Your data matches 23 different statistics following compositions of up to 3 maps.
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Mp00264: Graphs delete endpointsGraphs
Mp00157: Graphs connected complementGraphs
Mp00111: Graphs complementGraphs
St000264: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],3)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([],4)
=> ([],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(2,3)],4)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([],5)
=> ([],5)
=> ([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(3,4)],5)
=> ([],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(2,4),(3,4)],5)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,4),(2,3)],5)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> 3
([(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)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 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)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 3
([],6)
=> ([],6)
=> ([],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)
=> 3
([(4,5)],6)
=> ([],5)
=> ([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(3,5),(4,5)],6)
=> ([],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(2,5),(3,4)],6)
=> ([],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(2,5),(3,4),(4,5)],6)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,2),(3,5),(4,5)],6)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(0,5),(1,4),(2,3)],6)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],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)
=> 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 5
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,5),(1,2),(1,5),(2,4),(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)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St000455
Mp00157: Graphs connected complementGraphs
Mp00324: Graphs chromatic difference sequenceInteger compositions
Mp00184: Integer compositions to threshold graphGraphs
St000455: Graphs ⟶ ℤResult quality: 19% values known / values provided: 19%distinct values known / distinct values provided: 20%
Values
([],3)
=> ([],3)
=> [3] => ([],3)
=> ? = 3 - 3
([],4)
=> ([],4)
=> [4] => ([],4)
=> ? = 3 - 3
([(2,3)],4)
=> ([(2,3)],4)
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
([],5)
=> ([],5)
=> [5] => ([],5)
=> ? = 3 - 3
([(3,4)],5)
=> ([(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 3 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 3 - 3
([(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)
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
([],6)
=> ([],6)
=> [6] => ([],6)
=> ? = 3 - 3
([(4,5)],6)
=> ([(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(3,5),(4,5)],6)
=> ([(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(2,5),(3,4)],6)
=> ([(2,5),(3,4)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
=> ([(1,2),(3,5),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 3
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 3
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 3 - 3
([(5,6)],7)
=> ([(5,6)],7)
=> [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 0 = 3 - 3
Description
The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.
Matching statistic: St000781
Mp00037: Graphs to partition of connected componentsInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St000781: Integer partitions ⟶ ℤResult quality: 7% values known / values provided: 7%distinct values known / distinct values provided: 20%
Values
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 4 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 5 - 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1 = 3 - 2
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1 = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 5 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ?
=> ? = 6 - 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1 = 3 - 2
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1 = 3 - 2
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 1 = 3 - 2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 1 = 3 - 2
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 1 = 3 - 2
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
Description
The number of proper colouring schemes of a Ferrers diagram. A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1]. This statistic is the number of distinct such integer partitions that occur.
Matching statistic: St001901
Mp00037: Graphs to partition of connected componentsInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001901: Integer partitions ⟶ ℤResult quality: 7% values known / values provided: 7%distinct values known / distinct values provided: 20%
Values
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 4 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 5 - 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1 = 3 - 2
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1 = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 5 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ?
=> ? = 6 - 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1 = 3 - 2
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1 = 3 - 2
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 1 = 3 - 2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 1 = 3 - 2
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 1 = 3 - 2
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
Matching statistic: St001934
Mp00037: Graphs to partition of connected componentsInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001934: Integer partitions ⟶ ℤResult quality: 7% values known / values provided: 7%distinct values known / distinct values provided: 20%
Values
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 4 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 5 - 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 2
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1 = 3 - 2
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1 = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 5 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ?
=> ? = 6 - 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 2
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1 = 3 - 2
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1 = 3 - 2
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 1 = 3 - 2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 1 = 3 - 2
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 1 = 3 - 2
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1 = 3 - 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1 = 3 - 2
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1 = 3 - 2
Description
The number of monotone factorisations of genus zero of a permutation of given cycle type. A monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ with $\ell$ cycles, including fixed points, is a tuple of $r = n - \ell$ transpositions $$ (a_1, b_1),\dots,(a_r, b_r) $$ with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, whose product, in this order, is $\pi$. For example, the cycle $(2,3,1)$ has the two factorizations $(2,3)(1,3)$ and $(1,2)(2,3)$.
Matching statistic: St000205
Mp00037: Graphs to partition of connected componentsInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St000205: Integer partitions ⟶ ℤResult quality: 7% values known / values provided: 7%distinct values known / distinct values provided: 20%
Values
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 4 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 5 - 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 3 - 3
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 5 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ?
=> ? = 6 - 3
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 0 = 3 - 3
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 3 - 3
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 0 = 3 - 3
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 0 = 3 - 3
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. Given $\lambda$ count how many ''integer partitions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.
Matching statistic: St000206
Mp00037: Graphs to partition of connected componentsInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St000206: Integer partitions ⟶ ℤResult quality: 7% values known / values provided: 7%distinct values known / distinct values provided: 20%
Values
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 4 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 5 - 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 3 - 3
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 5 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ?
=> ? = 6 - 3
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 0 = 3 - 3
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 3 - 3
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 0 = 3 - 3
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 0 = 3 - 3
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. Given $\lambda$ count how many ''integer compositions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex. See also [[St000205]]. Each value in this statistic is greater than or equal to corresponding value in [[St000205]].
Matching statistic: St001175
Mp00037: Graphs to partition of connected componentsInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001175: Integer partitions ⟶ ℤResult quality: 7% values known / values provided: 7%distinct values known / distinct values provided: 20%
Values
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 4 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 5 - 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 3 - 3
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 3 - 3
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 5 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? = 3 - 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ?
=> ? = 6 - 3
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 4 - 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 3 - 3
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 0 = 3 - 3
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 3 - 3
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 0 = 3 - 3
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 0 = 3 - 3
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 3 - 3
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 3 - 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 3 - 3
Description
The size of a partition minus the hook length of the base cell. This is, the number of boxes in the diagram of a partition that are neither in the first row nor in the first column.
Mp00157: Graphs connected complementGraphs
Mp00266: Graphs connected vertex partitionsLattices
Mp00193: Lattices to posetPosets
St000068: Posets ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 20%
Values
([],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1 = 3 - 2
([],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 1 = 3 - 2
([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 3 - 2
([],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 1 = 3 - 2
([(3,4)],5)
=> ([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 3 - 2
([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1 = 3 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
=> ? = 3 - 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,15),(1,20),(1,21),(2,9),(2,10),(2,14),(2,18),(2,19),(3,8),(3,13),(3,17),(3,19),(3,21),(4,8),(4,12),(4,16),(4,18),(4,20),(5,7),(5,14),(5,15),(5,16),(5,17),(6,7),(6,10),(6,11),(6,12),(6,13),(7,31),(7,32),(8,30),(8,32),(9,30),(9,31),(10,22),(10,23),(10,31),(11,24),(11,25),(11,31),(12,22),(12,24),(12,32),(13,23),(13,25),(13,32),(14,26),(14,27),(14,31),(15,28),(15,29),(15,31),(16,26),(16,28),(16,32),(17,27),(17,29),(17,32),(18,22),(18,26),(18,30),(19,23),(19,27),(19,30),(20,24),(20,28),(20,30),(21,25),(21,29),(21,30),(22,33),(23,33),(24,33),(25,33),(26,33),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,15),(1,20),(1,21),(2,9),(2,10),(2,14),(2,18),(2,19),(3,8),(3,13),(3,17),(3,19),(3,21),(4,8),(4,12),(4,16),(4,18),(4,20),(5,7),(5,14),(5,15),(5,16),(5,17),(6,7),(6,10),(6,11),(6,12),(6,13),(7,31),(7,32),(8,30),(8,32),(9,30),(9,31),(10,22),(10,23),(10,31),(11,24),(11,25),(11,31),(12,22),(12,24),(12,32),(13,23),(13,25),(13,32),(14,26),(14,27),(14,31),(15,28),(15,29),(15,31),(16,26),(16,28),(16,32),(17,27),(17,29),(17,32),(18,22),(18,26),(18,30),(19,23),(19,27),(19,30),(20,24),(20,28),(20,30),(21,25),(21,29),(21,30),(22,33),(23,33),(24,33),(25,33),(26,33),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
=> ? = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 3 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
=> ? = 4 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
=> ? = 5 - 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(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)
=> 1 = 3 - 2
([],6)
=> ([],6)
=> ([],1)
=> ([],1)
=> 1 = 3 - 2
([(4,5)],6)
=> ([(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 3 - 2
([(3,5),(4,5)],6)
=> ([(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(2,5),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 3 - 2
([(2,5),(3,4)],6)
=> ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 3 - 2
([(1,2),(3,5),(4,5)],6)
=> ([(1,2),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 3 - 2
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1 = 3 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
=> ? = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 3 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,15),(1,20),(1,21),(2,9),(2,10),(2,14),(2,18),(2,19),(3,8),(3,13),(3,17),(3,19),(3,21),(4,8),(4,12),(4,16),(4,18),(4,20),(5,7),(5,14),(5,15),(5,16),(5,17),(6,7),(6,10),(6,11),(6,12),(6,13),(7,31),(7,32),(8,30),(8,32),(9,30),(9,31),(10,22),(10,23),(10,31),(11,24),(11,25),(11,31),(12,22),(12,24),(12,32),(13,23),(13,25),(13,32),(14,26),(14,27),(14,31),(15,28),(15,29),(15,31),(16,26),(16,28),(16,32),(17,27),(17,29),(17,32),(18,22),(18,26),(18,30),(19,23),(19,27),(19,30),(20,24),(20,28),(20,30),(21,25),(21,29),(21,30),(22,33),(23,33),(24,33),(25,33),(26,33),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,15),(1,20),(1,21),(2,9),(2,10),(2,14),(2,18),(2,19),(3,8),(3,13),(3,17),(3,19),(3,21),(4,8),(4,12),(4,16),(4,18),(4,20),(5,7),(5,14),(5,15),(5,16),(5,17),(6,7),(6,10),(6,11),(6,12),(6,13),(7,31),(7,32),(8,30),(8,32),(9,30),(9,31),(10,22),(10,23),(10,31),(11,24),(11,25),(11,31),(12,22),(12,24),(12,32),(13,23),(13,25),(13,32),(14,26),(14,27),(14,31),(15,28),(15,29),(15,31),(16,26),(16,28),(16,32),(17,27),(17,29),(17,32),(18,22),(18,26),(18,30),(19,23),(19,27),(19,30),(20,24),(20,28),(20,30),(21,25),(21,29),(21,30),(22,33),(23,33),(24,33),(25,33),(26,33),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,17),(1,24),(1,38),(1,40),(2,10),(2,16),(2,24),(2,37),(2,39),(3,12),(3,18),(3,23),(3,37),(3,40),(4,13),(4,19),(4,23),(4,38),(4,39),(5,15),(5,21),(5,22),(5,39),(5,40),(6,14),(6,20),(6,22),(6,37),(6,38),(7,9),(7,16),(7,17),(7,18),(7,19),(7,20),(7,21),(8,9),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,31),(9,32),(9,33),(9,34),(9,35),(9,36),(10,25),(10,31),(10,41),(10,43),(11,25),(11,32),(11,42),(11,44),(12,26),(12,33),(12,41),(12,44),(13,26),(13,34),(13,42),(13,43),(14,27),(14,35),(14,41),(14,42),(15,27),(15,36),(15,43),(15,44),(16,28),(16,31),(16,45),(16,47),(17,28),(17,32),(17,46),(17,48),(18,29),(18,33),(18,45),(18,48),(19,29),(19,34),(19,46),(19,47),(20,30),(20,35),(20,45),(20,46),(21,30),(21,36),(21,47),(21,48),(22,27),(22,30),(22,56),(23,26),(23,29),(23,56),(24,25),(24,28),(24,56),(25,49),(25,57),(26,50),(26,57),(27,51),(27,57),(28,49),(28,58),(29,50),(29,58),(30,51),(30,58),(31,49),(31,52),(31,54),(32,49),(32,53),(32,55),(33,50),(33,52),(33,55),(34,50),(34,53),(34,54),(35,51),(35,52),(35,53),(36,51),(36,54),(36,55),(37,41),(37,45),(37,56),(38,42),(38,46),(38,56),(39,43),(39,47),(39,56),(40,44),(40,48),(40,56),(41,52),(41,57),(42,53),(42,57),(43,54),(43,57),(44,55),(44,57),(45,52),(45,58),(46,53),(46,58),(47,54),(47,58),(48,55),(48,58),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,59),(56,57),(56,58),(57,59),(58,59)],60)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,17),(1,24),(1,38),(1,40),(2,10),(2,16),(2,24),(2,37),(2,39),(3,12),(3,18),(3,23),(3,37),(3,40),(4,13),(4,19),(4,23),(4,38),(4,39),(5,15),(5,21),(5,22),(5,39),(5,40),(6,14),(6,20),(6,22),(6,37),(6,38),(7,9),(7,16),(7,17),(7,18),(7,19),(7,20),(7,21),(8,9),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,31),(9,32),(9,33),(9,34),(9,35),(9,36),(10,25),(10,31),(10,41),(10,43),(11,25),(11,32),(11,42),(11,44),(12,26),(12,33),(12,41),(12,44),(13,26),(13,34),(13,42),(13,43),(14,27),(14,35),(14,41),(14,42),(15,27),(15,36),(15,43),(15,44),(16,28),(16,31),(16,45),(16,47),(17,28),(17,32),(17,46),(17,48),(18,29),(18,33),(18,45),(18,48),(19,29),(19,34),(19,46),(19,47),(20,30),(20,35),(20,45),(20,46),(21,30),(21,36),(21,47),(21,48),(22,27),(22,30),(22,56),(23,26),(23,29),(23,56),(24,25),(24,28),(24,56),(25,49),(25,57),(26,50),(26,57),(27,51),(27,57),(28,49),(28,58),(29,50),(29,58),(30,51),(30,58),(31,49),(31,52),(31,54),(32,49),(32,53),(32,55),(33,50),(33,52),(33,55),(34,50),(34,53),(34,54),(35,51),(35,52),(35,53),(36,51),(36,54),(36,55),(37,41),(37,45),(37,56),(38,42),(38,46),(38,56),(39,43),(39,47),(39,56),(40,44),(40,48),(40,56),(41,52),(41,57),(42,53),(42,57),(43,54),(43,57),(44,55),(44,57),(45,52),(45,58),(46,53),(46,58),(47,54),(47,58),(48,55),(48,58),(49,59),(50,59),(51,59),(52,59),(53,59),(54,59),(55,59),(56,57),(56,58),(57,59),(58,59)],60)
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,28),(1,29),(1,30),(2,9),(2,13),(2,18),(2,19),(2,30),(3,8),(3,12),(3,16),(3,17),(3,30),(4,11),(4,15),(4,17),(4,19),(4,29),(5,10),(5,14),(5,16),(5,18),(5,29),(6,12),(6,13),(6,14),(6,15),(6,28),(7,8),(7,9),(7,10),(7,11),(7,28),(8,20),(8,21),(8,32),(9,22),(9,23),(9,32),(10,20),(10,22),(10,33),(11,21),(11,23),(11,33),(12,24),(12,25),(12,32),(13,26),(13,27),(13,32),(14,24),(14,26),(14,33),(15,25),(15,27),(15,33),(16,20),(16,24),(16,31),(17,21),(17,25),(17,31),(18,22),(18,26),(18,31),(19,23),(19,27),(19,31),(20,34),(21,34),(22,34),(23,34),(24,34),(25,34),(26,34),(27,34),(28,32),(28,33),(29,31),(29,33),(30,31),(30,32),(31,34),(32,34),(33,34)],35)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,22),(1,23),(1,24),(1,25),(1,26),(1,27),(2,11),(2,15),(2,20),(2,21),(2,23),(2,50),(3,10),(3,14),(3,18),(3,19),(3,22),(3,50),(4,13),(4,17),(4,19),(4,21),(4,25),(4,49),(5,12),(5,16),(5,18),(5,20),(5,24),(5,49),(6,14),(6,15),(6,16),(6,17),(6,27),(6,48),(7,10),(7,11),(7,12),(7,13),(7,26),(7,48),(8,9),(8,48),(8,49),(8,50),(9,59),(9,60),(9,61),(10,28),(10,40),(10,41),(10,63),(11,29),(11,42),(11,43),(11,63),(12,30),(12,40),(12,42),(12,64),(13,31),(13,41),(13,43),(13,64),(14,32),(14,44),(14,45),(14,63),(15,33),(15,46),(15,47),(15,63),(16,34),(16,44),(16,46),(16,64),(17,35),(17,45),(17,47),(17,64),(18,36),(18,40),(18,44),(18,62),(19,37),(19,41),(19,45),(19,62),(20,38),(20,42),(20,46),(20,62),(21,39),(21,43),(21,47),(21,62),(22,28),(22,32),(22,36),(22,37),(22,59),(23,29),(23,33),(23,38),(23,39),(23,59),(24,30),(24,34),(24,36),(24,38),(24,60),(25,31),(25,35),(25,37),(25,39),(25,60),(26,28),(26,29),(26,30),(26,31),(26,61),(27,32),(27,33),(27,34),(27,35),(27,61),(28,51),(28,52),(28,66),(29,53),(29,54),(29,66),(30,51),(30,53),(30,67),(31,52),(31,54),(31,67),(32,55),(32,56),(32,66),(33,57),(33,58),(33,66),(34,55),(34,57),(34,67),(35,56),(35,58),(35,67),(36,51),(36,55),(36,65),(37,52),(37,56),(37,65),(38,53),(38,57),(38,65),(39,54),(39,58),(39,65),(40,51),(40,68),(41,52),(41,68),(42,53),(42,68),(43,54),(43,68),(44,55),(44,68),(45,56),(45,68),(46,57),(46,68),(47,58),(47,68),(48,61),(48,63),(48,64),(49,60),(49,62),(49,64),(50,59),(50,62),(50,63),(51,69),(52,69),(53,69),(54,69),(55,69),(56,69),(57,69),(58,69),(59,65),(59,66),(60,65),(60,67),(61,66),(61,67),(62,65),(62,68),(63,66),(63,68),(64,67),(64,68),(65,69),(66,69),(67,69),(68,69)],70)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,14),(1,18),(1,23),(1,24),(1,26),(1,32),(2,12),(2,13),(2,17),(2,21),(2,22),(2,25),(2,31),(3,11),(3,16),(3,20),(3,22),(3,24),(3,28),(3,34),(4,11),(4,15),(4,19),(4,21),(4,23),(4,27),(4,33),(5,10),(5,17),(5,18),(5,19),(5,20),(5,30),(5,36),(6,10),(6,13),(6,14),(6,15),(6,16),(6,29),(6,35),(7,9),(7,31),(7,32),(7,33),(7,34),(7,35),(7,36),(8,9),(8,25),(8,26),(8,27),(8,28),(8,29),(8,30),(9,88),(9,89),(9,90),(10,86),(10,87),(10,90),(11,85),(11,87),(11,89),(12,85),(12,86),(12,88),(13,37),(13,49),(13,61),(13,62),(13,86),(14,38),(14,50),(14,63),(14,64),(14,86),(15,39),(15,51),(15,61),(15,63),(15,87),(16,40),(16,52),(16,62),(16,64),(16,87),(17,41),(17,53),(17,65),(17,66),(17,86),(18,42),(18,54),(18,67),(18,68),(18,86),(19,43),(19,55),(19,65),(19,67),(19,87),(20,44),(20,56),(20,66),(20,68),(20,87),(21,45),(21,57),(21,61),(21,65),(21,85),(22,46),(22,58),(22,62),(22,66),(22,85),(23,47),(23,59),(23,63),(23,67),(23,85),(24,48),(24,60),(24,64),(24,68),(24,85),(25,37),(25,41),(25,45),(25,46),(25,88),(26,38),(26,42),(26,47),(26,48),(26,88),(27,39),(27,43),(27,45),(27,47),(27,89),(28,40),(28,44),(28,46),(28,48),(28,89),(29,37),(29,38),(29,39),(29,40),(29,90),(30,41),(30,42),(30,43),(30,44),(30,90),(31,49),(31,53),(31,57),(31,58),(31,88),(32,50),(32,54),(32,59),(32,60),(32,88),(33,51),(33,55),(33,57),(33,59),(33,89),(34,52),(34,56),(34,58),(34,60),(34,89),(35,49),(35,50),(35,51),(35,52),(35,90),(36,53),(36,54),(36,55),(36,56),(36,90),(37,69),(37,70),(37,92),(38,71),(38,72),(38,92),(39,69),(39,71),(39,93),(40,70),(40,72),(40,93),(41,73),(41,74),(41,92),(42,75),(42,76),(42,92),(43,73),(43,75),(43,93),(44,74),(44,76),(44,93),(45,69),(45,73),(45,94),(46,70),(46,74),(46,94),(47,71),(47,75),(47,94),(48,72),(48,76),(48,94),(49,77),(49,78),(49,92),(50,79),(50,80),(50,92),(51,77),(51,79),(51,93),(52,78),(52,80),(52,93),(53,81),(53,82),(53,92),(54,83),(54,84),(54,92),(55,81),(55,83),(55,93),(56,82),(56,84),(56,93),(57,77),(57,81),(57,94),(58,78),(58,82),(58,94),(59,79),(59,83),(59,94),(60,80),(60,84),(60,94),(61,69),(61,77),(61,91),(62,70),(62,78),(62,91),(63,71),(63,79),(63,91),(64,72),(64,80),(64,91),(65,73),(65,81),(65,91),(66,74),(66,82),(66,91),(67,75),(67,83),(67,91),(68,76),(68,84),(68,91),(69,95),(70,95),(71,95),(72,95),(73,95),(74,95),(75,95),(76,95),(77,95),(78,95),(79,95),(80,95),(81,95),(82,95),(83,95),(84,95),(85,91),(85,94),(86,91),(86,92),(87,91),(87,93),(88,92),(88,94),(89,93),(89,94),(90,92),(90,93),(91,95),(92,95),(93,95),(94,95)],96)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,14),(1,18),(1,23),(1,24),(1,26),(1,32),(2,12),(2,13),(2,17),(2,21),(2,22),(2,25),(2,31),(3,11),(3,16),(3,20),(3,22),(3,24),(3,28),(3,34),(4,11),(4,15),(4,19),(4,21),(4,23),(4,27),(4,33),(5,10),(5,17),(5,18),(5,19),(5,20),(5,30),(5,36),(6,10),(6,13),(6,14),(6,15),(6,16),(6,29),(6,35),(7,9),(7,31),(7,32),(7,33),(7,34),(7,35),(7,36),(8,9),(8,25),(8,26),(8,27),(8,28),(8,29),(8,30),(9,88),(9,89),(9,90),(10,86),(10,87),(10,90),(11,85),(11,87),(11,89),(12,85),(12,86),(12,88),(13,37),(13,49),(13,61),(13,62),(13,86),(14,38),(14,50),(14,63),(14,64),(14,86),(15,39),(15,51),(15,61),(15,63),(15,87),(16,40),(16,52),(16,62),(16,64),(16,87),(17,41),(17,53),(17,65),(17,66),(17,86),(18,42),(18,54),(18,67),(18,68),(18,86),(19,43),(19,55),(19,65),(19,67),(19,87),(20,44),(20,56),(20,66),(20,68),(20,87),(21,45),(21,57),(21,61),(21,65),(21,85),(22,46),(22,58),(22,62),(22,66),(22,85),(23,47),(23,59),(23,63),(23,67),(23,85),(24,48),(24,60),(24,64),(24,68),(24,85),(25,37),(25,41),(25,45),(25,46),(25,88),(26,38),(26,42),(26,47),(26,48),(26,88),(27,39),(27,43),(27,45),(27,47),(27,89),(28,40),(28,44),(28,46),(28,48),(28,89),(29,37),(29,38),(29,39),(29,40),(29,90),(30,41),(30,42),(30,43),(30,44),(30,90),(31,49),(31,53),(31,57),(31,58),(31,88),(32,50),(32,54),(32,59),(32,60),(32,88),(33,51),(33,55),(33,57),(33,59),(33,89),(34,52),(34,56),(34,58),(34,60),(34,89),(35,49),(35,50),(35,51),(35,52),(35,90),(36,53),(36,54),(36,55),(36,56),(36,90),(37,69),(37,70),(37,92),(38,71),(38,72),(38,92),(39,69),(39,71),(39,93),(40,70),(40,72),(40,93),(41,73),(41,74),(41,92),(42,75),(42,76),(42,92),(43,73),(43,75),(43,93),(44,74),(44,76),(44,93),(45,69),(45,73),(45,94),(46,70),(46,74),(46,94),(47,71),(47,75),(47,94),(48,72),(48,76),(48,94),(49,77),(49,78),(49,92),(50,79),(50,80),(50,92),(51,77),(51,79),(51,93),(52,78),(52,80),(52,93),(53,81),(53,82),(53,92),(54,83),(54,84),(54,92),(55,81),(55,83),(55,93),(56,82),(56,84),(56,93),(57,77),(57,81),(57,94),(58,78),(58,82),(58,94),(59,79),(59,83),(59,94),(60,80),(60,84),(60,94),(61,69),(61,77),(61,91),(62,70),(62,78),(62,91),(63,71),(63,79),(63,91),(64,72),(64,80),(64,91),(65,73),(65,81),(65,91),(66,74),(66,82),(66,91),(67,75),(67,83),(67,91),(68,76),(68,84),(68,91),(69,95),(70,95),(71,95),(72,95),(73,95),(74,95),(75,95),(76,95),(77,95),(78,95),(79,95),(80,95),(81,95),(82,95),(83,95),(84,95),(85,91),(85,94),(86,91),(86,92),(87,91),(87,93),(88,92),(88,94),(89,93),(89,94),(90,92),(90,93),(91,95),(92,95),(93,95),(94,95)],96)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,15),(1,20),(1,21),(1,23),(1,29),(1,69),(2,10),(2,14),(2,18),(2,19),(2,22),(2,28),(2,69),(3,13),(3,17),(3,19),(3,21),(3,25),(3,31),(3,68),(4,12),(4,16),(4,18),(4,20),(4,24),(4,30),(4,68),(5,14),(5,15),(5,16),(5,17),(5,27),(5,33),(5,67),(6,10),(6,11),(6,12),(6,13),(6,26),(6,32),(6,67),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,66),(8,22),(8,23),(8,24),(8,25),(8,26),(8,27),(8,66),(9,66),(9,67),(9,68),(9,69),(10,34),(10,46),(10,58),(10,59),(10,87),(11,35),(11,47),(11,60),(11,61),(11,87),(12,36),(12,48),(12,58),(12,60),(12,88),(13,37),(13,49),(13,59),(13,61),(13,88),(14,38),(14,50),(14,62),(14,63),(14,87),(15,39),(15,51),(15,64),(15,65),(15,87),(16,40),(16,52),(16,62),(16,64),(16,88),(17,41),(17,53),(17,63),(17,65),(17,88),(18,42),(18,54),(18,58),(18,62),(18,86),(19,43),(19,55),(19,59),(19,63),(19,86),(20,44),(20,56),(20,60),(20,64),(20,86),(21,45),(21,57),(21,61),(21,65),(21,86),(22,34),(22,38),(22,42),(22,43),(22,89),(23,35),(23,39),(23,44),(23,45),(23,89),(24,36),(24,40),(24,42),(24,44),(24,90),(25,37),(25,41),(25,43),(25,45),(25,90),(26,34),(26,35),(26,36),(26,37),(26,91),(27,38),(27,39),(27,40),(27,41),(27,91),(28,46),(28,50),(28,54),(28,55),(28,89),(29,47),(29,51),(29,56),(29,57),(29,89),(30,48),(30,52),(30,54),(30,56),(30,90),(31,49),(31,53),(31,55),(31,57),(31,90),(32,46),(32,47),(32,48),(32,49),(32,91),(33,50),(33,51),(33,52),(33,53),(33,91),(34,70),(34,71),(34,93),(35,72),(35,73),(35,93),(36,70),(36,72),(36,94),(37,71),(37,73),(37,94),(38,74),(38,75),(38,93),(39,76),(39,77),(39,93),(40,74),(40,76),(40,94),(41,75),(41,77),(41,94),(42,70),(42,74),(42,95),(43,71),(43,75),(43,95),(44,72),(44,76),(44,95),(45,73),(45,77),(45,95),(46,78),(46,79),(46,93),(47,80),(47,81),(47,93),(48,78),(48,80),(48,94),(49,79),(49,81),(49,94),(50,82),(50,83),(50,93),(51,84),(51,85),(51,93),(52,82),(52,84),(52,94),(53,83),(53,85),(53,94),(54,78),(54,82),(54,95),(55,79),(55,83),(55,95),(56,80),(56,84),(56,95),(57,81),(57,85),(57,95),(58,70),(58,78),(58,92),(59,71),(59,79),(59,92),(60,72),(60,80),(60,92),(61,73),(61,81),(61,92),(62,74),(62,82),(62,92),(63,75),(63,83),(63,92),(64,76),(64,84),(64,92),(65,77),(65,85),(65,92),(66,89),(66,90),(66,91),(67,87),(67,88),(67,91),(68,86),(68,88),(68,90),(69,86),(69,87),(69,89),(70,96),(71,96),(72,96),(73,96),(74,96),(75,96),(76,96),(77,96),(78,96),(79,96),(80,96),(81,96),(82,96),(83,96),(84,96),(85,96),(86,92),(86,95),(87,92),(87,93),(88,92),(88,94),(89,93),(89,95),(90,94),(90,95),(91,93),(91,94),(92,96),(93,96),(94,96),(95,96)],97)
=> ? = 3 - 2
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
=> ? = 4 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
=> ? = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,17),(1,18),(1,21),(1,22),(1,30),(1,32),(1,35),(1,36),(2,15),(2,16),(2,19),(2,20),(2,30),(2,31),(2,33),(2,34),(3,26),(3,27),(3,28),(3,29),(3,31),(3,32),(3,68),(4,12),(4,23),(4,25),(4,29),(4,34),(4,36),(4,70),(5,11),(5,23),(5,24),(5,28),(5,33),(5,35),(5,69),(6,10),(6,14),(6,19),(6,21),(6,24),(6,27),(6,70),(7,10),(7,13),(7,20),(7,22),(7,25),(7,26),(7,69),(8,11),(8,13),(8,15),(8,17),(8,68),(8,70),(9,12),(9,14),(9,16),(9,18),(9,68),(9,69),(10,39),(10,77),(10,78),(10,92),(11,62),(11,64),(11,79),(11,93),(12,63),(12,65),(12,80),(12,94),(13,58),(13,60),(13,78),(13,93),(14,59),(14,61),(14,77),(14,94),(15,58),(15,62),(15,66),(15,82),(15,85),(16,59),(16,63),(16,67),(16,81),(16,85),(17,60),(17,64),(17,66),(17,84),(17,86),(18,61),(18,65),(18,67),(18,83),(18,86),(19,49),(19,52),(19,59),(19,82),(19,92),(20,48),(20,53),(20,58),(20,81),(20,92),(21,51),(21,54),(21,61),(21,84),(21,92),(22,50),(22,55),(22,60),(22,83),(22,92),(23,37),(23,40),(23,41),(23,79),(23,80),(24,52),(24,54),(24,56),(24,77),(24,79),(25,53),(25,55),(25,57),(25,78),(25,80),(26,39),(26,48),(26,50),(26,57),(26,93),(27,39),(27,49),(27,51),(27,56),(27,94),(28,37),(28,44),(28,46),(28,56),(28,93),(29,37),(29,45),(29,47),(29,57),(29,94),(30,38),(30,42),(30,43),(30,66),(30,67),(30,92),(31,38),(31,44),(31,45),(31,48),(31,49),(31,85),(32,38),(32,46),(32,47),(32,50),(32,51),(32,86),(33,40),(33,42),(33,44),(33,52),(33,62),(33,81),(34,40),(34,43),(34,45),(34,53),(34,63),(34,82),(35,41),(35,42),(35,46),(35,54),(35,64),(35,83),(36,41),(36,43),(36,47),(36,55),(36,65),(36,84),(37,100),(37,103),(38,87),(38,95),(38,100),(39,95),(39,103),(40,88),(40,89),(40,100),(41,90),(41,91),(41,100),(42,75),(42,100),(42,101),(43,76),(43,100),(43,102),(44,71),(44,96),(44,100),(45,72),(45,97),(45,100),(46,73),(46,98),(46,100),(47,74),(47,99),(47,100),(48,72),(48,95),(48,96),(49,71),(49,95),(49,97),(50,74),(50,95),(50,98),(51,73),(51,95),(51,99),(52,71),(52,88),(52,101),(53,72),(53,89),(53,102),(54,73),(54,90),(54,101),(55,74),(55,91),(55,102),(56,71),(56,73),(56,103),(57,72),(57,74),(57,103),(58,96),(58,102),(59,97),(59,101),(60,98),(60,102),(61,99),(61,101),(62,75),(62,88),(62,96),(63,76),(63,89),(63,97),(64,75),(64,90),(64,98),(65,76),(65,91),(65,99),(66,75),(66,87),(66,102),(67,76),(67,87),(67,101),(68,85),(68,86),(68,93),(68,94),(69,77),(69,80),(69,81),(69,83),(69,93),(70,78),(70,79),(70,82),(70,84),(70,94),(71,104),(72,104),(73,104),(74,104),(75,104),(76,104),(77,101),(77,103),(78,102),(78,103),(79,88),(79,90),(79,103),(80,89),(80,91),(80,103),(81,89),(81,96),(81,101),(82,88),(82,97),(82,102),(83,91),(83,98),(83,101),(84,90),(84,99),(84,102),(85,87),(85,96),(85,97),(86,87),(86,98),(86,99),(87,104),(88,104),(89,104),(90,104),(91,104),(92,95),(92,101),(92,102),(93,96),(93,98),(93,103),(94,97),(94,99),(94,103),(95,104),(96,104),(97,104),(98,104),(99,104),(100,104),(101,104),(102,104),(103,104)],105)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,17),(1,18),(1,21),(1,22),(1,30),(1,32),(1,35),(1,36),(2,15),(2,16),(2,19),(2,20),(2,30),(2,31),(2,33),(2,34),(3,26),(3,27),(3,28),(3,29),(3,31),(3,32),(3,68),(4,12),(4,23),(4,25),(4,29),(4,34),(4,36),(4,70),(5,11),(5,23),(5,24),(5,28),(5,33),(5,35),(5,69),(6,10),(6,14),(6,19),(6,21),(6,24),(6,27),(6,70),(7,10),(7,13),(7,20),(7,22),(7,25),(7,26),(7,69),(8,11),(8,13),(8,15),(8,17),(8,68),(8,70),(9,12),(9,14),(9,16),(9,18),(9,68),(9,69),(10,39),(10,77),(10,78),(10,92),(11,62),(11,64),(11,79),(11,93),(12,63),(12,65),(12,80),(12,94),(13,58),(13,60),(13,78),(13,93),(14,59),(14,61),(14,77),(14,94),(15,58),(15,62),(15,66),(15,82),(15,85),(16,59),(16,63),(16,67),(16,81),(16,85),(17,60),(17,64),(17,66),(17,84),(17,86),(18,61),(18,65),(18,67),(18,83),(18,86),(19,49),(19,52),(19,59),(19,82),(19,92),(20,48),(20,53),(20,58),(20,81),(20,92),(21,51),(21,54),(21,61),(21,84),(21,92),(22,50),(22,55),(22,60),(22,83),(22,92),(23,37),(23,40),(23,41),(23,79),(23,80),(24,52),(24,54),(24,56),(24,77),(24,79),(25,53),(25,55),(25,57),(25,78),(25,80),(26,39),(26,48),(26,50),(26,57),(26,93),(27,39),(27,49),(27,51),(27,56),(27,94),(28,37),(28,44),(28,46),(28,56),(28,93),(29,37),(29,45),(29,47),(29,57),(29,94),(30,38),(30,42),(30,43),(30,66),(30,67),(30,92),(31,38),(31,44),(31,45),(31,48),(31,49),(31,85),(32,38),(32,46),(32,47),(32,50),(32,51),(32,86),(33,40),(33,42),(33,44),(33,52),(33,62),(33,81),(34,40),(34,43),(34,45),(34,53),(34,63),(34,82),(35,41),(35,42),(35,46),(35,54),(35,64),(35,83),(36,41),(36,43),(36,47),(36,55),(36,65),(36,84),(37,100),(37,103),(38,87),(38,95),(38,100),(39,95),(39,103),(40,88),(40,89),(40,100),(41,90),(41,91),(41,100),(42,75),(42,100),(42,101),(43,76),(43,100),(43,102),(44,71),(44,96),(44,100),(45,72),(45,97),(45,100),(46,73),(46,98),(46,100),(47,74),(47,99),(47,100),(48,72),(48,95),(48,96),(49,71),(49,95),(49,97),(50,74),(50,95),(50,98),(51,73),(51,95),(51,99),(52,71),(52,88),(52,101),(53,72),(53,89),(53,102),(54,73),(54,90),(54,101),(55,74),(55,91),(55,102),(56,71),(56,73),(56,103),(57,72),(57,74),(57,103),(58,96),(58,102),(59,97),(59,101),(60,98),(60,102),(61,99),(61,101),(62,75),(62,88),(62,96),(63,76),(63,89),(63,97),(64,75),(64,90),(64,98),(65,76),(65,91),(65,99),(66,75),(66,87),(66,102),(67,76),(67,87),(67,101),(68,85),(68,86),(68,93),(68,94),(69,77),(69,80),(69,81),(69,83),(69,93),(70,78),(70,79),(70,82),(70,84),(70,94),(71,104),(72,104),(73,104),(74,104),(75,104),(76,104),(77,101),(77,103),(78,102),(78,103),(79,88),(79,90),(79,103),(80,89),(80,91),(80,103),(81,89),(81,96),(81,101),(82,88),(82,97),(82,102),(83,91),(83,98),(83,101),(84,90),(84,99),(84,102),(85,87),(85,96),(85,97),(86,87),(86,98),(86,99),(87,104),(88,104),(89,104),(90,104),(91,104),(92,95),(92,101),(92,102),(93,96),(93,98),(93,103),(94,97),(94,99),(94,103),(95,104),(96,104),(97,104),(98,104),(99,104),(100,104),(101,104),(102,104),(103,104)],105)
=> ? = 5 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(1,13),(1,14),(1,44),(1,46),(2,9),(2,11),(2,12),(2,44),(2,45),(3,15),(3,24),(3,25),(3,26),(3,27),(3,44),(4,12),(4,17),(4,22),(4,23),(4,25),(4,46),(5,11),(5,16),(5,20),(5,21),(5,24),(5,46),(6,14),(6,19),(6,21),(6,23),(6,27),(6,45),(7,13),(7,18),(7,20),(7,22),(7,26),(7,45),(8,9),(8,10),(8,15),(8,16),(8,17),(8,18),(8,19),(9,36),(9,37),(9,47),(9,52),(10,38),(10,39),(10,47),(10,53),(11,36),(11,48),(11,62),(12,37),(12,49),(12,62),(13,38),(13,50),(13,63),(14,39),(14,51),(14,63),(15,32),(15,33),(15,34),(15,35),(15,47),(16,32),(16,36),(16,40),(16,41),(16,53),(17,33),(17,37),(17,42),(17,43),(17,53),(18,34),(18,38),(18,40),(18,42),(18,52),(19,35),(19,39),(19,41),(19,43),(19,52),(20,28),(20,40),(20,48),(20,50),(21,29),(21,41),(21,48),(21,51),(22,30),(22,42),(22,49),(22,50),(23,31),(23,43),(23,49),(23,51),(24,28),(24,29),(24,32),(24,62),(25,30),(25,31),(25,33),(25,62),(26,28),(26,30),(26,34),(26,63),(27,29),(27,31),(27,35),(27,63),(28,54),(28,66),(29,55),(29,66),(30,56),(30,66),(31,57),(31,66),(32,54),(32,55),(32,64),(33,56),(33,57),(33,64),(34,54),(34,56),(34,65),(35,55),(35,57),(35,65),(36,58),(36,64),(37,59),(37,64),(38,60),(38,65),(39,61),(39,65),(40,54),(40,58),(40,60),(41,55),(41,58),(41,61),(42,56),(42,59),(42,60),(43,57),(43,59),(43,61),(44,47),(44,62),(44,63),(45,48),(45,49),(45,52),(45,63),(46,50),(46,51),(46,53),(46,62),(47,64),(47,65),(48,58),(48,66),(49,59),(49,66),(50,60),(50,66),(51,61),(51,66),(52,58),(52,59),(52,65),(53,60),(53,61),(53,64),(54,67),(55,67),(56,67),(57,67),(58,67),(59,67),(60,67),(61,67),(62,64),(62,66),(63,65),(63,66),(64,67),(65,67),(66,67)],68)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(1,13),(1,14),(1,44),(1,46),(2,9),(2,11),(2,12),(2,44),(2,45),(3,15),(3,24),(3,25),(3,26),(3,27),(3,44),(4,12),(4,17),(4,22),(4,23),(4,25),(4,46),(5,11),(5,16),(5,20),(5,21),(5,24),(5,46),(6,14),(6,19),(6,21),(6,23),(6,27),(6,45),(7,13),(7,18),(7,20),(7,22),(7,26),(7,45),(8,9),(8,10),(8,15),(8,16),(8,17),(8,18),(8,19),(9,36),(9,37),(9,47),(9,52),(10,38),(10,39),(10,47),(10,53),(11,36),(11,48),(11,62),(12,37),(12,49),(12,62),(13,38),(13,50),(13,63),(14,39),(14,51),(14,63),(15,32),(15,33),(15,34),(15,35),(15,47),(16,32),(16,36),(16,40),(16,41),(16,53),(17,33),(17,37),(17,42),(17,43),(17,53),(18,34),(18,38),(18,40),(18,42),(18,52),(19,35),(19,39),(19,41),(19,43),(19,52),(20,28),(20,40),(20,48),(20,50),(21,29),(21,41),(21,48),(21,51),(22,30),(22,42),(22,49),(22,50),(23,31),(23,43),(23,49),(23,51),(24,28),(24,29),(24,32),(24,62),(25,30),(25,31),(25,33),(25,62),(26,28),(26,30),(26,34),(26,63),(27,29),(27,31),(27,35),(27,63),(28,54),(28,66),(29,55),(29,66),(30,56),(30,66),(31,57),(31,66),(32,54),(32,55),(32,64),(33,56),(33,57),(33,64),(34,54),(34,56),(34,65),(35,55),(35,57),(35,65),(36,58),(36,64),(37,59),(37,64),(38,60),(38,65),(39,61),(39,65),(40,54),(40,58),(40,60),(41,55),(41,58),(41,61),(42,56),(42,59),(42,60),(43,57),(43,59),(43,61),(44,47),(44,62),(44,63),(45,48),(45,49),(45,52),(45,63),(46,50),(46,51),(46,53),(46,62),(47,64),(47,65),(48,58),(48,66),(49,59),(49,66),(50,60),(50,66),(51,61),(51,66),(52,58),(52,59),(52,65),(53,60),(53,61),(53,64),(54,67),(55,67),(56,67),(57,67),(58,67),(59,67),(60,67),(61,67),(62,64),(62,66),(63,65),(63,66),(64,67),(65,67),(66,67)],68)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,15),(2,7),(2,8),(2,11),(2,14),(3,6),(3,8),(3,10),(3,13),(4,6),(4,7),(4,9),(4,12),(5,12),(5,13),(5,14),(5,15),(6,18),(6,22),(7,16),(7,22),(8,17),(8,22),(9,19),(9,22),(10,20),(10,22),(11,21),(11,22),(12,16),(12,18),(12,19),(13,17),(13,18),(13,20),(14,16),(14,17),(14,21),(15,19),(15,20),(15,21),(16,23),(17,23),(18,23),(19,23),(20,23),(21,23),(22,23)],24)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,15),(2,7),(2,8),(2,11),(2,14),(3,6),(3,8),(3,10),(3,13),(4,6),(4,7),(4,9),(4,12),(5,12),(5,13),(5,14),(5,15),(6,18),(6,22),(7,16),(7,22),(8,17),(8,22),(9,19),(9,22),(10,20),(10,22),(11,21),(11,22),(12,16),(12,18),(12,19),(13,17),(13,18),(13,20),(14,16),(14,17),(14,21),(15,19),(15,20),(15,21),(16,23),(17,23),(18,23),(19,23),(20,23),(21,23),(22,23)],24)
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(1,11),(1,12),(1,51),(1,52),(2,16),(2,20),(2,24),(2,28),(2,30),(2,52),(3,15),(3,19),(3,23),(3,28),(3,29),(3,51),(4,17),(4,21),(4,25),(4,27),(4,29),(4,52),(5,18),(5,22),(5,26),(5,27),(5,30),(5,51),(6,9),(6,11),(6,14),(6,19),(6,20),(6,21),(6,22),(7,9),(7,10),(7,13),(7,15),(7,16),(7,17),(7,18),(8,12),(8,13),(8,14),(8,23),(8,24),(8,25),(8,26),(9,37),(9,40),(9,69),(9,70),(10,37),(10,49),(10,53),(10,54),(11,37),(11,50),(11,55),(11,56),(12,49),(12,50),(12,57),(12,58),(13,40),(13,41),(13,42),(13,43),(13,44),(13,49),(14,40),(14,45),(14,46),(14,47),(14,48),(14,50),(15,33),(15,41),(15,53),(15,69),(16,34),(16,42),(16,54),(16,69),(17,33),(17,43),(17,54),(17,70),(18,34),(18,44),(18,53),(18,70),(19,35),(19,45),(19,55),(19,69),(20,36),(20,46),(20,56),(20,69),(21,35),(21,47),(21,56),(21,70),(22,36),(22,48),(22,55),(22,70),(23,31),(23,38),(23,41),(23,45),(23,57),(24,32),(24,38),(24,42),(24,46),(24,58),(25,31),(25,39),(25,43),(25,47),(25,58),(26,32),(26,39),(26,44),(26,48),(26,57),(27,39),(27,68),(27,70),(28,38),(28,68),(28,69),(29,31),(29,33),(29,35),(29,68),(30,32),(30,34),(30,36),(30,68),(31,60),(31,62),(31,71),(32,61),(32,63),(32,71),(33,60),(33,74),(34,61),(34,74),(35,62),(35,74),(36,63),(36,74),(37,59),(37,74),(38,71),(38,72),(39,71),(39,73),(40,59),(40,72),(40,73),(41,60),(41,64),(41,72),(42,61),(42,65),(42,72),(43,60),(43,65),(43,73),(44,61),(44,64),(44,73),(45,62),(45,66),(45,72),(46,63),(46,67),(46,72),(47,62),(47,67),(47,73),(48,63),(48,66),(48,73),(49,59),(49,64),(49,65),(50,59),(50,66),(50,67),(51,53),(51,55),(51,57),(51,68),(52,54),(52,56),(52,58),(52,68),(53,64),(53,74),(54,65),(54,74),(55,66),(55,74),(56,67),(56,74),(57,64),(57,66),(57,71),(58,65),(58,67),(58,71),(59,75),(60,75),(61,75),(62,75),(63,75),(64,75),(65,75),(66,75),(67,75),(68,71),(68,74),(69,72),(69,74),(70,73),(70,74),(71,75),(72,75),(73,75),(74,75)],76)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(1,11),(1,12),(1,51),(1,52),(2,16),(2,20),(2,24),(2,28),(2,30),(2,52),(3,15),(3,19),(3,23),(3,28),(3,29),(3,51),(4,17),(4,21),(4,25),(4,27),(4,29),(4,52),(5,18),(5,22),(5,26),(5,27),(5,30),(5,51),(6,9),(6,11),(6,14),(6,19),(6,20),(6,21),(6,22),(7,9),(7,10),(7,13),(7,15),(7,16),(7,17),(7,18),(8,12),(8,13),(8,14),(8,23),(8,24),(8,25),(8,26),(9,37),(9,40),(9,69),(9,70),(10,37),(10,49),(10,53),(10,54),(11,37),(11,50),(11,55),(11,56),(12,49),(12,50),(12,57),(12,58),(13,40),(13,41),(13,42),(13,43),(13,44),(13,49),(14,40),(14,45),(14,46),(14,47),(14,48),(14,50),(15,33),(15,41),(15,53),(15,69),(16,34),(16,42),(16,54),(16,69),(17,33),(17,43),(17,54),(17,70),(18,34),(18,44),(18,53),(18,70),(19,35),(19,45),(19,55),(19,69),(20,36),(20,46),(20,56),(20,69),(21,35),(21,47),(21,56),(21,70),(22,36),(22,48),(22,55),(22,70),(23,31),(23,38),(23,41),(23,45),(23,57),(24,32),(24,38),(24,42),(24,46),(24,58),(25,31),(25,39),(25,43),(25,47),(25,58),(26,32),(26,39),(26,44),(26,48),(26,57),(27,39),(27,68),(27,70),(28,38),(28,68),(28,69),(29,31),(29,33),(29,35),(29,68),(30,32),(30,34),(30,36),(30,68),(31,60),(31,62),(31,71),(32,61),(32,63),(32,71),(33,60),(33,74),(34,61),(34,74),(35,62),(35,74),(36,63),(36,74),(37,59),(37,74),(38,71),(38,72),(39,71),(39,73),(40,59),(40,72),(40,73),(41,60),(41,64),(41,72),(42,61),(42,65),(42,72),(43,60),(43,65),(43,73),(44,61),(44,64),(44,73),(45,62),(45,66),(45,72),(46,63),(46,67),(46,72),(47,62),(47,67),(47,73),(48,63),(48,66),(48,73),(49,59),(49,64),(49,65),(50,59),(50,66),(50,67),(51,53),(51,55),(51,57),(51,68),(52,54),(52,56),(52,58),(52,68),(53,64),(53,74),(54,65),(54,74),(55,66),(55,74),(56,67),(56,74),(57,64),(57,66),(57,71),(58,65),(58,67),(58,71),(59,75),(60,75),(61,75),(62,75),(63,75),(64,75),(65,75),(66,75),(67,75),(68,71),(68,74),(69,72),(69,74),(70,73),(70,74),(71,75),(72,75),(73,75),(74,75)],76)
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(1,11),(1,12),(1,51),(1,52),(2,16),(2,20),(2,24),(2,28),(2,30),(2,52),(3,15),(3,19),(3,23),(3,28),(3,29),(3,51),(4,17),(4,21),(4,25),(4,27),(4,29),(4,52),(5,18),(5,22),(5,26),(5,27),(5,30),(5,51),(6,9),(6,11),(6,14),(6,19),(6,20),(6,21),(6,22),(7,9),(7,10),(7,13),(7,15),(7,16),(7,17),(7,18),(8,12),(8,13),(8,14),(8,23),(8,24),(8,25),(8,26),(9,37),(9,40),(9,69),(9,70),(10,37),(10,49),(10,53),(10,54),(11,37),(11,50),(11,55),(11,56),(12,49),(12,50),(12,57),(12,58),(13,40),(13,41),(13,42),(13,43),(13,44),(13,49),(14,40),(14,45),(14,46),(14,47),(14,48),(14,50),(15,33),(15,41),(15,53),(15,69),(16,34),(16,42),(16,54),(16,69),(17,33),(17,43),(17,54),(17,70),(18,34),(18,44),(18,53),(18,70),(19,35),(19,45),(19,55),(19,69),(20,36),(20,46),(20,56),(20,69),(21,35),(21,47),(21,56),(21,70),(22,36),(22,48),(22,55),(22,70),(23,31),(23,38),(23,41),(23,45),(23,57),(24,32),(24,38),(24,42),(24,46),(24,58),(25,31),(25,39),(25,43),(25,47),(25,58),(26,32),(26,39),(26,44),(26,48),(26,57),(27,39),(27,68),(27,70),(28,38),(28,68),(28,69),(29,31),(29,33),(29,35),(29,68),(30,32),(30,34),(30,36),(30,68),(31,60),(31,62),(31,71),(32,61),(32,63),(32,71),(33,60),(33,74),(34,61),(34,74),(35,62),(35,74),(36,63),(36,74),(37,59),(37,74),(38,71),(38,72),(39,71),(39,73),(40,59),(40,72),(40,73),(41,60),(41,64),(41,72),(42,61),(42,65),(42,72),(43,60),(43,65),(43,73),(44,61),(44,64),(44,73),(45,62),(45,66),(45,72),(46,63),(46,67),(46,72),(47,62),(47,67),(47,73),(48,63),(48,66),(48,73),(49,59),(49,64),(49,65),(50,59),(50,66),(50,67),(51,53),(51,55),(51,57),(51,68),(52,54),(52,56),(52,58),(52,68),(53,64),(53,74),(54,65),(54,74),(55,66),(55,74),(56,67),(56,74),(57,64),(57,66),(57,71),(58,65),(58,67),(58,71),(59,75),(60,75),(61,75),(62,75),(63,75),(64,75),(65,75),(66,75),(67,75),(68,71),(68,74),(69,72),(69,74),(70,73),(70,74),(71,75),(72,75),(73,75),(74,75)],76)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(1,11),(1,12),(1,51),(1,52),(2,16),(2,20),(2,24),(2,28),(2,30),(2,52),(3,15),(3,19),(3,23),(3,28),(3,29),(3,51),(4,17),(4,21),(4,25),(4,27),(4,29),(4,52),(5,18),(5,22),(5,26),(5,27),(5,30),(5,51),(6,9),(6,11),(6,14),(6,19),(6,20),(6,21),(6,22),(7,9),(7,10),(7,13),(7,15),(7,16),(7,17),(7,18),(8,12),(8,13),(8,14),(8,23),(8,24),(8,25),(8,26),(9,37),(9,40),(9,69),(9,70),(10,37),(10,49),(10,53),(10,54),(11,37),(11,50),(11,55),(11,56),(12,49),(12,50),(12,57),(12,58),(13,40),(13,41),(13,42),(13,43),(13,44),(13,49),(14,40),(14,45),(14,46),(14,47),(14,48),(14,50),(15,33),(15,41),(15,53),(15,69),(16,34),(16,42),(16,54),(16,69),(17,33),(17,43),(17,54),(17,70),(18,34),(18,44),(18,53),(18,70),(19,35),(19,45),(19,55),(19,69),(20,36),(20,46),(20,56),(20,69),(21,35),(21,47),(21,56),(21,70),(22,36),(22,48),(22,55),(22,70),(23,31),(23,38),(23,41),(23,45),(23,57),(24,32),(24,38),(24,42),(24,46),(24,58),(25,31),(25,39),(25,43),(25,47),(25,58),(26,32),(26,39),(26,44),(26,48),(26,57),(27,39),(27,68),(27,70),(28,38),(28,68),(28,69),(29,31),(29,33),(29,35),(29,68),(30,32),(30,34),(30,36),(30,68),(31,60),(31,62),(31,71),(32,61),(32,63),(32,71),(33,60),(33,74),(34,61),(34,74),(35,62),(35,74),(36,63),(36,74),(37,59),(37,74),(38,71),(38,72),(39,71),(39,73),(40,59),(40,72),(40,73),(41,60),(41,64),(41,72),(42,61),(42,65),(42,72),(43,60),(43,65),(43,73),(44,61),(44,64),(44,73),(45,62),(45,66),(45,72),(46,63),(46,67),(46,72),(47,62),(47,67),(47,73),(48,63),(48,66),(48,73),(49,59),(49,64),(49,65),(50,59),(50,66),(50,67),(51,53),(51,55),(51,57),(51,68),(52,54),(52,56),(52,58),(52,68),(53,64),(53,74),(54,65),(54,74),(55,66),(55,74),(56,67),(56,74),(57,64),(57,66),(57,71),(58,65),(58,67),(58,71),(59,75),(60,75),(61,75),(62,75),(63,75),(64,75),(65,75),(66,75),(67,75),(68,71),(68,74),(69,72),(69,74),(70,73),(70,74),(71,75),(72,75),(73,75),(74,75)],76)
=> ? = 4 - 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
=> ? = 3 - 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,13),(4,15),(4,19),(4,20),(4,21),(4,60),(5,13),(5,14),(5,16),(5,17),(5,18),(5,59),(6,12),(6,14),(6,22),(6,23),(6,24),(6,60),(7,12),(7,15),(7,25),(7,26),(7,27),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,32),(9,33),(9,68),(9,71),(10,32),(10,34),(10,69),(10,72),(11,33),(11,34),(11,70),(11,73),(12,56),(12,57),(12,58),(12,80),(13,53),(13,54),(13,55),(13,80),(14,35),(14,36),(14,37),(14,80),(15,38),(15,39),(15,40),(15,80),(16,35),(16,41),(16,42),(16,53),(16,68),(17,36),(17,41),(17,43),(17,54),(17,69),(18,37),(18,42),(18,43),(18,55),(18,70),(19,38),(19,44),(19,45),(19,53),(19,71),(20,39),(20,44),(20,46),(20,54),(20,72),(21,40),(21,45),(21,46),(21,55),(21,73),(22,35),(22,47),(22,48),(22,56),(22,71),(23,36),(23,47),(23,49),(23,57),(23,72),(24,37),(24,48),(24,49),(24,58),(24,73),(25,38),(25,50),(25,51),(25,56),(25,68),(26,39),(26,50),(26,52),(26,57),(26,69),(27,40),(27,51),(27,52),(27,58),(27,70),(28,31),(28,32),(28,41),(28,44),(28,47),(28,50),(29,31),(29,33),(29,42),(29,45),(29,48),(29,51),(30,31),(30,34),(30,43),(30,46),(30,49),(30,52),(31,67),(31,84),(31,85),(32,67),(32,76),(32,79),(33,67),(33,74),(33,77),(34,67),(34,75),(34,78),(35,81),(35,84),(36,82),(36,84),(37,83),(37,84),(38,81),(38,85),(39,82),(39,85),(40,83),(40,85),(41,63),(41,76),(41,84),(42,61),(42,74),(42,84),(43,62),(43,75),(43,84),(44,63),(44,79),(44,85),(45,61),(45,77),(45,85),(46,62),(46,78),(46,85),(47,66),(47,79),(47,84),(48,64),(48,77),(48,84),(49,65),(49,78),(49,84),(50,66),(50,76),(50,85),(51,64),(51,74),(51,85),(52,65),(52,75),(52,85),(53,61),(53,63),(53,81),(54,62),(54,63),(54,82),(55,61),(55,62),(55,83),(56,64),(56,66),(56,81),(57,65),(57,66),(57,82),(58,64),(58,65),(58,83),(59,68),(59,69),(59,70),(59,80),(60,71),(60,72),(60,73),(60,80),(61,86),(62,86),(63,86),(64,86),(65,86),(66,86),(67,86),(68,74),(68,76),(68,81),(69,75),(69,76),(69,82),(70,74),(70,75),(70,83),(71,77),(71,79),(71,81),(72,78),(72,79),(72,82),(73,77),(73,78),(73,83),(74,86),(75,86),(76,86),(77,86),(78,86),(79,86),(80,81),(80,82),(80,83),(81,86),(82,86),(83,86),(84,86),(85,86)],87)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,18),(1,21),(1,24),(1,27),(1,29),(1,30),(2,10),(2,17),(2,20),(2,23),(2,26),(2,28),(2,30),(3,9),(3,16),(3,19),(3,22),(3,25),(3,28),(3,29),(4,13),(4,15),(4,19),(4,20),(4,21),(4,60),(5,13),(5,14),(5,16),(5,17),(5,18),(5,59),(6,12),(6,14),(6,22),(6,23),(6,24),(6,60),(7,12),(7,15),(7,25),(7,26),(7,27),(7,59),(8,9),(8,10),(8,11),(8,59),(8,60),(9,32),(9,33),(9,68),(9,71),(10,32),(10,34),(10,69),(10,72),(11,33),(11,34),(11,70),(11,73),(12,56),(12,57),(12,58),(12,80),(13,53),(13,54),(13,55),(13,80),(14,35),(14,36),(14,37),(14,80),(15,38),(15,39),(15,40),(15,80),(16,35),(16,41),(16,42),(16,53),(16,68),(17,36),(17,41),(17,43),(17,54),(17,69),(18,37),(18,42),(18,43),(18,55),(18,70),(19,38),(19,44),(19,45),(19,53),(19,71),(20,39),(20,44),(20,46),(20,54),(20,72),(21,40),(21,45),(21,46),(21,55),(21,73),(22,35),(22,47),(22,48),(22,56),(22,71),(23,36),(23,47),(23,49),(23,57),(23,72),(24,37),(24,48),(24,49),(24,58),(24,73),(25,38),(25,50),(25,51),(25,56),(25,68),(26,39),(26,50),(26,52),(26,57),(26,69),(27,40),(27,51),(27,52),(27,58),(27,70),(28,31),(28,32),(28,41),(28,44),(28,47),(28,50),(29,31),(29,33),(29,42),(29,45),(29,48),(29,51),(30,31),(30,34),(30,43),(30,46),(30,49),(30,52),(31,67),(31,84),(31,85),(32,67),(32,76),(32,79),(33,67),(33,74),(33,77),(34,67),(34,75),(34,78),(35,81),(35,84),(36,82),(36,84),(37,83),(37,84),(38,81),(38,85),(39,82),(39,85),(40,83),(40,85),(41,63),(41,76),(41,84),(42,61),(42,74),(42,84),(43,62),(43,75),(43,84),(44,63),(44,79),(44,85),(45,61),(45,77),(45,85),(46,62),(46,78),(46,85),(47,66),(47,79),(47,84),(48,64),(48,77),(48,84),(49,65),(49,78),(49,84),(50,66),(50,76),(50,85),(51,64),(51,74),(51,85),(52,65),(52,75),(52,85),(53,61),(53,63),(53,81),(54,62),(54,63),(54,82),(55,61),(55,62),(55,83),(56,64),(56,66),(56,81),(57,65),(57,66),(57,82),(58,64),(58,65),(58,83),(59,68),(59,69),(59,70),(59,80),(60,71),(60,72),(60,73),(60,80),(61,86),(62,86),(63,86),(64,86),(65,86),(66,86),(67,86),(68,74),(68,76),(68,81),(69,75),(69,76),(69,82),(70,74),(70,75),(70,83),(71,77),(71,79),(71,81),(72,78),(72,79),(72,82),(73,77),(73,78),(73,83),(74,86),(75,86),(76,86),(77,86),(78,86),(79,86),(80,81),(80,82),(80,83),(81,86),(82,86),(83,86),(84,86),(85,86)],87)
=> ? = 4 - 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(1,9),(1,36),(1,37),(2,12),(2,16),(2,21),(2,22),(2,37),(3,11),(3,15),(3,19),(3,20),(3,37),(4,14),(4,18),(4,20),(4,22),(4,36),(5,13),(5,17),(5,19),(5,21),(5,36),(6,9),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,10),(7,11),(7,12),(7,13),(7,14),(8,35),(8,38),(8,39),(9,35),(9,40),(9,41),(10,31),(10,32),(10,33),(10,34),(10,35),(11,23),(11,24),(11,31),(11,38),(12,25),(12,26),(12,32),(12,38),(13,23),(13,25),(13,33),(13,39),(14,24),(14,26),(14,34),(14,39),(15,27),(15,28),(15,31),(15,40),(16,29),(16,30),(16,32),(16,40),(17,27),(17,29),(17,33),(17,41),(18,28),(18,30),(18,34),(18,41),(19,23),(19,27),(19,48),(20,24),(20,28),(20,48),(21,25),(21,29),(21,48),(22,26),(22,30),(22,48),(23,42),(23,49),(24,43),(24,49),(25,44),(25,49),(26,45),(26,49),(27,42),(27,50),(28,43),(28,50),(29,44),(29,50),(30,45),(30,50),(31,42),(31,43),(31,46),(32,44),(32,45),(32,46),(33,42),(33,44),(33,47),(34,43),(34,45),(34,47),(35,46),(35,47),(36,39),(36,41),(36,48),(37,38),(37,40),(37,48),(38,46),(38,49),(39,47),(39,49),(40,46),(40,50),(41,47),(41,50),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,49),(48,50),(49,51),(50,51)],52)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,20),(1,21),(1,22),(1,23),(1,33),(1,61),(2,10),(2,16),(2,17),(2,18),(2,19),(2,32),(2,61),(3,13),(3,17),(3,21),(3,26),(3,27),(3,29),(3,60),(4,12),(4,16),(4,20),(4,24),(4,25),(4,28),(4,60),(5,15),(5,19),(5,23),(5,25),(5,27),(5,31),(5,59),(6,14),(6,18),(6,22),(6,24),(6,26),(6,30),(6,59),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,58),(8,12),(8,13),(8,14),(8,15),(8,58),(8,61),(9,10),(9,11),(9,58),(9,59),(9,60),(10,70),(10,71),(10,84),(11,72),(11,73),(11,84),(12,34),(12,35),(12,74),(12,82),(13,36),(13,37),(13,75),(13,82),(14,34),(14,36),(14,76),(14,83),(15,35),(15,37),(15,77),(15,83),(16,38),(16,39),(16,46),(16,70),(16,74),(17,40),(17,41),(17,47),(17,70),(17,75),(18,38),(18,40),(18,48),(18,71),(18,76),(19,39),(19,41),(19,49),(19,71),(19,77),(20,42),(20,43),(20,50),(20,72),(20,74),(21,44),(21,45),(21,51),(21,72),(21,75),(22,42),(22,44),(22,52),(22,73),(22,76),(23,43),(23,45),(23,53),(23,73),(23,77),(24,34),(24,38),(24,42),(24,54),(24,85),(25,35),(25,39),(25,43),(25,55),(25,85),(26,36),(26,40),(26,44),(26,56),(26,85),(27,37),(27,41),(27,45),(27,57),(27,85),(28,46),(28,50),(28,54),(28,55),(28,82),(29,47),(29,51),(29,56),(29,57),(29,82),(30,48),(30,52),(30,54),(30,56),(30,83),(31,49),(31,53),(31,55),(31,57),(31,83),(32,46),(32,47),(32,48),(32,49),(32,84),(33,50),(33,51),(33,52),(33,53),(33,84),(34,78),(34,90),(35,79),(35,90),(36,80),(36,90),(37,81),(37,90),(38,62),(38,78),(38,86),(39,63),(39,79),(39,86),(40,64),(40,80),(40,86),(41,65),(41,81),(41,86),(42,66),(42,78),(42,87),(43,67),(43,79),(43,87),(44,68),(44,80),(44,87),(45,69),(45,81),(45,87),(46,62),(46,63),(46,88),(47,64),(47,65),(47,88),(48,62),(48,64),(48,89),(49,63),(49,65),(49,89),(50,66),(50,67),(50,88),(51,68),(51,69),(51,88),(52,66),(52,68),(52,89),(53,67),(53,69),(53,89),(54,62),(54,66),(54,90),(55,63),(55,67),(55,90),(56,64),(56,68),(56,90),(57,65),(57,69),(57,90),(58,82),(58,83),(58,84),(59,71),(59,73),(59,83),(59,85),(60,70),(60,72),(60,82),(60,85),(61,74),(61,75),(61,76),(61,77),(61,84),(62,91),(63,91),(64,91),(65,91),(66,91),(67,91),(68,91),(69,91),(70,86),(70,88),(71,86),(71,89),(72,87),(72,88),(73,87),(73,89),(74,78),(74,79),(74,88),(75,80),(75,81),(75,88),(76,78),(76,80),(76,89),(77,79),(77,81),(77,89),(78,91),(79,91),(80,91),(81,91),(82,88),(82,90),(83,89),(83,90),(84,88),(84,89),(85,86),(85,87),(85,90),(86,91),(87,91),(88,91),(89,91),(90,91)],92)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,11),(1,20),(1,21),(1,22),(1,23),(1,33),(1,61),(2,10),(2,16),(2,17),(2,18),(2,19),(2,32),(2,61),(3,13),(3,17),(3,21),(3,26),(3,27),(3,29),(3,60),(4,12),(4,16),(4,20),(4,24),(4,25),(4,28),(4,60),(5,15),(5,19),(5,23),(5,25),(5,27),(5,31),(5,59),(6,14),(6,18),(6,22),(6,24),(6,26),(6,30),(6,59),(7,28),(7,29),(7,30),(7,31),(7,32),(7,33),(7,58),(8,12),(8,13),(8,14),(8,15),(8,58),(8,61),(9,10),(9,11),(9,58),(9,59),(9,60),(10,70),(10,71),(10,84),(11,72),(11,73),(11,84),(12,34),(12,35),(12,74),(12,82),(13,36),(13,37),(13,75),(13,82),(14,34),(14,36),(14,76),(14,83),(15,35),(15,37),(15,77),(15,83),(16,38),(16,39),(16,46),(16,70),(16,74),(17,40),(17,41),(17,47),(17,70),(17,75),(18,38),(18,40),(18,48),(18,71),(18,76),(19,39),(19,41),(19,49),(19,71),(19,77),(20,42),(20,43),(20,50),(20,72),(20,74),(21,44),(21,45),(21,51),(21,72),(21,75),(22,42),(22,44),(22,52),(22,73),(22,76),(23,43),(23,45),(23,53),(23,73),(23,77),(24,34),(24,38),(24,42),(24,54),(24,85),(25,35),(25,39),(25,43),(25,55),(25,85),(26,36),(26,40),(26,44),(26,56),(26,85),(27,37),(27,41),(27,45),(27,57),(27,85),(28,46),(28,50),(28,54),(28,55),(28,82),(29,47),(29,51),(29,56),(29,57),(29,82),(30,48),(30,52),(30,54),(30,56),(30,83),(31,49),(31,53),(31,55),(31,57),(31,83),(32,46),(32,47),(32,48),(32,49),(32,84),(33,50),(33,51),(33,52),(33,53),(33,84),(34,78),(34,90),(35,79),(35,90),(36,80),(36,90),(37,81),(37,90),(38,62),(38,78),(38,86),(39,63),(39,79),(39,86),(40,64),(40,80),(40,86),(41,65),(41,81),(41,86),(42,66),(42,78),(42,87),(43,67),(43,79),(43,87),(44,68),(44,80),(44,87),(45,69),(45,81),(45,87),(46,62),(46,63),(46,88),(47,64),(47,65),(47,88),(48,62),(48,64),(48,89),(49,63),(49,65),(49,89),(50,66),(50,67),(50,88),(51,68),(51,69),(51,88),(52,66),(52,68),(52,89),(53,67),(53,69),(53,89),(54,62),(54,66),(54,90),(55,63),(55,67),(55,90),(56,64),(56,68),(56,90),(57,65),(57,69),(57,90),(58,82),(58,83),(58,84),(59,71),(59,73),(59,83),(59,85),(60,70),(60,72),(60,82),(60,85),(61,74),(61,75),(61,76),(61,77),(61,84),(62,91),(63,91),(64,91),(65,91),(66,91),(67,91),(68,91),(69,91),(70,86),(70,88),(71,86),(71,89),(72,87),(72,88),(73,87),(73,89),(74,78),(74,79),(74,88),(75,80),(75,81),(75,88),(76,78),(76,80),(76,89),(77,79),(77,81),(77,89),(78,91),(79,91),(80,91),(81,91),(82,88),(82,90),(83,89),(83,90),(84,88),(84,89),(85,86),(85,87),(85,90),(86,91),(87,91),(88,91),(89,91),(90,91)],92)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,13),(1,15),(1,19),(1,23),(1,27),(1,31),(1,38),(1,39),(2,13),(2,14),(2,18),(2,22),(2,26),(2,30),(2,36),(2,37),(3,12),(3,17),(3,21),(3,25),(3,29),(3,33),(3,37),(3,39),(4,12),(4,16),(4,20),(4,24),(4,28),(4,32),(4,36),(4,38),(5,11),(5,22),(5,23),(5,24),(5,25),(5,35),(5,41),(6,11),(6,18),(6,19),(6,20),(6,21),(6,34),(6,40),(7,10),(7,26),(7,27),(7,28),(7,29),(7,34),(7,41),(8,10),(8,30),(8,31),(8,32),(8,33),(8,35),(8,40),(9,14),(9,15),(9,16),(9,17),(9,40),(9,41),(10,96),(10,100),(10,101),(11,96),(11,98),(11,99),(12,43),(12,97),(12,99),(12,101),(13,42),(13,97),(13,98),(13,100),(14,42),(14,44),(14,45),(14,80),(14,84),(15,42),(15,46),(15,47),(15,81),(15,85),(16,43),(16,44),(16,46),(16,82),(16,86),(17,43),(17,45),(17,47),(17,83),(17,87),(18,48),(18,49),(18,64),(18,80),(18,98),(19,50),(19,51),(19,65),(19,81),(19,98),(20,48),(20,50),(20,66),(20,82),(20,99),(21,49),(21,51),(21,67),(21,83),(21,99),(22,52),(22,53),(22,68),(22,84),(22,98),(23,54),(23,55),(23,69),(23,85),(23,98),(24,52),(24,54),(24,70),(24,86),(24,99),(25,53),(25,55),(25,71),(25,87),(25,99),(26,56),(26,57),(26,64),(26,84),(26,100),(27,58),(27,59),(27,65),(27,85),(27,100),(28,56),(28,58),(28,66),(28,86),(28,101),(29,57),(29,59),(29,67),(29,87),(29,101),(30,60),(30,61),(30,68),(30,80),(30,100),(31,62),(31,63),(31,69),(31,81),(31,100),(32,60),(32,62),(32,70),(32,82),(32,101),(33,61),(33,63),(33,71),(33,83),(33,101),(34,64),(34,65),(34,66),(34,67),(34,96),(35,68),(35,69),(35,70),(35,71),(35,96),(36,44),(36,48),(36,52),(36,56),(36,60),(36,97),(37,45),(37,49),(37,53),(37,57),(37,61),(37,97),(38,46),(38,50),(38,54),(38,58),(38,62),(38,97),(39,47),(39,51),(39,55),(39,59),(39,63),(39,97),(40,80),(40,81),(40,82),(40,83),(40,96),(41,84),(41,85),(41,86),(41,87),(41,96),(42,102),(42,105),(43,102),(43,106),(44,88),(44,92),(44,102),(45,89),(45,93),(45,102),(46,90),(46,94),(46,102),(47,91),(47,95),(47,102),(48,72),(48,88),(48,103),(49,73),(49,89),(49,103),(50,74),(50,90),(50,103),(51,75),(51,91),(51,103),(52,76),(52,92),(52,103),(53,77),(53,93),(53,103),(54,78),(54,94),(54,103),(55,79),(55,95),(55,103),(56,72),(56,92),(56,104),(57,73),(57,93),(57,104),(58,74),(58,94),(58,104),(59,75),(59,95),(59,104),(60,76),(60,88),(60,104),(61,77),(61,89),(61,104),(62,78),(62,90),(62,104),(63,79),(63,91),(63,104),(64,72),(64,73),(64,105),(65,74),(65,75),(65,105),(66,72),(66,74),(66,106),(67,73),(67,75),(67,106),(68,76),(68,77),(68,105),(69,78),(69,79),(69,105),(70,76),(70,78),(70,106),(71,77),(71,79),(71,106),(72,107),(73,107),(74,107),(75,107),(76,107),(77,107),(78,107),(79,107),(80,88),(80,89),(80,105),(81,90),(81,91),(81,105),(82,88),(82,90),(82,106),(83,89),(83,91),(83,106),(84,92),(84,93),(84,105),(85,94),(85,95),(85,105),(86,92),(86,94),(86,106),(87,93),(87,95),(87,106),(88,107),(89,107),(90,107),(91,107),(92,107),(93,107),(94,107),(95,107),(96,105),(96,106),(97,102),(97,103),(97,104),(98,103),(98,105),(99,103),(99,106),(100,104),(100,105),(101,104),(101,106),(102,107),(103,107),(104,107),(105,107),(106,107)],108)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,13),(1,15),(1,19),(1,23),(1,27),(1,31),(1,38),(1,39),(2,13),(2,14),(2,18),(2,22),(2,26),(2,30),(2,36),(2,37),(3,12),(3,17),(3,21),(3,25),(3,29),(3,33),(3,37),(3,39),(4,12),(4,16),(4,20),(4,24),(4,28),(4,32),(4,36),(4,38),(5,11),(5,22),(5,23),(5,24),(5,25),(5,35),(5,41),(6,11),(6,18),(6,19),(6,20),(6,21),(6,34),(6,40),(7,10),(7,26),(7,27),(7,28),(7,29),(7,34),(7,41),(8,10),(8,30),(8,31),(8,32),(8,33),(8,35),(8,40),(9,14),(9,15),(9,16),(9,17),(9,40),(9,41),(10,96),(10,100),(10,101),(11,96),(11,98),(11,99),(12,43),(12,97),(12,99),(12,101),(13,42),(13,97),(13,98),(13,100),(14,42),(14,44),(14,45),(14,80),(14,84),(15,42),(15,46),(15,47),(15,81),(15,85),(16,43),(16,44),(16,46),(16,82),(16,86),(17,43),(17,45),(17,47),(17,83),(17,87),(18,48),(18,49),(18,64),(18,80),(18,98),(19,50),(19,51),(19,65),(19,81),(19,98),(20,48),(20,50),(20,66),(20,82),(20,99),(21,49),(21,51),(21,67),(21,83),(21,99),(22,52),(22,53),(22,68),(22,84),(22,98),(23,54),(23,55),(23,69),(23,85),(23,98),(24,52),(24,54),(24,70),(24,86),(24,99),(25,53),(25,55),(25,71),(25,87),(25,99),(26,56),(26,57),(26,64),(26,84),(26,100),(27,58),(27,59),(27,65),(27,85),(27,100),(28,56),(28,58),(28,66),(28,86),(28,101),(29,57),(29,59),(29,67),(29,87),(29,101),(30,60),(30,61),(30,68),(30,80),(30,100),(31,62),(31,63),(31,69),(31,81),(31,100),(32,60),(32,62),(32,70),(32,82),(32,101),(33,61),(33,63),(33,71),(33,83),(33,101),(34,64),(34,65),(34,66),(34,67),(34,96),(35,68),(35,69),(35,70),(35,71),(35,96),(36,44),(36,48),(36,52),(36,56),(36,60),(36,97),(37,45),(37,49),(37,53),(37,57),(37,61),(37,97),(38,46),(38,50),(38,54),(38,58),(38,62),(38,97),(39,47),(39,51),(39,55),(39,59),(39,63),(39,97),(40,80),(40,81),(40,82),(40,83),(40,96),(41,84),(41,85),(41,86),(41,87),(41,96),(42,102),(42,105),(43,102),(43,106),(44,88),(44,92),(44,102),(45,89),(45,93),(45,102),(46,90),(46,94),(46,102),(47,91),(47,95),(47,102),(48,72),(48,88),(48,103),(49,73),(49,89),(49,103),(50,74),(50,90),(50,103),(51,75),(51,91),(51,103),(52,76),(52,92),(52,103),(53,77),(53,93),(53,103),(54,78),(54,94),(54,103),(55,79),(55,95),(55,103),(56,72),(56,92),(56,104),(57,73),(57,93),(57,104),(58,74),(58,94),(58,104),(59,75),(59,95),(59,104),(60,76),(60,88),(60,104),(61,77),(61,89),(61,104),(62,78),(62,90),(62,104),(63,79),(63,91),(63,104),(64,72),(64,73),(64,105),(65,74),(65,75),(65,105),(66,72),(66,74),(66,106),(67,73),(67,75),(67,106),(68,76),(68,77),(68,105),(69,78),(69,79),(69,105),(70,76),(70,78),(70,106),(71,77),(71,79),(71,106),(72,107),(73,107),(74,107),(75,107),(76,107),(77,107),(78,107),(79,107),(80,88),(80,89),(80,105),(81,90),(81,91),(81,105),(82,88),(82,90),(82,106),(83,89),(83,91),(83,106),(84,92),(84,93),(84,105),(85,94),(85,95),(85,105),(86,92),(86,94),(86,106),(87,93),(87,95),(87,106),(88,107),(89,107),(90,107),(91,107),(92,107),(93,107),(94,107),(95,107),(96,105),(96,106),(97,102),(97,103),(97,104),(98,103),(98,105),(99,103),(99,106),(100,104),(100,105),(101,104),(101,106),(102,107),(103,107),(104,107),(105,107),(106,107)],108)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,17),(1,21),(1,25),(1,29),(1,36),(1,37),(1,43),(2,12),(2,16),(2,20),(2,24),(2,28),(2,34),(2,35),(2,43),(3,15),(3,19),(3,23),(3,27),(3,31),(3,35),(3,37),(3,42),(4,14),(4,18),(4,22),(4,26),(4,30),(4,34),(4,36),(4,42),(5,11),(5,12),(5,13),(5,14),(5,15),(5,70),(5,71),(6,20),(6,21),(6,22),(6,23),(6,33),(6,69),(6,71),(7,16),(7,17),(7,18),(7,19),(7,33),(7,68),(7,70),(8,28),(8,29),(8,30),(8,31),(8,32),(8,68),(8,71),(9,24),(9,25),(9,26),(9,27),(9,32),(9,69),(9,70),(10,11),(10,42),(10,43),(10,68),(10,69),(11,80),(11,81),(11,103),(12,38),(12,39),(12,80),(12,82),(12,86),(13,40),(13,41),(13,80),(13,83),(13,87),(14,38),(14,40),(14,81),(14,84),(14,88),(15,39),(15,41),(15,81),(15,85),(15,89),(16,44),(16,45),(16,60),(16,82),(16,99),(17,46),(17,47),(17,61),(17,83),(17,99),(18,44),(18,46),(18,62),(18,84),(18,100),(19,45),(19,47),(19,63),(19,85),(19,100),(20,48),(20,49),(20,60),(20,86),(20,101),(21,50),(21,51),(21,61),(21,87),(21,101),(22,48),(22,50),(22,62),(22,88),(22,102),(23,49),(23,51),(23,63),(23,89),(23,102),(24,52),(24,53),(24,64),(24,82),(24,101),(25,54),(25,55),(25,65),(25,83),(25,101),(26,52),(26,54),(26,66),(26,84),(26,102),(27,53),(27,55),(27,67),(27,85),(27,102),(28,56),(28,57),(28,64),(28,86),(28,99),(29,58),(29,59),(29,65),(29,87),(29,99),(30,56),(30,58),(30,66),(30,88),(30,100),(31,57),(31,59),(31,67),(31,89),(31,100),(32,64),(32,65),(32,66),(32,67),(32,103),(33,60),(33,61),(33,62),(33,63),(33,103),(34,38),(34,44),(34,48),(34,52),(34,56),(34,98),(35,39),(35,45),(35,49),(35,53),(35,57),(35,98),(36,40),(36,46),(36,50),(36,54),(36,58),(36,98),(37,41),(37,47),(37,51),(37,55),(37,59),(37,98),(38,90),(38,94),(38,104),(39,91),(39,95),(39,104),(40,92),(40,96),(40,104),(41,93),(41,97),(41,104),(42,81),(42,98),(42,100),(42,102),(43,80),(43,98),(43,99),(43,101),(44,72),(44,90),(44,105),(45,73),(45,91),(45,105),(46,74),(46,92),(46,105),(47,75),(47,93),(47,105),(48,72),(48,94),(48,106),(49,73),(49,95),(49,106),(50,74),(50,96),(50,106),(51,75),(51,97),(51,106),(52,76),(52,90),(52,106),(53,77),(53,91),(53,106),(54,78),(54,92),(54,106),(55,79),(55,93),(55,106),(56,76),(56,94),(56,105),(57,77),(57,95),(57,105),(58,78),(58,96),(58,105),(59,79),(59,97),(59,105),(60,72),(60,73),(60,107),(61,74),(61,75),(61,107),(62,72),(62,74),(62,108),(63,73),(63,75),(63,108),(64,76),(64,77),(64,107),(65,78),(65,79),(65,107),(66,76),(66,78),(66,108),(67,77),(67,79),(67,108),(68,99),(68,100),(68,103),(69,101),(69,102),(69,103),(70,82),(70,83),(70,84),(70,85),(70,103),(71,86),(71,87),(71,88),(71,89),(71,103),(72,109),(73,109),(74,109),(75,109),(76,109),(77,109),(78,109),(79,109),(80,104),(80,107),(81,104),(81,108),(82,90),(82,91),(82,107),(83,92),(83,93),(83,107),(84,90),(84,92),(84,108),(85,91),(85,93),(85,108),(86,94),(86,95),(86,107),(87,96),(87,97),(87,107),(88,94),(88,96),(88,108),(89,95),(89,97),(89,108),(90,109),(91,109),(92,109),(93,109),(94,109),(95,109),(96,109),(97,109),(98,104),(98,105),(98,106),(99,105),(99,107),(100,105),(100,108),(101,106),(101,107),(102,106),(102,108),(103,107),(103,108),(104,109),(105,109),(106,109),(107,109),(108,109)],110)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,17),(1,21),(1,25),(1,29),(1,36),(1,37),(1,43),(2,12),(2,16),(2,20),(2,24),(2,28),(2,34),(2,35),(2,43),(3,15),(3,19),(3,23),(3,27),(3,31),(3,35),(3,37),(3,42),(4,14),(4,18),(4,22),(4,26),(4,30),(4,34),(4,36),(4,42),(5,11),(5,12),(5,13),(5,14),(5,15),(5,70),(5,71),(6,20),(6,21),(6,22),(6,23),(6,33),(6,69),(6,71),(7,16),(7,17),(7,18),(7,19),(7,33),(7,68),(7,70),(8,28),(8,29),(8,30),(8,31),(8,32),(8,68),(8,71),(9,24),(9,25),(9,26),(9,27),(9,32),(9,69),(9,70),(10,11),(10,42),(10,43),(10,68),(10,69),(11,80),(11,81),(11,103),(12,38),(12,39),(12,80),(12,82),(12,86),(13,40),(13,41),(13,80),(13,83),(13,87),(14,38),(14,40),(14,81),(14,84),(14,88),(15,39),(15,41),(15,81),(15,85),(15,89),(16,44),(16,45),(16,60),(16,82),(16,99),(17,46),(17,47),(17,61),(17,83),(17,99),(18,44),(18,46),(18,62),(18,84),(18,100),(19,45),(19,47),(19,63),(19,85),(19,100),(20,48),(20,49),(20,60),(20,86),(20,101),(21,50),(21,51),(21,61),(21,87),(21,101),(22,48),(22,50),(22,62),(22,88),(22,102),(23,49),(23,51),(23,63),(23,89),(23,102),(24,52),(24,53),(24,64),(24,82),(24,101),(25,54),(25,55),(25,65),(25,83),(25,101),(26,52),(26,54),(26,66),(26,84),(26,102),(27,53),(27,55),(27,67),(27,85),(27,102),(28,56),(28,57),(28,64),(28,86),(28,99),(29,58),(29,59),(29,65),(29,87),(29,99),(30,56),(30,58),(30,66),(30,88),(30,100),(31,57),(31,59),(31,67),(31,89),(31,100),(32,64),(32,65),(32,66),(32,67),(32,103),(33,60),(33,61),(33,62),(33,63),(33,103),(34,38),(34,44),(34,48),(34,52),(34,56),(34,98),(35,39),(35,45),(35,49),(35,53),(35,57),(35,98),(36,40),(36,46),(36,50),(36,54),(36,58),(36,98),(37,41),(37,47),(37,51),(37,55),(37,59),(37,98),(38,90),(38,94),(38,104),(39,91),(39,95),(39,104),(40,92),(40,96),(40,104),(41,93),(41,97),(41,104),(42,81),(42,98),(42,100),(42,102),(43,80),(43,98),(43,99),(43,101),(44,72),(44,90),(44,105),(45,73),(45,91),(45,105),(46,74),(46,92),(46,105),(47,75),(47,93),(47,105),(48,72),(48,94),(48,106),(49,73),(49,95),(49,106),(50,74),(50,96),(50,106),(51,75),(51,97),(51,106),(52,76),(52,90),(52,106),(53,77),(53,91),(53,106),(54,78),(54,92),(54,106),(55,79),(55,93),(55,106),(56,76),(56,94),(56,105),(57,77),(57,95),(57,105),(58,78),(58,96),(58,105),(59,79),(59,97),(59,105),(60,72),(60,73),(60,107),(61,74),(61,75),(61,107),(62,72),(62,74),(62,108),(63,73),(63,75),(63,108),(64,76),(64,77),(64,107),(65,78),(65,79),(65,107),(66,76),(66,78),(66,108),(67,77),(67,79),(67,108),(68,99),(68,100),(68,103),(69,101),(69,102),(69,103),(70,82),(70,83),(70,84),(70,85),(70,103),(71,86),(71,87),(71,88),(71,89),(71,103),(72,109),(73,109),(74,109),(75,109),(76,109),(77,109),(78,109),(79,109),(80,104),(80,107),(81,104),(81,108),(82,90),(82,91),(82,107),(83,92),(83,93),(83,107),(84,90),(84,92),(84,108),(85,91),(85,93),(85,108),(86,94),(86,95),(86,107),(87,96),(87,97),(87,107),(88,94),(88,96),(88,108),(89,95),(89,97),(89,108),(90,109),(91,109),(92,109),(93,109),(94,109),(95,109),(96,109),(97,109),(98,104),(98,105),(98,106),(99,105),(99,107),(100,105),(100,108),(101,106),(101,107),(102,106),(102,108),(103,107),(103,108),(104,109),(105,109),(106,109),(107,109),(108,109)],110)
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(1,40),(1,41),(2,15),(2,16),(2,17),(2,26),(2,27),(2,41),(3,12),(3,13),(3,14),(3,24),(3,25),(3,41),(4,21),(4,22),(4,23),(4,25),(4,27),(4,40),(5,18),(5,19),(5,20),(5,24),(5,26),(5,40),(6,11),(6,14),(6,17),(6,20),(6,23),(6,42),(7,10),(7,13),(7,16),(7,19),(7,22),(7,42),(8,9),(8,12),(8,15),(8,18),(8,21),(8,42),(9,43),(9,46),(9,49),(10,44),(10,47),(10,49),(11,45),(11,48),(11,49),(12,28),(12,31),(12,43),(12,50),(13,29),(13,32),(13,44),(13,50),(14,30),(14,33),(14,45),(14,50),(15,34),(15,37),(15,43),(15,51),(16,35),(16,38),(16,44),(16,51),(17,36),(17,39),(17,45),(17,51),(18,28),(18,34),(18,46),(18,52),(19,29),(19,35),(19,47),(19,52),(20,30),(20,36),(20,48),(20,52),(21,31),(21,37),(21,46),(21,53),(22,32),(22,38),(22,47),(22,53),(23,33),(23,39),(23,48),(23,53),(24,28),(24,29),(24,30),(24,58),(25,31),(25,32),(25,33),(25,58),(26,34),(26,35),(26,36),(26,58),(27,37),(27,38),(27,39),(27,58),(28,54),(28,61),(29,54),(29,62),(30,54),(30,63),(31,55),(31,61),(32,55),(32,62),(33,55),(33,63),(34,56),(34,61),(35,56),(35,62),(36,56),(36,63),(37,57),(37,61),(38,57),(38,62),(39,57),(39,63),(40,46),(40,47),(40,48),(40,58),(41,43),(41,44),(41,45),(41,58),(42,49),(42,50),(42,51),(42,52),(42,53),(43,59),(43,61),(44,59),(44,62),(45,59),(45,63),(46,60),(46,61),(47,60),(47,62),(48,60),(48,63),(49,59),(49,60),(50,54),(50,55),(50,59),(51,56),(51,57),(51,59),(52,54),(52,56),(52,60),(53,55),(53,57),(53,60),(54,64),(55,64),(56,64),(57,64),(58,61),(58,62),(58,63),(59,64),(60,64),(61,64),(62,64),(63,64)],65)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,10),(1,28),(1,29),(2,12),(2,16),(2,20),(2,22),(2,29),(3,11),(3,15),(3,20),(3,21),(3,28),(4,13),(4,17),(4,19),(4,21),(4,29),(5,14),(5,18),(5,19),(5,22),(5,28),(6,8),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(8,27),(8,34),(8,35),(9,27),(9,30),(9,31),(10,27),(10,32),(10,33),(11,23),(11,30),(11,34),(12,24),(12,31),(12,34),(13,23),(13,31),(13,35),(14,24),(14,30),(14,35),(15,25),(15,32),(15,34),(16,26),(16,33),(16,34),(17,25),(17,33),(17,35),(18,26),(18,32),(18,35),(19,35),(19,36),(20,34),(20,36),(21,23),(21,25),(21,36),(22,24),(22,26),(22,36),(23,37),(24,37),(25,37),(26,37),(27,37),(28,30),(28,32),(28,36),(29,31),(29,33),(29,36),(30,37),(31,37),(32,37),(33,37),(34,37),(35,37),(36,37)],38)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,10),(1,28),(1,29),(2,12),(2,16),(2,20),(2,22),(2,29),(3,11),(3,15),(3,20),(3,21),(3,28),(4,13),(4,17),(4,19),(4,21),(4,29),(5,14),(5,18),(5,19),(5,22),(5,28),(6,8),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(8,27),(8,34),(8,35),(9,27),(9,30),(9,31),(10,27),(10,32),(10,33),(11,23),(11,30),(11,34),(12,24),(12,31),(12,34),(13,23),(13,31),(13,35),(14,24),(14,30),(14,35),(15,25),(15,32),(15,34),(16,26),(16,33),(16,34),(17,25),(17,33),(17,35),(18,26),(18,32),(18,35),(19,35),(19,36),(20,34),(20,36),(21,23),(21,25),(21,36),(22,24),(22,26),(22,36),(23,37),(24,37),(25,37),(26,37),(27,37),(28,30),(28,32),(28,36),(29,31),(29,33),(29,36),(30,37),(31,37),(32,37),(33,37),(34,37),(35,37),(36,37)],38)
=> ? = 3 - 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,16),(1,20),(1,24),(1,30),(1,32),(2,15),(2,19),(2,23),(2,30),(2,31),(3,17),(3,21),(3,23),(3,29),(3,32),(4,18),(4,22),(4,24),(4,29),(4,31),(5,10),(5,13),(5,14),(5,17),(5,18),(5,30),(6,10),(6,11),(6,12),(6,15),(6,16),(6,29),(7,9),(7,11),(7,13),(7,19),(7,22),(7,32),(8,9),(8,12),(8,14),(8,20),(8,21),(8,31),(9,35),(9,36),(9,41),(10,33),(10,34),(10,41),(11,25),(11,38),(11,41),(12,26),(12,37),(12,41),(13,28),(13,39),(13,41),(14,27),(14,40),(14,41),(15,25),(15,33),(15,37),(16,26),(16,33),(16,38),(17,27),(17,34),(17,39),(18,28),(18,34),(18,40),(19,25),(19,35),(19,39),(20,26),(20,36),(20,40),(21,27),(21,36),(21,37),(22,28),(22,35),(22,38),(23,37),(23,39),(24,38),(24,40),(25,42),(26,42),(27,42),(28,42),(29,34),(29,37),(29,38),(30,33),(30,39),(30,40),(31,35),(31,37),(31,40),(32,36),(32,38),(32,39),(33,42),(34,42),(35,42),(36,42),(37,42),(38,42),(39,42),(40,42),(41,42)],43)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,16),(1,20),(1,24),(1,30),(1,32),(2,15),(2,19),(2,23),(2,30),(2,31),(3,17),(3,21),(3,23),(3,29),(3,32),(4,18),(4,22),(4,24),(4,29),(4,31),(5,10),(5,13),(5,14),(5,17),(5,18),(5,30),(6,10),(6,11),(6,12),(6,15),(6,16),(6,29),(7,9),(7,11),(7,13),(7,19),(7,22),(7,32),(8,9),(8,12),(8,14),(8,20),(8,21),(8,31),(9,35),(9,36),(9,41),(10,33),(10,34),(10,41),(11,25),(11,38),(11,41),(12,26),(12,37),(12,41),(13,28),(13,39),(13,41),(14,27),(14,40),(14,41),(15,25),(15,33),(15,37),(16,26),(16,33),(16,38),(17,27),(17,34),(17,39),(18,28),(18,34),(18,40),(19,25),(19,35),(19,39),(20,26),(20,36),(20,40),(21,27),(21,36),(21,37),(22,28),(22,35),(22,38),(23,37),(23,39),(24,38),(24,40),(25,42),(26,42),(27,42),(28,42),(29,34),(29,37),(29,38),(30,33),(30,39),(30,40),(31,35),(31,37),(31,40),(32,36),(32,38),(32,39),(33,42),(34,42),(35,42),(36,42),(37,42),(38,42),(39,42),(40,42),(41,42)],43)
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,17),(1,18),(1,23),(1,24),(1,32),(1,33),(1,36),(1,39),(2,14),(2,16),(2,20),(2,22),(2,31),(2,33),(2,35),(2,38),(3,13),(3,15),(3,19),(3,21),(3,31),(3,32),(3,34),(3,37),(4,12),(4,15),(4,16),(4,25),(4,26),(4,36),(4,75),(5,10),(5,13),(5,17),(5,27),(5,29),(5,35),(5,75),(6,11),(6,14),(6,18),(6,28),(6,30),(6,34),(6,75),(7,12),(7,21),(7,22),(7,29),(7,30),(7,39),(7,74),(8,10),(8,19),(8,23),(8,26),(8,28),(8,38),(8,74),(9,11),(9,20),(9,24),(9,25),(9,27),(9,37),(9,74),(10,42),(10,83),(10,85),(10,102),(11,41),(11,82),(11,86),(11,103),(12,43),(12,84),(12,87),(12,101),(13,46),(13,56),(13,70),(13,88),(13,102),(14,47),(14,57),(14,71),(14,89),(14,103),(15,44),(15,58),(15,68),(15,88),(15,101),(16,45),(16,59),(16,69),(16,89),(16,101),(17,49),(17,60),(17,72),(17,90),(17,102),(18,48),(18,61),(18,73),(18,90),(18,103),(19,52),(19,62),(19,68),(19,91),(19,102),(20,53),(20,63),(20,69),(20,92),(20,103),(21,50),(21,64),(21,70),(21,91),(21,101),(22,51),(22,65),(22,71),(22,92),(22,101),(23,55),(23,66),(23,73),(23,93),(23,102),(24,54),(24,67),(24,72),(24,93),(24,103),(25,58),(25,67),(25,69),(25,82),(25,87),(26,59),(26,66),(26,68),(26,83),(26,87),(27,56),(27,63),(27,72),(27,82),(27,85),(28,57),(28,62),(28,73),(28,83),(28,86),(29,60),(29,65),(29,70),(29,84),(29,85),(30,61),(30,64),(30,71),(30,84),(30,86),(31,40),(31,46),(31,47),(31,52),(31,53),(31,101),(32,40),(32,44),(32,48),(32,50),(32,54),(32,102),(33,40),(33,45),(33,49),(33,51),(33,55),(33,103),(34,41),(34,47),(34,48),(34,62),(34,64),(34,88),(35,42),(35,46),(35,49),(35,63),(35,65),(35,89),(36,43),(36,44),(36,45),(36,66),(36,67),(36,90),(37,41),(37,53),(37,54),(37,56),(37,58),(37,91),(38,42),(38,52),(38,55),(38,57),(38,59),(38,92),(39,43),(39,50),(39,51),(39,60),(39,61),(39,93),(40,104),(40,105),(40,106),(41,94),(41,97),(41,106),(42,95),(42,98),(42,105),(43,96),(43,99),(43,104),(44,78),(44,104),(44,108),(45,79),(45,104),(45,109),(46,76),(46,105),(46,107),(47,77),(47,106),(47,107),(48,80),(48,106),(48,108),(49,81),(49,105),(49,109),(50,80),(50,104),(50,111),(51,81),(51,104),(51,112),(52,77),(52,105),(52,110),(53,76),(53,106),(53,110),(54,78),(54,106),(54,111),(55,79),(55,105),(55,112),(56,76),(56,94),(56,111),(57,77),(57,95),(57,112),(58,78),(58,94),(58,110),(59,79),(59,95),(59,110),(60,81),(60,96),(60,111),(61,80),(61,96),(61,112),(62,77),(62,97),(62,108),(63,76),(63,98),(63,109),(64,80),(64,97),(64,107),(65,81),(65,98),(65,107),(66,79),(66,99),(66,108),(67,78),(67,99),(67,109),(68,108),(68,110),(69,109),(69,110),(70,107),(70,111),(71,107),(71,112),(72,109),(72,111),(73,108),(73,112),(74,85),(74,86),(74,87),(74,91),(74,92),(74,93),(75,82),(75,83),(75,84),(75,88),(75,89),(75,90),(76,113),(77,113),(78,113),(79,113),(80,113),(81,113),(82,94),(82,100),(82,109),(83,95),(83,100),(83,108),(84,96),(84,100),(84,107),(85,98),(85,100),(85,111),(86,97),(86,100),(86,112),(87,99),(87,100),(87,110),(88,94),(88,107),(88,108),(89,95),(89,107),(89,109),(90,96),(90,108),(90,109),(91,97),(91,110),(91,111),(92,98),(92,110),(92,112),(93,99),(93,111),(93,112),(94,113),(95,113),(96,113),(97,113),(98,113),(99,113),(100,113),(101,104),(101,107),(101,110),(102,105),(102,108),(102,111),(103,106),(103,109),(103,112),(104,113),(105,113),(106,113),(107,113),(108,113),(109,113),(110,113),(111,113),(112,113)],114)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,17),(1,18),(1,23),(1,24),(1,32),(1,33),(1,36),(1,39),(2,14),(2,16),(2,20),(2,22),(2,31),(2,33),(2,35),(2,38),(3,13),(3,15),(3,19),(3,21),(3,31),(3,32),(3,34),(3,37),(4,12),(4,15),(4,16),(4,25),(4,26),(4,36),(4,75),(5,10),(5,13),(5,17),(5,27),(5,29),(5,35),(5,75),(6,11),(6,14),(6,18),(6,28),(6,30),(6,34),(6,75),(7,12),(7,21),(7,22),(7,29),(7,30),(7,39),(7,74),(8,10),(8,19),(8,23),(8,26),(8,28),(8,38),(8,74),(9,11),(9,20),(9,24),(9,25),(9,27),(9,37),(9,74),(10,42),(10,83),(10,85),(10,102),(11,41),(11,82),(11,86),(11,103),(12,43),(12,84),(12,87),(12,101),(13,46),(13,56),(13,70),(13,88),(13,102),(14,47),(14,57),(14,71),(14,89),(14,103),(15,44),(15,58),(15,68),(15,88),(15,101),(16,45),(16,59),(16,69),(16,89),(16,101),(17,49),(17,60),(17,72),(17,90),(17,102),(18,48),(18,61),(18,73),(18,90),(18,103),(19,52),(19,62),(19,68),(19,91),(19,102),(20,53),(20,63),(20,69),(20,92),(20,103),(21,50),(21,64),(21,70),(21,91),(21,101),(22,51),(22,65),(22,71),(22,92),(22,101),(23,55),(23,66),(23,73),(23,93),(23,102),(24,54),(24,67),(24,72),(24,93),(24,103),(25,58),(25,67),(25,69),(25,82),(25,87),(26,59),(26,66),(26,68),(26,83),(26,87),(27,56),(27,63),(27,72),(27,82),(27,85),(28,57),(28,62),(28,73),(28,83),(28,86),(29,60),(29,65),(29,70),(29,84),(29,85),(30,61),(30,64),(30,71),(30,84),(30,86),(31,40),(31,46),(31,47),(31,52),(31,53),(31,101),(32,40),(32,44),(32,48),(32,50),(32,54),(32,102),(33,40),(33,45),(33,49),(33,51),(33,55),(33,103),(34,41),(34,47),(34,48),(34,62),(34,64),(34,88),(35,42),(35,46),(35,49),(35,63),(35,65),(35,89),(36,43),(36,44),(36,45),(36,66),(36,67),(36,90),(37,41),(37,53),(37,54),(37,56),(37,58),(37,91),(38,42),(38,52),(38,55),(38,57),(38,59),(38,92),(39,43),(39,50),(39,51),(39,60),(39,61),(39,93),(40,104),(40,105),(40,106),(41,94),(41,97),(41,106),(42,95),(42,98),(42,105),(43,96),(43,99),(43,104),(44,78),(44,104),(44,108),(45,79),(45,104),(45,109),(46,76),(46,105),(46,107),(47,77),(47,106),(47,107),(48,80),(48,106),(48,108),(49,81),(49,105),(49,109),(50,80),(50,104),(50,111),(51,81),(51,104),(51,112),(52,77),(52,105),(52,110),(53,76),(53,106),(53,110),(54,78),(54,106),(54,111),(55,79),(55,105),(55,112),(56,76),(56,94),(56,111),(57,77),(57,95),(57,112),(58,78),(58,94),(58,110),(59,79),(59,95),(59,110),(60,81),(60,96),(60,111),(61,80),(61,96),(61,112),(62,77),(62,97),(62,108),(63,76),(63,98),(63,109),(64,80),(64,97),(64,107),(65,81),(65,98),(65,107),(66,79),(66,99),(66,108),(67,78),(67,99),(67,109),(68,108),(68,110),(69,109),(69,110),(70,107),(70,111),(71,107),(71,112),(72,109),(72,111),(73,108),(73,112),(74,85),(74,86),(74,87),(74,91),(74,92),(74,93),(75,82),(75,83),(75,84),(75,88),(75,89),(75,90),(76,113),(77,113),(78,113),(79,113),(80,113),(81,113),(82,94),(82,100),(82,109),(83,95),(83,100),(83,108),(84,96),(84,100),(84,107),(85,98),(85,100),(85,111),(86,97),(86,100),(86,112),(87,99),(87,100),(87,110),(88,94),(88,107),(88,108),(89,95),(89,107),(89,109),(90,96),(90,108),(90,109),(91,97),(91,110),(91,111),(92,98),(92,110),(92,112),(93,99),(93,111),(93,112),(94,113),(95,113),(96,113),(97,113),(98,113),(99,113),(100,113),(101,104),(101,107),(101,110),(102,105),(102,108),(102,111),(103,106),(103,109),(103,112),(104,113),(105,113),(106,113),(107,113),(108,113),(109,113),(110,113),(111,113),(112,113)],114)
=> ? = 6 - 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,13),(1,22),(1,25),(1,26),(1,52),(2,10),(2,11),(2,22),(2,23),(2,24),(2,51),(3,16),(3,17),(3,24),(3,29),(3,30),(3,52),(4,14),(4,15),(4,23),(4,27),(4,28),(4,52),(5,20),(5,21),(5,26),(5,28),(5,30),(5,51),(6,18),(6,19),(6,25),(6,27),(6,29),(6,51),(7,9),(7,11),(7,13),(7,15),(7,17),(7,19),(7,21),(8,9),(8,10),(8,12),(8,14),(8,16),(8,18),(8,20),(9,31),(9,32),(9,33),(9,34),(9,75),(10,35),(10,37),(10,59),(10,75),(11,36),(11,38),(11,60),(11,75),(12,39),(12,41),(12,61),(12,75),(13,40),(13,42),(13,62),(13,75),(14,31),(14,35),(14,43),(14,45),(14,61),(15,31),(15,36),(15,44),(15,46),(15,62),(16,32),(16,37),(16,47),(16,49),(16,61),(17,32),(17,38),(17,48),(17,50),(17,62),(18,33),(18,39),(18,43),(18,47),(18,59),(19,33),(19,40),(19,44),(19,48),(19,60),(20,34),(20,41),(20,45),(20,49),(20,59),(21,34),(21,42),(21,46),(21,50),(21,60),(22,53),(22,54),(22,75),(23,35),(23,36),(23,53),(23,55),(24,37),(24,38),(24,53),(24,56),(25,39),(25,40),(25,54),(25,57),(26,41),(26,42),(26,54),(26,58),(27,43),(27,44),(27,55),(27,57),(28,45),(28,46),(28,55),(28,58),(29,47),(29,48),(29,56),(29,57),(30,49),(30,50),(30,56),(30,58),(31,63),(31,64),(31,77),(32,65),(32,66),(32,77),(33,63),(33,65),(33,78),(34,64),(34,66),(34,78),(35,67),(35,77),(36,68),(36,77),(37,69),(37,77),(38,70),(38,77),(39,71),(39,78),(40,72),(40,78),(41,73),(41,78),(42,74),(42,78),(43,63),(43,67),(43,71),(44,63),(44,68),(44,72),(45,64),(45,67),(45,73),(46,64),(46,68),(46,74),(47,65),(47,69),(47,71),(48,65),(48,70),(48,72),(49,66),(49,69),(49,73),(50,66),(50,70),(50,74),(51,54),(51,55),(51,56),(51,59),(51,60),(52,53),(52,57),(52,58),(52,61),(52,62),(53,76),(53,77),(54,76),(54,78),(55,67),(55,68),(55,76),(56,69),(56,70),(56,76),(57,71),(57,72),(57,76),(58,73),(58,74),(58,76),(59,67),(59,69),(59,78),(60,68),(60,70),(60,78),(61,71),(61,73),(61,77),(62,72),(62,74),(62,77),(63,79),(64,79),(65,79),(66,79),(67,79),(68,79),(69,79),(70,79),(71,79),(72,79),(73,79),(74,79),(75,77),(75,78),(76,79),(77,79),(78,79)],80)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,13),(1,22),(1,25),(1,26),(1,52),(2,10),(2,11),(2,22),(2,23),(2,24),(2,51),(3,16),(3,17),(3,24),(3,29),(3,30),(3,52),(4,14),(4,15),(4,23),(4,27),(4,28),(4,52),(5,20),(5,21),(5,26),(5,28),(5,30),(5,51),(6,18),(6,19),(6,25),(6,27),(6,29),(6,51),(7,9),(7,11),(7,13),(7,15),(7,17),(7,19),(7,21),(8,9),(8,10),(8,12),(8,14),(8,16),(8,18),(8,20),(9,31),(9,32),(9,33),(9,34),(9,75),(10,35),(10,37),(10,59),(10,75),(11,36),(11,38),(11,60),(11,75),(12,39),(12,41),(12,61),(12,75),(13,40),(13,42),(13,62),(13,75),(14,31),(14,35),(14,43),(14,45),(14,61),(15,31),(15,36),(15,44),(15,46),(15,62),(16,32),(16,37),(16,47),(16,49),(16,61),(17,32),(17,38),(17,48),(17,50),(17,62),(18,33),(18,39),(18,43),(18,47),(18,59),(19,33),(19,40),(19,44),(19,48),(19,60),(20,34),(20,41),(20,45),(20,49),(20,59),(21,34),(21,42),(21,46),(21,50),(21,60),(22,53),(22,54),(22,75),(23,35),(23,36),(23,53),(23,55),(24,37),(24,38),(24,53),(24,56),(25,39),(25,40),(25,54),(25,57),(26,41),(26,42),(26,54),(26,58),(27,43),(27,44),(27,55),(27,57),(28,45),(28,46),(28,55),(28,58),(29,47),(29,48),(29,56),(29,57),(30,49),(30,50),(30,56),(30,58),(31,63),(31,64),(31,77),(32,65),(32,66),(32,77),(33,63),(33,65),(33,78),(34,64),(34,66),(34,78),(35,67),(35,77),(36,68),(36,77),(37,69),(37,77),(38,70),(38,77),(39,71),(39,78),(40,72),(40,78),(41,73),(41,78),(42,74),(42,78),(43,63),(43,67),(43,71),(44,63),(44,68),(44,72),(45,64),(45,67),(45,73),(46,64),(46,68),(46,74),(47,65),(47,69),(47,71),(48,65),(48,70),(48,72),(49,66),(49,69),(49,73),(50,66),(50,70),(50,74),(51,54),(51,55),(51,56),(51,59),(51,60),(52,53),(52,57),(52,58),(52,61),(52,62),(53,76),(53,77),(54,76),(54,78),(55,67),(55,68),(55,76),(56,69),(56,70),(56,76),(57,71),(57,72),(57,76),(58,73),(58,74),(58,76),(59,67),(59,69),(59,78),(60,68),(60,70),(60,78),(61,71),(61,73),(61,77),(62,72),(62,74),(62,77),(63,79),(64,79),(65,79),(66,79),(67,79),(68,79),(69,79),(70,79),(71,79),(72,79),(73,79),(74,79),(75,77),(75,78),(76,79),(77,79),(78,79)],80)
=> ? = 4 - 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,13),(1,22),(1,25),(1,26),(1,52),(2,10),(2,11),(2,22),(2,23),(2,24),(2,51),(3,16),(3,17),(3,24),(3,29),(3,30),(3,52),(4,14),(4,15),(4,23),(4,27),(4,28),(4,52),(5,20),(5,21),(5,26),(5,28),(5,30),(5,51),(6,18),(6,19),(6,25),(6,27),(6,29),(6,51),(7,9),(7,11),(7,13),(7,15),(7,17),(7,19),(7,21),(8,9),(8,10),(8,12),(8,14),(8,16),(8,18),(8,20),(9,31),(9,32),(9,33),(9,34),(9,75),(10,35),(10,37),(10,59),(10,75),(11,36),(11,38),(11,60),(11,75),(12,39),(12,41),(12,61),(12,75),(13,40),(13,42),(13,62),(13,75),(14,31),(14,35),(14,43),(14,45),(14,61),(15,31),(15,36),(15,44),(15,46),(15,62),(16,32),(16,37),(16,47),(16,49),(16,61),(17,32),(17,38),(17,48),(17,50),(17,62),(18,33),(18,39),(18,43),(18,47),(18,59),(19,33),(19,40),(19,44),(19,48),(19,60),(20,34),(20,41),(20,45),(20,49),(20,59),(21,34),(21,42),(21,46),(21,50),(21,60),(22,53),(22,54),(22,75),(23,35),(23,36),(23,53),(23,55),(24,37),(24,38),(24,53),(24,56),(25,39),(25,40),(25,54),(25,57),(26,41),(26,42),(26,54),(26,58),(27,43),(27,44),(27,55),(27,57),(28,45),(28,46),(28,55),(28,58),(29,47),(29,48),(29,56),(29,57),(30,49),(30,50),(30,56),(30,58),(31,63),(31,64),(31,77),(32,65),(32,66),(32,77),(33,63),(33,65),(33,78),(34,64),(34,66),(34,78),(35,67),(35,77),(36,68),(36,77),(37,69),(37,77),(38,70),(38,77),(39,71),(39,78),(40,72),(40,78),(41,73),(41,78),(42,74),(42,78),(43,63),(43,67),(43,71),(44,63),(44,68),(44,72),(45,64),(45,67),(45,73),(46,64),(46,68),(46,74),(47,65),(47,69),(47,71),(48,65),(48,70),(48,72),(49,66),(49,69),(49,73),(50,66),(50,70),(50,74),(51,54),(51,55),(51,56),(51,59),(51,60),(52,53),(52,57),(52,58),(52,61),(52,62),(53,76),(53,77),(54,76),(54,78),(55,67),(55,68),(55,76),(56,69),(56,70),(56,76),(57,71),(57,72),(57,76),(58,73),(58,74),(58,76),(59,67),(59,69),(59,78),(60,68),(60,70),(60,78),(61,71),(61,73),(61,77),(62,72),(62,74),(62,77),(63,79),(64,79),(65,79),(66,79),(67,79),(68,79),(69,79),(70,79),(71,79),(72,79),(73,79),(74,79),(75,77),(75,78),(76,79),(77,79),(78,79)],80)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(1,13),(1,22),(1,25),(1,26),(1,52),(2,10),(2,11),(2,22),(2,23),(2,24),(2,51),(3,16),(3,17),(3,24),(3,29),(3,30),(3,52),(4,14),(4,15),(4,23),(4,27),(4,28),(4,52),(5,20),(5,21),(5,26),(5,28),(5,30),(5,51),(6,18),(6,19),(6,25),(6,27),(6,29),(6,51),(7,9),(7,11),(7,13),(7,15),(7,17),(7,19),(7,21),(8,9),(8,10),(8,12),(8,14),(8,16),(8,18),(8,20),(9,31),(9,32),(9,33),(9,34),(9,75),(10,35),(10,37),(10,59),(10,75),(11,36),(11,38),(11,60),(11,75),(12,39),(12,41),(12,61),(12,75),(13,40),(13,42),(13,62),(13,75),(14,31),(14,35),(14,43),(14,45),(14,61),(15,31),(15,36),(15,44),(15,46),(15,62),(16,32),(16,37),(16,47),(16,49),(16,61),(17,32),(17,38),(17,48),(17,50),(17,62),(18,33),(18,39),(18,43),(18,47),(18,59),(19,33),(19,40),(19,44),(19,48),(19,60),(20,34),(20,41),(20,45),(20,49),(20,59),(21,34),(21,42),(21,46),(21,50),(21,60),(22,53),(22,54),(22,75),(23,35),(23,36),(23,53),(23,55),(24,37),(24,38),(24,53),(24,56),(25,39),(25,40),(25,54),(25,57),(26,41),(26,42),(26,54),(26,58),(27,43),(27,44),(27,55),(27,57),(28,45),(28,46),(28,55),(28,58),(29,47),(29,48),(29,56),(29,57),(30,49),(30,50),(30,56),(30,58),(31,63),(31,64),(31,77),(32,65),(32,66),(32,77),(33,63),(33,65),(33,78),(34,64),(34,66),(34,78),(35,67),(35,77),(36,68),(36,77),(37,69),(37,77),(38,70),(38,77),(39,71),(39,78),(40,72),(40,78),(41,73),(41,78),(42,74),(42,78),(43,63),(43,67),(43,71),(44,63),(44,68),(44,72),(45,64),(45,67),(45,73),(46,64),(46,68),(46,74),(47,65),(47,69),(47,71),(48,65),(48,70),(48,72),(49,66),(49,69),(49,73),(50,66),(50,70),(50,74),(51,54),(51,55),(51,56),(51,59),(51,60),(52,53),(52,57),(52,58),(52,61),(52,62),(53,76),(53,77),(54,76),(54,78),(55,67),(55,68),(55,76),(56,69),(56,70),(56,76),(57,71),(57,72),(57,76),(58,73),(58,74),(58,76),(59,67),(59,69),(59,78),(60,68),(60,70),(60,78),(61,71),(61,73),(61,77),(62,72),(62,74),(62,77),(63,79),(64,79),(65,79),(66,79),(67,79),(68,79),(69,79),(70,79),(71,79),(72,79),(73,79),(74,79),(75,77),(75,78),(76,79),(77,79),(78,79)],80)
=> ? = 3 - 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(1,14),(1,19),(1,24),(1,25),(1,26),(1,27),(2,10),(2,16),(2,23),(2,25),(2,28),(2,32),(2,33),(3,9),(3,15),(3,22),(3,24),(3,28),(3,30),(3,31),(4,12),(4,18),(4,21),(4,27),(4,29),(4,31),(4,33),(5,11),(5,17),(5,20),(5,26),(5,29),(5,30),(5,32),(6,11),(6,12),(6,14),(6,22),(6,23),(6,34),(7,9),(7,10),(7,13),(7,20),(7,21),(7,34),(8,15),(8,16),(8,17),(8,18),(8,19),(8,34),(9,47),(9,48),(9,76),(9,84),(10,49),(10,50),(10,77),(10,84),(11,51),(11,53),(11,78),(11,85),(12,52),(12,54),(12,79),(12,85),(13,43),(13,44),(13,75),(13,84),(14,45),(14,46),(14,75),(14,85),(15,55),(15,57),(15,58),(15,61),(15,76),(16,55),(16,59),(16,60),(16,62),(16,77),(17,56),(17,57),(17,59),(17,63),(17,78),(18,56),(18,58),(18,60),(18,64),(18,79),(19,61),(19,62),(19,63),(19,64),(19,75),(20,43),(20,47),(20,49),(20,65),(20,78),(21,44),(21,48),(21,50),(21,65),(21,79),(22,45),(22,51),(22,52),(22,66),(22,76),(23,46),(23,53),(23,54),(23,66),(23,77),(24,39),(24,40),(24,45),(24,61),(24,84),(25,41),(25,42),(25,46),(25,62),(25,84),(26,39),(26,41),(26,43),(26,63),(26,85),(27,40),(27,42),(27,44),(27,64),(27,85),(28,37),(28,38),(28,55),(28,66),(28,84),(29,35),(29,36),(29,56),(29,65),(29,85),(30,35),(30,37),(30,39),(30,47),(30,51),(30,57),(31,35),(31,38),(31,40),(31,48),(31,52),(31,58),(32,36),(32,37),(32,41),(32,49),(32,53),(32,59),(33,36),(33,38),(33,42),(33,50),(33,54),(33,60),(34,75),(34,76),(34,77),(34,78),(34,79),(35,71),(35,88),(35,90),(36,72),(36,89),(36,90),(37,73),(37,86),(37,90),(38,74),(38,87),(38,90),(39,67),(39,86),(39,88),(40,68),(40,87),(40,88),(41,69),(41,86),(41,89),(42,70),(42,87),(42,89),(43,86),(43,92),(44,87),(44,92),(45,88),(45,91),(46,89),(46,91),(47,71),(47,80),(47,86),(48,71),(48,81),(48,87),(49,72),(49,82),(49,86),(50,72),(50,83),(50,87),(51,73),(51,80),(51,88),(52,74),(52,81),(52,88),(53,73),(53,82),(53,89),(54,74),(54,83),(54,89),(55,90),(55,91),(56,90),(56,92),(57,67),(57,80),(57,90),(58,68),(58,81),(58,90),(59,69),(59,82),(59,90),(60,70),(60,83),(60,90),(61,67),(61,68),(61,91),(62,69),(62,70),(62,91),(63,67),(63,69),(63,92),(64,68),(64,70),(64,92),(65,71),(65,72),(65,92),(66,73),(66,74),(66,91),(67,93),(68,93),(69,93),(70,93),(71,93),(72,93),(73,93),(74,93),(75,91),(75,92),(76,80),(76,81),(76,91),(77,82),(77,83),(77,91),(78,80),(78,82),(78,92),(79,81),(79,83),(79,92),(80,93),(81,93),(82,93),(83,93),(84,86),(84,87),(84,91),(85,88),(85,89),(85,92),(86,93),(87,93),(88,93),(89,93),(90,93),(91,93),(92,93)],94)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(1,14),(1,19),(1,24),(1,25),(1,26),(1,27),(2,10),(2,16),(2,23),(2,25),(2,28),(2,32),(2,33),(3,9),(3,15),(3,22),(3,24),(3,28),(3,30),(3,31),(4,12),(4,18),(4,21),(4,27),(4,29),(4,31),(4,33),(5,11),(5,17),(5,20),(5,26),(5,29),(5,30),(5,32),(6,11),(6,12),(6,14),(6,22),(6,23),(6,34),(7,9),(7,10),(7,13),(7,20),(7,21),(7,34),(8,15),(8,16),(8,17),(8,18),(8,19),(8,34),(9,47),(9,48),(9,76),(9,84),(10,49),(10,50),(10,77),(10,84),(11,51),(11,53),(11,78),(11,85),(12,52),(12,54),(12,79),(12,85),(13,43),(13,44),(13,75),(13,84),(14,45),(14,46),(14,75),(14,85),(15,55),(15,57),(15,58),(15,61),(15,76),(16,55),(16,59),(16,60),(16,62),(16,77),(17,56),(17,57),(17,59),(17,63),(17,78),(18,56),(18,58),(18,60),(18,64),(18,79),(19,61),(19,62),(19,63),(19,64),(19,75),(20,43),(20,47),(20,49),(20,65),(20,78),(21,44),(21,48),(21,50),(21,65),(21,79),(22,45),(22,51),(22,52),(22,66),(22,76),(23,46),(23,53),(23,54),(23,66),(23,77),(24,39),(24,40),(24,45),(24,61),(24,84),(25,41),(25,42),(25,46),(25,62),(25,84),(26,39),(26,41),(26,43),(26,63),(26,85),(27,40),(27,42),(27,44),(27,64),(27,85),(28,37),(28,38),(28,55),(28,66),(28,84),(29,35),(29,36),(29,56),(29,65),(29,85),(30,35),(30,37),(30,39),(30,47),(30,51),(30,57),(31,35),(31,38),(31,40),(31,48),(31,52),(31,58),(32,36),(32,37),(32,41),(32,49),(32,53),(32,59),(33,36),(33,38),(33,42),(33,50),(33,54),(33,60),(34,75),(34,76),(34,77),(34,78),(34,79),(35,71),(35,88),(35,90),(36,72),(36,89),(36,90),(37,73),(37,86),(37,90),(38,74),(38,87),(38,90),(39,67),(39,86),(39,88),(40,68),(40,87),(40,88),(41,69),(41,86),(41,89),(42,70),(42,87),(42,89),(43,86),(43,92),(44,87),(44,92),(45,88),(45,91),(46,89),(46,91),(47,71),(47,80),(47,86),(48,71),(48,81),(48,87),(49,72),(49,82),(49,86),(50,72),(50,83),(50,87),(51,73),(51,80),(51,88),(52,74),(52,81),(52,88),(53,73),(53,82),(53,89),(54,74),(54,83),(54,89),(55,90),(55,91),(56,90),(56,92),(57,67),(57,80),(57,90),(58,68),(58,81),(58,90),(59,69),(59,82),(59,90),(60,70),(60,83),(60,90),(61,67),(61,68),(61,91),(62,69),(62,70),(62,91),(63,67),(63,69),(63,92),(64,68),(64,70),(64,92),(65,71),(65,72),(65,92),(66,73),(66,74),(66,91),(67,93),(68,93),(69,93),(70,93),(71,93),(72,93),(73,93),(74,93),(75,91),(75,92),(76,80),(76,81),(76,91),(77,82),(77,83),(77,91),(78,80),(78,82),(78,92),(79,81),(79,83),(79,92),(80,93),(81,93),(82,93),(83,93),(84,86),(84,87),(84,91),(85,88),(85,89),(85,92),(86,93),(87,93),(88,93),(89,93),(90,93),(91,93),(92,93)],94)
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,14),(1,20),(1,21),(1,24),(1,27),(1,30),(2,10),(2,13),(2,19),(2,21),(2,23),(2,26),(2,29),(3,9),(3,12),(3,19),(3,20),(3,22),(3,25),(3,28),(4,12),(4,13),(4,14),(4,17),(4,18),(4,56),(5,15),(5,16),(5,22),(5,23),(5,24),(5,56),(6,16),(6,18),(6,28),(6,29),(6,30),(6,55),(7,15),(7,17),(7,25),(7,26),(7,27),(7,55),(8,9),(8,10),(8,11),(8,55),(8,56),(9,31),(9,32),(9,63),(9,66),(10,31),(10,33),(10,64),(10,67),(11,32),(11,33),(11,65),(11,68),(12,34),(12,37),(12,63),(12,72),(13,35),(13,38),(13,64),(13,72),(14,36),(14,39),(14,65),(14,72),(15,49),(15,50),(15,51),(15,73),(16,52),(16,53),(16,54),(16,73),(17,34),(17,35),(17,36),(17,73),(18,37),(18,38),(18,39),(18,73),(19,31),(19,42),(19,45),(19,48),(19,72),(20,32),(20,40),(20,43),(20,46),(20,72),(21,33),(21,41),(21,44),(21,47),(21,72),(22,46),(22,48),(22,49),(22,52),(22,63),(23,47),(23,48),(23,50),(23,53),(23,64),(24,46),(24,47),(24,51),(24,54),(24,65),(25,34),(25,40),(25,42),(25,49),(25,66),(26,35),(26,41),(26,42),(26,50),(26,67),(27,36),(27,40),(27,41),(27,51),(27,68),(28,37),(28,43),(28,45),(28,52),(28,66),(29,38),(29,44),(29,45),(29,53),(29,67),(30,39),(30,43),(30,44),(30,54),(30,68),(31,71),(31,79),(32,69),(32,79),(33,70),(33,79),(34,74),(34,77),(35,75),(35,77),(36,76),(36,77),(37,74),(37,78),(38,75),(38,78),(39,76),(39,78),(40,57),(40,69),(40,77),(41,58),(41,70),(41,77),(42,59),(42,71),(42,77),(43,60),(43,69),(43,78),(44,61),(44,70),(44,78),(45,62),(45,71),(45,78),(46,57),(46,60),(46,79),(47,58),(47,61),(47,79),(48,59),(48,62),(48,79),(49,57),(49,59),(49,74),(50,58),(50,59),(50,75),(51,57),(51,58),(51,76),(52,60),(52,62),(52,74),(53,61),(53,62),(53,75),(54,60),(54,61),(54,76),(55,66),(55,67),(55,68),(55,73),(56,63),(56,64),(56,65),(56,73),(57,80),(58,80),(59,80),(60,80),(61,80),(62,80),(63,74),(63,79),(64,75),(64,79),(65,76),(65,79),(66,69),(66,71),(66,74),(67,70),(67,71),(67,75),(68,69),(68,70),(68,76),(69,80),(70,80),(71,80),(72,77),(72,78),(72,79),(73,74),(73,75),(73,76),(74,80),(75,80),(76,80),(77,80),(78,80),(79,80)],81)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(1,14),(1,20),(1,21),(1,24),(1,27),(1,30),(2,10),(2,13),(2,19),(2,21),(2,23),(2,26),(2,29),(3,9),(3,12),(3,19),(3,20),(3,22),(3,25),(3,28),(4,12),(4,13),(4,14),(4,17),(4,18),(4,56),(5,15),(5,16),(5,22),(5,23),(5,24),(5,56),(6,16),(6,18),(6,28),(6,29),(6,30),(6,55),(7,15),(7,17),(7,25),(7,26),(7,27),(7,55),(8,9),(8,10),(8,11),(8,55),(8,56),(9,31),(9,32),(9,63),(9,66),(10,31),(10,33),(10,64),(10,67),(11,32),(11,33),(11,65),(11,68),(12,34),(12,37),(12,63),(12,72),(13,35),(13,38),(13,64),(13,72),(14,36),(14,39),(14,65),(14,72),(15,49),(15,50),(15,51),(15,73),(16,52),(16,53),(16,54),(16,73),(17,34),(17,35),(17,36),(17,73),(18,37),(18,38),(18,39),(18,73),(19,31),(19,42),(19,45),(19,48),(19,72),(20,32),(20,40),(20,43),(20,46),(20,72),(21,33),(21,41),(21,44),(21,47),(21,72),(22,46),(22,48),(22,49),(22,52),(22,63),(23,47),(23,48),(23,50),(23,53),(23,64),(24,46),(24,47),(24,51),(24,54),(24,65),(25,34),(25,40),(25,42),(25,49),(25,66),(26,35),(26,41),(26,42),(26,50),(26,67),(27,36),(27,40),(27,41),(27,51),(27,68),(28,37),(28,43),(28,45),(28,52),(28,66),(29,38),(29,44),(29,45),(29,53),(29,67),(30,39),(30,43),(30,44),(30,54),(30,68),(31,71),(31,79),(32,69),(32,79),(33,70),(33,79),(34,74),(34,77),(35,75),(35,77),(36,76),(36,77),(37,74),(37,78),(38,75),(38,78),(39,76),(39,78),(40,57),(40,69),(40,77),(41,58),(41,70),(41,77),(42,59),(42,71),(42,77),(43,60),(43,69),(43,78),(44,61),(44,70),(44,78),(45,62),(45,71),(45,78),(46,57),(46,60),(46,79),(47,58),(47,61),(47,79),(48,59),(48,62),(48,79),(49,57),(49,59),(49,74),(50,58),(50,59),(50,75),(51,57),(51,58),(51,76),(52,60),(52,62),(52,74),(53,61),(53,62),(53,75),(54,60),(54,61),(54,76),(55,66),(55,67),(55,68),(55,73),(56,63),(56,64),(56,65),(56,73),(57,80),(58,80),(59,80),(60,80),(61,80),(62,80),(63,74),(63,79),(64,75),(64,79),(65,76),(65,79),(66,69),(66,71),(66,74),(67,70),(67,71),(67,75),(68,69),(68,70),(68,76),(69,80),(70,80),(71,80),(72,77),(72,78),(72,79),(73,74),(73,75),(73,76),(74,80),(75,80),(76,80),(77,80),(78,80),(79,80)],81)
=> ? = 3 - 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,16),(1,19),(1,21),(1,22),(1,25),(2,9),(2,15),(2,18),(2,20),(2,22),(2,24),(3,8),(3,14),(3,17),(3,20),(3,21),(3,23),(4,11),(4,12),(4,13),(4,23),(4,24),(4,25),(5,8),(5,9),(5,10),(5,11),(5,26),(6,13),(6,17),(6,18),(6,19),(6,26),(7,12),(7,14),(7,15),(7,16),(7,26),(8,30),(8,51),(8,58),(9,31),(9,52),(9,58),(10,32),(10,53),(10,58),(11,30),(11,31),(11,32),(11,54),(12,39),(12,40),(12,41),(12,54),(13,42),(13,43),(13,44),(13,54),(14,33),(14,34),(14,39),(14,51),(15,33),(15,35),(15,40),(15,52),(16,34),(16,35),(16,41),(16,53),(17,36),(17,37),(17,42),(17,51),(18,36),(18,38),(18,43),(18,52),(19,37),(19,38),(19,44),(19,53),(20,29),(20,33),(20,36),(20,58),(21,27),(21,34),(21,37),(21,58),(22,28),(22,35),(22,38),(22,58),(23,27),(23,29),(23,30),(23,39),(23,42),(24,28),(24,29),(24,31),(24,40),(24,43),(25,27),(25,28),(25,32),(25,41),(25,44),(26,51),(26,52),(26,53),(26,54),(27,45),(27,48),(27,59),(28,46),(28,49),(28,59),(29,47),(29,50),(29,59),(30,55),(30,59),(31,56),(31,59),(32,57),(32,59),(33,47),(33,60),(34,45),(34,60),(35,46),(35,60),(36,50),(36,60),(37,48),(37,60),(38,49),(38,60),(39,45),(39,47),(39,55),(40,46),(40,47),(40,56),(41,45),(41,46),(41,57),(42,48),(42,50),(42,55),(43,49),(43,50),(43,56),(44,48),(44,49),(44,57),(45,61),(46,61),(47,61),(48,61),(49,61),(50,61),(51,55),(51,60),(52,56),(52,60),(53,57),(53,60),(54,55),(54,56),(54,57),(55,61),(56,61),(57,61),(58,59),(58,60),(59,61),(60,61)],62)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,16),(1,19),(1,21),(1,22),(1,25),(2,9),(2,15),(2,18),(2,20),(2,22),(2,24),(3,8),(3,14),(3,17),(3,20),(3,21),(3,23),(4,11),(4,12),(4,13),(4,23),(4,24),(4,25),(5,8),(5,9),(5,10),(5,11),(5,26),(6,13),(6,17),(6,18),(6,19),(6,26),(7,12),(7,14),(7,15),(7,16),(7,26),(8,30),(8,51),(8,58),(9,31),(9,52),(9,58),(10,32),(10,53),(10,58),(11,30),(11,31),(11,32),(11,54),(12,39),(12,40),(12,41),(12,54),(13,42),(13,43),(13,44),(13,54),(14,33),(14,34),(14,39),(14,51),(15,33),(15,35),(15,40),(15,52),(16,34),(16,35),(16,41),(16,53),(17,36),(17,37),(17,42),(17,51),(18,36),(18,38),(18,43),(18,52),(19,37),(19,38),(19,44),(19,53),(20,29),(20,33),(20,36),(20,58),(21,27),(21,34),(21,37),(21,58),(22,28),(22,35),(22,38),(22,58),(23,27),(23,29),(23,30),(23,39),(23,42),(24,28),(24,29),(24,31),(24,40),(24,43),(25,27),(25,28),(25,32),(25,41),(25,44),(26,51),(26,52),(26,53),(26,54),(27,45),(27,48),(27,59),(28,46),(28,49),(28,59),(29,47),(29,50),(29,59),(30,55),(30,59),(31,56),(31,59),(32,57),(32,59),(33,47),(33,60),(34,45),(34,60),(35,46),(35,60),(36,50),(36,60),(37,48),(37,60),(38,49),(38,60),(39,45),(39,47),(39,55),(40,46),(40,47),(40,56),(41,45),(41,46),(41,57),(42,48),(42,50),(42,55),(43,49),(43,50),(43,56),(44,48),(44,49),(44,57),(45,61),(46,61),(47,61),(48,61),(49,61),(50,61),(51,55),(51,60),(52,56),(52,60),(53,57),(53,60),(54,55),(54,56),(54,57),(55,61),(56,61),(57,61),(58,59),(58,60),(59,61),(60,61)],62)
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,16),(1,19),(1,21),(1,22),(1,25),(2,9),(2,15),(2,18),(2,20),(2,22),(2,24),(3,8),(3,14),(3,17),(3,20),(3,21),(3,23),(4,11),(4,12),(4,13),(4,23),(4,24),(4,25),(5,8),(5,9),(5,10),(5,11),(5,26),(6,13),(6,17),(6,18),(6,19),(6,26),(7,12),(7,14),(7,15),(7,16),(7,26),(8,30),(8,51),(8,58),(9,31),(9,52),(9,58),(10,32),(10,53),(10,58),(11,30),(11,31),(11,32),(11,54),(12,39),(12,40),(12,41),(12,54),(13,42),(13,43),(13,44),(13,54),(14,33),(14,34),(14,39),(14,51),(15,33),(15,35),(15,40),(15,52),(16,34),(16,35),(16,41),(16,53),(17,36),(17,37),(17,42),(17,51),(18,36),(18,38),(18,43),(18,52),(19,37),(19,38),(19,44),(19,53),(20,29),(20,33),(20,36),(20,58),(21,27),(21,34),(21,37),(21,58),(22,28),(22,35),(22,38),(22,58),(23,27),(23,29),(23,30),(23,39),(23,42),(24,28),(24,29),(24,31),(24,40),(24,43),(25,27),(25,28),(25,32),(25,41),(25,44),(26,51),(26,52),(26,53),(26,54),(27,45),(27,48),(27,59),(28,46),(28,49),(28,59),(29,47),(29,50),(29,59),(30,55),(30,59),(31,56),(31,59),(32,57),(32,59),(33,47),(33,60),(34,45),(34,60),(35,46),(35,60),(36,50),(36,60),(37,48),(37,60),(38,49),(38,60),(39,45),(39,47),(39,55),(40,46),(40,47),(40,56),(41,45),(41,46),(41,57),(42,48),(42,50),(42,55),(43,49),(43,50),(43,56),(44,48),(44,49),(44,57),(45,61),(46,61),(47,61),(48,61),(49,61),(50,61),(51,55),(51,60),(52,56),(52,60),(53,57),(53,60),(54,55),(54,56),(54,57),(55,61),(56,61),(57,61),(58,59),(58,60),(59,61),(60,61)],62)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,16),(1,19),(1,21),(1,22),(1,25),(2,9),(2,15),(2,18),(2,20),(2,22),(2,24),(3,8),(3,14),(3,17),(3,20),(3,21),(3,23),(4,11),(4,12),(4,13),(4,23),(4,24),(4,25),(5,8),(5,9),(5,10),(5,11),(5,26),(6,13),(6,17),(6,18),(6,19),(6,26),(7,12),(7,14),(7,15),(7,16),(7,26),(8,30),(8,51),(8,58),(9,31),(9,52),(9,58),(10,32),(10,53),(10,58),(11,30),(11,31),(11,32),(11,54),(12,39),(12,40),(12,41),(12,54),(13,42),(13,43),(13,44),(13,54),(14,33),(14,34),(14,39),(14,51),(15,33),(15,35),(15,40),(15,52),(16,34),(16,35),(16,41),(16,53),(17,36),(17,37),(17,42),(17,51),(18,36),(18,38),(18,43),(18,52),(19,37),(19,38),(19,44),(19,53),(20,29),(20,33),(20,36),(20,58),(21,27),(21,34),(21,37),(21,58),(22,28),(22,35),(22,38),(22,58),(23,27),(23,29),(23,30),(23,39),(23,42),(24,28),(24,29),(24,31),(24,40),(24,43),(25,27),(25,28),(25,32),(25,41),(25,44),(26,51),(26,52),(26,53),(26,54),(27,45),(27,48),(27,59),(28,46),(28,49),(28,59),(29,47),(29,50),(29,59),(30,55),(30,59),(31,56),(31,59),(32,57),(32,59),(33,47),(33,60),(34,45),(34,60),(35,46),(35,60),(36,50),(36,60),(37,48),(37,60),(38,49),(38,60),(39,45),(39,47),(39,55),(40,46),(40,47),(40,56),(41,45),(41,46),(41,57),(42,48),(42,50),(42,55),(43,49),(43,50),(43,56),(44,48),(44,49),(44,57),(45,61),(46,61),(47,61),(48,61),(49,61),(50,61),(51,55),(51,60),(52,56),(52,60),(53,57),(53,60),(54,55),(54,56),(54,57),(55,61),(56,61),(57,61),(58,59),(58,60),(59,61),(60,61)],62)
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,15),(1,16),(1,17),(1,18),(1,54),(1,55),(2,10),(2,13),(2,14),(2,20),(2,55),(2,57),(3,10),(3,11),(3,12),(3,19),(3,54),(3,56),(4,12),(4,16),(4,23),(4,24),(4,26),(4,30),(4,57),(5,11),(5,15),(5,21),(5,22),(5,25),(5,29),(5,57),(6,14),(6,18),(6,22),(6,24),(6,28),(6,32),(6,56),(7,13),(7,17),(7,21),(7,23),(7,27),(7,31),(7,56),(8,19),(8,27),(8,28),(8,29),(8,30),(8,33),(8,55),(9,20),(9,25),(9,26),(9,31),(9,32),(9,33),(9,54),(10,58),(10,59),(10,78),(11,42),(11,58),(11,60),(11,64),(12,43),(12,58),(12,61),(12,65),(13,44),(13,59),(13,62),(13,66),(14,45),(14,59),(14,63),(14,67),(15,38),(15,39),(15,60),(15,80),(16,40),(16,41),(16,61),(16,80),(17,38),(17,40),(17,62),(17,79),(18,39),(18,41),(18,63),(18,79),(19,42),(19,43),(19,68),(19,78),(20,44),(20,45),(20,69),(20,78),(21,38),(21,46),(21,50),(21,64),(21,66),(22,39),(22,47),(22,51),(22,64),(22,67),(23,40),(23,48),(23,52),(23,65),(23,66),(24,41),(24,49),(24,53),(24,65),(24,67),(25,34),(25,50),(25,51),(25,60),(25,69),(26,35),(26,52),(26,53),(26,61),(26,69),(27,36),(27,46),(27,48),(27,62),(27,68),(28,37),(28,47),(28,49),(28,63),(28,68),(29,34),(29,42),(29,46),(29,47),(29,80),(30,35),(30,43),(30,48),(30,49),(30,80),(31,36),(31,44),(31,50),(31,52),(31,79),(32,37),(32,45),(32,51),(32,53),(32,79),(33,34),(33,35),(33,36),(33,37),(33,78),(34,70),(34,71),(34,86),(35,72),(35,73),(35,86),(36,70),(36,72),(36,87),(37,71),(37,73),(37,87),(38,82),(38,84),(39,82),(39,85),(40,83),(40,84),(41,83),(41,85),(42,74),(42,86),(43,75),(43,86),(44,76),(44,87),(45,77),(45,87),(46,70),(46,74),(46,84),(47,71),(47,74),(47,85),(48,72),(48,75),(48,84),(49,73),(49,75),(49,85),(50,70),(50,76),(50,82),(51,71),(51,77),(51,82),(52,72),(52,76),(52,83),(53,73),(53,77),(53,83),(54,60),(54,61),(54,78),(54,79),(55,62),(55,63),(55,78),(55,80),(56,59),(56,64),(56,65),(56,68),(56,79),(57,58),(57,66),(57,67),(57,69),(57,80),(58,81),(58,86),(59,81),(59,87),(60,82),(60,86),(61,83),(61,86),(62,84),(62,87),(63,85),(63,87),(64,74),(64,81),(64,82),(65,75),(65,81),(65,83),(66,76),(66,81),(66,84),(67,77),(67,81),(67,85),(68,74),(68,75),(68,87),(69,76),(69,77),(69,86),(70,88),(71,88),(72,88),(73,88),(74,88),(75,88),(76,88),(77,88),(78,86),(78,87),(79,82),(79,83),(79,87),(80,84),(80,85),(80,86),(81,88),(82,88),(83,88),(84,88),(85,88),(86,88),(87,88)],89)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,15),(1,16),(1,17),(1,18),(1,54),(1,55),(2,10),(2,13),(2,14),(2,20),(2,55),(2,57),(3,10),(3,11),(3,12),(3,19),(3,54),(3,56),(4,12),(4,16),(4,23),(4,24),(4,26),(4,30),(4,57),(5,11),(5,15),(5,21),(5,22),(5,25),(5,29),(5,57),(6,14),(6,18),(6,22),(6,24),(6,28),(6,32),(6,56),(7,13),(7,17),(7,21),(7,23),(7,27),(7,31),(7,56),(8,19),(8,27),(8,28),(8,29),(8,30),(8,33),(8,55),(9,20),(9,25),(9,26),(9,31),(9,32),(9,33),(9,54),(10,58),(10,59),(10,78),(11,42),(11,58),(11,60),(11,64),(12,43),(12,58),(12,61),(12,65),(13,44),(13,59),(13,62),(13,66),(14,45),(14,59),(14,63),(14,67),(15,38),(15,39),(15,60),(15,80),(16,40),(16,41),(16,61),(16,80),(17,38),(17,40),(17,62),(17,79),(18,39),(18,41),(18,63),(18,79),(19,42),(19,43),(19,68),(19,78),(20,44),(20,45),(20,69),(20,78),(21,38),(21,46),(21,50),(21,64),(21,66),(22,39),(22,47),(22,51),(22,64),(22,67),(23,40),(23,48),(23,52),(23,65),(23,66),(24,41),(24,49),(24,53),(24,65),(24,67),(25,34),(25,50),(25,51),(25,60),(25,69),(26,35),(26,52),(26,53),(26,61),(26,69),(27,36),(27,46),(27,48),(27,62),(27,68),(28,37),(28,47),(28,49),(28,63),(28,68),(29,34),(29,42),(29,46),(29,47),(29,80),(30,35),(30,43),(30,48),(30,49),(30,80),(31,36),(31,44),(31,50),(31,52),(31,79),(32,37),(32,45),(32,51),(32,53),(32,79),(33,34),(33,35),(33,36),(33,37),(33,78),(34,70),(34,71),(34,86),(35,72),(35,73),(35,86),(36,70),(36,72),(36,87),(37,71),(37,73),(37,87),(38,82),(38,84),(39,82),(39,85),(40,83),(40,84),(41,83),(41,85),(42,74),(42,86),(43,75),(43,86),(44,76),(44,87),(45,77),(45,87),(46,70),(46,74),(46,84),(47,71),(47,74),(47,85),(48,72),(48,75),(48,84),(49,73),(49,75),(49,85),(50,70),(50,76),(50,82),(51,71),(51,77),(51,82),(52,72),(52,76),(52,83),(53,73),(53,77),(53,83),(54,60),(54,61),(54,78),(54,79),(55,62),(55,63),(55,78),(55,80),(56,59),(56,64),(56,65),(56,68),(56,79),(57,58),(57,66),(57,67),(57,69),(57,80),(58,81),(58,86),(59,81),(59,87),(60,82),(60,86),(61,83),(61,86),(62,84),(62,87),(63,85),(63,87),(64,74),(64,81),(64,82),(65,75),(65,81),(65,83),(66,76),(66,81),(66,84),(67,77),(67,81),(67,85),(68,74),(68,75),(68,87),(69,76),(69,77),(69,86),(70,88),(71,88),(72,88),(73,88),(74,88),(75,88),(76,88),(77,88),(78,86),(78,87),(79,82),(79,83),(79,87),(80,84),(80,85),(80,86),(81,88),(82,88),(83,88),(84,88),(85,88),(86,88),(87,88)],89)
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,20),(1,21),(1,22),(1,33),(2,9),(2,17),(2,18),(2,19),(2,33),(3,8),(3,14),(3,15),(3,16),(3,33),(4,13),(4,16),(4,19),(4,22),(4,32),(5,12),(5,15),(5,18),(5,21),(5,32),(6,11),(6,14),(6,17),(6,20),(6,32),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,23),(8,24),(8,25),(8,40),(9,26),(9,27),(9,28),(9,40),(10,29),(10,30),(10,31),(10,40),(11,23),(11,26),(11,29),(11,41),(12,24),(12,27),(12,30),(12,41),(13,25),(13,28),(13,31),(13,41),(14,23),(14,34),(14,37),(15,24),(15,35),(15,37),(16,25),(16,36),(16,37),(17,26),(17,34),(17,38),(18,27),(18,35),(18,38),(19,28),(19,36),(19,38),(20,29),(20,34),(20,39),(21,30),(21,35),(21,39),(22,31),(22,36),(22,39),(23,42),(23,45),(24,43),(24,45),(25,44),(25,45),(26,42),(26,46),(27,43),(27,46),(28,44),(28,46),(29,42),(29,47),(30,43),(30,47),(31,44),(31,47),(32,37),(32,38),(32,39),(32,41),(33,34),(33,35),(33,36),(33,40),(34,42),(34,48),(35,43),(35,48),(36,44),(36,48),(37,45),(37,48),(38,46),(38,48),(39,47),(39,48),(40,42),(40,43),(40,44),(41,45),(41,46),(41,47),(42,49),(43,49),(44,49),(45,49),(46,49),(47,49),(48,49)],50)
=> ? = 4 - 2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([],7)
=> ([],7)
=> ([],1)
=> ([],1)
=> 1 = 3 - 2
([(5,6)],7)
=> ([(5,6)],7)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 3 - 2
([(4,6),(5,6)],7)
=> ([(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(3,6),(4,6),(5,6)],7)
=> ([(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 3 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
=> ([(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(3,6),(4,5)],7)
=> ([(3,6),(4,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(3,6),(4,5),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 3 - 2
([(2,3),(4,6),(5,6)],7)
=> ([(2,3),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 3 - 2
([(4,5),(4,6),(5,6)],7)
=> ([(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1 = 3 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
=> ([(1,2),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
=> ([(1,6),(2,6),(3,5),(4,5)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(1,6),(2,5),(3,4)],7)
=> ([(1,6),(2,5),(3,4)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 3 - 2
([(1,2),(3,6),(4,5),(5,6)],7)
=> ([(1,2),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(0,3),(1,2),(4,6),(5,6)],7)
=> ([(0,3),(1,2),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,5),(4,5),(4,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> 1 = 3 - 2
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> 1 = 3 - 2
([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> 1 = 3 - 2
([(0,3),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> 1 = 3 - 2
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)
=> 1 = 3 - 2
Description
The number of minimal elements in a poset.
Mp00157: Graphs connected complementGraphs
Mp00243: Graphs weak duplicate orderPosets
Mp00195: Posets order idealsLattices
St001719: Lattices ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 20%
Values
([],3)
=> ([],3)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 3 - 2
([],4)
=> ([],4)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 3 - 2
([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([],5)
=> ([],5)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 3 - 2
([(3,4)],5)
=> ([(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(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)
=> ? = 3 - 2
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 1 = 3 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 1 = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],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)
=> 1 = 3 - 2
([(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)
=> ([],5)
=> ?
=> ? = 4 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([],5)
=> ?
=> ? = 5 - 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(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)
=> ? = 3 - 2
([],6)
=> ([],6)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 3 - 2
([(4,5)],6)
=> ([(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(3,5),(4,5)],6)
=> ([(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(2,5),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(2,5),(3,4)],6)
=> ([(2,5),(3,4)],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)
=> ? = 3 - 2
([(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> ([(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)
=> ? = 3 - 2
([(1,2),(3,5),(4,5)],6)
=> ([(1,2),(3,5),(4,5)],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)
=> ? = 3 - 2
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(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)
=> 1 = 3 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(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)
=> ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ?
=> ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(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)
=> 1 = 3 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(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)
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(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)
=> 1 = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(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)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],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)
=> 1 = 3 - 2
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ([],6)
=> ?
=> ? = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ?
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> ?
=> ? = 4 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ?
=> ? = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ?
=> ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ?
=> ? = 5 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(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)
=> ? = 3 - 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5)],6)
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(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),(18,1)],19)
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],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)
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],5)
=> ?
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(3,4)],5)
=> ?
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(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)
=> ? = 4 - 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],5)
=> ?
=> ? = 3 - 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(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)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],6)
=> ?
=> ? = 4 - 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5)],6)
=> ?
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(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)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(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)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(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)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],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)
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ?
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(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)
=> ? = 3 - 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(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)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([],6)
=> ?
=> ? = 6 - 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> ([],6)
=> ?
=> ? = 4 - 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ?
=> ? = 3 - 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
=> ([(3,4),(3,5)],6)
=> ?
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4)],6)
=> ?
=> ? = 3 - 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(3,4),(4,5)],6)
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5)],6)
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(3,4),(3,5)],6)
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([],6)
=> ?
=> ? = 4 - 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> ([(4,5)],6)
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(3,4)],5)
=> ?
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(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)
=> ? = 3 - 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([],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)
=> 1 = 3 - 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],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)
=> 1 = 3 - 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],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)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],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)
=> 1 = 3 - 2
([],7)
=> ([],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 3 - 2
([(5,6)],7)
=> ([(5,6)],7)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(4,6),(5,6)],7)
=> ([(4,6),(5,6)],7)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(3,6),(4,6),(5,6)],7)
=> ([(3,6),(4,6),(5,6)],7)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
=> ([(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(4,5),(4,6),(5,6)],7)
=> ([(4,5),(4,6),(5,6)],7)
=> ([(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)
=> 1 = 3 - 2
([(3,5),(3,6),(4,5),(4,6)],7)
=> ([(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(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)
=> 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(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)
=> 1 = 3 - 2
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(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)
=> 1 = 3 - 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([],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)
=> 1 = 3 - 2
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(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)
=> 1 = 3 - 2
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 3 - 2
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(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)
=> 1 = 3 - 2
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([],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)
=> 1 = 3 - 2
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(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)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ([],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)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([],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)
=> 1 = 3 - 2
Description
The number of shortest chains of small intervals from the bottom to the top in a lattice. An interval $[a, b]$ in a lattice is small if $b$ is a join of elements covering $a$.
The following 13 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001845The number of join irreducibles minus the rank of a lattice. St001651The Frankl number of a lattice. St001820The size of the image of the pop stack sorting operator. St001846The number of elements which do not have a complement in the lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001330The hat guessing number of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001703The villainy of a graph. St001545The second Elser number of a connected graph. St001877Number of indecomposable injective modules with projective dimension 2. St001490The number of connected components of a skew partition.