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-----------------------------------------------------------------------------
Statistic identifier: St001786
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
Description: The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order.
Alternatively, remark that the monomials of the polynomial $\prod_{k=1}^n (z_1+\dots +z_k)$ are in bijection with Dyck paths, regarded as superdiagonal paths, with $n$ east steps: the exponent of $z_i$ is the number of north steps before the $i$-th east step, see [2]. Thus, this statistic records the coefficients of the monomials.
A formula for the coefficient of $z_1^{a_1}\dots z_n^{a_n}$ is provided in [3]:
$$
c_{(a_1,\dots,a_n)} = \prod_{k=1}^{n-1} \frac{n-k+1 - \sum_{i=k+1}^n a_i}{a_k!}.
$$
This polynomial arises in a partial symmetrization process as follows, see [1]. For $w\in\frak{S}_n$, let $w\cdot F(x_1,\dots,x_n)=F(x_{w(1)},\dots,x_{w(n)})$. Furthermore, let
$$G(\mathbf{x},\mathbf{z}) = \prod_{k=1}^n\frac{x_1z_1+x_2z_2+\cdots+x_kz_k}{x_k-x_{k+1}}.$$
Then $\sum_{w\in\frak{S}_{n+1}}w\cdot G = \prod_{k=1}^n (z_1+\dots +z_k)$.
-----------------------------------------------------------------------------
References: [1] Amdeberhan, T. Counting monomials and the Catalan numbers [[MathOverflow:420887]]
[2] The coefficients in the expansion x_1(x_1 + x_2)...(x_1 + x_2 + ... + x_n), given row by row. [[OEIS:A347917]]
[3] Fried, S. On the coefficients of the distinct monomials in the expansion of $x_1(x_1+x_2)\cdots (x_1+x_2+\cdots +x_n)$ [[arXiv:2111.07331]]
-----------------------------------------------------------------------------
Code:
def statistic(D):
n = D.semilength()
a = []
i = 0
for e in D:
if e == 0:
a.append(i)
i = 0
else:
i += 1
return prod((n-k-sum(a[k+1:]))/factorial(a[k]) for k in range(len(a)-1))
-----------------------------------------------------------------------------
Statistic values:
[1,0] => 1
[1,0,1,0] => 1
[1,1,0,0] => 1
[1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,0] => 9
[1,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,0,1,0,1,0,1,1,0,0,0] => 12
[1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,0,0] => 12
[1,1,0,1,0,1,1,0,1,0,0,0] => 18
[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] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,0] => 12
[1,1,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,0,1,1,0,1,0,0,0,1,0] => 9
[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] => 27
[1,1,0,1,1,0,1,1,0,0,0,0] => 18
[1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => 12
[1,1,0,1,1,1,0,1,0,0,0,0] => 16
[1,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => 12
[1,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,1,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,1,0,1,0,1,0,0,1,0,0] => 18
[1,1,1,0,1,0,1,0,1,0,0,0] => 27
[1,1,1,0,1,0,1,1,0,0,0,0] => 18
[1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => 12
[1,1,1,0,1,1,0,0,1,0,0,0] => 18
[1,1,1,0,1,1,0,1,0,0,0,0] => 24
[1,1,1,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => 9
[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] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,0,1,1,0,0,0,0,0] => 10
[1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 12
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 12
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 18
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 12
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 18
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 27
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 12
[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] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 18
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 27
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 18
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 12
[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] => 24
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[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] => 12
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 24
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 36
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 16
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 12
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 24
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 18
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 18
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 36
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 54
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 36
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 16
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 24
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 32
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 12
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 24
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 18
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 18
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 27
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 12
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 9
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 18
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 36
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 27
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 27
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 54
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 81
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 54
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 18
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 36
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 54
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 72
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 30
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 16
[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] => 12
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 24
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 36
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 24
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 32
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 48
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 64
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 40
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 15
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 20
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 25
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 12
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 12
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 18
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 12
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 18
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 27
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 18
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 16
[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] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 12
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 24
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 18
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 18
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 27
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 12
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 9
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 18
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 36
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 27
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 27
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 54
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 81
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 54
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 18
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 36
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 54
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 72
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 30
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 12
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 24
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 18
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 18
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 36
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 54
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 36
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 24
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 48
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 72
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 96
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 60
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 20
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 30
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 40
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 50
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 9
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 12
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 18
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 27
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 18
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 18
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 24
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 16
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[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] => 36
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 24
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 32
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 48
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 64
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 40
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 20
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 30
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 40
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 50
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 20
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 9
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 12
[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] => 10
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 15
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 20
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 25
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 12
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 12
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 18
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 18
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 12
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 24
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 16
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 24
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 72
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 48
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 12
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 24
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 27
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 36
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 27
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 54
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 81
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 36
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 72
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 24
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 48
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 20
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 40
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 27
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 24
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 36
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 32
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 64
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 20
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 20
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 25
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 27
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 18
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 16
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 12
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => 12
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 64
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 48
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 24
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 48
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 72
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 32
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 12
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 48
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => 36
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 36
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 108
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 72
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => 16
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 32
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 48
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 64
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 20
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 48
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => 36
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => 36
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => 24
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => 18
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 72
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 108
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 162
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => 144
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => 32
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => 24
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 72
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 96
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 128
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 80
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => 20
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 30
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 50
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 12
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 48
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => 36
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => 36
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => 24
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 18
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => 36
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 27
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => 24
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => 36
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => 48
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => 15
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 9
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 18
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 72
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 27
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 81
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => 162
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 243
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => 162
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 72
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => 288
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => 150
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => 45
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => 32
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => 24
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => 24
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => 16
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => 12
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 108
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => 72
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 48
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 144
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 192
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 256
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 120
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 200
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 80
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => 20
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => 15
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 45
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => 50
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 75
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => 100
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 125
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 75
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 12
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 18
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => 24
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 30
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 36
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => 24
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => 24
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => 16
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => 24
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => 18
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => 16
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => 10
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 24
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => 18
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 18
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 12
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => 81
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => 16
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => 12
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => 25
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 9
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 12
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 24
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 48
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 27
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 18
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 18
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 36
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 72
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 27
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 27
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => 81
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 81
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 162
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 243
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 162
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => 162
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => 216
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 90
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 18
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 72
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => 162
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => 108
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 144
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => 216
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 288
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => 180
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => 90
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => 120
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 150
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 45
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 18
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => 162
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => 108
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 108
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => 144
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 60
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 48
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => 96
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => 216
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => 144
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 192
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => 288
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 384
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => 240
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => 180
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => 240
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 300
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => 120
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 40
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => 90
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => 60
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 80
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => 120
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 160
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 100
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => 100
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => 150
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 200
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 250
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 150
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 30
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 45
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 60
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 75
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 90
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => 12
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => 12
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => 12
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => 16
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 54
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 81
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => 54
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => 54
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => 72
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 30
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => 54
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => 36
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => 72
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => 96
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => 60
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => 30
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => 40
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 50
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 32
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 24
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 108
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => 72
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => 72
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 96
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 40
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 16
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 64
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 144
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => 96
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 128
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 192
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 256
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 160
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 40
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 120
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => 160
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 200
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 80
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 90
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => 60
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => 120
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 160
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 100
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 100
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 150
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 200
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 250
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 150
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 20
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 40
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 60
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 80
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 100
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 120
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 35
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => 9
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 27
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => 18
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 18
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => 24
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => 36
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => 24
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 48
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 64
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => 40
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => 20
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 30
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => 40
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 50
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 20
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => 30
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 45
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 30
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 40
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 60
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 80
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 50
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 25
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 50
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 75
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 100
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 125
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 75
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 30
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 45
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 60
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 75
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 90
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 35
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => 12
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 15
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 20
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 25
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 12
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 18
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 24
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 30
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 36
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 21
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 21
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 21
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 35
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 36
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 15
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 25
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 125
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 15
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 64
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 128
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 96
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 96
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 144
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 64
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 96
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => 144
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 216
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 144
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 64
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 96
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 128
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 40
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 96
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 324
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 144
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 192
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 256
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 60
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => 216
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 486
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 216
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 288
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 512
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 90
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 96
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 54
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 36
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 486
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 729
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 324
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 432
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1024
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 135
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 175
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 216
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 126
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 14
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 35
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 42
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 49
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 64
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 96
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 486
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 729
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 960
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 63
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 28
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 243
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => 384
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => 324
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 432
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => 384
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1024
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 640
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => 140
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => 56
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => 81
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => 192
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => 256
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 375
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => 315
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => 70
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => 175
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 245
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => 70
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => 125
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => 90
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => 90
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => 72
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => 126
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 42
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 126
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 147
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => 56
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 12
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => 30
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => 36
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 14
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 49
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 28
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 64
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 24
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 36
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 72
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 24
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 72
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 48
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 162
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 40
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 144
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 243
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 80
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 256
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 32
[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] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 12
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 24
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 48
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 243
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 81
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 27
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 81
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 81
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 243
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 81
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 32
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 48
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 32
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 16
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 32
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 64
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 15
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => 10
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => 27
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => 18
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => 12
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => 36
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => 18
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => 12
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 16
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 28
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 49
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => 216
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 64
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 128
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 256
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 128
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 432
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 729
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1458
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1024
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 32
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 64
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 128
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 1875
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => 625
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 2560
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1024
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 192
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => 36
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 196
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => 49
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 16
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => 84
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => 126
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 126
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 84
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 36
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2187
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 432
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 288
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 192
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 625
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 128
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 256
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 512
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1024
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2048
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4096
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 4096
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 648
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => 98
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 343
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 27
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 81
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 54
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 18
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 288
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 432
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 972
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1458
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2187
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 192
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 288
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 432
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 648
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 972
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 729
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 900
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 600
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 384
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 600
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 300
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 216
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 144
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 216
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 108
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 600
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 400
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 192
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 300
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 120
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 144
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 96
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 54
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 96
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 48
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 81
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 54
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 54
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 36
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 144
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 96
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 54
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 96
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 48
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 900
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 600
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 384
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 600
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 300
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 216
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 144
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 216
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 108
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 600
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 400
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 192
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 300
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 120
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 729
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 224
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 64
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => 14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => 56
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 56
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 196
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 512
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 9375
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 3125
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => 45
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => 18
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 81
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 384
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 576
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 864
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1296
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1944
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2916
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 4374
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 6561
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 6561
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 16200
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 10800
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 7500
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 10800
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 5400
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 4800
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 3200
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 4800
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 2400
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 10800
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 7200
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 3750
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 5400
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 2160
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 2700
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 1800
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 1152
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 1800
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 900
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 1728
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 1152
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 864
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 576
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 2700
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 1800
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 864
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 1350
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 540
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 10800
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 7200
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 5000
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 7200
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 3600
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 2400
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 1600
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 2400
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 960
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 5400
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 3600
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 1500
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 2160
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 720
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1800
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 1200
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 768
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 1200
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 600
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 432
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 288
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 432
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 216
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 1200
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 800
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 384
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 600
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 240
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 648
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 432
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 243
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 432
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 216
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 432
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 288
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 162
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 288
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 144
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 648
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 432
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 432
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 288
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 243
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 162
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 432
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 288
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 216
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 144
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 1800
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 1200
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 768
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 1200
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 600
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 432
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 288
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 432
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 216
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 1200
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 800
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 384
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 600
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 240
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 16200
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 10800
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 7500
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 10800
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 5400
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 4800
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 3200
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 4800
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 2400
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 10800
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 7200
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 3750
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 5400
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 2160
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 2700
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 1800
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 1152
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 1800
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 900
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1728
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 1152
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 864
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 576
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 2700
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 1800
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 864
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 1350
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 540
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 10800
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 7200
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 5000
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 7200
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 3600
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 2400
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 1600
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2400
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 960
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 5400
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 3600
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 1500
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 2160
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 720
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 11
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Created: Apr 25, 2022 at 10:03 by Martin Rubey
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Last Updated: Apr 26, 2022 at 17:11 by Martin Rubey