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Your data matches 10 different statistics following compositions of up to 3 maps.
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(click to perform a complete search on your data)
Matching statistic: St000100
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],2)
=> 2
([(0,1)],2)
=> 1
([],3)
=> 6
([(1,2)],3)
=> 3
([(0,1),(0,2)],3)
=> 2
([(0,2),(2,1)],3)
=> 1
([(0,2),(1,2)],3)
=> 2
([],4)
=> 24
([(2,3)],4)
=> 12
([(1,2),(1,3)],4)
=> 8
([(0,1),(0,2),(0,3)],4)
=> 6
([(0,2),(0,3),(3,1)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(1,2),(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> 2
([(1,3),(2,3)],4)
=> 8
([(0,3),(1,3),(3,2)],4)
=> 2
([(0,3),(1,3),(2,3)],4)
=> 6
([(0,3),(1,2)],4)
=> 6
([(0,3),(1,2),(1,3)],4)
=> 5
([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> 1
([(0,3),(1,2),(2,3)],4)
=> 3
([],5)
=> 120
([(3,4)],5)
=> 60
([(2,3),(2,4)],5)
=> 40
([(1,2),(1,3),(1,4)],5)
=> 30
([(0,1),(0,2),(0,3),(0,4)],5)
=> 24
([(0,2),(0,3),(0,4),(4,1)],5)
=> 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 6
([(1,3),(1,4),(4,2)],5)
=> 15
([(0,3),(0,4),(4,1),(4,2)],5)
=> 8
([(1,2),(1,3),(2,4),(3,4)],5)
=> 10
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
([(2,3),(3,4)],5)
=> 20
([(1,4),(4,2),(4,3)],5)
=> 10
([(0,4),(4,1),(4,2),(4,3)],5)
=> 6
([(2,4),(3,4)],5)
=> 40
([(1,4),(2,4),(4,3)],5)
=> 10
([(0,4),(1,4),(4,2),(4,3)],5)
=> 4
([(1,4),(2,4),(3,4)],5)
=> 30
([(0,4),(1,4),(2,4),(4,3)],5)
=> 6
([(0,4),(1,4),(2,4),(3,4)],5)
=> 24
([(0,4),(1,4),(2,3)],5)
=> 20
([(0,4),(1,3),(2,3),(2,4)],5)
=> 16
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 14
Description
The number of linear extensions of a poset.
Matching statistic: St001034
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001034: Dyck paths ⟶ ℤResult quality: 32% ●values known / values provided: 45%●distinct values known / distinct values provided: 32%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001034: Dyck paths ⟶ ℤResult quality: 32% ●values known / values provided: 45%●distinct values known / distinct values provided: 32%
Values
([],2)
=> [2]
=> [1,0,1,0]
=> 2
([(0,1)],2)
=> [1]
=> [1,0]
=> 1
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> 6
([(1,2)],3)
=> [3]
=> [1,0,1,0,1,0]
=> 3
([(0,1),(0,2)],3)
=> [2]
=> [1,0,1,0]
=> 2
([(0,2),(2,1)],3)
=> [1]
=> [1,0]
=> 1
([(0,2),(1,2)],3)
=> [2]
=> [1,0,1,0]
=> 2
([],4)
=> [4,4,4,4,4,4]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> 24
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 12
([(1,2),(1,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> 8
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> 6
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,0,1,0,1,0]
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,0,1,0]
=> 2
([(1,2),(2,3)],4)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> 4
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> 2
([(1,3),(2,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> 8
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> 2
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> 6
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 6
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> 5
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> 4
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1,0]
=> 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,0,1,0,1,0]
=> 3
([],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(3,4)],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(2,3),(2,4)],5)
=> [10,10,10,10]
=> [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(0,4)],5)
=> [4,4,4,4,4,4]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> 24
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> 6
([(1,3),(1,4),(4,2)],5)
=> [15]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> 8
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> 10
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,0,1,0]
=> 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> 4
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> 20
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> 10
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> 6
([(2,4),(3,4)],5)
=> [10,10,10,10]
=> [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> 10
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> 4
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> 6
([(0,4),(1,4),(2,4),(3,4)],5)
=> [4,4,4,4,4,4]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> 24
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> 20
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> 12
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> 2
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> 8
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 12
([(1,4),(2,3)],5)
=> [5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> 30
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> 9
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> 5
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> 20
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> 6
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([(1,4),(2,3),(3,4)],5)
=> [15]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {14,14,15,15,16,16,18,18,25,30,30,40,40,60,120}
([],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,4),(3,5)],6)
=> [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(2,5)],6)
=> [18,18,18,18,18,18,18,18,18,18]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(1,5)],6)
=> [24,24,24,24,24,24]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [10,10,10,10]
=> [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(1,5),(5,2)],6)
=> [24,24,24]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [10,10,10,10]
=> [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [48]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [18,18]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(4,5)],6)
=> [18,18,18,18,18]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(1,5),(5,2),(5,3)],6)
=> [48]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(3,5),(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(2,5),(3,5),(5,4)],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]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(1,5),(4,3),(5,2)],6)
=> [24,12]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [18,12]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,4),(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(3,4),(3,5)],6)
=> [6,6,6,6,6,6,6,6,6,6]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,5),(5,2),(5,3),(5,4)],6)
=> [18,18]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(4,5),(5,2),(5,3)],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]
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,5),(4,5)],6)
=> [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,5),(3,5),(5,4)],6)
=> [6,6,6,6,6,6,6,6,6,6]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
Description
The area of the parallelogram polyomino associated with the Dyck path.
The (bivariate) generating function is given in [1].
Matching statistic: St000293
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000293: Binary words ⟶ ℤResult quality: 27% ●values known / values provided: 40%●distinct values known / distinct values provided: 27%
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000293: Binary words ⟶ ℤResult quality: 27% ●values known / values provided: 40%●distinct values known / distinct values provided: 27%
Values
([],2)
=> [2]
=> [1,1]
=> 110 => 2
([(0,1)],2)
=> [1]
=> [1]
=> 10 => 1
([],3)
=> [3,3]
=> [2,2,2]
=> 11100 => 6
([(1,2)],3)
=> [3]
=> [1,1,1]
=> 1110 => 3
([(0,1),(0,2)],3)
=> [2]
=> [1,1]
=> 110 => 2
([(0,2),(2,1)],3)
=> [1]
=> [1]
=> 10 => 1
([(0,2),(1,2)],3)
=> [2]
=> [1,1]
=> 110 => 2
([],4)
=> [4,4,4,4,4,4]
=> [6,6,6,6]
=> 1111000000 => ? = 24
([(2,3)],4)
=> [4,4,4]
=> [3,3,3,3]
=> 1111000 => 12
([(1,2),(1,3)],4)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 111111110 => 8
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [2,2,2]
=> 11100 => 6
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,1,1]
=> 1110 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,1]
=> 110 => 2
([(1,2),(2,3)],4)
=> [4]
=> [1,1,1,1]
=> 11110 => 4
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,1]
=> 110 => 2
([(1,3),(2,3)],4)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 111111110 => 8
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,1]
=> 110 => 2
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [2,2,2]
=> 11100 => 6
([(0,3),(1,2)],4)
=> [4,2]
=> [2,2,1,1]
=> 110110 => 6
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2,2,1]
=> 11010 => 5
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2,2]
=> 1100 => 4
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1]
=> 10 => 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,1,1]
=> 1110 => 3
([],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> [24,24,24,24,24]
=> 11111000000000000000000000000 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(3,4)],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> [12,12,12,12,12]
=> 11111000000000000 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,3),(2,4)],5)
=> [10,10,10,10]
=> [4,4,4,4,4,4,4,4,4,4]
=> 11111111110000 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> 11111111111111100 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(0,4)],5)
=> [4,4,4,4,4,4]
=> [6,6,6,6]
=> 1111000000 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [3,3,3,3]
=> 1111000 => 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 111111110 => 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [2,2,2]
=> 11100 => 6
([(1,3),(1,4),(4,2)],5)
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> 1111111111111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 111111110 => 8
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [2,2,2,2,2]
=> 1111100 => 10
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,1]
=> 110 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2,2,1,1]
=> 110110 => 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2,2,1]
=> 11010 => 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2,2]
=> 1100 => 4
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [4,4,4,4,4]
=> 111110000 => 20
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [2,2,2,2,2]
=> 1111100 => 10
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [2,2,2]
=> 11100 => 6
([(2,4),(3,4)],5)
=> [10,10,10,10]
=> [4,4,4,4,4,4,4,4,4,4]
=> 11111111110000 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [2,2,2,2,2]
=> 1111100 => 10
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2,2]
=> 1100 => 4
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> 11111111111111100 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [2,2,2]
=> 11100 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
=> [4,4,4,4,4,4]
=> [6,6,6,6]
=> 1111000000 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> 111111111100 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [2,2,2,2,1,1,1,1,1,1,1,1]
=> 11110111111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> 111111111111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [2,2,2,2,2,2]
=> 11111100 => 12
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,1]
=> 110 => 2
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 111111110 => 8
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [3,3,3,3,1,1,1,1,1,1]
=> 1111001111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [3,3,3,3]
=> 1111000 => 12
([(1,4),(2,3)],5)
=> [5,5,5,5,5,5]
=> [6,6,6,6,6]
=> 11111000000 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]
=> 111110011111111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [2,2,2,2,1]
=> 1111010 => 9
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2,2,1]
=> 11010 => 5
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [4,4,4,4,4]
=> 111110000 => 20
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1]
=> 1111110 => 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2,2]
=> 1100 => 4
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> [1,1,1,1,1,1,1]
=> 11111110 => 7
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> 111111111100 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [3,3,3,3,1,1,1,1,1,1]
=> 1111001111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> [1,1,1,1]
=> 11110 => 4
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [3,3,3,2]
=> 1110100 => 11
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> [1,1,1]
=> 1110 => 3
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [2,2,2,2,1,1,1,1,1,1,1,1]
=> 11110111111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> 111111111111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3),(3,4)],5)
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> 1111111111111110 => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> [120,120,120,120,120,120]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> [60,60,60,60,60,60]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,4),(3,5)],6)
=> [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
=> [20,20,20,20,20,20,20,20,20,20,20,20]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(2,5)],6)
=> [18,18,18,18,18,18,18,18,18,18]
=> [10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(1,5)],6)
=> [24,24,24,24,24,24]
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> [24,24,24,24,24]
=> 11111000000000000000000000000 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> [12,12,12,12,12]
=> 11111000000000000 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [10,10,10,10]
=> [4,4,4,4,4,4,4,4,4,4]
=> 11111111110000 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> 11111111111111100 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [4,4,4,4,4,4]
=> [6,6,6,6]
=> 1111000000 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(1,5),(5,2)],6)
=> [24,24,24]
=> [3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [10,10,10,10]
=> [4,4,4,4,4,4,4,4,4,4]
=> 11111111110000 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [48]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [18,18]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> 111111111100 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [2,2,2,2,1,1,1,1,1,1,1,1]
=> 11110111111110 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> 111111111111110 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [3,3,3,3,1,1,1,1,1,1]
=> 1111001111110 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [5,5,5,5,5,5]
=> [6,6,6,6,6]
=> 11111000000 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]
=> 111110011111111110 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(4,5)],6)
=> [18,18,18,18,18]
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(1,5),(5,2),(5,3)],6)
=> [48]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> 11111111111111100 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(3,5),(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6]
=> [10,10,10,10,10,10]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> 1111111111110 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(1,5),(4,3),(5,2)],6)
=> [24,12]
=> [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [18,12]
=> ?
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ? => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> 111111111100 => ? ∊ {12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
Description
The number of inversions of a binary word.
Matching statistic: St000290
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
St000290: Binary words ⟶ ℤResult quality: 27% ●values known / values provided: 39%●distinct values known / distinct values provided: 27%
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
St000290: Binary words ⟶ ℤResult quality: 27% ●values known / values provided: 39%●distinct values known / distinct values provided: 27%
Values
([],2)
=> [2]
=> 100 => 010 => 2
([(0,1)],2)
=> [1]
=> 10 => 10 => 1
([],3)
=> [3,3]
=> 11000 => 01010 => 6
([(1,2)],3)
=> [3]
=> 1000 => 0010 => 3
([(0,1),(0,2)],3)
=> [2]
=> 100 => 010 => 2
([(0,2),(2,1)],3)
=> [1]
=> 10 => 10 => 1
([(0,2),(1,2)],3)
=> [2]
=> 100 => 010 => 2
([],4)
=> [4,4,4,4,4,4]
=> 1111110000 => ? => ? = 24
([(2,3)],4)
=> [4,4,4]
=> 1110000 => 0101010 => 12
([(1,2),(1,3)],4)
=> [8]
=> 100000000 => 000000010 => 8
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> 11000 => 01010 => 6
([(0,2),(0,3),(3,1)],4)
=> [3]
=> 1000 => 0010 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> 100 => 010 => 2
([(1,2),(2,3)],4)
=> [4]
=> 10000 => 00010 => 4
([(0,3),(3,1),(3,2)],4)
=> [2]
=> 100 => 010 => 2
([(1,3),(2,3)],4)
=> [8]
=> 100000000 => 000000010 => 8
([(0,3),(1,3),(3,2)],4)
=> [2]
=> 100 => 010 => 2
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> 11000 => 01010 => 6
([(0,3),(1,2)],4)
=> [4,2]
=> 100100 => 100010 => 6
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> 10100 => 10010 => 5
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> 1100 => 1010 => 4
([(0,3),(2,1),(3,2)],4)
=> [1]
=> 10 => 10 => 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> 1000 => 0010 => 3
([],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> 11111111111111111111111100000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(3,4)],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> 11111111111100000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,3),(2,4)],5)
=> [10,10,10,10]
=> 11110000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> 11000000000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(0,4)],5)
=> [4,4,4,4,4,4]
=> 1111110000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> 1110000 => 0101010 => 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> 100000000 => 000000010 => 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> 11000 => 01010 => 6
([(1,3),(1,4),(4,2)],5)
=> [15]
=> 1000000000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> 100000000 => 000000010 => 8
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> 1100000 => 0001010 => 10
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> 100 => 010 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> 100100 => 100010 => 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> 10100 => 10010 => 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> 1100 => 1010 => 4
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> 111100000 => 010101010 => 20
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> 1100000 => 0001010 => 10
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> 11000 => 01010 => 6
([(2,4),(3,4)],5)
=> [10,10,10,10]
=> 11110000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> 1100000 => 0001010 => 10
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> 1100 => 1010 => 4
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> 11000000000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> 11000 => 01010 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
=> [4,4,4,4,4,4]
=> 1111110000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> 110000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> 10000000010000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> 100000000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> 11000000 => 00001010 => 12
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> 100 => 010 => 2
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> 100000000 => 000000010 => 8
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> 1000000110000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> 1110000 => 0101010 => 12
([(1,4),(2,3)],5)
=> [5,5,5,5,5,5]
=> 11111100000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> 100000000001100000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> 1010000 => 0010010 => 9
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> 10100 => 10010 => 5
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> 111100000 => 010101010 => 20
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> 1000000 => 0000010 => 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> 1100 => 1010 => 4
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> 10000000 => 00000010 => 7
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> 110000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> 1000000110000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> 10000 => 00010 => 4
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> 1101000 => 1001010 => 11
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> 1000 => 0010 => 3
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> 10000000010000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> 100000000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3),(3,4)],5)
=> [15]
=> 1000000000000000 => ? => ? ∊ {14,14,15,15,16,16,18,18,20,20,24,24,25,30,30,30,40,40,60,120}
([],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,4),(3,5)],6)
=> [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(2,5)],6)
=> [18,18,18,18,18,18,18,18,18,18]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(1,5)],6)
=> [24,24,24,24,24,24]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> 11111111111111111111111100000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> 11111111111100000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [10,10,10,10]
=> 11110000000000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> 11000000000000000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [4,4,4,4,4,4]
=> 1111110000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(1,5),(5,2)],6)
=> [24,24,24]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [10,10,10,10]
=> 11110000000000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [48]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [18,18]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> 110000000000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> 10000000010000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> 100000000000000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> 1000000110000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [5,5,5,5,5,5]
=> 11111100000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> 100000000001100000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(4,5)],6)
=> [18,18,18,18,18]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(1,5),(5,2),(5,3)],6)
=> [48]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> 11000000000000000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(3,5),(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> 1000000000000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(1,5),(4,3),(5,2)],6)
=> [24,12]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [18,12]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ? => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> 110000000000 => ? => ? ∊ {11,11,12,12,12,12,12,12,12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
Description
The major index of a binary word.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
Matching statistic: St000395
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St000395: Dyck paths ⟶ ℤResult quality: 19% ●values known / values provided: 33%●distinct values known / distinct values provided: 19%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St000395: Dyck paths ⟶ ℤResult quality: 19% ●values known / values provided: 33%●distinct values known / distinct values provided: 19%
Values
([],2)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([(0,1)],2)
=> [1]
=> [1,0]
=> [1,0]
=> 1
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 6
([(1,2)],3)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 3
([(0,1),(0,2)],3)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([(0,2),(2,1)],3)
=> [1]
=> [1,0]
=> [1,0]
=> 1
([(0,2),(1,2)],3)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([],4)
=> [4,4,4,4,4,4]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
=> ? ∊ {8,8,24}
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 12
([(1,2),(1,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,24}
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 6
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([(1,2),(2,3)],4)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 4
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([(1,3),(2,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,24}
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 6
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 6
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 5
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 4
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1,0]
=> [1,0]
=> 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 3
([],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(3,4)],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,3),(2,4)],5)
=> [10,10,10,10]
=> [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(0,4)],5)
=> [4,4,4,4,4,4]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 6
([(1,3),(1,4),(4,2)],5)
=> [15]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 10
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 4
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 10
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 6
([(2,4),(3,4)],5)
=> [10,10,10,10]
=> [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 10
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 4
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 6
([(0,4),(1,4),(2,4),(3,4)],5)
=> [4,4,4,4,4,4]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 12
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 12
([(1,4),(2,3)],5)
=> [5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 9
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 5
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 4
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 7
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 4
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> 11
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 12
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 8
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 9
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 6
([(1,4),(3,2),(4,3)],5)
=> [5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 2
([(1,4),(2,3),(3,4)],5)
=> [15]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 3
([],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ?
=> ?
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ?
=> ?
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,4),(3,5)],6)
=> [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
=> ?
=> ?
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(2,5)],6)
=> [18,18,18,18,18,18,18,18,18,18]
=> ?
=> ?
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(1,5)],6)
=> [24,24,24,24,24,24]
=> ?
=> ?
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [10,10,10,10]
=> [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [4,4,4,4,4,4]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(1,5),(5,2)],6)
=> [24,24,24]
=> ?
=> ?
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [10,10,10,10]
=> [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [48]
=> ?
=> ?
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [18,18]
=> ?
=> ?
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [5,5,5,5,5,5]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0]
=> ? ∊ {8,8,8,8,8,8,10,10,11,11,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
Description
The sum of the heights of the peaks of a Dyck path.
Matching statistic: St000228
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000228: Integer partitions ⟶ ℤResult quality: 16% ●values known / values provided: 32%●distinct values known / distinct values provided: 16%
St000228: Integer partitions ⟶ ℤResult quality: 16% ●values known / values provided: 32%●distinct values known / distinct values provided: 16%
Values
([],2)
=> [2]
=> 2
([(0,1)],2)
=> [1]
=> 1
([],3)
=> [3,3]
=> 6
([(1,2)],3)
=> [3]
=> 3
([(0,1),(0,2)],3)
=> [2]
=> 2
([(0,2),(2,1)],3)
=> [1]
=> 1
([(0,2),(1,2)],3)
=> [2]
=> 2
([],4)
=> [4,4,4,4,4,4]
=> ? ∊ {12,24}
([(2,3)],4)
=> [4,4,4]
=> ? ∊ {12,24}
([(1,2),(1,3)],4)
=> [8]
=> 8
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> 6
([(0,2),(0,3),(3,1)],4)
=> [3]
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> 2
([(1,2),(2,3)],4)
=> [4]
=> 4
([(0,3),(3,1),(3,2)],4)
=> [2]
=> 2
([(1,3),(2,3)],4)
=> [8]
=> 8
([(0,3),(1,3),(3,2)],4)
=> [2]
=> 2
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> 6
([(0,3),(1,2)],4)
=> [4,2]
=> 6
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> 5
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> 4
([(0,3),(2,1),(3,2)],4)
=> [1]
=> 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> 3
([],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(3,4)],5)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,3),(2,4)],5)
=> [10,10,10,10]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(0,4)],5)
=> [4,4,4,4,4,4]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> 6
([(1,3),(1,4),(4,2)],5)
=> [15]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> 8
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> 10
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> 4
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> 10
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> 6
([(2,4),(3,4)],5)
=> [10,10,10,10]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> 10
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> 4
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> 6
([(0,4),(1,4),(2,4),(3,4)],5)
=> [4,4,4,4,4,4]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> 2
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> 8
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3)],5)
=> [5,5,5,5,5,5]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> 9
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> 5
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> 4
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> 7
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> 4
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> 3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> 8
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> 8
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> 9
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> 6
([(1,4),(3,2),(4,3)],5)
=> [5]
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> 2
([(1,4),(2,3),(3,4)],5)
=> [15]
=> ? ∊ {11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> 3
([],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(4,5)],6)
=> [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,4),(3,5)],6)
=> [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(2,5)],6)
=> [18,18,18,18,18,18,18,18,18,18]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(1,5)],6)
=> [24,24,24,24,24,24]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [5,5,5,5,5,5,5,5,5,5,5,5]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [10,10,10,10]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [4,4,4,4,4,4]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(1,5),(5,2)],6)
=> [24,24,24]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [10,10,10,10]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [48]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [18,18]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [5,5,5,5,5,5]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> ? ∊ {11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
Description
The size of a partition.
This statistic is the constant statistic of the level sets.
Matching statistic: St000071
Values
([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
([],3)
=> ([(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),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 6
([(1,2)],3)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
([(0,1),(0,2)],3)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(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)
=> 24
([(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
=> 12
([(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> 8
([(0,1),(0,2),(0,3)],4)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> 6
([(0,2),(0,3),(3,1)],4)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 2
([(1,2),(2,3)],4)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 2
([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> 8
([(0,3),(1,3),(3,2)],4)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 2
([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 6
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> 5
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 3
([],5)
=> ?
=> ?
=> ? ∊ {60,120}
([(3,4)],5)
=> ?
=> ?
=> ? ∊ {60,120}
([(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
=> ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
=> 40
([(1,2),(1,3),(1,4)],5)
=> ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
=> ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
=> 30
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
=> ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
=> 24
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
=> ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
=> 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> 6
([(1,3),(1,4),(4,2)],5)
=> ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14)
=> ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14)
=> 15
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
=> ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
=> 8
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)
=> ([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)
=> 10
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> 4
([(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)
=> ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)
=> 20
([(1,4),(4,2),(4,3)],5)
=> ([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)
=> ([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)
=> 10
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
=> ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
=> 6
([(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
=> 40
([(1,4),(2,4),(4,3)],5)
=> ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)
=> ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)
=> 10
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> 4
([(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
=> 30
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
=> ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
=> 6
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> 24
([(0,4),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
=> ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
=> 20
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
=> ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
=> 16
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
=> ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
=> 14
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
=> ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
=> 12
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> 2
([],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(4,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,4),(3,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(2,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(1,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(1,3),(1,4),(1,5),(1,6),(2,7),(3,8),(3,9),(3,10),(4,10),(4,12),(4,13),(5,9),(5,11),(5,13),(6,8),(6,11),(6,12),(8,14),(8,15),(9,14),(9,16),(10,15),(10,16),(11,14),(11,17),(12,15),(12,17),(13,16),(13,17),(14,18),(15,18),(16,18),(17,2),(17,18),(18,7)],19)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(1,5),(5,2)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,7),(2,14),(3,4),(3,5),(3,6),(3,14),(4,10),(4,12),(4,13),(5,9),(5,11),(5,13),(6,8),(6,11),(6,12),(8,15),(8,16),(9,15),(9,17),(10,16),(10,17),(11,15),(11,18),(12,16),(12,18),(13,17),(13,18),(14,8),(14,9),(14,10),(15,19),(16,19),(17,19),(18,1),(18,19),(19,7)],20)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(0,1),(1,3),(1,4),(1,5),(2,11),(3,10),(3,13),(4,10),(4,12),(5,6),(5,12),(5,13),(6,8),(6,9),(8,15),(9,15),(10,2),(10,14),(11,7),(12,8),(12,14),(13,9),(13,14),(14,11),(14,15),(15,7)],16)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,6),(1,11),(1,12),(2,9),(3,8),(4,7),(4,11),(5,7),(5,12),(6,1),(6,4),(6,5),(7,13),(8,10),(9,10),(11,3),(11,13),(12,2),(12,13),(13,8),(13,9)],14)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,10),(2,9),(3,8),(3,11),(4,7),(4,11),(5,7),(5,8),(6,3),(6,4),(6,5),(7,12),(8,12),(9,10),(11,2),(11,12),(12,1),(12,9)],13)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,7),(2,7),(3,9),(3,10),(4,8),(4,10),(5,8),(5,9),(6,3),(6,4),(6,5),(8,11),(9,11),(10,11),(11,1),(11,2)],12)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> ([(0,6),(1,11),(1,12),(2,10),(3,7),(3,9),(4,7),(4,8),(5,1),(5,8),(5,9),(6,3),(6,4),(6,5),(7,14),(8,11),(8,14),(9,12),(9,14),(11,13),(12,13),(13,10),(14,2),(14,13)],15)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(1,11),(2,7),(2,8),(3,8),(3,9),(4,7),(4,9),(5,1),(5,10),(6,2),(6,3),(6,4),(7,12),(8,12),(9,5),(9,12),(10,11),(12,10)],13)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> ([(0,1),(1,2),(1,3),(1,4),(2,12),(2,13),(3,6),(3,13),(3,14),(4,5),(4,12),(4,14),(5,8),(5,10),(6,9),(6,11),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18)],19)
=> ([(0,1),(1,2),(1,3),(1,4),(2,12),(2,13),(3,6),(3,13),(3,14),(4,5),(4,12),(4,14),(5,8),(5,10),(6,9),(6,11),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18)],19)
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> ([(0,1),(1,3),(1,4),(1,5),(2,8),(2,9),(3,10),(3,13),(4,10),(4,12),(5,6),(5,12),(5,13),(6,7),(6,11),(7,14),(8,15),(9,15),(10,16),(11,8),(11,14),(12,7),(12,16),(13,2),(13,11),(13,16),(14,15),(16,9),(16,14)],17)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,9),(1,12),(2,8),(2,12),(3,7),(3,11),(4,7),(4,10),(5,8),(5,9),(6,1),(6,2),(6,5),(7,14),(8,13),(9,13),(10,14),(11,14),(12,3),(12,4),(12,13),(13,10),(13,11)],15)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(4,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(1,5),(5,2),(5,3)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> ([(0,1),(1,2),(1,3),(2,13),(3,4),(3,5),(3,6),(3,13),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,14),(7,15),(8,14),(8,16),(9,15),(9,16),(10,14),(10,17),(11,15),(11,17),(12,16),(12,17),(13,7),(13,8),(13,9),(14,18),(15,18),(16,18),(17,18)],19)
=> ([(0,1),(1,2),(1,3),(2,13),(3,4),(3,5),(3,6),(3,13),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,14),(7,15),(8,14),(8,16),(9,15),(9,16),(10,14),(10,17),(11,15),(11,17),(12,16),(12,17),(13,7),(13,8),(13,9),(14,18),(15,18),(16,18),(17,18)],19)
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(2,4),(3,5),(4,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> ([(0,4),(0,6),(1,10),(2,8),(2,12),(3,8),(3,11),(4,7),(5,1),(5,9),(6,2),(6,3),(6,7),(7,11),(7,12),(8,5),(8,13),(9,10),(11,13),(12,13),(13,9)],14)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(1,5),(4,3),(5,2)],6)
=> ([(0,1),(0,2),(1,14),(2,3),(2,4),(2,14),(3,6),(3,13),(3,15),(4,5),(4,12),(4,15),(5,8),(5,10),(6,9),(6,11),(7,19),(8,17),(9,18),(10,7),(10,17),(11,7),(11,18),(12,8),(12,16),(13,9),(13,16),(14,12),(14,13),(15,10),(15,11),(15,16),(16,17),(16,18),(17,19),(18,19)],20)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> ([(0,1),(0,2),(1,14),(2,3),(2,5),(2,14),(3,9),(3,13),(4,8),(4,10),(5,6),(5,12),(5,13),(6,7),(6,11),(7,15),(8,16),(9,17),(10,16),(11,10),(11,15),(12,7),(12,17),(13,4),(13,11),(13,17),(14,9),(14,12),(15,16),(17,8),(17,15)],18)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(1,13),(2,3),(2,4),(2,13),(3,8),(3,12),(4,7),(4,12),(5,10),(5,11),(6,9),(6,11),(7,15),(8,15),(9,14),(10,14),(11,14),(12,5),(12,6),(12,15),(13,7),(13,8),(15,9),(15,10)],16)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ([(0,6),(1,9),(2,9),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(7,8),(9,4),(9,5)],10)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
=> ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,5),(3,6),(3,13),(4,12),(5,9),(5,11),(6,9),(6,10),(7,15),(8,15),(9,14),(10,7),(10,14),(11,8),(11,14),(12,7),(12,8),(13,10),(13,11),(13,12),(14,15)],16)
=> ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,5),(3,6),(3,13),(4,12),(5,9),(5,11),(6,9),(6,10),(7,15),(8,15),(9,14),(10,7),(10,14),(11,8),(11,14),(12,7),(12,8),(13,10),(13,11),(13,12),(14,15)],16)
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> ([(0,6),(1,12),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,3),(5,4),(5,12),(6,1),(6,5),(7,14),(8,10),(8,14),(9,11),(9,14),(10,13),(11,13),(12,2),(12,8),(12,9),(14,13)],15)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> ([(0,6),(1,11),(2,8),(2,10),(3,8),(3,9),(4,7),(5,4),(5,11),(6,1),(6,5),(7,9),(7,10),(8,12),(9,12),(10,12),(11,2),(11,3),(11,7)],13)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,6),(1,10),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,1),(6,2),(7,11),(8,11),(9,11),(10,3),(10,4),(10,5)],12)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,4),(4,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(3,4),(3,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,5),(5,2),(5,3),(5,4)],6)
=> ([(0,2),(0,3),(1,4),(1,5),(1,6),(1,14),(2,13),(3,1),(3,13),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,15),(7,16),(8,15),(8,17),(9,16),(9,17),(10,15),(10,18),(11,16),(11,18),(12,17),(12,18),(13,14),(14,7),(14,8),(14,9),(15,19),(16,19),(17,19),(18,19)],20)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> ([(0,5),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,6),(6,1),(6,2),(6,3),(6,4),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17)],18)
=> ([(0,5),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,6),(6,1),(6,2),(6,3),(6,4),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17)],18)
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(2,3),(3,5),(5,4)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,12),(1,13),(2,8),(2,9),(3,2),(3,14),(3,15),(4,7),(4,11),(5,7),(5,10),(6,1),(6,10),(6,11),(7,16),(8,17),(9,17),(10,12),(10,16),(11,13),(11,16),(12,14),(12,18),(13,15),(13,18),(14,8),(14,19),(15,9),(15,19),(16,18),(18,19),(19,17)],20)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(1,4),(4,5),(5,2),(5,3)],6)
=> ([(0,3),(0,5),(1,7),(1,10),(2,7),(2,9),(3,8),(4,6),(4,11),(5,4),(5,8),(6,1),(6,2),(6,12),(7,13),(8,11),(9,13),(10,13),(11,12),(12,9),(12,10)],14)
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> ([(0,5),(1,8),(1,9),(2,7),(2,9),(3,7),(3,8),(4,6),(5,4),(6,1),(6,2),(6,3),(7,10),(8,10),(9,10)],11)
=> ([(0,5),(1,8),(1,9),(2,7),(2,9),(3,7),(3,8),(4,6),(5,4),(6,1),(6,2),(6,3),(7,10),(8,10),(9,10)],11)
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
([(3,5),(4,5)],6)
=> ?
=> ?
=> ? ∊ {5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,26,26,26,26,26,27,27,28,28,28,28,28,28,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,32,32,32,32,33,33,33,33,35,35,36,36,36,36,36,36,36,36,37,37,38,38,38,40,40,40,40,40,40,40,40,40,42,42,42,42,44,45,45,48,48,48,48,48,48,48,48,48,48,52,52,52,52,54,54,54,54,57,60,60,60,60,60,60,60,60,60,61,64,64,66,66,66,70,70,72,72,72,72,75,76,80,80,80,84,84,84,84,90,90,90,90,90,96,96,108,108,120,120,120,120,120,120,144,144,150,180,180,180,240,240,360,720}
Description
The number of maximal chains in a poset.
Matching statistic: St001645
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,6}
([(0,2),(2,1)],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,6}
([],4)
=> ([(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)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,2),(1,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(0,1),(0,2),(0,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(1,2),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,3,4,5,6,6,6,8,12,24}
([],5)
=> ([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
([(3,4)],5)
=> ([(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),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(1,4)],5)
=> ([(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)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(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)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,3),(1,4),(4,2)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(3,4)],5)
=> ([(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)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(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)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(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)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(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)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(0,4),(1,2),(1,3)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,3),(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),(1,3),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,2,3,4,4,4,4,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(1,4),(3,2),(4,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,3),(1,4),(4,2)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 1
([],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)
=> ([(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)
=> ([(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
([(4,5)],6)
=> ([(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)
=> ([(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
([(3,4),(3,5)],6)
=> ([(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)
=> ([(0,3),(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)
=> ([(0,3),(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
([(3,4),(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),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(2,3),(3,5),(5,4)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(3,5),(4,5)],6)
=> ([(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)
=> ([(0,3),(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)
=> ([(0,3),(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
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(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),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16
([(0,5),(1,5),(2,3),(2,4)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(2,5),(3,4)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(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
([(2,5),(3,4),(3,5)],6)
=> ([(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)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(1,4),(1,5),(2,3),(2,5)],6)
=> ([(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),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(0,4),(0,5),(1,3),(1,5),(5,2)],6)
=> ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16
([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(0,4),(0,5),(1,2),(1,3)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(0,4),(1,3),(1,5),(4,2),(4,5)],6)
=> ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16
([(1,3),(2,4),(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),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
([(1,5),(3,4),(4,2),(5,3)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 8
Description
The pebbling number of a connected graph.
Matching statistic: St000909
Values
([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
([],3)
=> ([(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),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 6
([(1,2)],3)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
([(0,1),(0,2)],3)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(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)
=> ? ∊ {8,8,12,24}
([(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
=> ? ∊ {8,8,12,24}
([(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {8,8,12,24}
([(0,1),(0,2),(0,3)],4)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> 6
([(0,2),(0,3),(3,1)],4)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 2
([(1,2),(2,3)],4)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 2
([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? ∊ {8,8,12,24}
([(0,3),(1,3),(3,2)],4)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 2
([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 6
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> 5
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 3
([],5)
=> ?
=> ?
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(3,4)],5)
=> ?
=> ?
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
=> ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(1,4)],5)
=> ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
=> ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
=> ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
=> ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,3),(1,4),(4,2)],5)
=> ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14)
=> ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
=> ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)
=> ([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> 4
([(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)
=> ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(4,2),(4,3)],5)
=> ([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)
=> ([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
=> ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(4,3)],5)
=> ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)
=> ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> 4
([(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
=> ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
=> ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
=> ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
=> ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
=> ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> 2
([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
=> ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14)
=> ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13)
=> ([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)
=> ([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16)
=> ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
=> ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> 5
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
=> ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> 4
([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,3)],5)
=> ([(0,2),(0,3),(1,11),(2,1),(2,12),(3,4),(3,5),(3,12),(4,8),(4,10),(5,8),(5,9),(6,14),(7,14),(8,13),(9,6),(9,13),(10,7),(10,13),(11,6),(11,7),(12,9),(12,10),(12,11),(13,14)],15)
=> ([(0,2),(0,3),(1,11),(2,1),(2,12),(3,4),(3,5),(3,12),(4,8),(4,10),(5,8),(5,9),(6,14),(7,14),(8,13),(9,6),(9,13),(10,7),(10,13),(11,6),(11,7),(12,9),(12,10),(12,11),(13,14)],15)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14)
=> ([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> 4
([(0,4),(1,2),(1,3),(3,4)],5)
=> ([(0,4),(0,5),(1,8),(2,7),(2,9),(3,7),(3,10),(4,6),(5,2),(5,3),(5,6),(6,9),(6,10),(7,11),(9,11),(10,1),(10,11),(11,8)],12)
=> ([(0,4),(0,5),(1,8),(2,7),(2,9),(3,7),(3,10),(4,6),(5,2),(5,3),(5,6),(6,9),(6,10),(7,11),(9,11),(10,1),(10,11),(11,8)],12)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> 3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(2,7),(2,9),(3,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,8),(6,9),(7,10),(8,10),(9,10),(10,1)],11)
=> ([(0,4),(0,5),(2,7),(2,9),(3,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,8),(6,9),(7,10),(8,10),(9,10),(10,1)],11)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,4)],5)
=> ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13)
=> ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,4),(0,5),(1,7),(1,9),(2,7),(2,8),(3,6),(4,10),(5,3),(5,10),(6,8),(6,9),(7,11),(8,11),(9,11),(10,1),(10,2),(10,6)],12)
=> ([(0,4),(0,5),(1,7),(1,9),(2,7),(2,8),(3,6),(4,10),(5,3),(5,10),(6,8),(6,9),(7,11),(8,11),(9,11),(10,1),(10,2),(10,6)],12)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11)
=> ([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> 6
([(1,4),(3,2),(4,3)],5)
=> ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> 2
([(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,1),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8)],14)
=> ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,1),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8)],14)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> 3
([(0,3),(1,4),(4,2)],5)
=> ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> 3
([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ? ∊ {5,6,6,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 1
Description
The number of maximal chains of maximal size in a poset.
Matching statistic: St001879
Values
([],2)
=> ? ∊ {1,2}
([(0,1)],2)
=> ? ∊ {1,2}
([],3)
=> ? ∊ {1,2,3,6}
([(1,2)],3)
=> ? ∊ {1,2,3,6}
([(0,1),(0,2)],3)
=> ? ∊ {1,2,3,6}
([(0,2),(2,1)],3)
=> 2
([(0,2),(1,2)],3)
=> ? ∊ {1,2,3,6}
([],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(2,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(1,2),(1,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,1),(0,2),(0,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,2),(0,3),(3,1)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(1,2),(2,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,3),(3,1),(3,2)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(1,3),(2,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,3),(1,3),(3,2)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,3),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,3),(1,2)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,3),(1,2),(1,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([(0,3),(2,1),(3,2)],4)
=> 3
([(0,3),(1,2),(2,3)],4)
=> ? ∊ {1,2,2,2,3,4,5,6,6,6,8,8,12,24}
([],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,3),(2,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(0,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(0,4),(4,1)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
([(1,3),(1,4),(4,2)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(4,1),(4,2)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,3),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(4,2),(4,3)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(4,1),(4,2),(4,3)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(2,4),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(4,3)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(4,2),(4,3)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(4,3)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,3),(2,3),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,2,2,2,2,3,3,3,4,4,4,4,5,6,6,6,6,6,6,7,7,8,8,8,8,8,9,10,10,10,10,11,12,12,12,12,14,14,15,15,16,16,18,18,20,20,20,20,24,24,25,30,30,30,40,40,60,120}
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 8
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 7
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
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