- FindStat

Identifier

Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001203: Dyck paths ⟶ ℤ (values match St000306The bounce count of a Dyck path.)

Values

[1,0] => [1] => [1,0] => [1,0] => 1

[1,0,1,0] => [1,2] => [1,0,1,0] => [1,1,0,0] => 1

[1,1,0,0] => [2,1] => [1,1,0,0] => [1,0,1,0] => 2

[1,0,1,0,1,0] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1

[1,0,1,1,0,0] => [1,3,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2

[1,1,0,0,1,0] => [2,1,3] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2

[1,1,0,1,0,0] => [2,3,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3

[1,1,1,0,0,0] => [3,2,1] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 2

[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1

[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 2

[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2

[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 3

[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2

[1,1,0,0,1,0,1,0] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 2

[1,1,0,0,1,1,0,0] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 3

[1,1,0,1,0,0,1,0] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3

[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4

[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => 3

[1,1,1,0,0,0,1,0] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2

[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 3

[1,1,1,0,1,0,0,0] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 2

[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 2

[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 2

[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 2

[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3

[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2

[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 2

[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3

[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 3

[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4

[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => 3

[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 2

[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 2

[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 2

[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 2

[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3

[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3

[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 4

[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 3

[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 3

[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 4

[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 4

[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5

[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 4

[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 3

[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 4

[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 3

[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 3

[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 2

[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3

[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3

[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4

[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => 3

[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 2

[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 3

[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2

[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 2

[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 3

[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1

[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2

[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2

[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2

[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3

[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3

[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3

[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2

[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2

[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2

[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2

[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3

[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3

[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4

[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3

[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3

[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4

[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4

[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5

[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 4

[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3

[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 4

[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2

[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3

[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3

[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3

[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2

[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3

[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2

>>> Load all 625 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2

[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3

[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2

[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2

[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3

[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3

[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4

[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3

[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3

[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4

[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [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

[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5

[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 4

[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3

[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 4

[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3

[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 4

[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4

[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5

[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4

[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4

[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5

[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5

[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5

[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4

[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 5

[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4

[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4

[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3

[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 4

[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 4

[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 5

[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4

[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3

[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3

[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2

[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3

[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3

[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4

[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3

[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3

[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 4

[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 4

[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4

[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3

[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4

[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2

[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3

[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3

[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4

[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3

[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2

[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3

[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3

[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4

[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3

[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3

[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3

[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2

[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2

[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2

[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3

[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3

[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4

[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 3

[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3

[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4

[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4

[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3

[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4

[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3

[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 3

[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2

[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2

[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3

[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2

[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2

[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2

[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3

[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3

[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4

[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3

[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3

[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4

[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4

[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5

[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4

[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3

[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4

[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4

[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4

[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5

[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4

[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4

[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5

[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5

[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4

[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5

[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4

[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4

[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3

[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4

[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4

[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5

[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4

[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3

[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3

[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 3

[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4

[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 3

[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3

[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4

[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4

[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3

[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4

[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3

[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4

[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3

[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3

[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2

[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3

[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4

[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3

[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2

[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3

[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4

[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3

[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4

[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 5

[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5

[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4

[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 5

[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4

[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4

[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5

[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4

[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4

[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4

[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 5

[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5

[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5

[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4

[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5

[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4

[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4

[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5

[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5

[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5

[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5

[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4

[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5

[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5

[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4

[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3

[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4

[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4

[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5

[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4

[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4

[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 5

[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5

[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4

[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4

[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3

[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4

[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3

[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4

[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4

[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4

[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 3

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 3

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5

[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 4

[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 3

[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4

[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 5

[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 5

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5

[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4

[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3

[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 4

[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2

[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3

[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3

[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4

[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3

[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3

[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4

[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2

[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3

[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2

[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3

[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3

[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3

[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2

[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3

[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3

[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2

[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = q + 3\ q^{2} + q^{3}$

$F_{4} = q + 7\ q^{2} + 5\ q^{3} + q^{4}$

$F_{5} = q + 16\ q^{2} + 17\ q^{3} + 7\ q^{4} + q^{5}$

$F_{6} = q + 39\ q^{2} + 51\ q^{3} + 31\ q^{4} + 9\ q^{5} + q^{6}$

$F_{7} = q + 104\ q^{2} + 149\ q^{3} + 114\ q^{4} + 49\ q^{5} + 11\ q^{6} + q^{7}$

Description

We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series

$L=[c_0,c_1,...,c_{n-1}]$ such that

$n=c_0 < c_i$ for all

$i > 0$ a Dyck path as follows:
In the list

$L$ delete the first entry

$c_0$ and substract from all other entries

$n-1$ and then append the last element 1 (this was suggested by Christian Stump). The result is a Kupisch series of an LNakayama algebra.
Example:
[5,6,6,6,6] goes into [2,2,2,2,1].
Now associate to the CNakayama algebra with the above properties the Dyck path corresponding to the Kupisch series of the LNakayama algebra.
The statistic return the global dimension of the CNakayama algebra divided by 2.

Map

Delest-Viennot-inverse

Description

Return the Dyck path obtained by applying the inverse of Delest-Viennot's bijection to the corresponding parallelogram polyomino.
Let

$D$ be a Dyck path of semilength

$n$ . The parallelogram polyomino

$\gamma(D)$ is defined as follows: let

$\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to

$D$ . Then, the upper path of

$\gamma(D)$ corresponds to the sequence of steps of

$\tilde D$ with even indices, and the lower path of

$\gamma(D)$ corresponds to the sequence of steps of

$\tilde D$ with odd indices.
The Delest-Viennot bijection

$\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path

$(\beta^{(-1)}\circ\gamma)(D)$ .

Map

to non-crossing permutation

Description

Sends a Dyck path

$D$ with valley at positions

$\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation

$\pi$ having descents

$\{i_1,\ldots,i_k\}$ and whose inverse has descents

$\{j_1,\ldots,j_k\}$ .
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to

$n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..

Map

left-to-right-maxima to Dyck path

Description

The left-to-right maxima of a permutation as a Dyck path.
Let

$(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are

$c_1, c_1+c_2, \dots, c_1+\dots+c_k$ .
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.