Identifier
-
Mp00222:
Dyck paths
—peaks-to-valleys⟶
Dyck paths
St000306: Dyck paths ⟶ ℤ (values match St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: )
Values
[1,0] => [1,0] => 0
[1,0,1,0] => [1,1,0,0] => 0
[1,1,0,0] => [1,0,1,0] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,1,0,1,0,0] => [1,0,1,0,1,0] => 2
[1,1,1,0,0,0] => [1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
>>> Load all 808 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[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
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,7,5,1 1,15,18,7,1 1,31,57,33,9,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + q^{2}$
$F_{4} = 1 + 7\ q + 5\ q^{2} + q^{3}$
$F_{5} = 1 + 15\ q + 18\ q^{2} + 7\ q^{3} + q^{4}$
$F_{6} = 1 + 31\ q + 57\ q^{2} + 33\ q^{3} + 9\ q^{4} + q^{5}$
Description
The bounce count of a Dyck path.
For a Dyck path $D$ of length $2n$, this is the number of points $(i,i)$ for $1 \leq i < n$ that are touching points of the bounce path of $D$.
For a Dyck path $D$ of length $2n$, this is the number of points $(i,i)$ for $1 \leq i < n$ that are touching points of the bounce path of $D$.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
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