Identifier
Values
([],1) => [1] => [1,0,1,0] => [1,0,1,0] => 0
([],2) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,1)],2) => [1] => [1,0,1,0] => [1,0,1,0] => 0
([],3) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(1,2)],3) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,1),(0,2)],3) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,2),(2,1)],3) => [1] => [1,0,1,0] => [1,0,1,0] => 0
([(0,2),(1,2)],3) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(2,3)],4) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(0,1),(0,2),(0,3)],4) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,2),(0,3),(3,1)],4) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,1),(0,2),(1,3),(2,3)],4) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(1,2),(2,3)],4) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(3,1),(3,2)],4) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,3),(1,3),(3,2)],4) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,3),(1,3),(2,3)],4) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,3),(1,2)],4) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,3),(1,2),(1,3)],4) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,3),(2,1),(3,2)],4) => [1] => [1,0,1,0] => [1,0,1,0] => 0
([(0,3),(1,2),(2,3)],4) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,2),(0,3),(0,4),(4,1)],5) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(1,2),(1,3),(2,4),(3,4)],5) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,3),(0,4),(3,2),(4,1)],5) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(1,4),(4,2),(4,3)],5) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,4),(4,1),(4,2),(4,3)],5) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(1,4),(2,4),(4,3)],5) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,4),(1,4),(4,2),(4,3)],5) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,4),(1,4),(2,3),(4,2)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(0,4),(1,2),(1,4),(2,3)],5) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,4),(1,2),(1,4),(4,3)],5) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,2),(0,4),(3,1),(4,3)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(1,2),(1,3),(3,4)],5) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,3),(1,2),(1,4),(3,4)],5) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(1,4),(3,2),(4,3)],5) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,3),(3,4),(4,1),(4,2)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,4),(1,2),(2,4),(4,3)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,3),(1,4),(4,2)],5) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,4),(3,2),(4,1),(4,3)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,4),(1,2),(2,3),(2,4)],5) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,4),(2,3),(3,1),(4,2)],5) => [1] => [1,0,1,0] => [1,0,1,0] => 0
([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,4),(1,2),(2,3),(3,4)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
>>> Load all 289 entries. <<<
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(1,5),(3,4),(4,2),(5,3)],6) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => [1,0,1,0] => [1,0,1,0] => 0
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,5),(1,3),(1,4),(3,6),(4,5),(5,6),(6,2)],7) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,2),(0,6),(1,5),(1,6),(2,3),(3,5),(5,4),(6,4)],7) => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => [6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7) => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6)],7) => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) => [7,4,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7) => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,5),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4)],7) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7) => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7) => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => [1,0,1,0] => [1,0,1,0] => 0
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 1
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Description
The convexity degree of the parallelogram polyomino associated with the Dyck path.
A parallelogram polyomino is $k$-convex if $k$ is the maximal number of turns an axis-parallel path must take to connect two cells of the polyomino.
For example, any rotation of a Ferrers shape has convexity degree at most one.
The (bivariate) generating function is given in Theorem 2 of [1].
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.