- FindStat

Identifier

Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St000476: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

[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] => 4

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

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

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

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

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

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

[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 5

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

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

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

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

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

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

[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5

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

[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5

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

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

[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5

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

[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6

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

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

[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5

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

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

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

[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5

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

[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5

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

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

[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6

[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 5

[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 7

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

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

[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 6

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

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

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

[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5

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

[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 7

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

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

[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6

[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5

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

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

[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5

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

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

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

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

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5

[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6

[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

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

[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6

[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5

[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 7

[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5

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

[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6

[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5

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

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

[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5

[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6

[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5

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

[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 7

[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 6

[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 8

[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5

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

[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 7

[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5

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

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

[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 6

[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5

[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 8

[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5

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

[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 7

[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6

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

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

>>> Load all 625 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6

[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5

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

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

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

[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5

[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6

[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5

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

[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6

[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5

[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 7

[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5

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

[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6

[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5

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

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

[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 7

[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 6

[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 7

[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 6

[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5

[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 8

[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 7

[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 9

[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

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

[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 8

[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5

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

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

[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 7

[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 6

[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9

[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5

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

[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 8

[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 6

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

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

[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7

[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 5

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

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

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

[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6

[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5

[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6

[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5

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

[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 8

[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 7

[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 9

[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5

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

[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8

[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 5

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

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

[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 7

[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6

[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 10

[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 6

[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 5

[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8

[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7

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

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

[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7

[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 6

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

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

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

[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6

[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5

[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 9

[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5

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

[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8

[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 7

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

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

[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 7

[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6

[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 5

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

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

[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6

[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5

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

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

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

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

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6

[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6

[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5

[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7

[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6

[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5

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

[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 6

[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 7

[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 6

[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5

[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 8

[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 7

[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 9

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6

[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5

[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 8

[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6

[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5

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

[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 6

[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 9

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 6

[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5

[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 8

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 7

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5

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

[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6

[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 5

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

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

[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6

[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 7

[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 6

[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5

[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7

[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6

[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 8

[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 6

[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5

[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 7

[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 6

[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 5

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

[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 8

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 7

[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 8

[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 7

[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 6

[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 9

[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 8

[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 10

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6

[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5

[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 9

[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6

[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 5

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

[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 8

[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 7

[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 10

[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6

[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 5

[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 9

[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 5

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

[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 8

[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 6

[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 5

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

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

[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 6

[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 7

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 6

[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5

[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 9

[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 8

[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 10

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6

[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 5

[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 9

[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 6

[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 5

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

[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 8

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 7

[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 11

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7

[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 6

[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 9

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5

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

[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7

[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 5

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

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

[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7

[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6

[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 10

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6

[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 5

[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9

[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 8

[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 5

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

[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 8

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 7

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6

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

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

[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 6

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 5

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

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

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

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6

[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 7

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 6

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 7

[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 6

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 8

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 6

[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5

[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 7

[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 6

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 5

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

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 7

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 6

[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 6

[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 8

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 7

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 9

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 6

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 5

[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 8

[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6

[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 5

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

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 7

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 6

[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 9

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6

[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 8

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 5

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

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 6

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 5

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

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

[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 7

[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 8

[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 7

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 6

[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8

[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 7

[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 9

[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 7

[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6

[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 8

[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 7

[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 6

[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 5

[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 9

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8

[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 9

[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 8

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 7

[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 10

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 9

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 11

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5

[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 10

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 5

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

[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 9

[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 8

[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 11

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 6

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 5

[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 10

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 7

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 5

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

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 9

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 5

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

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

[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 8

[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 7

[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 8

[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 7

[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 6

[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 10

[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 9

[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 11

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 6

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 5

[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 10

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 6

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 5

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

[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 9

[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 8

[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 12

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 7

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 6

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 10

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 8

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 5

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

[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 5

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

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

[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 8

[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 7

[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 11

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6

[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 5

[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 10

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 8

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 5

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

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 9

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 7

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6

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

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

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 8

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 6

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 5

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

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

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

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 7

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 6

[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 5

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 7

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 6

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 8

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6

[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 5

[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 7

[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 6

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 5

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

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 9

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 8

[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 9

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 8

[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 10

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 9

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 11

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 5

[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 10

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 5

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

[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 9

[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8

[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 11

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 5

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 10

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 5

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

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 6

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 5

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

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

[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 8

[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 7

[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 8

[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7

[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 6

[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 11

[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 10

[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 12

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 6

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 11

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 7

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 6

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 5

[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 9

[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8

[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 13

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 8

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 7

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 10

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 9

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 5

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

[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 9

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 8

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 5

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

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

[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8

[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 7

[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 12

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 7

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 6

[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 9

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 5

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

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 9

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 8

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 6

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

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

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 5

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

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

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

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 6

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 6

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5

[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 10

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 9

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 11

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 6

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 5

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 10

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 6

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 5

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

[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9

[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 8

[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 13

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 8

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7

[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 9

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5

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

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 9

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 8

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 5

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

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

[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 8

[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 12

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 7

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 6

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 10

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 6

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 5

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 9

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 8

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 7

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

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

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 8

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 6

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

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

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

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 10

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 9

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5

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

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 9

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 7

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

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

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 7

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 5

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

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

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 5

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

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

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

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

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$F_{1} = q$

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

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

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

$F_{5} = q + 4\ q^{2} + 9\ q^{3} + 12\ q^{4} + 10\ q^{5} + 4\ q^{6} + 2\ q^{7}$

$F_{6} = q + 5\ q^{2} + 14\ q^{3} + 25\ q^{4} + 31\ q^{5} + 26\ q^{6} + 16\ q^{7} + 9\ q^{8} + 4\ q^{9} + q^{10}$

$F_{7} = q + 6\ q^{2} + 20\ q^{3} + 44\ q^{4} + 70\ q^{5} + 82\ q^{6} + 74\ q^{7} + 54\ q^{8} + 38\ q^{9} + 22\ q^{10} + 12\ q^{11} + 4\ q^{12} + 2\ q^{13}$

Description

The sum of the semi-lengths of tunnels before a valley of a Dyck path.
For each valley

$v$ in a Dyck path

$D$ there is a corresponding tunnel, which
is the factor

$T_v = s_i\dots s_j$ of

$D$ where

$s_i$ is the step after the first intersection of

$D$ with the line

$y = ht(v)$ to the left of

$s_j$ . This statistic is

$\sum_v (j_v-i_v)/2.$

Map

prime Dyck path

Description

Return the Dyck path obtained by adding an initial up and a final down step.

Map

promotion

Description

The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength

$n$ are in bijection with standard Young tableaux of shape

$(n^2)$ , see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.