Identifier
Values
[1] => [1,0,1,0] => [1,1,0,0] => ([],2) => 2
[2] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => ([(1,2)],3) => 1
[1,1] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => ([(0,2),(1,2)],3) => 2
[3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 1
[2,1] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => ([],3) => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => ([(0,3),(1,3),(3,2)],4) => 2
[4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 1
[3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => ([(0,3),(1,2),(2,3)],4) => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3)],4) => 3
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => ([(0,4),(1,4),(2,3),(4,2)],5) => 2
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 1
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => ([(0,3),(1,3),(2,3)],4) => 3
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => ([(0,4),(4,1),(4,2),(4,3)],5) => 3
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 2
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 1
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => ([(0,4),(1,2),(2,4),(4,3)],5) => 1
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 3
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 3
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 2
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 1
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 1
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 2
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,4),(2,4),(4,3)],5) => 3
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 3
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 1
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 2
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 1
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 1
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 2
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 3
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 2
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 4
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 3
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 3
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 2
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 3
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 3
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 3
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 1
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 3
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 3
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 3
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 3
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 2
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 1
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 1
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 2
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 3
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 3
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 2
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 2
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 3
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 4
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => 3
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7) => 2
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => 2
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 1
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 2
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 2
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 2
>>> Load all 312 entries. <<<
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7) => 3
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 4
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 3
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 3
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 2
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 3
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 3
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 3
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 2
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 2
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 2
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 2
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 3
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 2
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7) => 3
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 3
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 3
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 2
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 3
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 4
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 2
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 3
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 4
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 2
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 1
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 3
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => 2
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => ([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 3
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => 4
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 3
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 2
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 3
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => 3
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 5
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => 2
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 4
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 3
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 2
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 3
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 4
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 2
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => 2
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => 2
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) => 2
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => 2
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 2
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 4
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 3
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 3
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 4
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 2
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => 2
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => 2
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 3
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => 2
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 4
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 2
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 2
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 4
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 2
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7) => 3
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7) => 2
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7) => 2
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7) => 2
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 2
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 2
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7) => 3
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 4
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 2
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => 2
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 2
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => 2
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 3
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 2
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 4
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 4
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 2
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 2
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7) => 3
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) => 2
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => 2
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => 2
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => 2
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => ([(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) => 4
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 3
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7) => 3
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 4
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 2
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => 2
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 3
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 3
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 4
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 5
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => ([(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => ([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 3
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 2
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 2
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 2
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => 2
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 2
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 3
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 2
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 3
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => ([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => 2
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 3
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 3
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 3
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7) => 2
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 3
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 3
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 2
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => 4
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 3
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 2
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 3
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => ([],7) => 7
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 6
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 5
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 4
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 5
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 5
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => ([(3,6),(4,6),(5,6)],7) => 3
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 3
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => 3
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5),(2,6)],7) => 4
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 4
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => ([(4,6),(5,6)],7) => 4
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 3
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => 3
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) => 3
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => ([(3,4),(3,5),(3,6)],7) => 3
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 3
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 2
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => ([(5,6)],7) => 5
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 4
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 4
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 4
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => ([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 3
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 3
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 4
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => ([(2,6),(3,6),(4,5),(4,6)],7) => 2
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => ([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 2
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => ([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 3
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => ([(4,5),(4,6)],7) => 4
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 3
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 3
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 3
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => ([(3,5),(3,6),(4,5),(4,6)],7) => 3
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => ([(3,6),(4,5),(4,6)],7) => 3
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Description
The distinguishing number of a poset.
This is the minimal number of colours needed to colour the vertices of a poset, such that only the trivial automorphism of the poset preserves the colouring.
See also St000469The distinguishing number of a graph., which is the same concept for graphs.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
Map
Hessenberg poset
Description
The Hessenberg poset of a Dyck path.
Let $D$ be a Dyck path of semilength $n$, regarded as a subdiagonal path from $(0,0)$ to $(n,n)$, and let $\boldsymbol{m}_i$ be the $x$-coordinate of the $i$-th up step.
Then the Hessenberg poset (or natural unit interval order) corresponding to $D$ has elements $\{1,\dots,n\}$ with $i < j$ if $j < \boldsymbol{m}_i$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.