Identifier
-
Mp00296:
Dyck paths
—Knuth-Krattenthaler⟶
Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000288: Binary words ⟶ ℤ
Values
[1,0] => [1,0] => [1] => 1 => 1
[1,0,1,0] => [1,1,0,0] => [2] => 10 => 1
[1,1,0,0] => [1,0,1,0] => [1,1] => 11 => 2
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [3] => 100 => 1
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [2,1] => 101 => 2
[1,1,0,0,1,0] => [1,0,1,0,1,0] => [1,1,1] => 111 => 3
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,2] => 110 => 2
[1,1,1,0,0,0] => [1,1,0,0,1,0] => [2,1] => 101 => 2
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [4] => 1000 => 1
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [3,1] => 1001 => 2
[1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0] => [2,1,1] => 1011 => 3
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [2,2] => 1010 => 2
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [3,1] => 1001 => 2
[1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0] => [1,2,1] => 1101 => 3
[1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => 1111 => 4
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => [1,2,1] => 1101 => 3
[1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [1,3] => 1100 => 2
[1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [1,1,2] => 1110 => 3
[1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0] => [2,1,1] => 1011 => 3
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => [2,1,1] => 1011 => 3
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0] => [2,2] => 1010 => 2
[1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => [3,1] => 1001 => 2
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [5] => 10000 => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [4,1] => 10001 => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [3,1,1] => 10011 => 3
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => [3,2] => 10010 => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [4,1] => 10001 => 2
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [2,2,1] => 10101 => 3
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => 10111 => 4
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => [2,2,1] => 10101 => 3
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [2,3] => 10100 => 2
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => [2,1,2] => 10110 => 3
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [3,1,1] => 10011 => 3
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => [3,1,1] => 10011 => 3
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => [3,2] => 10010 => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [4,1] => 10001 => 2
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 11001 => 3
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => 11011 => 4
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => 11111 => 5
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 11101 => 4
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 11011 => 4
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [1,3,1] => 11001 => 3
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => 11011 => 4
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => [1,3,1] => 11001 => 3
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,4] => 11000 => 2
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [1,2,2] => 11010 => 3
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 11110 => 4
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => 11101 => 4
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 11100 => 3
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 11010 => 3
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => [2,2,1] => 10101 => 3
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => 10111 => 4
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 10111 => 4
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 10101 => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => 10111 => 4
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 10110 => 3
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [2,2,1] => 10101 => 3
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,3] => 10100 => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => [2,1,2] => 10110 => 3
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => [3,1,1] => 10011 => 3
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [3,1,1] => 10011 => 3
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 10011 => 3
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2] => 10010 => 2
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => [4,1] => 10001 => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6] => 100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => 100001 => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => 100011 => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => 100010 => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => 100001 => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => 100101 => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => 100111 => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => 100101 => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => 100100 => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => 100110 => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => 100011 => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => 100011 => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => 100010 => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => 100001 => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => 101001 => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => 101011 => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => 101111 => 5
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => 101101 => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => 101011 => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => 101001 => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => 101011 => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => 101001 => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,4] => 101000 => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => 101010 => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => 101110 => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => 101101 => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => 101100 => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => 101010 => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => 100101 => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => 100111 => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => 100111 => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => 100101 => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => 100111 => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => 100110 => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => 100101 => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => 100100 => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => 100110 => 3
>>> Load all 2134 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => 100011 => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => 100011 => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => 100011 => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => 100010 => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => 100001 => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => 110001 => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => 110011 => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => 110111 => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => 110101 => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => 110011 => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => 111011 => 5
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 111111 => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => 111011 => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 111001 => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 111101 => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => 110111 => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 110111 => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 110101 => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 110011 => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => 110001 => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => 110011 => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => 110111 => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => 110101 => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => 110011 => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => 110001 => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => 110011 => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => 110001 => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 110000 => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => 110010 => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => 110110 => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => 110101 => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => 110100 => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => 110010 => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => 111010 => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 111110 => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => 111011 => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => 111001 => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => 111101 => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => 111010 => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => 111001 => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 111000 => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 111100 => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => 110110 => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 110110 => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => 110101 => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 110100 => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 110010 => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => 101001 => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => 101011 => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => 101111 => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => 101101 => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => 101011 => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => 101011 => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => 101111 => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => 101011 => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => 101001 => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 101101 => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => 101111 => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => 101111 => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => 101101 => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => 101011 => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => 101010 => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => 101110 => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => 101011 => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => 101001 => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => 101101 => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => 101010 => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => 101001 => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 101000 => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 101100 => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => 101110 => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => 101110 => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => 101101 => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => 101100 => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => 101010 => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => 100101 => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => 100111 => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => 100111 => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => 100101 => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => 100111 => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => 100111 => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 100111 => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 100101 => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => 100111 => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => 100110 => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 100110 => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => 100101 => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 100100 => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => 100110 => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => 100011 => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => 100011 => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => 100011 => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => 100011 => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => 100010 => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => 100001 => 2
[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] => [7] => 1000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => 1000001 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => 1000010 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => 1000001 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3] => 1000100 => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,1,2] => 1000110 => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => 1000010 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => 1000001 => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => 1001001 => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => 1001111 => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => 1001101 => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => 1001001 => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => 1001001 => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => 1001000 => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => 1001010 => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,2] => 1001110 => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => 1001101 => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => 1001100 => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => 1001010 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,2] => 1000110 => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3] => 1000100 => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,2] => 1000110 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => 1000010 => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => 1000001 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => 1010001 => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,1] => 1010011 => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1] => 1010111 => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,2,2,1] => 1010101 => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,1] => 1010011 => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => 1011011 => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => 1011111 => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => 1011011 => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => 1011001 => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => 1011101 => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1] => 1010111 => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => 1010111 => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,1] => 1010101 => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,1] => 1010011 => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => 1010001 => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,1,1] => 1010011 => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1] => 1010111 => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,1] => 1010101 => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,1] => 1010011 => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => 1010001 => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,1] => 1010011 => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => 1010001 => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5] => 1010000 => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => 1010010 => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1,2] => 1010110 => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,1] => 1010101 => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,3] => 1010100 => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => 1010010 => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => 1011010 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,2] => 1011110 => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => 1011011 => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => 1011001 => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => 1011101 => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => 1011010 => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => 1011001 => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => 1011000 => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => 1011100 => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,2,1,2] => 1010110 => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,1,2] => 1010110 => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,1] => 1010101 => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,3] => 1010100 => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => 1010010 => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => 1001001 => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => 1001111 => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => 1001101 => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => 1001111 => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => 1001001 => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => 1001101 => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => 1001111 => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => 1001111 => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => 1001101 => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => 1001010 => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,2] => 1001110 => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 1001011 => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => 1001001 => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => 1001101 => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => 1001010 => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => 1001001 => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => 1001000 => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => 1001100 => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,2] => 1001110 => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2] => 1001110 => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => 1001101 => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => 1001100 => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => 1001010 => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => 1000111 => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,2] => 1000110 => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2] => 1000110 => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => 1000101 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3] => 1000100 => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,1,2] => 1000110 => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => 1000011 => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => 1000010 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1] => 1000001 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => 1100001 => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => 1101111 => 6
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => 1101001 => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => 1101101 => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => 1110011 => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => 1110111 => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => 1111111 => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => 1111011 => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => 1110111 => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => 1110011 => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => 1110111 => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => 1110011 => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => 1110001 => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => 1110101 => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => 1111101 => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => 1111011 => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => 1111001 => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => 1110101 => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => 1101111 => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 1101111 => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 1101111 => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => 1101101 => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => 1101001 => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => 1101101 => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => 1100001 => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => 1101111 => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => 1101001 => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => 1101101 => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => 1100001 => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => 1100111 => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => 1100001 => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => 1100011 => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => 1100001 => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => 1100000 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => 1100010 => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => 1100110 => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => 1100100 => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => 1100010 => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => 1101010 => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => 1101110 => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => 1101001 => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => 1101101 => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => 1101010 => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => 1101001 => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => 1101000 => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => 1101100 => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => 1100110 => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => 1100110 => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => 1100100 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => 1100010 => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => 1110010 => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => 1110110 => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => 1111110 => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => 1111010 => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => 1110110 => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => 1110011 => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => 1110111 => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => 1110011 => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,4,1] => 1110001 => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => 1110101 => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,2,1] => 1111101 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => 1111011 => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,3,1] => 1111001 => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => 1110101 => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => 1110010 => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => 1110110 => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => 1110011 => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => 1110001 => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => 1110101 => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => 1110010 => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => 1110001 => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => 1110000 => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,2,3] => 1110100 => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => 1111100 => 5
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,2,2] => 1111010 => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => 1111001 => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => 1111000 => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => 1110100 => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => 1101010 => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => 1101110 => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => 1101110 => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => 1101010 => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => 1101110 => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => 1101101 => 5
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => 1101011 => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => 1101001 => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => 1101101 => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => 1101100 => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => 1101010 => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => 1101001 => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => 1101000 => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => 1101100 => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => 1100110 => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => 1100110 => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => 1100110 => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => 1100101 => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => 1100100 => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => 1100010 => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => 1010001 => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => 1011111 => 6
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => 1011001 => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => 1011101 => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1011111 => 6
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => 1010001 => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1011101 => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 1011001 => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => 1011111 => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1011111 => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1011111 => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1011101 => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 1011001 => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1011101 => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => 1010010 => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => 1010110 => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1011110 => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 1011010 => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => 1010110 => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => 1010111 => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => 1010001 => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 1011101 => 5
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 1011001 => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => 1010010 => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => 1010110 => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => 1010011 => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => 1010001 => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => 1010010 => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => 1010001 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => 1010000 => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => 1010100 => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 1011100 => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 1011010 => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 1011001 => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => 1011000 => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => 1010100 => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => 1011010 => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => 1011110 => 5
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1011110 => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 1011010 => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1011110 => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 1011101 => 5
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 1011011 => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 1011001 => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => 1011101 => 5
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 1011100 => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 1011010 => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 1011001 => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => 1011000 => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => 1011100 => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => 1010110 => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => 1010110 => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => 1010110 => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => 1010101 => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => 1010100 => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => 1010010 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => 1001001 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => 1001001 => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 1001001 => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => 5
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => 1001010 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => 1001110 => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 1001110 => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 1001010 => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => 1001110 => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 1001011 => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => 1001001 => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 1001100 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => 1001010 => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => 1001001 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => 1001000 => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => 1001100 => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => 1001110 => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => 1001110 => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => 1001110 => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => 1001101 => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => 1001100 => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => 1001010 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => 1000101 => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => 1000101 => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => 1000101 => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1000101 => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => 1000111 => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => 1000110 => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => 1000110 => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => 1000110 => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => 1000101 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => 1000100 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => 1000110 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => 1000011 => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => 1000011 => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => 1000011 => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => 1000011 => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => 1000011 => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => 1000010 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => 1000001 => 2
[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] => [8] => 10000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => 10000001 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,2] => 10000010 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => 10000001 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,3] => 10000100 => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,2] => 10000010 => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => 10000001 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,4] => 10001000 => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,3] => 10001100 => 3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,3] => 10000100 => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,2] => 10000010 => 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] => [7,1] => 10000001 => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,5] => 10010000 => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 10010010 => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,2,3] => 10010100 => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,2] => 10010010 => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,4] => 10011000 => 3
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,2,3] => 10010100 => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3,2] => 10010010 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4] => 10001000 => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,3] => 10001100 => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,3] => 10001100 => 3
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,3] => 10000100 => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,2] => 10000010 => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => 10000001 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,5,1] => 10100001 => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,3,1] => 10101001 => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => 10111111 => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,4,1] => 10110001 => 4
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => 10101001 => 4
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,5,1] => 10100001 => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,5,1] => 10100001 => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,5,1] => 10100001 => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,5,1] => 10100001 => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,6] => 10100000 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,2] => 10100010 => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,3] => 10100100 => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,4,2] => 10100010 => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,4] => 10101000 => 3
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,3] => 10100100 => 3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,4,2] => 10100010 => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => 10110010 => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => 10111110 => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,4,1] => 10110001 => 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => 10110010 => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,1,4,1] => 10110001 => 4
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => 10110010 => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,1] => 10110001 => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,5] => 10110000 => 3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,2,3] => 10110100 => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,3] => 10111100 => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,4] => 10111000 => 4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,2,3] => 10110100 => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => 10101000 => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,3] => 10100100 => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,4,2] => 10100010 => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,3,2] => 10010010 => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,2] => 10010010 => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2] => 10010010 => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,1] => 10010001 => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,5] => 10010000 => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,3] => 10010100 => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 10011000 => 3
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,2,3] => 10010100 => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 10011000 => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,2,3] => 10010100 => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,3,2] => 10010010 => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => 5
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,2,1,1] => 10001011 => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,3] => 10001100 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,1] => 10001001 => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4] => 10001000 => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,3] => 10001100 => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => 4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 10001101 => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,3] => 10001100 => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,2,2] => 10001010 => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,1,1,1] => 10000111 => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,2,1] => 10000101 => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,3] => 10000100 => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,1,2] => 10000110 => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1] => 10000011 => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,2] => 10000010 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => 10000001 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => 11000001 => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => 7
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1] => 11101111 => 7
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => 11110111 => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1] => 11110111 => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => 11110011 => 6
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => 11111011 => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 11101111 => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 11101111 => 7
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1] => 11101111 => 7
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => 11100001 => 4
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,2,1,2,1] => 11101101 => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,2,3,1] => 11101001 => 5
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => 11110101 => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => 11111101 => 7
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => 11110111 => 7
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,3,1,1] => 11110011 => 6
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => 11111011 => 7
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,2,2,1] => 11110101 => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1] => 11110011 => 6
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => 11110001 => 5
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => 11111001 => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 11101101 => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 11101101 => 6
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => 11101001 => 5
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => 7
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => 7
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => 7
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => 7
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,6,1] => 11000001 => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => 11011111 => 7
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,6,1] => 11000001 => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1] => 11001111 => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,6,1] => 11000001 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => 11000111 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,6,1] => 11000001 => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1] => 11000011 => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => 11000001 => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => 11000000 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => 11000010 => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => 11000100 => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => 11000010 => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4] => 11001000 => 3
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => 11001100 => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => 11000100 => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => 11000010 => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,2,3,2] => 11010010 => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,2] => 11011110 => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,2,2] => 11011010 => 5
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => 11010010 => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => 11010010 => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5] => 11010000 => 3
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,2,2,3] => 11010100 => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,3] => 11011100 => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,2,1,2,2] => 11011010 => 5
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,1,4] => 11011000 => 4
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,2,2,3] => 11010100 => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,1,3] => 11001100 => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,4] => 11001000 => 3
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => 11001100 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => 11000100 => 3
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,5,2] => 11000010 => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => 11100010 => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,3,1,2] => 11100110 => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,2,1,1,2] => 11101110 => 6
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,2,2] => 11101010 => 5
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,2] => 11100110 => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => 11110110 => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => 11111110 => 7
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,2,1,2] => 11110110 => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => 11110010 => 5
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => 11111010 => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 11101110 => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 11101110 => 6
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => 11101010 => 5
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 11100110 => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1] => 11101111 => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,5,1] => 11100001 => 4
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,2,1,2,1] => 11101101 => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,3,1] => 11101001 => 5
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,2,1] => 11110101 => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,2,1] => 11111101 => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => 11110111 => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1] => 11110011 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => 11111011 => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,2,2,1] => 11110101 => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1] => 11110011 => 6
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,4,1] => 11110001 => 5
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,3,1] => 11111001 => 6
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 11101101 => 6
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 11101101 => 6
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,3,1] => 11101001 => 5
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,4,2] => 11100010 => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,3,1,2] => 11100110 => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => 11101110 => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,2,2,2] => 11101010 => 5
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,3,1,2] => 11100110 => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1] => 11100111 => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,5,1] => 11100001 => 4
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,2,1] => 11101101 => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1] => 11101011 => 6
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,2,3,1] => 11101001 => 5
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,4,2] => 11100010 => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,2] => 11100110 => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,4,1,1] => 11100011 => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,5,1] => 11100001 => 4
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,3,2,1] => 11100101 => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,4,2] => 11100010 => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,5,1] => 11100001 => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => 11100000 => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,3,3] => 11100100 => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,3] => 11101100 => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,2,2,2] => 11101010 => 5
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,3,1] => 11101001 => 5
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,2,4] => 11101000 => 4
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,3,3] => 11100100 => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => 11110100 => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => 11111100 => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,2] => 11110110 => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,3,2] => 11110010 => 5
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,2,2] => 11111010 => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,2,2,1] => 11110101 => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1] => 11110011 => 6
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,4,1] => 11110001 => 5
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,3,1] => 11111001 => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,2,3] => 11110100 => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,3,2] => 11110010 => 5
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,4,1] => 11110001 => 5
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => 11110000 => 4
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => 11111000 => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,2,1,3] => 11101100 => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => 11101100 => 5
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,2,2] => 11101010 => 5
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,3,1] => 11101001 => 5
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => 11101000 => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => 11100100 => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,2] => 11010010 => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,2] => 11011110 => 6
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => 11011010 => 5
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 11011110 => 6
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => 11010010 => 4
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 11011010 => 5
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 11011110 => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 11011110 => 6
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 11011010 => 5
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => 11010111 => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 11011101 => 6
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 11011011 => 6
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => 11010100 => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 11011100 => 5
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => 11010110 => 5
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,2] => 11010010 => 4
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 11011010 => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => 11010101 => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,1,1] => 11010011 => 5
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,2,3] => 11010100 => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,2] => 11010010 => 4
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,1] => 11010001 => 4
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => 11010000 => 3
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 11011000 => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,3] => 11011100 => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 11011100 => 5
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 11011010 => 5
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 11011001 => 5
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 11011000 => 4
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,2,2,3] => 11010100 => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,2,1,1] => 11001011 => 5
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 11001101 => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,3,1,3] => 11001100 => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 11001100 => 4
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,2,2] => 11001010 => 4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,3,1] => 11001001 => 4
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => 11001000 => 3
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,3,1,3] => 11001100 => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 11000110 => 4
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,2,1] => 11000101 => 4
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => 11000100 => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => 11000010 => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,5,1] => 10100001 => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => 7
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => 10100001 => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => 7
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => 7
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => 10100010 => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => 6
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 10110010 => 4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,5,1] => 10100001 => 3
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,2] => 10100010 => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => 10100111 => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,5,1] => 10100001 => 3
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => 10100010 => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => 10100011 => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,5,1] => 10100001 => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => 10100010 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,1] => 10100001 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => 10100000 => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,3] => 10100100 => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => 10101000 => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,3] => 10100100 => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 10110100 => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 10111100 => 5
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 10110010 => 4
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 10110100 => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 10110010 => 4
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 10110000 => 3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 10111000 => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 10101000 => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => 10100100 => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => 10110010 => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => 6
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 10110010 => 4
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => 6
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => 6
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => 6
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => 6
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 10110100 => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 10111100 => 5
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 10110110 => 5
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 10110010 => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 10110101 => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 10110011 => 5
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 10110100 => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 10110010 => 4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 10110001 => 4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 10110000 => 3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 10111000 => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,3] => 10111100 => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 10111100 => 5
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 10111010 => 5
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 10111001 => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 10111000 => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,2,3] => 10110100 => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => 5
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => 10101001 => 4
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 10101000 => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 10100110 => 4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => 10100101 => 4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,3] => 10100100 => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => 10100010 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => 10010001 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => 10010001 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 10010001 => 3
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,3,2] => 10010010 => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 10010010 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => 5
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1] => 10010001 => 3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 10010100 => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,3,2] => 10010010 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => 10010011 => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => 10010001 => 3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,3] => 10010100 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => 10010010 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => 10010001 => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => 10010000 => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => 10011000 => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 10011000 => 3
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,3] => 10010100 => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => 5
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 10011001 => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 10011000 => 3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => 10010110 => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => 10010101 => 4
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => 10010100 => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => 10010010 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => 10001001 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => 10001001 => 3
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => 10001001 => 3
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 10001001 => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => 5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => 10001010 => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,2,2] => 10001010 => 3
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 10001010 => 3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,2,1,1] => 10001011 => 4
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,1] => 10001001 => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,3] => 10001100 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 10001100 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,2,2] => 10001010 => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => 10001001 => 3
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 10001000 => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => 10001100 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => 10001110 => 4
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 10001101 => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => 10001100 => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => 10001010 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => 10000101 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => 10000101 => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => 10000101 => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => 10000101 => 3
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 10000101 => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => 10000111 => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => 10000110 => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => 10000110 => 3
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => 10000110 => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 10000110 => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => 10000101 => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => 10000100 => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => 10000110 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => 10000011 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => 10000011 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => 10000011 => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => 10000011 => 3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => 10000011 => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => 10000011 => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => 10000010 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => 10000001 => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2] => 100000110 => 3
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,2] => 100000010 => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [7,1,2] => 1000000110 => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,1,2] => 100001110 => 4
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2] => 100000110 => 3
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,2] => 1000000010 => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => 3
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,3] => 100000100 => 2
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [7,3] => 1000000100 => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4] => 100001000 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,1,2] => 100011110 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => 110000000 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,4,4] => 110001000 => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5] => 110010000 => 3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,6] => 110100000 => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5] => 110010000 => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => 111000000 => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => 110100000 => 3
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => 110001000 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => 101000000 => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => 101010000 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => 100100010 => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => 100100000 => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,4,2] => 100100010 => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => 100010001 => 3
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,1,3] => 100011100 => 4
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [4,2,1,2] => 100010110 => 4
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [4,2,3] => 100010100 => 3
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,3,2] => 100010010 => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => 3
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => 3
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [5,2,2] => 100001010 => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [6,1,2] => 100000110 => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 100000100 => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2] => 100000110 => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => 100000010 => 2
[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] => [9] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,2] => 100000010 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,3] => 100000100 => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,4] => 100001000 => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,5] => 100010000 => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,6] => 100100000 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,7] => 101000000 => 2
[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] => [10] => 1000000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,2] => 1000000010 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [7,3] => 1000000100 => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,4,1] => 100010001 => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [9,2] => 10000000010 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,2] => 100000010 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [6,3] => 100000100 => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,4,1] => 100010001 => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [6,1,2] => 100000110 => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5] => 100010000 => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,3,2] => 100110010 => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,6] => 100100000 => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5] => 100010000 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,4,1] => 100010001 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,4,1] => 100010001 => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,3,2] => 110010010 => 4
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2] => 1000000110 => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => 1000000010 => 2
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => [6,2,2] => 1000001010 => 3
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,2] => 10000000010 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [4,4,1] => 100010001 => 3
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4] => 1100001000 => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => 111111110 => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,2,1] => 111111101 => 8
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => 1111111110 => 9
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,2,1] => 110111101 => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,2,1] => 1111111101 => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,5,4] => 1100001000 => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,1,1,5] => 1011110000 => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3] => 100100100 => 3
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [3,4,2] => 100100010 => 3
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,3,2] => 100010010 => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [5,2,2] => 100001010 => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,1,2] => 100000110 => 3
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searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,6,6,1 1,10,20,10,1 1,15,50,50,15,1 1,21,105,175,105,21,1 1,28,196,490,490,196,28,1
F1=q
F2=q+q2
F3=q+3 q2+q3
F4=q+6 q2+6 q3+q4
F5=q+10 q2+20 q3+10 q4+q5
F6=q+15 q2+50 q3+50 q4+15 q5+q6
F7=q+21 q2+105 q3+175 q4+105 q5+21 q6+q7
F8=q+28 q2+196 q3+490 q4+490 q5+196 q6+28 q7+q8
Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
This is also known as the Hamming weight of the word.
Map
to binary word
Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer i as the word 10…0 consisting of a one followed by i−1 zeros, the binary word of a composition (i1,…,ik) is the concatenation of of words for i1,…,ik.
The image of this map contains precisely the words which do not begin with a 0.
Encoding a positive integer i as the word 10…0 consisting of a one followed by i−1 zeros, the binary word of a composition (i1,…,ik) is the concatenation of of words for i1,…,ik.
The image of this map contains precisely the words which do not begin with a 0.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
Knuth-Krattenthaler
Description
The map that sends the Dyck path to a 321-avoiding permutation, then applies the Robinson-Schensted correspondence and finally interprets the first row of the insertion tableau and the second row of the recording tableau as up steps.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and 321-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and 321-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
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