),(58,78),(58,82),(58,94),(59,79),(59,83),(59,94),(60,80),(60,84),(60,94),(61,69),(61,77),(61,91),(62,70),(62,78),(62,91),(63,71),(63,79),(63,91),(64,72),(64,80),(64,91),(65,73),(65,81),(65,91),(66,74),(66,82),(66,91),(67,75),(67,83),(67,91),(68,76),(68,84),(68,91),(69,95),(70,95),(71,95),(72,95),(73,95),(74,95),(75,95),(76,95),(77,95),(78,95),(79,95),(80,95),(81,95),(82,95),(83,95),(84,95),(85,91),(85,94),(86,91),(86,92),(87,91),(87,93),(88,92),(88,94),(89,93),(89,94),(90,92),(90,93),(91,95),(92,95),(93,95),(94,95)],96)
 => ? = 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,5),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
([(0,1),(0,4),(0,5),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,3),(0,4),(0,5),(1,2),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 1
Description
The size of the image of the pop stack sorting operator. The pop stack sorting operator is defined by Pop↓L(x)=x∧⋀{y∈L∣y⋖. This statistic returns the size of Pop_L^\downarrow(L)\}.
Matching statistic: St001846
(load all 8 compositions to match this statistic)
Mapping
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001846: Lattices ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 50%
Values
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(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
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 0 = 1 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(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
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(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
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,15),(1,20),(1,21),(2,9),(2,10),(2,14),(2,18),(2,19),(3,8),(3,13),(3,17),(3,19),(3,21),(4,8),(4,12),(4,16),(4,18),(4,20),(5,7),(5,14),(5,15),(5,16),(5,17),(6,7),(6,10),(6,11),(6,12),(6,13),(7,31),(7,32),(8,30),(8,32),(9,30),(9,31),(10,22),(10,23),(10,31),(11,24),(11,25),(11,31),(12,22),(12,24),(12,32),(13,23),(13,25),(13,32),(14,26),(14,27),(14,31),(15,28),(15,29),(15,31),(16,26),(16,28),(16,32),(17,27),(17,29),(17,32),(18,22),(18,26),(18,30),(19,23),(19,27),(19,30),(20,24),(20,28),(20,30),(21,25),(21,29),(21,30),(22,33),(23,33),(24,33),(25,33),(26,33),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,15),(2,7),(2,8),(2,11),(2,14),(3,6),(3,8),(3,10),(3,13),(4,6),(4,7),(4,9),(4,12),(5,12),(5,13),(5,14),(5,15),(6,18),(6,22),(7,16),(7,22),(8,17),(8,22),(9,19),(9,22),(10,20),(10,22),(11,21),(11,22),(12,16),(12,18),(12,19),(13,17),(13,18),(13,20),(14,16),(14,17),(14,21),(15,19),(15,20),(15,21),(16,23),(17,23),(18,23),(19,23),(20,23),(21,23),(22,23)],24)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],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),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(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),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
 => ? = 1 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(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
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,12),(1,15),(1,28),(1,31),(1,34),(2,11),(2,14),(2,28),(2,30),(2,33),(3,10),(3,13),(3,28),(3,29),(3,32),(4,10),(4,16),(4,19),(4,21),(4,30),(4,31),(5,11),(5,17),(5,20),(5,22),(5,29),(5,31),(6,12),(6,18),(6,23),(6,24),(6,29),(6,30),(7,13),(7,16),(7,20),(7,23),(7,33),(7,34),(8,14),(8,17),(8,19),(8,24),(8,32),(8,34),(9,15),(9,18),(9,21),(9,22),(9,32),(9,33),(10,25),(10,35),(10,45),(11,26),(11,36),(11,45),(12,27),(12,37),(12,45),(13,25),(13,38),(13,44),(14,26),(14,39),(14,44),(15,27),(15,40),(15,44),(16,25),(16,42),(16,43),(17,26),(17,41),(17,43),(18,27),(18,41),(18,42),(19,35),(19,39),(19,43),(20,36),(20,38),(20,43),(21,35),(21,40),(21,42),(22,36),(22,40),(22,41),(23,37),(23,38),(23,42),(24,37),(24,39),(24,41),(25,46),(26,46),(27,46),(28,44),(28,45),(29,38),(29,41),(29,45),(30,39),(30,42),(30,45),(31,40),(31,43),(31,45),(32,35),(32,41),(32,44),(33,36),(33,42),(33,44),(34,37),(34,43),(34,44),(35,46),(36,46),(37,46),(38,46),(39,46),(40,46),(41,46),(42,46),(43,46),(44,46),(45,46)],47)
 => ? = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(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),(1,14),(1,18),(1,22),(1,28),(1,30),(1,36),(1,37),(1,66),(2,13),(2,17),(2,21),(2,27),(2,29),(2,34),(2,35),(2,66),(3,12),(3,20),(3,24),(3,26),(3,32),(3,35),(3,37),(3,67),(4,11),(4,19),(4,23),(4,25),(4,31),(4,34),(4,36),(4,67),(5,16),(5,19),(5,20),(5,27),(5,28),(5,39),(5,40),(6,15),(6,17),(6,18),(6,25),(6,26),(6,38),(6,40),(7,29),(7,30),(7,31),(7,32),(7,33),(7,40),(7,41),(8,21),(8,22),(8,23),(8,24),(8,33),(8,38),(8,39),(9,11),(9,12),(9,15),(9,39),(9,41),(9,66),(10,13),(10,14),(10,16),(10,38),(10,41),(10,67),(11,42),(11,74),(11,80),(11,94),(12,43),(12,75),(12,81),(12,94),(13,44),(13,76),(13,78),(13,95),(14,45),(14,77),(14,79),(14,95),(15,42),(15,43),(15,72),(15,98),(16,44),(16,45),(16,73),(16,98),(17,46),(17,47),(17,72),(17,78),(17,82),(18,48),(18,49),(18,72),(18,79),(18,83),(19,50),(19,52),(19,73),(19,80),(19,84),(20,51),(20,53),(20,73),(20,81),(20,85),(21,54),(21,55),(21,64),(21,78),(21,97),(22,56),(22,57),(22,65),(22,79),(22,97),(23,54),(23,56),(23,62),(23,80),(23,96),(24,55),(24,57),(24,63),(24,81),(24,96),(25,42),(25,46),(25,48),(25,84),(25,96),(26,43),(26,47),(26,49),(26,85),(26,96),(27,44),(27,50),(27,51),(27,82),(27,97),(28,45),(28,52),(28,53),(28,83),(28,97),(29,58),(29,59),(29,64),(29,82),(29,95),(30,60),(30,61),(30,65),(30,83),(30,95),(31,58),(31,60),(31,62),(31,84),(31,94),(32,59),(32,61),(32,63),(32,85),(32,94),(33,62),(33,63),(33,64),(33,65),(33,98),(34,46),(34,50),(34,54),(34,58),(34,74),(34,76),(35,47),(35,51),(35,55),(35,59),(35,75),(35,76),(36,48),(36,52),(36,56),(36,60),(36,74),(36,77),(37,49),(37,53),(37,57),(37,61),(37,75),(37,77),(38,78),(38,79),(38,96),(38,98),(39,80),(39,81),(39,97),(39,98),(40,82),(40,83),(40,84),(40,85),(40,98),(41,94),(41,95),(41,98),(42,90),(42,104),(43,91),(43,104),(44,92),(44,105),(45,93),(45,105),(46,86),(46,90),(46,99),(47,87),(47,91),(47,99),(48,88),(48,90),(48,100),(49,89),(49,91),(49,100),(50,86),(50,92),(50,101),(51,87),(51,92),(51,102),(52,88),(52,93),(52,101),(53,89),(53,93),(53,102),(54,68),(54,99),(54,101),(55,69),(55,99),(55,102),(56,70),(56,100),(56,101),(57,71),(57,100),(57,102),(58,68),(58,86),(58,103),(59,69),(59,87),(59,103),(60,70),(60,88),(60,103),(61,71),(61,89),(61,103),(62,68),(62,70),(62,104),(63,69),(63,71),(63,104),(64,68),(64,69),(64,105),(65,70),(65,71),(65,105),(66,72),(66,74),(66,75),(66,95),(66,97),(67,73),(67,76),(67,77),(67,94),(67,96),(68,106),(69,106),(70,106),(71,106),(72,90),(72,91),(72,105),(73,92),(73,93),(73,104),(74,90),(74,101),(74,103),(75,91),(75,102),(75,103),(76,92),(76,99),(76,103),(77,93),(77,100),(77,103),(78,99),(78,105),(79,100),(79,105),(80,101),(80,104),(81,102),(81,104),(82,86),(82,87),(82,105),(83,88),(83,89),(83,105),(84,86),(84,88),(84,104),(85,87),(85,89),(85,104),(86,106),(87,106),(88,106),(89,106),(90,106),(91,106),(92,106),(93,106),(94,103),(94,104),(95,103),(95,105),(96,99),(96,100),(96,104),(97,101),(97,102),(97,105),(98,104),(98,105),(99,106),(100,106),(101,106),(102,106),(103,106),(104,106),(105,106)],107)
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(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
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(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
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(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
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(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)
 => ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(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),(0,10),(0,11),(1,15),(1,21),(1,29),(1,30),(1,35),(1,36),(1,44),(1,45),(1,93),(2,14),(2,20),(2,26),(2,28),(2,32),(2,34),(2,43),(2,45),(2,92),(3,13),(3,19),(3,25),(3,27),(3,31),(3,33),(3,43),(3,44),(3,91),(4,16),(4,19),(4,28),(4,29),(4,37),(4,39),(4,46),(4,48),(4,90),(5,17),(5,20),(5,27),(5,30),(5,38),(5,40),(5,47),(5,48),(5,89),(6,18),(6,21),(6,25),(6,26),(6,41),(6,42),(6,46),(6,47),(6,88),(7,22),(7,23),(7,33),(7,34),(7,37),(7,38),(7,88),(7,93),(8,22),(8,24),(8,31),(8,35),(8,39),(8,41),(8,89),(8,92),(9,23),(9,24),(9,32),(9,36),(9,40),(9,42),(9,90),(9,91),(10,12),(10,16),(10,17),(10,18),(10,91),(10,92),(10,93),(11,12),(11,13),(11,14),(11,15),(11,88),(11,89),(11,90),(12,120),(12,121),(12,122),(13,52),(13,53),(13,99),(13,101),(13,120),(14,52),(14,54),(14,100),(14,102),(14,121),(15,53),(15,54),(15,103),(15,104),(15,122),(16,55),(16,57),(16,108),(16,109),(16,120),(17,56),(17,57),(17,107),(17,110),(17,121),(18,55),(18,56),(18,105),(18,106),(18,122),(19,64),(19,66),(19,117),(19,118),(19,120),(20,65),(20,67),(20,117),(20,119),(20,121),(21,68),(21,69),(21,118),(21,119),(21,122),(22,51),(22,70),(22,73),(22,124),(22,128),(23,51),(23,71),(23,74),(23,123),(23,127),(24,51),(24,72),(24,75),(24,125),(24,126),(25,58),(25,61),(25,76),(25,101),(25,105),(25,118),(26,58),(26,62),(26,77),(26,102),(26,106),(26,119),(27,59),(27,61),(27,78),(27,99),(27,107),(27,117),(28,60),(28,62),(28,79),(28,100),(28,108),(28,117),(29,60),(29,63),(29,80),(29,104),(29,109),(29,118),(30,59),(30,63),(30,81),(30,103),(30,110),(30,119),(31,66),(31,70),(31,76),(31,83),(31,99),(31,126),(32,67),(32,71),(32,77),(32,84),(32,100),(32,126),(33,64),(33,70),(33,78),(33,82),(33,101),(33,127),(34,65),(34,71),(34,79),(34,82),(34,102),(34,128),(35,69),(35,72),(35,80),(35,83),(35,103),(35,128),(36,68),(36,72),(36,81),(36,84),(36,104),(36,127),(37,64),(37,73),(37,79),(37,87),(37,109),(37,123),(38,65),(38,74),(38,78),(38,87),(38,110),(38,124),(39,66),(39,73),(39,80),(39,85),(39,108),(39,125),(40,67),(40,74),(40,81),(40,86),(40,107),(40,125),(41,69),(41,75),(41,76),(41,85),(41,106),(41,124),(42,68),(42,75),(42,77),(42,86),(42,105),(42,123),(43,49),(43,52),(43,58),(43,82),(43,117),(43,126),(44,49),(44,53),(44,59),(44,83),(44,118),(44,127),(45,49),(45,54),(45,60),(45,84),(45,119),(45,128),(46,50),(46,55),(46,62),(46,85),(46,118),(46,123),(47,50),(47,56),(47,61),(47,86),(47,119),(47,124),(48,50),(48,57),(48,63),(48,87),(48,117),(48,125),(49,97),(49,139),(49,140),(50,98),(50,138),(50,140),(51,138),(51,139),(52,97),(52,113),(52,143),(53,97),(53,111),(53,141),(54,97),(54,112),(54,142),(55,98),(55,115),(55,141),(56,98),(56,114),(56,142),(57,98),(57,116),(57,143),(58,113),(58,137),(58,140),(59,111),(59,135),(59,140),(60,112),(60,136),(60,140),(61,114),(61,132),(61,140),(62,115),(62,133),(62,140),(63,116),(63,134),(63,140),(64,94),(64,129),(64,141),(65,95),(65,129),(65,142),(66,94),(66,130),(66,143),(67,95),(67,131),(67,143),(68,96),(68,131),(68,141),(69,96),(69,130),(69,142),(70,94),(70,132),(70,139),(71,95),(71,133),(71,139),(72,96),(72,134),(72,139),(73,94),(73,136),(73,138),(74,95),(74,135),(74,138),(75,96),(75,137),(75,138),(76,130),(76,132),(76,137),(77,131),(77,133),(77,137),(78,129),(78,132),(78,135),(79,129),(79,133),(79,136),(80,130),(80,134),(80,136),(81,131),(81,134),(81,135),(82,113),(82,129),(82,139),(83,111),(83,130),(83,139),(84,112),(84,131),(84,139),(85,115),(85,130),(85,138),(86,114),(86,131),(86,138),(87,116),(87,129),(87,138),(88,101),(88,102),(88,122),(88,123),(88,124),(89,99),(89,103),(89,121),(89,124),(89,125),(90,100),(90,104),(90,120),(90,123),(90,125),(91,105),(91,107),(91,120),(91,126),(91,127),(92,106),(92,108),(92,121),(92,126),(92,128),(93,109),(93,110),(93,122),(93,127),(93,128),(94,144),(95,144),(96,144),(97,144),(98,144),(99,111),(99,132),(99,143),(100,112),(100,133),(100,143),(101,113),(101,132),(101,141),(102,113),(102,133),(102,142),(103,111),(103,134),(103,142),(104,112),(104,134),(104,141),(105,114),(105,137),(105,141),(106,115),(106,137),(106,142),(107,114),(107,135),(107,143),(108,115),(108,136),(108,143),(109,116),(109,136),(109,141),(110,116),(110,135),(110,142),(111,144),(112,144),(113,144),(114,144),(115,144),(116,144),(117,129),(117,140),(117,143),(118,130),(118,140),(118,141),(119,131),(119,140),(119,142),(120,141),(120,143),(121,142),(121,143),(122,141),(122,142),(123,133),(123,138),(123,141),(124,132),(124,138),(124,142),(125,134),(125,138),(125,143),(126,137),(126,139),(126,143),(127,135),(127,139),(127,141),(128,136),(128,139),(128,142),(129,144),(130,144),(131,144),(132,144),(133,144),(134,144),(135,144),(136,144),(137,144),(138,144),(139,144),(140,144),(141,144),(142,144),(143,144)],145)
 => ? = 1 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(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),(0,10),(1,13),(1,18),(1,28),(1,30),(1,32),(1,35),(1,36),(1,72),(2,12),(2,17),(2,27),(2,29),(2,32),(2,33),(2,34),(2,71),(3,17),(3,20),(3,21),(3,30),(3,31),(3,37),(3,38),(3,73),(4,18),(4,19),(4,22),(4,29),(4,31),(4,39),(4,40),(4,74),(5,16),(5,24),(5,26),(5,34),(5,36),(5,38),(5,40),(5,75),(6,15),(6,23),(6,25),(6,33),(6,35),(6,37),(6,39),(6,75),(7,11),(7,15),(7,16),(7,19),(7,20),(7,71),(7,72),(8,14),(8,22),(8,23),(8,24),(8,27),(8,72),(8,73),(9,14),(9,21),(9,25),(9,26),(9,28),(9,71),(9,74),(10,11),(10,12),(10,13),(10,73),(10,74),(10,75),(11,84),(11,99),(11,100),(12,41),(12,82),(12,85),(12,99),(13,41),(13,83),(13,86),(13,100),(14,58),(14,59),(14,101),(14,102),(15,54),(15,56),(15,84),(15,87),(15,89),(16,55),(16,57),(16,84),(16,88),(16,90),(17,44),(17,45),(17,85),(17,91),(17,98),(18,46),(18,47),(18,86),(18,92),(18,98),(19,54),(19,55),(19,68),(19,92),(19,99),(20,56),(20,57),(20,68),(20,91),(20,100),(21,64),(21,65),(21,70),(21,91),(21,102),(22,66),(22,67),(22,69),(22,92),(22,102),(23,58),(23,60),(23,66),(23,89),(23,103),(24,59),(24,61),(24,67),(24,90),(24,103),(25,58),(25,62),(25,64),(25,87),(25,104),(26,59),(26,63),(26,65),(26,88),(26,104),(27,60),(27,61),(27,69),(27,85),(27,101),(28,62),(28,63),(28,70),(28,86),(28,101),(29,50),(29,51),(29,69),(29,98),(29,99),(30,52),(30,53),(30,70),(30,98),(30,100),(31,48),(31,49),(31,68),(31,98),(31,102),(32,41),(32,42),(32,43),(32,98),(32,101),(33,42),(33,44),(33,50),(33,60),(33,82),(33,87),(34,43),(34,45),(34,51),(34,61),(34,82),(34,88),(35,42),(35,46),(35,52),(35,62),(35,83),(35,89),(36,43),(36,47),(36,53),(36,63),(36,83),(36,90),(37,44),(37,48),(37,52),(37,56),(37,64),(37,103),(38,45),(38,49),(38,53),(38,57),(38,65),(38,103),(39,46),(39,48),(39,50),(39,54),(39,66),(39,104),(40,47),(40,49),(40,51),(40,55),(40,67),(40,104),(41,97),(41,114),(42,97),(42,105),(42,107),(43,97),(43,106),(43,108),(44,93),(44,105),(44,109),(45,94),(45,106),(45,109),(46,95),(46,105),(46,110),(47,96),(47,106),(47,110),(48,80),(48,105),(48,113),(49,81),(49,106),(49,113),(50,76),(50,105),(50,111),(51,77),(51,106),(51,111),(52,78),(52,105),(52,112),(53,79),(53,106),(53,112),(54,80),(54,95),(54,111),(55,81),(55,96),(55,111),(56,80),(56,93),(56,112),(57,81),(57,94),(57,112),(58,107),(58,113),(59,108),(59,113),(60,76),(60,107),(60,109),(61,77),(61,108),(61,109),(62,78),(62,107),(62,110),(63,79),(63,108),(63,110),(64,78),(64,93),(64,113),(65,79),(65,94),(65,113),(66,76),(66,95),(66,113),(67,77),(67,96),(67,113),(68,80),(68,81),(68,114),(69,76),(69,77),(69,114),(70,78),(70,79),(70,114),(71,87),(71,88),(71,91),(71,99),(71,101),(72,89),(72,90),(72,92),(72,100),(72,101),(73,85),(73,100),(73,102),(73,103),(74,86),(74,99),(74,102),(74,104),(75,82),(75,83),(75,84),(75,103),(75,104),(76,115),(77,115),(78,115),(79,115),(80,115),(81,115),(82,97),(82,109),(82,111),(83,97),(83,110),(83,112),(84,111),(84,112),(85,109),(85,114),(86,110),(86,114),(87,93),(87,107),(87,111),(88,94),(88,108),(88,111),(89,95),(89,107),(89,112),(90,96),(90,108),(90,112),(91,93),(91,94),(91,114),(92,95),(92,96),(92,114),(93,115),(94,115),(95,115),(96,115),(97,115),(98,105),(98,106),(98,114),(99,111),(99,114),(100,112),(100,114),(101,107),(101,108),(101,114),(102,113),(102,114),(103,109),(103,112),(103,113),(104,110),(104,111),(104,113),(105,115),(106,115),(107,115),(108,115),(109,115),(110,115),(111,115),(112,115),(113,115),(114,115)],116)
 => ? = 1 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,16),(1,17),(1,18),(1,34),(1,35),(1,40),(1,41),(1,42),(1,43),(2,14),(2,15),(2,18),(2,32),(2,33),(2,36),(2,37),(2,38),(2,39),(3,12),(3,21),(3,23),(3,27),(3,31),(3,37),(3,41),(3,79),(4,12),(4,20),(4,22),(4,26),(4,30),(4,36),(4,40),(4,78),(5,13),(5,20),(5,24),(5,28),(5,31),(5,38),(5,42),(5,76),(6,13),(6,21),(6,25),(6,29),(6,30),(6,39),(6,43),(6,77),(7,19),(7,28),(7,29),(7,33),(7,35),(7,78),(7,79),(8,19),(8,26),(8,27),(8,32),(8,34),(8,76),(8,77),(9,11),(9,14),(9,16),(9,22),(9,25),(9,76),(9,79),(10,11),(10,15),(10,17),(10,23),(10,24),(10,77),(10,78),(11,105),(11,106),(11,107),(12,44),(12,106),(12,108),(12,111),(13,45),(13,105),(13,108),(13,112),(14,60),(14,63),(14,89),(14,92),(14,107),(15,61),(15,62),(15,90),(15,91),(15,107),(16,64),(16,67),(16,93),(16,96),(16,107),(17,65),(17,66),(17,94),(17,95),(17,107),(18,46),(18,47),(18,107),(18,111),(18,112),(19,48),(19,49),(19,109),(19,110),(20,68),(20,70),(20,85),(20,87),(20,108),(21,69),(21,71),(21,86),(21,88),(21,108),(22,50),(22,60),(22,64),(22,85),(22,106),(23,51),(23,61),(23,65),(23,86),(23,106),(24,51),(24,62),(24,66),(24,87),(24,105),(25,50),(25,63),(25,67),(25,88),(25,105),(26,44),(26,52),(26,56),(26,85),(26,109),(27,44),(27,53),(27,57),(27,86),(27,110),(28,45),(28,54),(28,58),(28,87),(28,110),(29,45),(29,55),(29,59),(29,88),(29,109),(30,50),(30,72),(30,74),(30,108),(30,109),(31,51),(31,73),(31,75),(31,108),(31,110),(32,46),(32,48),(32,52),(32,53),(32,89),(32,90),(33,47),(33,48),(33,54),(33,55),(33,91),(33,92),(34,46),(34,49),(34,56),(34,57),(34,93),(34,94),(35,47),(35,49),(35,58),(35,59),(35,95),(35,96),(36,52),(36,60),(36,68),(36,72),(36,91),(36,111),(37,53),(37,61),(37,69),(37,73),(37,92),(37,111),(38,54),(38,62),(38,68),(38,73),(38,89),(38,112),(39,55),(39,63),(39,69),(39,72),(39,90),(39,112),(40,56),(40,64),(40,70),(40,74),(40,95),(40,111),(41,57),(41,65),(41,71),(41,75),(41,96),(41,111),(42,58),(42,66),(42,70),(42,75),(42,93),(42,112),(43,59),(43,67),(43,71),(43,74),(43,94),(43,112),(44,113),(44,122),(45,114),(45,122),(46,84),(46,113),(46,120),(47,84),(47,114),(47,121),(48,84),(48,115),(48,116),(49,84),(49,117),(49,118),(50,80),(50,82),(50,122),(51,81),(51,83),(51,122),(52,97),(52,113),(52,115),(53,98),(53,113),(53,116),(54,99),(54,114),(54,116),(55,100),(55,114),(55,115),(56,101),(56,113),(56,117),(57,102),(57,113),(57,118),(58,103),(58,114),(58,118),(59,104),(59,114),(59,117),(60,80),(60,97),(60,121),(61,81),(61,98),(61,121),(62,81),(62,99),(62,120),(63,80),(63,100),(63,120),(64,82),(64,101),(64,121),(65,83),(65,102),(65,121),(66,83),(66,103),(66,120),(67,82),(67,104),(67,120),(68,97),(68,99),(68,119),(69,98),(69,100),(69,119),(70,101),(70,103),(70,119),(71,102),(71,104),(71,119),(72,80),(72,115),(72,119),(73,81),(73,116),(73,119),(74,82),(74,117),(74,119),(75,83),(75,118),(75,119),(76,85),(76,89),(76,93),(76,105),(76,110),(77,86),(77,90),(77,94),(77,105),(77,109),(78,87),(78,91),(78,95),(78,106),(78,109),(79,88),(79,92),(79,96),(79,106),(79,110),(80,123),(81,123),(82,123),(83,123),(84,123),(85,97),(85,101),(85,122),(86,98),(86,102),(86,122),(87,99),(87,103),(87,122),(88,100),(88,104),(88,122),(89,97),(89,116),(89,120),(90,98),(90,115),(90,120),(91,99),(91,115),(91,121),(92,100),(92,116),(92,121),(93,101),(93,118),(93,120),(94,102),(94,117),(94,120),(95,103),(95,117),(95,121),(96,104),(96,118),(96,121),(97,123),(98,123),(99,123),(100,123),(101,123),(102,123),(103,123),(104,123),(105,120),(105,122),(106,121),(106,122),(107,120),(107,121),(108,119),(108,122),(109,115),(109,117),(109,122),(110,116),(110,118),(110,122),(111,113),(111,119),(111,121),(112,114),(112,119),(112,120),(113,123),(114,123),(115,123),(116,123),(117,123),(118,123),(119,123),(120,123),(121,123),(122,123)],124)
 => ? = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(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),(1,21),(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
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(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)
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(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),(1,16),(1,20),(1,24),(1,30),(1,32),(2,15),(2,19),(2,23),(2,30),(2,31),(3,17),(3,21),(3,23),(3,29),(3,32),(4,18),(4,22),(4,24),(4,29),(4,31),(5,10),(5,13),(5,14),(5,17),(5,18),(5,30),(6,10),(6,11),(6,12),(6,15),(6,16),(6,29),(7,9),(7,11),(7,13),(7,19),(7,22),(7,32),(8,9),(8,12),(8,14),(8,20),(8,21),(8,31),(9,35),(9,36),(9,41),(10,33),(10,34),(10,41),(11,25),(11,38),(11,41),(12,26),(12,37),(12,41),(13,28),(13,39),(13,41),(14,27),(14,40),(14,41),(15,25),(15,33),(15,37),(16,26),(16,33),(16,38),(17,27),(17,34),(17,39),(18,28),(18,34),(18,40),(19,25),(19,35),(19,39),(20,26),(20,36),(20,40),(21,27),(21,36),(21,37),(22,28),(22,35),(22,38),(23,37),(23,39),(24,38),(24,40),(25,42),(26,42),(27,42),(28,42),(29,34),(29,37),(29,38),(30,33),(30,39),(30,40),(31,35),(31,37),(31,40),(32,36),(32,38),(32,39),(33,42),(34,42),(35,42),(36,42),(37,42),(38,42),(39,42),(40,42),(41,42)],43)
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(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),(0,8),(0,9),(0,10),(1,20),(1,29),(1,30),(1,34),(1,35),(1,39),(1,40),(1,75),(2,19),(2,24),(2,28),(2,31),(2,33),(2,37),(2,40),(2,72),(3,18),(3,23),(3,27),(3,31),(3,32),(3,36),(3,39),(3,71),(4,17),(4,21),(4,26),(4,32),(4,34),(4,37),(4,38),(4,73),(5,16),(5,22),(5,25),(5,33),(5,35),(5,36),(5,38),(5,74),(6,12),(6,14),(6,16),(6,21),(6,23),(6,72),(6,75),(7,11),(7,15),(7,17),(7,22),(7,24),(7,71),(7,75),(8,11),(8,13),(8,18),(8,25),(8,29),(8,72),(8,73),(9,12),(9,13),(9,19),(9,26),(9,30),(9,71),(9,74),(10,14),(10,15),(10,20),(10,27),(10,28),(10,73),(10,74),(11,61),(11,81),(11,83),(11,105),(12,62),(12,82),(12,84),(12,104),(13,65),(13,81),(13,82),(13,101),(14,63),(14,84),(14,85),(14,103),(15,64),(15,83),(15,85),(15,102),(16,52),(16,55),(16,84),(16,87),(16,92),(17,51),(17,56),(17,83),(17,86),(17,93),(18,53),(18,57),(18,81),(18,88),(18,90),(19,54),(19,58),(19,82),(19,89),(19,91),(20,59),(20,60),(20,85),(20,94),(20,95),(21,52),(21,62),(21,66),(21,93),(21,103),(22,51),(22,61),(22,67),(22,92),(22,102),(23,55),(23,63),(23,66),(23,88),(23,104),(24,56),(24,64),(24,67),(24,89),(24,105),(25,53),(25,61),(25,69),(25,87),(25,101),(26,54),(26,62),(26,70),(26,86),(26,101),(27,59),(27,63),(27,68),(27,90),(27,102),(28,60),(28,64),(28,68),(28,91),(28,103),(29,57),(29,65),(29,69),(29,94),(29,105),(30,58),(30,65),(30,70),(30,95),(30,104),(31,41),(31,42),(31,48),(31,68),(31,88),(31,89),(32,41),(32,43),(32,46),(32,66),(32,86),(32,90),(33,42),(33,44),(33,47),(33,67),(33,87),(33,91),(34,43),(34,45),(34,50),(34,70),(34,93),(34,94),(35,44),(35,45),(35,49),(35,69),(35,92),(35,95),(36,42),(36,46),(36,49),(36,53),(36,55),(36,102),(37,41),(37,47),(37,50),(37,54),(37,56),(37,103),(38,45),(38,46),(38,47),(38,51),(38,52),(38,101),(39,43),(39,48),(39,49),(39,57),(39,59),(39,104),(40,44),(40,48),(40,50),(40,58),(40,60),(40,105),(41,97),(41,106),(41,111),(42,96),(42,107),(42,111),(43,99),(43,108),(43,111),(44,100),(44,109),(44,111),(45,98),(45,110),(45,111),(46,76),(46,111),(46,112),(47,77),(47,111),(47,113),(48,80),(48,111),(48,114),(49,78),(49,111),(49,115),(50,79),(50,111),(50,116),(51,77),(51,98),(51,112),(52,76),(52,98),(52,113),(53,78),(53,96),(53,112),(54,79),(54,97),(54,113),(55,76),(55,96),(55,115),(56,77),(56,97),(56,116),(57,78),(57,99),(57,114),(58,79),(58,100),(58,114),(59,80),(59,99),(59,115),(60,80),(60,100),(60,116),(61,109),(61,112),(62,108),(62,113),(63,106),(63,115),(64,107),(64,116),(65,110),(65,114),(66,76),(66,106),(66,108),(67,77),(67,107),(67,109),(68,80),(68,106),(68,107),(69,78),(69,109),(69,110),(70,79),(70,108),(70,110),(71,81),(71,86),(71,89),(71,102),(71,104),(72,82),(72,87),(72,88),(72,103),(72,105),(73,83),(73,90),(73,94),(73,101),(73,103),(74,84),(74,91),(74,95),(74,101),(74,102),(75,85),(75,92),(75,93),(75,104),(75,105),(76,117),(77,117),(78,117),(79,117),(80,117),(81,112),(81,114),(82,113),(82,114),(83,112),(83,116),(84,113),(84,115),(85,115),(85,116),(86,97),(86,108),(86,112),(87,96),(87,109),(87,113),(88,96),(88,106),(88,114),(89,97),(89,107),(89,114),(90,99),(90,106),(90,112),(91,100),(91,107),(91,113),(92,98),(92,109),(92,115),(93,98),(93,108),(93,116),(94,99),(94,110),(94,116),(95,100),(95,110),(95,115),(96,117),(97,117),(98,117),(99,117),(100,117),(101,110),(101,112),(101,113),(102,107),(102,112),(102,115),(103,106),(103,113),(103,116),(104,108),(104,114),(104,115),(105,109),(105,114),(105,116),(106,117),(107,117),(108,117),(109,117),(110,117),(111,117),(112,117),(113,117),(114,117),(115,117),(116,117)],118)
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(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),(1,15),(1,16),(1,17),(1,18),(1,54),(1,55),(2,10),(2,13),(2,14),(2,20),(2,55),(2,57),(3,10),(3,11),(3,12),(3,19),(3,54),(3,56),(4,12),(4,16),(4,23),(4,24),(4,26),(4,30),(4,57),(5,11),(5,15),(5,21),(5,22),(5,25),(5,29),(5,57),(6,14),(6,18),(6,22),(6,24),(6,28),(6,32),(6,56),(7,13),(7,17),(7,21),(7,23),(7,27),(7,31),(7,56),(8,19),(8,27),(8,28),(8,29),(8,30),(8,33),(8,55),(9,20),(9,25),(9,26),(9,31),(9,32),(9,33),(9,54),(10,58),(10,59),(10,78),(11,42),(11,58),(11,60),(11,64),(12,43),(12,58),(12,61),(12,65),(13,44),(13,59),(13,62),(13,66),(14,45),(14,59),(14,63),(14,67),(15,38),(15,39),(15,60),(15,80),(16,40),(16,41),(16,61),(16,80),(17,38),(17,40),(17,62),(17,79),(18,39),(18,41),(18,63),(18,79),(19,42),(19,43),(19,68),(19,78),(20,44),(20,45),(20,69),(20,78),(21,38),(21,46),(21,50),(21,64),(21,66),(22,39),(22,47),(22,51),(22,64),(22,67),(23,40),(23,48),(23,52),(23,65),(23,66),(24,41),(24,49),(24,53),(24,65),(24,67),(25,34),(25,50),(25,51),(25,60),(25,69),(26,35),(26,52),(26,53),(26,61),(26,69),(27,36),(27,46),(27,48),(27,62),(27,68),(28,37),(28,47),(28,49),(28,63),(28,68),(29,34),(29,42),(29,46),(29,47),(29,80),(30,35),(30,43),(30,48),(30,49),(30,80),(31,36),(31,44),(31,50),(31,52),(31,79),(32,37),(32,45),(32,51),(32,53),(32,79),(33,34),(33,35),(33,36),(33,37),(33,78),(34,70),(34,71),(34,86),(35,72),(35,73),(35,86),(36,70),(36,72),(36,87),(37,71),(37,73),(37,87),(38,82),(38,84),(39,82),(39,85),(40,83),(40,84),(41,83),(41,85),(42,74),(42,86),(43,75),(43,86),(44,76),(44,87),(45,77),(45,87),(46,70),(46,74),(46,84),(47,71),(47,74),(47,85),(48,72),(48,75),(48,84),(49,73),(49,75),(49,85),(50,70),(50,76),(50,82),(51,71),(51,77),(51,82),(52,72),(52,76),(52,83),(53,73),(53,77),(53,83),(54,60),(54,61),(54,78),(54,79),(55,62),(55,63),(55,78),(55,80),(56,59),(56,64),(56,65),(56,68),(56,79),(57,58),(57,66),(57,67),(57,69),(57,80),(58,81),(58,86),(59,81),(59,87),(60,82),(60,86),(61,83),(61,86),(62,84),(62,87),(63,85),(63,87),(64,74),(64,81),(64,82),(65,75),(65,81),(65,83),(66,76),(66,81),(66,84),(67,77),(67,81),(67,85),(68,74),(68,75),(68,87),(69,76),(69,77),(69,86),(70,88),(71,88),(72,88),(73,88),(74,88),(75,88),(76,88),(77,88),(78,86),(78,87),(79,82),(79,83),(79,87),(80,84),(80,85),(80,86),(81,88),(82,88),(83,88),(84,88),(85,88),(86,88),(87,88)],89)
 => ? = 1 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(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),(0,8),(0,9),(1,17),(1,18),(1,21),(1,22),(1,30),(1,32),(1,35),(1,36),(2,15),(2,16),(2,19),(2,20),(2,30),(2,31),(2,33),(2,34),(3,26),(3,27),(3,28),(3,29),(3,31),(3,32),(3,68),(4,12),(4,23),(4,25),(4,29),(4,34),(4,36),(4,70),(5,11),(5,23),(5,24),(5,28),(5,33),(5,35),(5,69),(6,10),(6,14),(6,19),(6,21),(6,24),(6,27),(6,70),(7,10),(7,13),(7,20),(7,22),(7,25),(7,26),(7,69),(8,11),(8,13),(8,15),(8,17),(8,68),(8,70),(9,12),(9,14),(9,16),(9,18),(9,68),(9,69),(10,39),(10,77),(10,78),(10,92),(11,62),(11,64),(11,79),(11,93),(12,63),(12,65),(12,80),(12,94),(13,58),(13,60),(13,78),(13,93),(14,59),(14,61),(14,77),(14,94),(15,58),(15,62),(15,66),(15,82),(15,85),(16,59),(16,63),(16,67),(16,81),(16,85),(17,60),(17,64),(17,66),(17,84),(17,86),(18,61),(18,65),(18,67),(18,83),(18,86),(19,49),(19,52),(19,59),(19,82),(19,92),(20,48),(20,53),(20,58),(20,81),(20,92),(21,51),(21,54),(21,61),(21,84),(21,92),(22,50),(22,55),(22,60),(22,83),(22,92),(23,37),(23,40),(23,41),(23,79),(23,80),(24,52),(24,54),(24,56),(24,77),(24,79),(25,53),(25,55),(25,57),(25,78),(25,80),(26,39),(26,48),(26,50),(26,57),(26,93),(27,39),(27,49),(27,51),(27,56),(27,94),(28,37),(28,44),(28,46),(28,56),(28,93),(29,37),(29,45),(29,47),(29,57),(29,94),(30,38),(30,42),(30,43),(30,66),(30,67),(30,92),(31,38),(31,44),(31,45),(31,48),(31,49),(31,85),(32,38),(32,46),(32,47),(32,50),(32,51),(32,86),(33,40),(33,42),(33,44),(33,52),(33,62),(33,81),(34,40),(34,43),(34,45),(34,53),(34,63),(34,82),(35,41),(35,42),(35,46),(35,54),(35,64),(35,83),(36,41),(36,43),(36,47),(36,55),(36,65),(36,84),(37,100),(37,103),(38,87),(38,95),(38,100),(39,95),(39,103),(40,88),(40,89),(40,100),(41,90),(41,91),(41,100),(42,75),(42,100),(42,101),(43,76),(43,100),(43,102),(44,71),(44,96),(44,100),(45,72),(45,97),(45,100),(46,73),(46,98),(46,100),(47,74),(47,99),(47,100),(48,72),(48,95),(48,96),(49,71),(49,95),(49,97),(50,74),(50,95),(50,98),(51,73),(51,95),(51,99),(52,71),(52,88),(52,101),(53,72),(53,89),(53,102),(54,73),(54,90),(54,101),(55,74),(55,91),(55,102),(56,71),(56,73),(56,103),(57,72),(57,74),(57,103),(58,96),(58,102),(59,97),(59,101),(60,98),(60,102),(61,99),(61,101),(62,75),(62,88),(62,96),(63,76),(63,89),(63,97),(64,75),(64,90),(64,98),(65,76),(65,91),(65,99),(66,75),(66,87),(66,102),(67,76),(67,87),(67,101),(68,85),(68,86),(68,93),(68,94),(69,77),(69,80),(69,81),(69,83),(69,93),(70,78),(70,79),(70,82),(70,84),(70,94),(71,104),(72,104),(73,104),(74,104),(75,104),(76,104),(77,101),(77,103),(78,102),(78,103),(79,88),(79,90),(79,103),(80,89),(80,91),(80,103),(81,89),(81,96),(81,101),(82,88),(82,97),(82,102),(83,91),(83,98),(83,101),(84,90),(84,99),(84,102),(85,87),(85,96),(85,97),(86,87),(86,98),(86,99),(87,104),(88,104),(89,104),(90,104),(91,104),(92,95),(92,101),(92,102),(93,96),(93,98),(93,103),(94,97),(94,99),(94,103),(95,104),(96,104),(97,104),(98,104),(99,104),(100,104),(101,104),(102,104),(103,104)],105)
 => ? = 1 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(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),(1,18),(1,19),(1,20),(1,21),(1,34),(1,57),(2,12),(2,13),(2,16),(2,17),(2,34),(2,56),(3,10),(3,11),(3,14),(3,15),(3,34),(3,55),(4,15),(4,17),(4,24),(4,25),(4,28),(4,29),(4,57),(5,14),(5,16),(5,22),(5,23),(5,26),(5,27),(5,57),(6,11),(6,19),(6,23),(6,25),(6,32),(6,33),(6,56),(7,10),(7,18),(7,22),(7,24),(7,30),(7,31),(7,56),(8,13),(8,21),(8,27),(8,29),(8,31),(8,33),(8,55),(9,12),(9,20),(9,26),(9,28),(9,30),(9,32),(9,55),(10,35),(10,37),(10,62),(10,83),(11,36),(11,38),(11,63),(11,83),(12,39),(12,41),(12,64),(12,84),(13,40),(13,42),(13,65),(13,84),(14,35),(14,36),(14,58),(14,82),(15,37),(15,38),(15,59),(15,82),(16,39),(16,40),(16,60),(16,82),(17,41),(17,42),(17,61),(17,82),(18,43),(18,44),(18,66),(18,83),(19,45),(19,46),(19,67),(19,83),(20,43),(20,45),(20,68),(20,84),(21,44),(21,46),(21,69),(21,84),(22,35),(22,47),(22,48),(22,60),(22,66),(23,36),(23,49),(23,50),(23,60),(23,67),(24,37),(24,51),(24,52),(24,61),(24,66),(25,38),(25,53),(25,54),(25,61),(25,67),(26,39),(26,47),(26,49),(26,58),(26,68),(27,40),(27,48),(27,50),(27,58),(27,69),(28,41),(28,51),(28,53),(28,59),(28,68),(29,42),(29,52),(29,54),(29,59),(29,69),(30,43),(30,47),(30,51),(30,62),(30,64),(31,44),(31,48),(31,52),(31,62),(31,65),(32,45),(32,49),(32,53),(32,63),(32,64),(33,46),(33,50),(33,54),(33,63),(33,65),(34,82),(34,83),(34,84),(35,70),(35,85),(36,71),(36,85),(37,72),(37,85),(38,73),(38,85),(39,74),(39,86),(40,75),(40,86),(41,76),(41,86),(42,77),(42,86),(43,78),(43,87),(44,79),(44,87),(45,80),(45,87),(46,81),(46,87),(47,70),(47,74),(47,78),(48,70),(48,75),(48,79),(49,71),(49,74),(49,80),(50,71),(50,75),(50,81),(51,72),(51,76),(51,78),(52,72),(52,77),(52,79),(53,73),(53,76),(53,80),(54,73),(54,77),(54,81),(55,58),(55,59),(55,62),(55,63),(55,84),(56,60),(56,61),(56,64),(56,65),(56,83),(57,66),(57,67),(57,68),(57,69),(57,82),(58,70),(58,71),(58,86),(59,72),(59,73),(59,86),(60,74),(60,75),(60,85),(61,76),(61,77),(61,85),(62,70),(62,72),(62,87),(63,71),(63,73),(63,87),(64,74),(64,76),(64,87),(65,75),(65,77),(65,87),(66,78),(66,79),(66,85),(67,80),(67,81),(67,85),(68,78),(68,80),(68,86),(69,79),(69,81),(69,86),(70,88),(71,88),(72,88),(73,88),(74,88),(75,88),(76,88),(77,88),(78,88),(79,88),(80,88),(81,88),(82,85),(82,86),(83,85),(83,87),(84,86),(84,87),(85,88),(86,88),(87,88)],89)
 => ? = 1 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(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
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
 => ? = 1 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,14),(1,18),(1,23),(1,24),(1,26),(1,32),(2,12),(2,13),(2,17),(2,21),(2,22),(2,25),(2,31),(3,11),(3,16),(3,20),(3,22),(3,24),(3,28),(3,34),(4,11),(4,15),(4,19),(4,21),(4,23),(4,27),(4,33),(5,10),(5,17),(5,18),(5,19),(5,20),(5,30),(5,36),(6,10),(6,13),(6,14),(6,15),(6,16),(6,29),(6,35),(7,9),(7,31),(7,32),(7,33),(7,34),(7,35),(7,36),(8,9),(8,25),(8,26),(8,27),(8,28),(8,29),(8,30),(9,88),(9,89),(9,90),(10,86),(10,87),(10,90),(11,85),(11,87),(11,89),(12,85),(12,86),(12,88),(13,37),(13,49),(13,61),(13,62),(13,86),(14,38),(14,50),(14,63),(14,64),(14,86),(15,39),(15,51),(15,61),(15,63),(15,87),(16,40),(16,52),(16,62),(16,64),(16,87),(17,41),(17,53),(17,65),(17,66),(17,86),(18,42),(18,54),(18,67),(18,68),(18,86),(19,43),(19,55),(19,65),(19,67),(19,87),(20,44),(20,56),(20,66),(20,68),(20,87),(21,45),(21,57),(21,61),(21,65),(21,85),(22,46),(22,58),(22,62),(22,66),(22,85),(23,47),(23,59),(23,63),(23,67),(23,85),(24,48),(24,60),(24,64),(24,68),(24,85),(25,37),(25,41),(25,45),(25,46),(25,88),(26,38),(26,42),(26,47),(26,48),(26,88),(27,39),(27,43),(27,45),(27,47),(27,89),(28,40),(28,44),(28,46),(28,48),(28,89),(29,37),(29,38),(29,39),(29,40),(29,90),(30,41),(30,42),(30,43),(30,44),(30,90),(31,49),(31,53),(31,57),(31,58),(31,88),(32,50),(32,54),(32,59),(32,60),(32,88),(33,51),(33,55),(33,57),(33,59),(33,89),(34,52),(34,56),(34,58),(34,60),(34,89),(35,49),(35,50),(35,51),(35,52),(35,90),(36,53),(36,54),(36,55),(36,56),(36,90),(37,69),(37,70),(37,92),(38,71),(38,72),(38,92),(39,69),(39,71),(39,93),(40,70),(40,72),(40,93),(41,73),(41,74),(41,92),(42,75),(42,76),(42,92),(43,73),(43,75),(43,93),(44,74),(44,76),(44,93),(45,69),(45,73),(45,94),(46,70),(46,74),(46,94),(47,71),(47,75),(47,94),(48,72),(48,76),(48,94),(49,77),(49,78),(49,92),(50,79),(50,80),(50,92),(51,77),(51,79),(51,93),(52,78),(52,80),(52,93),(53,81),(53,82),(53,92),(54,83),(54,84),(54,92),(55,81),(55,83),(55,93),(56,82),(56,84),(56,93),(57,77),(57,81),(57,94),(58,78),(58,82),(58,94),(59,79),(59,83),(59,94),(60,80),(60,84),(60,94),(61,69),(61,77),(61,91),(62,70),(62,78),(62,91),(63,71),(63,79),(63,91),(64,72),(64,80),(64,91),(65,73),(65,81),(65,91),(66,74),(66,82),(66,91),(67,75),(67,83),(67,91),(68,76),(68,84),(68,91),(69,95),(70,95),(71,95),(72,95),(73,95),(74,95),(75,95),(76,95),(77,95),(78,95),(79,95),(80,95),(81,95),(82,95),(83,95),(84,95),(85,91),(85,94),(86,91),(86,92),(87,91),(87,93),(88,92),(88,94),(89,93),(89,94),(90,92),(90,93),(91,95),(92,95),(93,95),(94,95)],96)
 => ? = 1 - 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,5),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(0,5),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,4),(0,5),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(0,5),(1,2),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([],1)
 => 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: St001330
Mapping
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 50%
Values
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ? = 1 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,1),(0,2),(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),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,1),(0,2),(0,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,5),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,1),(0,4),(0,5),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,2),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(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),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(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)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 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)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(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)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 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.
The following 67 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001871The number of triconnected components of a graph. St001196The global dimension of A minus the global dimension of eAe for the corresponding Nakayama algebra with minimal faithful projective-injective module eA. St000264The girth of a graph, which is not a tree. St001597The Frobenius rank of a skew partition. St001193The dimension of Ext_A^1(A/AeA,A) in the corresponding Nakayama algebra A such that eA is a minimal faithful projective-injective module. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001198The number of simple modules in the algebra eAe with projective dimension at most 1 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St001206The maximal dimension of an indecomposable projective eAe-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module eA. St000455The second largest eigenvalue of a graph if it is integral. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001720The minimal length of a chain of small intervals in a lattice. St001195The global dimension of the algebra A/AfA of the corresponding Nakayama algebra A with minimal left faithful projective-injective module Af. St001618The cardinality of the Frattini sublattice of a lattice. St001845The number of join irreducibles minus the rank of a lattice. St001638The book thickness of a graph. St000287The number of connected components of a graph. St001518The number of graphs with the same ordinary spectrum as the given graph. St001890The maximum magnitude of the Möbius function of a poset. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000315The number of isolated vertices of a graph. St001651The Frankl number of a lattice. St001570The minimal number of edges to add to make a graph Hamiltonian. St000068The number of minimal elements in a poset. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St001432The order dimension of the partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St001175The size of a partition minus the hook length of the base cell. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001626The number of maximal proper sublattices of a lattice. St000699The toughness times the least common multiple of 1,. St000049The number of set partitions whose sorted block sizes correspond to the partition. St000146The Andrews-Garvan crank of a partition. St000256The number of parts from which one can substract 2 and still get an integer partition. St000275Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition. St000783The side length of the largest staircase partition fitting into a partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St000143The largest repeated part of a partition. St000185The weighted size of a partition. St000312The number of leaves in a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001214The aft of an integer partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition.