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-----------------------------------------------------------------------------
Statistic identifier: St000027
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
Description: The major index of a Dyck path.
This is the sum over all $i+j$ for which $(i,j)$ is a valley of $D$.
The generating function of the major index yields '''MacMahon''' 's $q$-Catalan numbers
$$\sum_{D \in \mathfrak{D}_n} q^{\operatorname{maj}(D)} = \frac{1}{[n+1]_q}\begin{bmatrix} 2n \\ n \end{bmatrix}_q,$$
where $[k]_q := 1+q+\ldots+q^{k-1}$ is the usual $q$-extension of the integer $k$, $[k]_q!:= [1]_q[2]_q \cdots [k]_q$ is the $q$-factorial of $k$ and $\left[\begin{smallmatrix} k \\ l \end{smallmatrix}\right]_q:=[k]_q!/[l]_q![k-l]_q!$ is the $q$-binomial coefficient.
The major index was first studied by P.A.MacMahon in [1], where he proved this generating function identity.
There is a bijection $\psi$ between Dyck paths and '''noncrossing permutations''' which simultaneously sends the area of a Dyck path [[St000012]] to the number of inversions [[St000018]], and the major index of the Dyck path to $n(n-1)$ minus the sum of the major index and the major index of the inverse [2].
For the major index on other collections, see [[St000004]] for permutations and [[St000290]] for binary words.
-----------------------------------------------------------------------------
References: [1] MacMahon, P. A. Combinatory analysis [[MathSciNet:0141605]]
[2] Stump, C. More bijective Catalan combinatorics on permutations and on signed permutations [[arXiv:0808.2822]]
-----------------------------------------------------------------------------
Code:
def statistic(x):
return x.major_index()
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1,0] => 0
[1,0,1,0] => 2
[1,1,0,0] => 0
[1,0,1,0,1,0] => 6
[1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => 4
[1,1,0,1,0,0] => 3
[1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => 12
[1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0] => 10
[1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0] => 9
[1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => 20
[1,0,1,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,0,1,1,0,1,0,0] => 13
[1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0] => 16
[1,0,1,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,0] => 15
[1,0,1,1,0,1,0,1,0,0] => 14
[1,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0] => 18
[1,1,0,0,1,0,1,1,0,0] => 10
[1,1,0,0,1,1,0,0,1,0] => 12
[1,1,0,0,1,1,0,1,0,0] => 11
[1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0] => 17
[1,1,0,1,0,0,1,1,0,0] => 9
[1,1,0,1,0,1,0,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,0] => 15
[1,1,0,1,0,1,1,0,0,0] => 8
[1,1,0,1,1,0,0,0,1,0] => 11
[1,1,0,1,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,0,0,0] => 9
[1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0] => 14
[1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,0] => 13
[1,1,1,0,0,1,0,1,0,0] => 12
[1,1,1,0,0,1,1,0,0,0] => 5
[1,1,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,0,1,0,0] => 11
[1,1,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => 30
[1,0,1,0,1,0,1,0,1,1,0,0] => 20
[1,0,1,0,1,0,1,1,0,0,1,0] => 22
[1,0,1,0,1,0,1,1,0,1,0,0] => 21
[1,0,1,0,1,0,1,1,1,0,0,0] => 12
[1,0,1,0,1,1,0,0,1,0,1,0] => 24
[1,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,0,1,1,0,1,0,0,1,0] => 23
[1,0,1,0,1,1,0,1,0,1,0,0] => 22
[1,0,1,0,1,1,0,1,1,0,0,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,0,1,0,1,1,1,0,0,1,0,0] => 15
[1,0,1,0,1,1,1,0,1,0,0,0] => 14
[1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => 26
[1,0,1,1,0,0,1,0,1,1,0,0] => 16
[1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,1,0,0,1,1,0,1,0,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,0] => 25
[1,0,1,1,0,1,0,0,1,1,0,0] => 15
[1,0,1,1,0,1,0,1,0,0,1,0] => 24
[1,0,1,1,0,1,0,1,0,1,0,0] => 23
[1,0,1,1,0,1,0,1,1,0,0,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,0] => 17
[1,0,1,1,0,1,1,0,0,1,0,0] => 16
[1,0,1,1,0,1,1,0,1,0,0,0] => 15
[1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => 20
[1,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,1,0,0,1,0] => 19
[1,0,1,1,1,0,0,1,0,1,0,0] => 18
[1,0,1,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,0] => 18
[1,0,1,1,1,0,1,0,0,1,0,0] => 17
[1,0,1,1,1,0,1,0,1,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,1,1,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => 28
[1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,0,0,1,0,1,1,0,0,1,0] => 20
[1,1,0,0,1,0,1,1,0,1,0,0] => 19
[1,1,0,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,1,0,0,1,0,1,0] => 22
[1,1,0,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,1,0,0,1,0] => 21
[1,1,0,0,1,1,0,1,0,1,0,0] => 20
[1,1,0,0,1,1,0,1,1,0,0,0] => 11
[1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,1,0,0,1,1,1,0,0,1,0,0] => 13
[1,1,0,0,1,1,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => 27
[1,1,0,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,1,0,0,1,1,0,0,1,0] => 19
[1,1,0,1,0,0,1,1,0,1,0,0] => 18
[1,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,1,0,0,1,0,1,0] => 26
[1,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,0] => 25
[1,1,0,1,0,1,0,1,0,1,0,0] => 24
[1,1,0,1,0,1,0,1,1,0,0,0] => 15
[1,1,0,1,0,1,1,0,0,0,1,0] => 18
[1,1,0,1,0,1,1,0,0,1,0,0] => 17
[1,1,0,1,0,1,1,0,1,0,0,0] => 16
[1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => 21
[1,1,0,1,1,0,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,1,0,0,1,0] => 20
[1,1,0,1,1,0,0,1,0,1,0,0] => 19
[1,1,0,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,1,1,0,1,0,0,0,1,0] => 19
[1,1,0,1,1,0,1,0,0,1,0,0] => 18
[1,1,0,1,1,0,1,0,1,0,0,0] => 17
[1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,1,1,1,0,0,0,0,1,0] => 13
[1,1,0,1,1,1,0,0,0,1,0,0] => 12
[1,1,0,1,1,1,0,0,1,0,0,0] => 11
[1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => 24
[1,1,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,1,0,0,0,1,1,0,0,1,0] => 16
[1,1,1,0,0,0,1,1,0,1,0,0] => 15
[1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => 23
[1,1,1,0,0,1,0,0,1,1,0,0] => 13
[1,1,1,0,0,1,0,1,0,0,1,0] => 22
[1,1,1,0,0,1,0,1,0,1,0,0] => 21
[1,1,1,0,0,1,0,1,1,0,0,0] => 12
[1,1,1,0,0,1,1,0,0,0,1,0] => 15
[1,1,1,0,0,1,1,0,0,1,0,0] => 14
[1,1,1,0,0,1,1,0,1,0,0,0] => 13
[1,1,1,0,0,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => 22
[1,1,1,0,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,0,1,0,0,1,0] => 21
[1,1,1,0,1,0,0,1,0,1,0,0] => 20
[1,1,1,0,1,0,0,1,1,0,0,0] => 11
[1,1,1,0,1,0,1,0,0,0,1,0] => 20
[1,1,1,0,1,0,1,0,0,1,0,0] => 19
[1,1,1,0,1,0,1,0,1,0,0,0] => 18
[1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => 14
[1,1,1,0,1,1,0,0,0,1,0,0] => 13
[1,1,1,0,1,1,0,0,1,0,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,1,0,1,1,1,0,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => 18
[1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => 17
[1,1,1,1,0,0,0,1,0,1,0,0] => 16
[1,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,0,0,1,0] => 16
[1,1,1,1,0,0,1,0,0,1,0,0] => 15
[1,1,1,1,0,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => 15
[1,1,1,1,0,1,0,0,0,1,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,0] => 13
[1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 42
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 30
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 32
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 31
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 20
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 34
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 22
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 33
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 32
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 21
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 24
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 23
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 22
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 12
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 36
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 24
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 26
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 25
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 14
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 35
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 23
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 34
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 33
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 22
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 25
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 24
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 23
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 28
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 16
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 27
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 26
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 15
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 26
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 25
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 24
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 14
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 18
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 17
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 16
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 15
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 38
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 26
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 28
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 27
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 16
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 30
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 18
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 29
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 28
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 20
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 19
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 37
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 25
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 27
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 26
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 36
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 24
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 35
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 34
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 23
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 26
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 25
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 24
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 29
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 17
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 28
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 27
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 16
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 27
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 26
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 25
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 15
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 19
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 18
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 17
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 32
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 20
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 22
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 21
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 10
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 31
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 19
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 30
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 29
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 18
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 21
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 20
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 19
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 30
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 18
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 29
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 28
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 17
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 28
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 27
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 26
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 20
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 19
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 18
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 17
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 24
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 23
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 22
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 22
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 21
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 20
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 21
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 20
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 19
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 18
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 40
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 28
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 30
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 29
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 18
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 32
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 20
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 31
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 30
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 19
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 22
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 21
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 20
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 34
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 22
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 24
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 23
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 12
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 33
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 21
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 32
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 31
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 20
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 23
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 22
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 21
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 26
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 14
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 25
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 24
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 13
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 24
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 23
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 22
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 16
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 15
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 14
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 39
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 27
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 29
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 28
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 17
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 31
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 19
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 30
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 29
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 18
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 21
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 20
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 19
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 38
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 26
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 28
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 27
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 37
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 25
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 36
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 35
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 24
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 27
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 26
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 25
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 15
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 30
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 18
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 29
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 28
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 17
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 28
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 27
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 26
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 16
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 20
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 19
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 18
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 17
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 33
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 21
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 23
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 22
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 11
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 32
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 20
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 31
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 30
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 19
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 22
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 21
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 20
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 31
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 19
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 30
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 29
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 18
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 29
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 28
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 27
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 17
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 21
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 20
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 19
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 18
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 9
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 25
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 13
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 24
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 23
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 12
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 23
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 22
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 21
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 22
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 21
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 20
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 19
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 10
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 15
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 14
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 12
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 11
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 36
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 24
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 26
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 25
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 14
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 28
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 16
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 27
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 26
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 15
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 18
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 17
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 16
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 35
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 23
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 25
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 24
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 13
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 34
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 22
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 33
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 32
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 21
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 24
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 23
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 22
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 12
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 27
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 15
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 26
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 25
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 14
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 25
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 24
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 23
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 13
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 17
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 16
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 15
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 14
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 34
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 22
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 24
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 23
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 12
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 33
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 21
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 32
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 31
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 20
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 23
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 22
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 21
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 32
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 20
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 31
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 30
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 19
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 30
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 29
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 28
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 18
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 22
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 21
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 20
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 19
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 26
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 14
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 25
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 24
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 13
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 24
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 23
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 22
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 23
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 22
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 21
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 20
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 11
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 16
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 15
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 13
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 30
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 18
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 20
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 19
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 29
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 17
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 28
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 27
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 16
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 19
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 18
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 17
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 28
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 16
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 27
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 26
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 15
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 26
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 25
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 24
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 14
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 18
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 17
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 16
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 15
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 27
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 15
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 26
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 25
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 25
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 24
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 23
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 13
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 24
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 23
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 22
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 21
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 17
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 16
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 15
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 14
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 13
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 22
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 21
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 20
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 20
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 19
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 18
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 19
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 18
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 17
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 18
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 17
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 15
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 12
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 56
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 42
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 44
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 43
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 30
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 46
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 32
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 45
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 44
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 31
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 34
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 33
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 32
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 20
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 48
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 34
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 36
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 35
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 22
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 47
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 33
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 46
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 45
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 32
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 35
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 34
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 33
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 21
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 38
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 24
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 37
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 36
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 23
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 36
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 35
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 34
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 22
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 26
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 25
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 24
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 23
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 50
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 36
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 38
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 37
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 24
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 40
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 26
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 39
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 38
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 25
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 28
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 27
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 26
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 14
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 49
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 35
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 37
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 36
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 23
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 48
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 34
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 47
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 46
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 33
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 36
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 35
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 34
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 22
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 39
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 25
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 38
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 37
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 24
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 37
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 36
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 35
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 23
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 27
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 26
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 25
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 24
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 42
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 28
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 30
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 29
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 16
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 41
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 27
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 40
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 39
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 26
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 29
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 28
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 27
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 15
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 40
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 26
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 39
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 38
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 25
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 38
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 37
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 36
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 24
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 28
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 27
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 26
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 25
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 14
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 32
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 18
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 31
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 30
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 17
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 30
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 29
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 28
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 16
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 29
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 28
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 27
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 26
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 15
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 20
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 19
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 18
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 17
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 16
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 52
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 38
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 40
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 39
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 26
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 42
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 28
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 41
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 40
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 27
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 30
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 29
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 28
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 16
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 44
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 30
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 32
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 31
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 43
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 29
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 42
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 41
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 28
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 31
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 30
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 29
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 34
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 20
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 33
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 32
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 19
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 32
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 31
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 30
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 18
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 22
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 21
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 20
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 19
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 51
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 37
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 39
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 38
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 25
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 41
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 27
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 40
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 39
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 26
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 29
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 28
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 27
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 15
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 50
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 36
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 38
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 37
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 24
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 49
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 35
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 48
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 47
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 34
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 37
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 36
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 35
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 23
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 40
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 26
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 39
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 38
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 25
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 38
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 37
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 36
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 24
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 28
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 27
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 26
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 25
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 43
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 29
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 31
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 30
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 17
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 42
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 28
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 41
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 40
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 27
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 30
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 29
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 28
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 16
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 41
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 27
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 40
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 39
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 26
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 39
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 38
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 37
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 25
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 29
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 28
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 27
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 26
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 15
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 33
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 19
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 32
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 31
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 31
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 30
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 29
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 17
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 30
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 29
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 28
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 27
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 16
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 21
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 20
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 19
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 17
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 46
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 32
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 34
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 33
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 20
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 36
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 22
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 35
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 34
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 21
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 24
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 23
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 22
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 45
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 31
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 33
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 32
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 19
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 44
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 30
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 43
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 42
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 29
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 32
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 31
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 30
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 18
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 35
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 21
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 34
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 33
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 20
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 33
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 32
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 31
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 19
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 23
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 22
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 21
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 20
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 44
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 30
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 32
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 31
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 18
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 43
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 29
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 42
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 41
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 28
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 31
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 30
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 29
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 17
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 42
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 28
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 41
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 40
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 27
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 40
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 39
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 38
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 26
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 30
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 29
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 28
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 27
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 34
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 20
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 33
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 32
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 19
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 32
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 31
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 30
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 18
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 31
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 30
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 29
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 28
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 17
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 22
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 21
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 20
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 19
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 38
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 24
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 26
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 25
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 37
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 23
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 36
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 35
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 22
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 25
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 24
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 23
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 36
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 22
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 35
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 34
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 21
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 34
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 33
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 32
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 20
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 24
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 23
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 22
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 21
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 35
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 21
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 34
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 33
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 20
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 33
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 32
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 31
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 19
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 32
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 31
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 30
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 29
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 18
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 23
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 22
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 21
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 20
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 19
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 28
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 14
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 27
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 26
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 26
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 25
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 24
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 25
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 24
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 23
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 22
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 24
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 23
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 22
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 21
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 20
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 16
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 14
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 54
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 40
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 42
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 41
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 28
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 44
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 30
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 43
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 42
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 29
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 32
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 31
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 30
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 18
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 46
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 32
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 34
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 33
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 20
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 45
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 31
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 44
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 43
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 30
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 33
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 32
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 31
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 19
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 36
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 22
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 35
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 34
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 21
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 34
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 33
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 32
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 20
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 24
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 23
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 22
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 21
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 48
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 34
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 36
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 35
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 22
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 38
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 24
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 37
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 36
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 23
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 26
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 25
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 24
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 47
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 33
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 35
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 34
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 21
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 46
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 32
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 45
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 44
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 31
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 34
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 33
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 32
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 20
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 37
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 23
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 36
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 35
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 22
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 35
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 34
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 33
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 21
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 25
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 24
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 23
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 22
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 40
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 26
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 28
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 27
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 39
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 25
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 38
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 37
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 24
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 27
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 26
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 25
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 13
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 38
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 24
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 37
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 36
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 23
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 36
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 35
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 34
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 22
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 26
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 25
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 24
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 23
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 30
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 16
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 29
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 28
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 15
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 28
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 27
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 26
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 27
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 26
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 25
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 24
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 18
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 17
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 16
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 15
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 53
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 39
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 41
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 40
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 27
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 43
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 29
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 42
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 41
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 28
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 31
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 30
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 29
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 17
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 30
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 32
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 51
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 37
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 50
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 36
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 49
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 48
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 35
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 37
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 36
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 24
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 39
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 37
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 44
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 41
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 47
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 43
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 32
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 32
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 34
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 15
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 13
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 12
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 50
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 36
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 37
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 20
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 47
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 46
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 45
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 38
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 24
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 24
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 34
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 44
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 35
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 46
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 43
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 44
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 30
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 42
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 41
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 40
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 28
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 24
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 24
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 36
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 16
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 24
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 13
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 18
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 16
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 15
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 14
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 13
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 20
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 20
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 36
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 38
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 24
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 26
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 24
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 22
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 17
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 24
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 13
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 19
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 18
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 17
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 16
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 14
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 20
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 22
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 20
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 19
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 21
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 19
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 18
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 28
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 27
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 24
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 14
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 20
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 19
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 18
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 17
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 16
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 12
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 23
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 22
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 20
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 22
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 21
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 19
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 18
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 21
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 20
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 18
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 17
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 13
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 12
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 11
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 16
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 24
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 25
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 23
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 13
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 22
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 24
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 14
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 18
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 21
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 22
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 20
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 16
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 14
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 63
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 48
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 50
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 49
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 58
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 14
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 13
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 60
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 59
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 55
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 54
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 4
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 22
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 17
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 24
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 23
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 15
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 14
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 56
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 57
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 45
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 44
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 22
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 52
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 62
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 32
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 16
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 70
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 54
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 56
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 20
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 66
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 65
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 64
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 63
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 55
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 54
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 53
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 53
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 56
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 58
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 61
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 47
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 49
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 59
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 32
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 40
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 41
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 39
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 33
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 31
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 18
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 27
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 13
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 26
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 16
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 4
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 20
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 24
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 16
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 72
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 73
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 80
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 77
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 24
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 36
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 88
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 70
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 84
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 81
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 63
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 11
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 71
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 17
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 26
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 70
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 40
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 42
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 43
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 44
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 46
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 44
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 46
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 46
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 48
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 46
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 48
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 49
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 50
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 52
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 45
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 47
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 48
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 49
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 51
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 48
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 50
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 50
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 52
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 49
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 51
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 52
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 53
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 55
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 48
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 50
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 51
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 52
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 54
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 52
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 54
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 54
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 56
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 54
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 56
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 57
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 58
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 60
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 72
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 19
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 45
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 35
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 20
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 90
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 91
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 99
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 108
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 19
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 88
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 18
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 40
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 26
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 57
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 59
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 60
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 61
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 63
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 61
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 63
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 63
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 65
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 63
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 65
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 66
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 67
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 69
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 62
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 64
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 65
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 66
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 68
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 65
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 67
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 67
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 69
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 66
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 68
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 69
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 70
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 72
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 65
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 67
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 68
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 69
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 71
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 69
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 71
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 71
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 73
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 71
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 73
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 74
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 75
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 77
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 63
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 65
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 66
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 67
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 69
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 67
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 69
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 69
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 71
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 69
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 71
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 72
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 73
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 75
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 67
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 69
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 70
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 71
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 73
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 69
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 71
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 72
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 73
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 75
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 69
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 71
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 71
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 73
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 72
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 74
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 73
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 75
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 75
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 77
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 69
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 71
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 72
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 73
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 75
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 73
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 75
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 75
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 77
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 75
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 77
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 78
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 79
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 81
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 67
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 69
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 70
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 71
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 73
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 71
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 73
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 73
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 75
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 73
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 75
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 76
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 77
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 79
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 72
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 74
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 75
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 76
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 78
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 75
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 77
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 77
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 79
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 76
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 78
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 79
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 80
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 82
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 75
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 77
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 78
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 79
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 81
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 79
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 81
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 81
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 83
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 81
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 83
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 84
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 85
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 87
-----------------------------------------------------------------------------
Created: Jun 10, 2012 at 08:35 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Feb 12, 2018 at 22:26 by Martin Rubey