***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- 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