Identifier
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
[1,0] => [1,0] => [2,1] => [2,1] => [1,1,0,0]
[1,0,1,0] => [1,0,1,0] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[1,1,0,0] => [1,1,0,0] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[1,0,1,0,1,0] => [1,0,1,0,1,0] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[1,0,1,1,0,0] => [1,0,1,1,0,0] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[1,1,0,0,1,0] => [1,1,0,0,1,0] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[1,1,1,0,0,0] => [1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [7,5,4,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [7,5,4,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
>>> Load all 1055 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [7,4,3,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [7,4,3,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [7,4,3,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [7,5,4,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [7,5,4,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [8,5,4,3,2,1,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [8,5,4,3,2,1,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [8,7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [8,5,4,3,2,1,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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] => [5,1,2,3,6,7,8,4] => [8,4,3,2,1,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [8,6,5,3,2,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [8,6,5,3,2,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [8,7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [8,4,3,2,1,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [8,7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [8,7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [8,4,3,2,1,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [8,7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [8,4,3,2,1,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,3,2,1,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [8,6,5,4,2,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [8,6,5,4,2,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,5,4,2,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,5,4,2,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,5,4,2,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [8,6,5,3,2,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [8,6,5,3,2,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [8,7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [8,7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,3,2,1,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [8,7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [8,6,5,2,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [8,6,5,2,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [8,7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [8,7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,3,2,1,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [8,7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [8,7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,3,2,1,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,3,2,1,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,1,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,6,4,3,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,6,4,3,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,6,4,3,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,6,4,3,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,6,4,3,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,6,4,3,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [8,6,5,4,2,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [8,6,5,4,2,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,5,4,2,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,5,4,2,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,5,4,2,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [8,7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [8,6,5,2,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [8,6,5,2,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [8,7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,1,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [8,6,5,4,1,2,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [8,7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [8,6,5,4,1,2,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [8,5,4,1,2,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [8,7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [8,7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [8,5,4,1,2,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [8,5,4,1,2,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [8,7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [8,7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [8,6,5,2,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [8,6,5,2,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [8,7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [8,7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,1,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [8,6,5,1,2,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [8,6,5,1,2,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [8,7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [8,7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,1,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,1,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,1,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [9,8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [9,6,5,4,3,2,1,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => [9,8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [9,8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [9,6,5,4,3,2,1,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8] => [9,8,5,4,3,2,1,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [9,6,5,4,3,2,1,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [9,5,4,3,2,1,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8] => [9,8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => [9,8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8] => [9,8,5,4,3,2,1,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [9,5,4,3,2,1,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8] => [9,8,5,4,3,2,1,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [9,5,4,3,2,1,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [9,5,4,3,2,1,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8] => [9,8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => [9,8,7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => [9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => [9,8,7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8] => [9,8,7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => [9,8,7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,8,1,3,4,5,6,9,7] => [9,7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,8,1,3,4,5,6,9,7] => [9,7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,9,3,5,6,7,8] => [9,8,7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => [9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,9,3,5,6,7,8] => [9,8,7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8] => [9,8,7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,9,1,4,5,6,7,8] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,9,3,5,6,7,8] => [9,8,7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8] => [9,8,7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,9,1,5,6,7,8] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,9,1,6,7,8] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[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] => [2,3,4,5,6,9,1,7,8] => [9,8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => [9,8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => [10,9,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,11,1,10] => [11,10,1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,10,12,1,11] => [12,11,1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => [10,9,8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => [11,9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[] => [] => [1] => [1] => [1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [10,8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [10,8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [10,8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [10,8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11,10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => [11,9,8,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [10,7,6,5,4,3,2,1,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => [11,9,8,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [10,8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => [12,10,9,8,7,6,5,4,3,2,1,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => [12,10,9,8,7,6,5,4,3,2,1,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [10,7,6,5,4,3,2,1,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => [12,10,8,6,4,2,1,3,5,7,9,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => [12,10,8,6,4,2,1,3,5,7,9,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,1,2,3,4,5,6,10,7,9] => [10,9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [10,8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => [10,9,8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => [10,9,8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,10,2,4,5,6,7,8,9] => [10,9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => [10,8,7,6,5,4,2,1,3,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [10,9,8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,10,1,3,4,5,6,7,8,9] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,9,1,3,4,5,6,7,10,8] => [10,8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,10,1,4,5,6,7,8,9] => [10,9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,10,1,5,6,7,8,9] => [10,9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,10,1,6,7,8,9] => [10,9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,10,1,7,8,9] => [10,9,8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,11,1,3,4,5,6,7,8,9,10] => [11,10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,10,2,4,5,6,7,8,9] => [10,9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [10,9,8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,9,1,3,4,5,6,7,10,8] => [10,8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => [10,8,7,6,5,4,2,1,3,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => [10,8,7,6,5,4,2,1,3,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => [10,8,7,6,5,4,2,1,3,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => [11,9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => [11,9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [10,9,8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => [10,9,8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [10,8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [10,9,8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,12,1] => [12,1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => [11,9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [10,7,6,5,4,3,2,1,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => [10,9,8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => [12,10,8,6,4,2,1,3,5,7,9,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,1,2,3,4,5,6,10,7,9] => [10,9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [10,9,8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => [12,10,8,6,4,2,1,3,5,7,9,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [10,8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => [12,10,8,6,4,2,1,3,5,7,9,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [10,9,8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => [11,9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => [11,9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => [12,10,8,6,4,2,1,3,5,7,9,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
Map
bounce path
Description
Sends a Dyck path D of length 2n to its bounce path.
This path is formed by starting at the endpoint (n,n) of D and travelling west until encountering the first vertical step of D, then south until hitting the diagonal, then west again to hit D, etc. until the point (0,0) is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint (n,n) of D and travelling west until encountering the first vertical step of D, then south until hitting the diagonal, then west again to hit D, etc. until the point (0,0) is reached.
This map is the first part of the zeta map Mp00030zeta map.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
inverse first fundamental transformation
Description
Let σ=(i11⋯i1k1)⋯(iℓ1⋯iℓkℓ) be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps σ to the permutation [i11,…,i1k1,…,iℓ1,…,iℓkℓ] in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps σ to the permutation [i11,…,i1k1,…,iℓ1,…,iℓkℓ] in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
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