Identifier
  • Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
    St000015: Dyck paths ⟶ ℤ (values match St000053The number of valleys of the Dyck path., St001068Number of torsionless simple modules in the corresponding Nakayama algebra., St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra.)
Values
[1] => [1,0] => 1
[1,2] => [1,0,1,0] => 2
[2,1] => [1,1,0,0] => 1
[1,2,3] => [1,0,1,0,1,0] => 3
[1,3,2] => [1,0,1,1,0,0] => 2
[2,1,3] => [1,1,0,0,1,0] => 2
[2,3,1] => [1,1,0,1,0,0] => 2
[3,1,2] => [1,1,1,0,0,0] => 1
[3,2,1] => [1,1,1,0,0,0] => 1
[1,2,3,4] => [1,0,1,0,1,0,1,0] => 4
[1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[1,3,2,4] => [1,0,1,1,0,0,1,0] => 3
[1,3,4,2] => [1,0,1,1,0,1,0,0] => 3
[1,4,2,3] => [1,0,1,1,1,0,0,0] => 2
[1,4,3,2] => [1,0,1,1,1,0,0,0] => 2
[2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[2,1,4,3] => [1,1,0,0,1,1,0,0] => 2
[2,3,1,4] => [1,1,0,1,0,0,1,0] => 3
[2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[2,4,1,3] => [1,1,0,1,1,0,0,0] => 2
[2,4,3,1] => [1,1,0,1,1,0,0,0] => 2
[3,1,2,4] => [1,1,1,0,0,0,1,0] => 2
[3,1,4,2] => [1,1,1,0,0,1,0,0] => 2
[3,2,1,4] => [1,1,1,0,0,0,1,0] => 2
[3,2,4,1] => [1,1,1,0,0,1,0,0] => 2
[3,4,1,2] => [1,1,1,0,1,0,0,0] => 2
[3,4,2,1] => [1,1,1,0,1,0,0,0] => 2
[4,1,2,3] => [1,1,1,1,0,0,0,0] => 1
[4,1,3,2] => [1,1,1,1,0,0,0,0] => 1
[4,2,1,3] => [1,1,1,1,0,0,0,0] => 1
[4,2,3,1] => [1,1,1,1,0,0,0,0] => 1
[4,3,1,2] => [1,1,1,1,0,0,0,0] => 1
[4,3,2,1] => [1,1,1,1,0,0,0,0] => 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 4
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 4
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 4
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 3
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 2
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 4
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 4
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => 3
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 3
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => 3
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => 3
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 3
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => 3
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 2
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 3
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 2
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => 2
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 2
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 3
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 2
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => 2
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 3
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => 3
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => 3
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 3
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 2
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 2
>>> Load all 873 entries. <<<
[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => 2
[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 2
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => 2
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 2
[4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => 2
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 2
[4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 2
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,3,6,2,5,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,4,6,5,2,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,5,6,3,2,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => 4
[2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => 4
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => 4
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => 4
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 4
[2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 4
[2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 4
[2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4
[2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 4
[2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4
[2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3
[2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3
[2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[2,5,1,6,4,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3
[2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3
[2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3
[2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3
[2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,6,1,4,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,6,3,1,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4
[3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[3,1,5,6,4,2] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,1,6,2,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,1,6,4,2,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,1,6,4,5,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4
[3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,2,6,5,1,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
[3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
[3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[3,4,6,1,5,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[3,5,1,6,4,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[3,5,2,1,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[3,5,4,1,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[3,5,6,1,4,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[3,5,6,4,1,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,1,2,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,1,4,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,1,5,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,2,1,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,2,1,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,4,1,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,4,2,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,5,1,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,1,2,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,1,3,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[4,1,5,3,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[4,1,5,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,1,6,3,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,1,6,3,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,1,6,5,2,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[4,2,1,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,2,6,3,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,3,6,2,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[4,5,1,3,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[4,5,1,6,3,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[4,5,2,1,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,1,2,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,1,3,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,1,3,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,1,5,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,2,1,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,3,1,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,5,1,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,5,2,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,5,3,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,1,2,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,1,3,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,3,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,1,3,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,1,4,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,1,4,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,1,6,2,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,1,6,3,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,1,6,3,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,1,6,4,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,2,1,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,2,1,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,2,3,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,2,4,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,2,6,1,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,2,6,3,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,3,1,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,4,1,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
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Description
The number of peaks of a Dyck path.
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.