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-----------------------------------------------------------------------------
Statistic identifier: St001104
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
Description: The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group.
Following Stembridge [1, cor.4.7], the highest weight words indexing the irreducibles in $\mathfrak{gl_n}^{\otimes r}$ are ''staircase tableaux'' of length $2r$: sequences $(\gamma^{(0)},\dots,\gamma^{(2r)})$ of vectors in $\mathbb Z^n$ with decreasing entries, such that $\gamma^{(2i+1)}$ is obtained from $\gamma^{(2i)}$ by adding a unit vector and $\gamma^{(2i)}$ is obtained from $\gamma^{(2i-1)}$ by subtracting a unit vector.
For $n=2$, the staircase tableaux whose final element is the zero vector are in natural correspondence with Dyck paths: adding the first or subtracting the second unit vector is translated to an up step, whereas adding the second or subtracting the first unit vector is translated to a down step.
A Dyck path can be transformed into a ''bicoloured Motzkin path'' by replacing double up steps (double down, up-down, down-up steps) with up steps (down, coloured level, level steps). Note that the resulting path cannot have coloured level steps at height zero.
In this context, say that a bicoloured Motzkin path has a $\mathfrak{gl}_2$-''descent'' between the following pairs of steps:
* an up step followed by a level step
* an up step followed by a down step, if the final height is not zero
* a coloured level step followed by any non-coloured step.
Then, conjecturally, the quasisymmetric expansion of the Frobenius character of the symmetric group $\mathfrak S_r$ acting on $\mathfrak{gl}_2^{\otimes r}$, is
$$
\sum_M F_{Des(M)},
$$
where the sum is over all length $r$ prefixes of bicoloured Motzkin paths, $Des(M)$ is the set of indices of descents of the path $M$ and $F_D$ is Gessel's fundamental quasisymmetric function.
The statistic recorded here is the number of $\mathfrak{gl}_2$-descents in the bicoloured Motzkin path corresponding to the Dyck path.
Restricting to Motzkin paths without coloured steps one obtains the quasisymmetric expansion for the Frobenius character of $\mathfrak S_r$ acting on $\mathfrak{sl}_2^{\otimes r}$. In this case, the conjecture was shown by Braunsteiner [2].
-----------------------------------------------------------------------------
References: [1] Stembridge, J. R. Rational tableaux and the tensor algebra of ${\rm gl}_n$ [[MathSciNet:0899903]]
[2] Braunsteiner, J. A Sundaram type bijection for $\mathrm {SO}(3)$: vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux [[arXiv:1801.03780]]
-----------------------------------------------------------------------------
Code:
def statistic(W):
h = 0 # h before old
D = []
for i in range(W.semilength()-1):
old = W[2*i], W[2*i+1]
new = W[2*i+2], W[2*i+3]
# print h, old, new
if old == (1,1): # up
h += 1
# level or down not on height 1
if new == (0,1) or (new == (0,0) and h > 1):
D.append(i+1)
elif old == (1,0): # dotted
if new != (1,0):
D.append(i+1)
elif old == (0,1): # level
if new == (0,0):
D.append(i+1)
elif old == (0,0): # down
h -= 1
return len(D)
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1,0] => 0
[1,0,1,0] => 0
[1,1,0,0] => 0
[1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0] => 0
[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] => 3
[1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0] => 2
[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] => 1
[1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => 0
[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] => 3
[1,0,1,0,1,1,1,0,0,0] => 2
[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] => 3
[1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => 0
[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] => 2
[1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => 2
[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] => 2
[1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => 2
[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] => 2
[1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => 0
[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] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => 2
[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] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => 2
[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] => 2
[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] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => 3
[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] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => 3
[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] => 3
[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] => 0
[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] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => 2
[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] => 1
[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] => 3
[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] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => 2
[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] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => 2
[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] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => 2
[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] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => 1
[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] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[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] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[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] => 2
[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] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[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] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[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] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[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] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[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] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[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] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[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] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[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] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[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] => 0
[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] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[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] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[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] => 0
[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] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[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] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[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] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[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] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[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] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[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] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[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] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 4
[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] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[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] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[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] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 3
[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] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[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] => 2
[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] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[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] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[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] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[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] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[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] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[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] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[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] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[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] => 0
[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] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[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
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[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] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[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] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 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] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[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] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[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] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 3
[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
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 3
[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] => 2
[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] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 2
[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] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[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
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 7
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 7
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 7
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 6
-----------------------------------------------------------------------------
Created: Feb 12, 2018 at 21:20 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Feb 12, 2018 at 21:52 by Martin Rubey