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------------------------------------------------------------------------
Map identifier: Mp00242

------------------------------------------------------------------------
Map name: Hessenberg poset

------------------------------------------------------------------------
Domain: Dyck paths

------------------------------------------------------------------------
Codomain: Posets

------------------------------------------------------------------------
Description: The Hessenberg poset of a Dyck path.

Let $D$ be a Dyck path of semilength $n$, regarded as a subdiagonal path from $(0,0)$ to $(n,n)$, and let $\boldsymbol{m}_i$ be the $x$-coordinate of the $i$-th up step.

Then the Hessenberg poset (or natural unit interval order) corresponding to $D$ has elements $\{1,\dots,n\}$ with $i < j$ if $j < \boldsymbol{m}_i$.

------------------------------------------------------------------------
References: [1]   Shareshian, J., Wachs, M. L. Chromatic quasisymmetric functions [[MathSciNet:3488041]]

------------------------------------------------------------------------
Code:

def mapping(D):
    D = DyckWord(D)
    m = [a+i for i, a in enumerate(reversed(D.to_area_sequence()), 1)]
    return Poset([list(range(1, D.semilength()+1)), lambda i, j: j > m[i-1]])


------------------------------------------------------------------------
Map images:

[1,0]                             => ([],1)
[1,0,1,0]                         => ([(0,1)],2)
[1,1,0,0]                         => ([],2)
[1,0,1,0,1,0]                     => ([(0,2),(2,1)],3)
[1,0,1,1,0,0]                     => ([(0,2),(1,2)],3)
[1,1,0,0,1,0]                     => ([(0,1),(0,2)],3)
[1,1,0,1,0,0]                     => ([(1,2)],3)
[1,1,1,0,0,0]                     => ([],3)
[1,0,1,0,1,0,1,0]                 => ([(0,3),(2,1),(3,2)],4)
[1,0,1,0,1,1,0,0]                 => ([(0,3),(1,3),(3,2)],4)
[1,0,1,1,0,0,1,0]                 => ([(0,1),(0,2),(1,3),(2,3)],4)
[1,0,1,1,0,1,0,0]                 => ([(0,3),(1,2),(2,3)],4)
[1,0,1,1,1,0,0,0]                 => ([(0,3),(1,3),(2,3)],4)
[1,1,0,0,1,0,1,0]                 => ([(0,3),(3,1),(3,2)],4)
[1,1,0,0,1,1,0,0]                 => ([(0,2),(0,3),(1,2),(1,3)],4)
[1,1,0,1,0,0,1,0]                 => ([(0,2),(0,3),(3,1)],4)
[1,1,0,1,0,1,0,0]                 => ([(0,3),(1,2),(1,3)],4)
[1,1,0,1,1,0,0,0]                 => ([(1,3),(2,3)],4)
[1,1,1,0,0,0,1,0]                 => ([(0,1),(0,2),(0,3)],4)
[1,1,1,0,0,1,0,0]                 => ([(1,2),(1,3)],4)
[1,1,1,0,1,0,0,0]                 => ([(2,3)],4)
[1,1,1,1,0,0,0,0]                 => ([],4)
[1,0,1,0,1,0,1,0,1,0]             => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,0,1,1,0,0]             => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,0,1,0,1,1,0,0,1,0]             => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[1,0,1,0,1,1,0,1,0,0]             => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,0,1,1,1,0,0,0]             => ([(0,4),(1,4),(2,4),(4,3)],5)
[1,0,1,1,0,0,1,0,1,0]             => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[1,0,1,1,0,0,1,1,0,0]             => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[1,0,1,1,0,1,0,0,1,0]             => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[1,0,1,1,0,1,0,1,0,0]             => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[1,0,1,1,0,1,1,0,0,0]             => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,0,1,0]             => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
[1,0,1,1,1,0,0,1,0,0]             => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[1,0,1,1,1,0,1,0,0,0]             => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,1,0,0,0,0]             => ([(0,4),(1,4),(2,4),(3,4)],5)
[1,1,0,0,1,0,1,0,1,0]             => ([(0,3),(3,4),(4,1),(4,2)],5)
[1,1,0,0,1,0,1,1,0,0]             => ([(0,4),(1,4),(4,2),(4,3)],5)
[1,1,0,0,1,1,0,0,1,0]             => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[1,1,0,0,1,1,0,1,0,0]             => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[1,1,0,0,1,1,1,0,0,0]             => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[1,1,0,1,0,0,1,0,1,0]             => ([(0,4),(3,2),(4,1),(4,3)],5)
[1,1,0,1,0,0,1,1,0,0]             => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[1,1,0,1,0,1,0,0,1,0]             => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
[1,1,0,1,0,1,0,1,0,0]             => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[1,1,0,1,0,1,1,0,0,0]             => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[1,1,0,1,1,0,0,0,1,0]             => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
[1,1,0,1,1,0,0,1,0,0]             => ([(0,4),(1,2),(1,3),(3,4)],5)
[1,1,0,1,1,0,1,0,0,0]             => ([(0,4),(1,4),(2,3),(2,4)],5)
[1,1,0,1,1,1,0,0,0,0]             => ([(1,4),(2,4),(3,4)],5)
[1,1,1,0,0,0,1,0,1,0]             => ([(0,4),(4,1),(4,2),(4,3)],5)
[1,1,1,0,0,0,1,1,0,0]             => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
[1,1,1,0,0,1,0,0,1,0]             => ([(0,3),(0,4),(4,1),(4,2)],5)
[1,1,1,0,0,1,0,1,0,0]             => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
[1,1,1,0,0,1,1,0,0,0]             => ([(1,3),(1,4),(2,3),(2,4)],5)
[1,1,1,0,1,0,0,0,1,0]             => ([(0,2),(0,3),(0,4),(4,1)],5)
[1,1,1,0,1,0,0,1,0,0]             => ([(0,4),(1,2),(1,3),(1,4)],5)
[1,1,1,0,1,0,1,0,0,0]             => ([(1,4),(2,3),(2,4)],5)
[1,1,1,0,1,1,0,0,0,0]             => ([(2,4),(3,4)],5)
[1,1,1,1,0,0,0,0,1,0]             => ([(0,1),(0,2),(0,3),(0,4)],5)
[1,1,1,1,0,0,0,1,0,0]             => ([(1,2),(1,3),(1,4)],5)
[1,1,1,1,0,0,1,0,0,0]             => ([(2,3),(2,4)],5)
[1,1,1,1,0,1,0,0,0,0]             => ([(3,4)],5)
[1,1,1,1,1,0,0,0,0,0]             => ([],5)
[1,0,1,0,1,0,1,0,1,0,1,0]         => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,0,1,0,1,1,0,0]         => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,0,1,0,1,0,1,1,0,0,1,0]         => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[1,0,1,0,1,0,1,1,0,1,0,0]         => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,0,1,1,1,0,0,0]         => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[1,0,1,0,1,1,0,0,1,0,1,0]         => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[1,0,1,0,1,1,0,0,1,1,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[1,0,1,0,1,1,0,1,0,0,1,0]         => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[1,0,1,0,1,1,0,1,0,1,0,0]         => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[1,0,1,0,1,1,0,1,1,0,0,0]         => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,0,1,0,1,1,1,0,0,0,1,0]         => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
[1,0,1,0,1,1,1,0,0,1,0,0]         => ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[1,0,1,0,1,1,1,0,1,0,0,0]         => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[1,0,1,0,1,1,1,1,0,0,0,0]         => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[1,0,1,1,0,0,1,0,1,0,1,0]         => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[1,0,1,1,0,0,1,0,1,1,0,0]         => ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[1,0,1,1,0,0,1,1,0,0,1,0]         => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[1,0,1,1,0,0,1,1,0,1,0,0]         => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[1,0,1,1,0,0,1,1,1,0,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[1,0,1,1,0,1,0,0,1,0,1,0]         => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[1,0,1,1,0,1,0,0,1,1,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[1,0,1,1,0,1,0,1,0,0,1,0]         => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,1,0,1,0,0]         => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
[1,0,1,1,0,1,0,1,1,0,0,0]         => ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
[1,0,1,1,0,1,1,0,0,0,1,0]         => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,0,1,0,0]         => ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,1,0,0,0]         => ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
[1,0,1,1,0,1,1,1,0,0,0,0]         => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[1,0,1,1,1,0,0,0,1,0,1,0]         => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[1,0,1,1,1,0,0,0,1,1,0,0]         => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0,1,0]         => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
[1,0,1,1,1,0,0,1,0,1,0,0]         => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,1,1,0,0,0]         => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,0,0,1,0]         => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
[1,0,1,1,1,0,1,0,0,1,0,0]         => ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,1,0,0,0]         => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,1,0,0,0,0]         => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,1,1,0,0,0,0,1,0]         => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,0,0,1,0,0]         => ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,0,1,0,0,0]         => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,1,0,0,0,0]         => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,1,1,1,1,0,0,0,0,0]         => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[1,1,0,0,1,0,1,0,1,0,1,0]         => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
[1,1,0,0,1,0,1,0,1,1,0,0]         => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
[1,1,0,0,1,0,1,1,0,0,1,0]         => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
[1,1,0,0,1,0,1,1,0,1,0,0]         => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
[1,1,0,0,1,0,1,1,1,0,0,0]         => ([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
[1,1,0,0,1,1,0,0,1,0,1,0]         => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[1,1,0,0,1,1,0,0,1,1,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
[1,1,0,0,1,1,0,1,0,0,1,0]         => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[1,1,0,0,1,1,0,1,0,1,0,0]         => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
[1,1,0,0,1,1,0,1,1,0,0,0]         => ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,0,1,1,1,0,0,0,1,0]         => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,0,1,1,1,0,0,1,0,0]         => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,0,1,1,1,0,1,0,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[1,1,0,0,1,1,1,1,0,0,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,0,0,1,0,1,0,1,0]         => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
[1,1,0,1,0,0,1,0,1,1,0,0]         => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
[1,1,0,1,0,0,1,1,0,0,1,0]         => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[1,1,0,1,0,0,1,1,0,1,0,0]         => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
[1,1,0,1,0,0,1,1,1,0,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[1,1,0,1,0,1,0,0,1,0,1,0]         => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
[1,1,0,1,0,1,0,0,1,1,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
[1,1,0,1,0,1,0,1,0,0,1,0]         => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
[1,1,0,1,0,1,0,1,0,1,0,0]         => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[1,1,0,1,0,1,0,1,1,0,0,0]         => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)
[1,1,0,1,0,1,1,0,0,0,1,0]         => ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,0,1,1,0,0,1,0,0]         => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)
[1,1,0,1,0,1,1,0,1,0,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,1,1,0,0,0,0]         => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,1,0,0,0,1,0,1,0]         => ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[1,1,0,1,1,0,0,0,1,1,0,0]         => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
[1,1,0,1,1,0,0,1,0,0,1,0]         => ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)
[1,1,0,1,1,0,0,1,0,1,0,0]         => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)
[1,1,0,1,1,0,0,1,1,0,0,0]         => ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)
[1,1,0,1,1,0,1,0,0,0,1,0]         => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
[1,1,0,1,1,0,1,0,0,1,0,0]         => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
[1,1,0,1,1,0,1,0,1,0,0,0]         => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,1,1,0,0,0,0]         => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,1,1,0,0,0,0,1,0]         => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,0,0,1,0,0]         => ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,0,1,0,0,0]         => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
[1,1,0,1,1,1,0,1,0,0,0,0]         => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
[1,1,0,1,1,1,1,0,0,0,0,0]         => ([(1,5),(2,5),(3,5),(4,5)],6)
[1,1,1,0,0,0,1,0,1,0,1,0]         => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
[1,1,1,0,0,0,1,0,1,1,0,0]         => ([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
[1,1,1,0,0,0,1,1,0,0,1,0]         => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,0,0,1,1,0,1,0,0]         => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,0,0,1,1,1,0,0,0]         => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,0,1,0,0,1,0,1,0]         => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
[1,1,1,0,0,1,0,0,1,1,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
[1,1,1,0,0,1,0,1,0,0,1,0]         => ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
[1,1,1,0,0,1,0,1,0,1,0,0]         => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)
[1,1,1,0,0,1,0,1,1,0,0,0]         => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,0,1,1,0,0,0,1,0]         => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,0,0,1,1,0,0,1,0,0]         => ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6)
[1,1,1,0,0,1,1,0,1,0,0,0]         => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,0,1,1,1,0,0,0,0]         => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,0,1,0,0,0,1,0,1,0]         => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
[1,1,1,0,1,0,0,0,1,1,0,0]         => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[1,1,1,0,1,0,0,1,0,0,1,0]         => ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
[1,1,1,0,1,0,0,1,0,1,0,0]         => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
[1,1,1,0,1,0,0,1,1,0,0,0]         => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,1,0,1,0,0,0,1,0]         => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
[1,1,1,0,1,0,1,0,0,1,0,0]         => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
[1,1,1,0,1,0,1,0,1,0,0,0]         => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,1,0,1,1,0,0,0,0]         => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,0,1,1,0,0,0,0,1,0]         => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
[1,1,1,0,1,1,0,0,0,1,0,0]         => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6)
[1,1,1,0,1,1,0,0,1,0,0,0]         => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,0,1,1,0,1,0,0,0,0]         => ([(1,5),(2,5),(3,4),(3,5)],6)
[1,1,1,0,1,1,1,0,0,0,0,0]         => ([(2,5),(3,5),(4,5)],6)
[1,1,1,1,0,0,0,0,1,0,1,0]         => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
[1,1,1,1,0,0,0,0,1,1,0,0]         => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[1,1,1,1,0,0,0,1,0,0,1,0]         => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
[1,1,1,1,0,0,0,1,0,1,0,0]         => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[1,1,1,1,0,0,0,1,1,0,0,0]         => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,1,0,0,1,0,0,0,1,0]         => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
[1,1,1,1,0,0,1,0,0,1,0,0]         => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[1,1,1,1,0,0,1,0,1,0,0,0]         => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,1,0,0,1,1,0,0,0,0]         => ([(2,4),(2,5),(3,4),(3,5)],6)
[1,1,1,1,0,1,0,0,0,0,1,0]         => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
[1,1,1,1,0,1,0,0,0,1,0,0]         => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[1,1,1,1,0,1,0,0,1,0,0,0]         => ([(1,5),(2,3),(2,4),(2,5)],6)
[1,1,1,1,0,1,0,1,0,0,0,0]         => ([(2,5),(3,4),(3,5)],6)
[1,1,1,1,0,1,1,0,0,0,0,0]         => ([(3,5),(4,5)],6)
[1,1,1,1,1,0,0,0,0,0,1,0]         => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
[1,1,1,1,1,0,0,0,0,1,0,0]         => ([(1,2),(1,3),(1,4),(1,5)],6)
[1,1,1,1,1,0,0,0,1,0,0,0]         => ([(2,3),(2,4),(2,5)],6)
[1,1,1,1,1,0,0,1,0,0,0,0]         => ([(3,4),(3,5)],6)
[1,1,1,1,1,0,1,0,0,0,0,0]         => ([(4,5)],6)
[1,1,1,1,1,1,0,0,0,0,0,0]         => ([],6)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]     => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]     => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]     => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]     => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]     => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]     => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]     => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]     => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]     => ([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]     => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]     => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]     => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]     => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]     => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]     => ([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]     => ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]     => ([(0,5),(1,3),(1,4),(3,6),(4,5),(5,6),(6,2)],7)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]     => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]     => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]     => ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]     => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]     => ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]     => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]     => ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]     => ([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]     => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]     => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]     => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]     => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]     => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]     => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]     => ([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]     => ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]     => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]     => ([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]     => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]     => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]     => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]     => ([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]     => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]     => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]     => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(4,3),(5,4),(6,3)],7)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]     => ([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]     => ([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]     => ([(0,6),(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]     => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]     => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]     => ([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]     => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]     => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,3),(5,3),(6,3)],7)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]     => ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]     => ([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]     => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]     => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]     => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]     => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]     => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]     => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]     => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]     => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]     => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]     => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]     => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]     => ([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]     => ([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]     => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]     => ([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]     => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]     => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]     => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]     => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]     => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]     => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]     => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]     => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]     => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]     => ([(0,6),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]     => ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]     => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]     => ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]     => ([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]     => ([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]     => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]     => ([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]     => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]     => ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]     => ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]     => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]     => ([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]     => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]     => ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]     => ([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]     => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]     => ([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]     => ([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]     => ([(0,2),(0,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]     => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]     => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]     => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]     => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]     => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]     => ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]     => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]     => ([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]     => ([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]     => ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]     => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]     => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]     => ([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]     => ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]     => ([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]     => ([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]     => ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]     => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]     => ([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]     => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]     => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]     => ([(0,4),(0,6),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]     => ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]     => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,2),(5,6)],7)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]     => ([(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]     => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,6),(4,6),(5,3),(5,6)],7)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]     => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]     => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]     => ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]     => ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]     => ([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]     => ([(0,5),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4)],7)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]     => ([(0,2),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3)],7)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]     => ([(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]     => ([(0,2),(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(6,5)],7)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]     => ([(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3),(5,4)],7)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]     => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]     => ([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]     => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]     => ([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,5)],7)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,6)],7)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]     => ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]     => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]     => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]     => ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]     => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]     => ([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]     => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]     => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]     => ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]     => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]     => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]     => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]     => ([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]     => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]     => ([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]     => ([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]     => ([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]     => ([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]     => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]     => ([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]     => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]     => ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]     => ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]     => ([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]     => ([(0,4),(2,5),(2,6),(3,1),(3,5),(3,6),(4,2),(4,3)],7)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,1),(3,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]     => ([(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4)],7)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]     => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]     => ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]     => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]     => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]     => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(6,3),(6,4)],7)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]     => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6)],7)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]     => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]     => ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]     => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]     => ([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]     => ([(0,5),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4)],7)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(1,4),(2,4),(2,5),(2,6),(3,1),(3,5),(3,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]     => ([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3)],7)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]     => ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]     => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]     => ([(0,5),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4)],7)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,3),(6,2),(6,3)],7)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]     => ([(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,2),(4,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]     => ([(0,2),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(6,3)],7)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]     => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5)],7)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6)],7)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]     => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]     => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]     => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]     => ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]     => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(5,2),(6,2)],7)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]     => ([(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]     => ([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(6,3)],7)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]     => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]     => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6)],7)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]     => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]     => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6)],7)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]     => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]     => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]     => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]     => ([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]     => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]     => ([(1,6),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]     => ([(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]     => ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]     => ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]     => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]     => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]     => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]     => ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]     => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]     => ([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5)],7)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]     => ([(0,2),(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]     => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]     => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]     => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]     => ([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]     => ([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4)],7)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]     => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]     => ([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5)],7)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]     => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]     => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]     => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]     => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]     => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]     => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]     => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]     => ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]     => ([(0,2),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3)],7)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]     => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]     => ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]     => ([(0,2),(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4)],7)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]     => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]     => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(4,5)],7)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]     => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]     => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]     => ([(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]     => ([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]     => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]     => ([(1,6),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]     => ([(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]     => ([(3,6),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]     => ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]     => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]     => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]     => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]     => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]     => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]     => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]     => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]     => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]     => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]     => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]     => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]     => ([(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]     => ([(3,5),(3,6),(4,5),(4,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]     => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]     => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]     => ([(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]     => ([(2,6),(3,4),(3,5),(3,6)],7)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]     => ([(3,6),(4,5),(4,6)],7)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]     => ([(4,6),(5,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]     => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]     => ([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]     => ([(2,3),(2,4),(2,5),(2,6)],7)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]     => ([(3,4),(3,5),(3,6)],7)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]     => ([(4,5),(4,6)],7)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]     => ([(5,6)],7)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]     => ([],7)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => ([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,7),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,3),(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(7,5)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => ([(0,7),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,7),(1,7),(3,6),(4,6),(5,2),(6,5),(7,3),(7,4)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(5,4),(6,5),(7,5)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(5,3),(6,5),(7,5)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,6),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(7,5)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(3,5),(4,2),(5,4),(6,5),(7,3)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,5)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => ([(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(5,6),(6,3),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,7),(3,6),(4,6),(5,1),(6,7),(7,5)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,7),(1,3),(1,4),(3,7),(4,6),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(4,7),(5,7),(6,7),(7,2)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => ([(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => ([(0,5),(0,6),(1,3),(1,5),(1,6),(3,7),(4,2),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(5,7),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => ([(0,6),(1,3),(1,4),(1,6),(3,7),(4,7),(5,2),(6,7),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => ([(0,7),(1,6),(2,3),(2,6),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => ([(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,7),(1,7),(2,4),(2,5),(4,7),(5,7),(6,3),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(3,7),(4,7),(5,3),(5,4),(6,5),(7,2)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,7),(1,2),(2,7),(3,6),(4,6),(6,5),(7,3),(7,4)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(6,5),(7,3),(7,4)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7),(7,1)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(3,2),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(5,7),(6,7),(7,1)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(1,3),(1,7),(3,5),(3,6),(4,2),(5,4),(6,4),(7,5),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => ([(0,7),(1,7),(2,5),(2,6),(4,3),(5,4),(6,4),(7,5),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(6,5),(7,5)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,7),(1,7),(2,6),(3,6),(5,3),(6,4),(7,2),(7,5)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,2),(7,1)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,5),(0,7),(1,2),(2,5),(2,7),(3,6),(5,6),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(6,5),(7,3)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(3,4),(4,2),(5,4),(6,5),(7,3),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7),(7,1)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(4,2),(5,4),(6,4),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,5),(0,7),(1,4),(1,7),(2,4),(2,7),(4,5),(5,6),(6,3),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(6,1),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,5),(0,7),(1,3),(1,4),(3,7),(4,5),(4,7),(5,6),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => ([(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7),(7,1)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(3,2),(4,3),(5,4),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => ([(0,4),(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(6,7),(7,1)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,6),(0,7),(1,3),(1,6),(1,7),(3,5),(4,2),(5,4),(6,5),(7,4)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(4,3),(5,4),(6,5),(7,4)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,5),(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,6),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,7),(1,5),(1,7),(2,4),(2,5),(4,7),(5,6),(6,3),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,5),(2,7),(3,5),(3,7),(5,6),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(1,4),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,4),(3,7),(4,6),(6,5),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(3,7),(4,6),(6,5),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5),(7,2)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7),(7,1)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => ([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7),(7,2)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => ([(0,6),(1,7),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(5,7),(6,2),(6,3),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => ([(0,3),(0,4),(1,7),(3,5),(3,6),(4,1),(4,5),(4,6),(5,7),(6,7),(7,2)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(4,7),(5,7),(6,7),(7,2)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7),(7,3)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,4),(2,7),(4,5),(4,6),(5,7),(6,7),(7,3)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,7),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => ([(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(4,7),(5,7),(6,2),(7,3)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(4,7),(5,7),(6,7),(7,2)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7),(7,3)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,7),(3,7),(4,6),(5,1),(5,6),(6,7),(7,2)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,7),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,7),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => ([(0,7),(1,6),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,7),(7,1)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,5),(2,7),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,6),(3,7),(4,7),(6,7),(7,5)],8)
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => ([(0,7),(1,6),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,7),(7,2)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => ([(0,5),(0,6),(1,7),(2,7),(3,7),(5,7),(6,1),(6,2),(6,3),(7,4)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,7),(7,2)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => ([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7),(7,3)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(4,7),(5,7),(6,1),(6,2),(7,3)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,7),(3,7),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => ([(0,7),(1,5),(1,6),(2,3),(2,5),(2,6),(3,7),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(3,7),(4,7),(5,7),(6,1),(7,2)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,7),(7,5)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => ([(0,7),(1,6),(2,3),(2,4),(2,6),(3,7),(4,7),(6,7),(7,5)],8)
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => ([(0,7),(1,7),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,2),(5,3),(7,4)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(1,2),(2,7),(3,6),(4,6),(5,3),(5,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(7,3)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,5),(4,2),(4,3),(6,4),(7,4)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,2),(1,6),(2,7),(3,5),(4,5),(6,7),(7,3),(7,4)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,5),(2,5),(3,7),(4,7),(5,6),(6,3),(6,4)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => ([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(5,2),(5,3),(6,4),(7,4)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => ([(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(6,3),(6,4),(7,3),(7,4)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => ([(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(4,2),(5,3),(6,3),(7,5),(7,6)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => ([(0,1),(0,2),(1,7),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,7),(1,6),(1,7),(2,6),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,7),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,7),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8)
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,1),(4,2),(4,3),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,2),(7,2)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,1),(4,2),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(2,7),(4,6),(4,7),(5,6),(5,7),(6,3),(7,3)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,1),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => ([(0,6),(0,7),(1,4),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,6),(4,1),(5,3),(6,2),(6,4)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => ([(0,7),(1,7),(2,6),(3,6),(4,3),(5,2),(5,4),(7,5)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => ([(0,7),(1,2),(2,7),(3,6),(4,6),(5,4),(7,3),(7,5)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => ([(0,7),(1,7),(2,7),(3,5),(4,6),(5,6),(7,3),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => ([(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(4,3),(5,6),(7,1)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(3,2),(5,4),(6,3),(6,5),(7,3),(7,5)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(1,3),(1,7),(2,5),(3,4),(3,6),(4,2),(6,5),(7,4),(7,6)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => ([(0,7),(1,7),(2,4),(2,6),(3,5),(4,3),(6,5),(7,4),(7,6)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,1)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => ([(0,7),(1,7),(2,6),(3,5),(4,2),(4,5),(5,6),(7,3),(7,4)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,1),(7,5)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => ([(0,3),(1,6),(1,7),(2,4),(3,6),(3,7),(5,4),(6,5),(7,2),(7,5)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(6,4),(7,3),(7,4)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(4,3),(5,3),(6,2),(6,4),(7,4),(7,5)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,1),(0,3),(1,2),(1,5),(2,6),(2,7),(3,5),(3,7),(5,6),(6,4),(7,4)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(4,3),(5,3),(6,4),(7,4),(7,5)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => ([(0,5),(0,7),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(1,7),(2,4),(2,7),(3,6),(3,7),(4,6),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,6),(1,7),(2,5),(2,7),(3,6),(3,7),(5,4),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(5,4),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,7),(2,5),(2,7),(3,5),(3,7),(4,1),(4,2),(4,3),(5,6),(7,6)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => ([(0,3),(0,5),(0,6),(1,3),(1,5),(1,6),(3,7),(4,2),(5,4),(5,7),(6,4),(6,7),(7,2)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,7),(2,5),(2,7),(3,5),(3,7),(4,1),(4,2),(5,6),(7,6)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,6),(1,2),(1,4),(1,6),(2,5),(2,7),(4,7),(5,3),(6,5),(6,7),(7,3)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(4,7),(5,3),(6,5),(6,7),(7,3)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,6),(2,6),(2,7),(3,6),(3,7),(4,1),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => ([(0,6),(0,7),(1,4),(1,6),(2,3),(2,4),(3,6),(3,7),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,7),(3,4),(3,7),(4,6),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3),(6,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => ([(0,7),(1,7),(2,6),(3,5),(4,5),(5,6),(7,2),(7,3),(7,4)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(5,4),(6,3),(7,3)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => ([(0,5),(1,7),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => ([(0,5),(0,7),(1,5),(1,7),(2,4),(3,6),(5,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,5),(2,6),(2,7),(3,1),(3,6),(3,7),(5,4),(6,5),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(4,3),(5,4),(6,3),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => ([(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(5,4),(6,5),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,5),(1,6),(2,7),(3,5),(3,6),(5,7),(6,4),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(5,4),(6,5),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(6,5),(7,4)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(4,7),(5,7),(6,2),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,7),(2,7),(3,5),(3,7),(4,1),(4,2),(4,5),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,4),(1,5),(1,6),(2,6),(2,7),(4,7),(5,7),(6,3),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => ([(0,6),(0,7),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,7),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,7),(2,7),(3,5),(3,7),(4,1),(4,5),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => ([(0,2),(0,3),(0,5),(1,5),(1,6),(2,7),(3,6),(3,7),(5,7),(6,4),(7,4)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => ([(0,6),(0,7),(1,4),(1,6),(2,3),(2,4),(2,6),(3,7),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => ([(0,7),(1,6),(1,7),(2,4),(2,6),(3,4),(3,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(2,7),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(3,7),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,4),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,2),(7,2)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(1,7),(2,7),(3,6),(4,7),(5,1),(5,2),(5,3),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,7),(4,7),(5,7),(6,3),(7,3)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => ([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,3),(7,3)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,7),(5,1),(5,2),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,7),(3,7),(5,7),(6,4),(7,4)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => ([(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(3,7),(4,6),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,5),(7,5)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => ([(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => ([(0,7),(1,7),(2,5),(2,7),(3,4),(3,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,7),(3,7),(4,7),(5,2),(5,3),(5,4),(6,5)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,2),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => ([(0,6),(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => ([(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,7),(3,7),(4,7),(5,2),(5,3),(6,4),(6,5)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => ([(0,3),(0,4),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,1),(6,2)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => ([(0,5),(0,6),(1,4),(2,7),(3,7),(4,5),(4,6),(5,7),(6,2),(6,3)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,7),(2,5),(2,6),(3,1),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(5,3),(5,4),(6,2),(6,3),(6,4)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,1),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,4),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => ([(0,3),(0,5),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,2),(5,3),(6,2),(6,3)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => ([(0,2),(0,3),(0,4),(1,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(2,5),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,7),(3,7),(4,7),(5,2),(6,3),(6,4),(6,5)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,1)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => ([(0,3),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,2)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(5,3),(6,4),(7,4)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,4)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(2,6),(3,1),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(6,3)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => ([(0,3),(0,5),(0,6),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,7),(5,4),(6,4),(7,4)],8)
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => ([(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,3),(6,2),(6,3)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,7),(2,5),(3,5),(3,6),(4,1),(4,2),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(5,7),(6,3)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,7),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,4),(2,7),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => ([(0,7),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(0,7),(1,2),(1,3),(1,4),(2,7),(3,6),(4,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,7),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => ([(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => ([(0,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,2),(6,2)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(3,7),(4,7),(5,7),(6,3)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => ([(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(0,7),(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,7),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => ([(0,7),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(4,7),(5,6),(7,6)],8)
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3)],8)
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,7),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => ([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,7),(2,7),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,7),(2,7),(3,5),(3,6),(4,1),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => ([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => ([(0,7),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => ([(0,2),(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => ([(0,7),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,7),(3,7),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => ([(0,7),(1,6),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => ([(0,7),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => ([(0,7),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => ([(0,7),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => ([(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => ([(0,7),(1,7),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,6),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,7),(1,7),(4,6),(5,4),(6,2),(6,3),(7,5)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,7),(4,7),(5,6),(6,1),(6,2),(7,5)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(1,4),(4,7),(5,6),(6,2),(6,3),(7,5)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => ([(0,7),(1,7),(2,7),(5,6),(6,3),(6,4),(7,5)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,6),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(7,5)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,4),(6,5),(7,5)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,4),(0,5),(3,7),(4,7),(5,3),(6,1),(6,2),(7,6)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,7),(1,4),(1,7),(4,6),(5,2),(5,3),(6,5),(7,6)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => ([(0,7),(1,6),(2,6),(3,4),(3,5),(6,7),(7,3)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(6,2),(7,6)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => ([(0,7),(1,4),(1,5),(4,7),(5,7),(6,2),(6,3),(7,6)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => ([(0,7),(1,7),(2,5),(5,7),(6,3),(6,4),(7,6)],8)
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,5),(1,7),(2,7),(5,6),(6,1),(6,2),(7,3),(7,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,7),(1,7),(2,6),(3,6),(6,4),(6,5),(7,2),(7,3)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1),(7,2)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,5),(0,6),(1,4),(4,5),(4,6),(5,7),(6,7),(7,2),(7,3)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(5,3),(5,4),(6,5),(7,5)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,6),(1,7),(2,7),(5,2),(6,1),(6,5),(7,3),(7,4)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(4,7),(5,7),(6,4),(7,2),(7,3)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,4),(0,5),(3,7),(4,6),(5,3),(5,6),(6,7),(7,1),(7,2)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,5),(0,6),(1,4),(1,6),(4,5),(5,7),(6,7),(7,2),(7,3)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => ([(0,7),(1,5),(1,7),(2,5),(2,7),(5,6),(6,3),(6,4),(7,6)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(3,7),(4,6),(5,6),(6,7),(7,1),(7,2)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,6),(1,4),(1,5),(4,7),(5,6),(6,7),(7,2),(7,3)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,7),(3,6),(6,4),(6,5),(7,6)],8)
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,6),(6,4),(6,5),(7,6)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => ([(0,6),(1,7),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7),(7,2),(7,3)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => ([(0,5),(0,6),(1,7),(2,7),(5,7),(6,1),(6,2),(7,3),(7,4)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,7),(5,7),(6,7),(7,3),(7,4)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => ([(0,4),(0,5),(0,6),(1,7),(4,7),(5,7),(6,1),(7,2),(7,3)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => ([(0,6),(1,2),(1,3),(1,6),(2,7),(3,7),(6,7),(7,4),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => ([(0,7),(1,6),(2,3),(2,6),(3,7),(6,7),(7,4),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,6),(3,6),(6,7),(7,4),(7,5)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(0,6),(3,7),(4,7),(5,7),(6,7),(7,1),(7,2)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(7,5),(7,6)],8)
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,3),(5,1),(5,2)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(7,4)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(7,1),(7,2)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,7),(1,2),(2,7),(3,5),(3,6),(4,5),(4,6),(7,3),(7,4)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(7,3),(7,4)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,1),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,1),(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(1,2),(1,7),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => ([(0,7),(1,7),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,2),(4,5),(5,1),(5,3)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,3),(7,2),(7,4)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(6,1),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,3),(1,4),(1,7),(2,5),(2,6),(3,4),(3,7),(4,2),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(6,4),(6,5),(7,3)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,5),(2,6),(2,7),(3,2),(3,5),(4,1),(4,3),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,7),(6,2),(6,7),(7,3),(7,4)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,7),(2,1),(2,6),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,5),(1,7),(2,6),(2,7),(5,6),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,7),(5,6),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,7),(2,4),(2,7),(3,4),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,2),(0,3),(1,6),(1,7),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,5),(2,5),(3,6),(3,7),(4,1),(4,2),(4,3),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(4,6),(5,6),(6,2),(6,3),(7,2),(7,3)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,5),(2,6),(2,7),(3,5),(4,1),(4,2),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,5),(0,7),(1,2),(1,5),(1,7),(2,6),(5,6),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,6),(1,5),(1,7),(2,5),(2,7),(5,6),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(3,7),(4,1),(4,7),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,7),(1,4),(1,7),(2,3),(2,4),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,7),(1,7),(2,4),(2,7),(3,4),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,7),(1,2),(1,3),(1,4),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,7),(1,7),(2,3),(2,4),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => ([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(5,3),(5,4),(6,3),(6,4),(7,3),(7,4)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(5,1),(5,4)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,6),(1,7),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,3),(5,1),(5,2),(5,4)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,1),(4,5),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => ([(0,5),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => ([(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => ([(0,6),(0,7),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,6),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => ([(0,7),(1,7),(4,3),(5,6),(6,2),(6,4),(7,5)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,7),(4,7),(5,2),(6,1),(6,5),(7,6)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => ([(0,7),(1,7),(2,7),(5,4),(6,3),(6,5),(7,6)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => ([(0,6),(2,7),(3,7),(5,1),(6,2),(6,3),(7,4),(7,5)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,7),(6,7),(7,2),(7,4)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => ([(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,3),(7,5)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,4),(1,6),(4,7),(5,3),(6,7),(7,2),(7,5)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => ([(0,7),(1,6),(2,6),(4,5),(6,7),(7,3),(7,4)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(7,2),(7,6)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => ([(0,7),(1,3),(1,4),(3,7),(4,7),(6,2),(7,5),(7,6)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => ([(0,7),(1,7),(2,4),(4,7),(6,3),(7,5),(7,6)],8)
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => ([(0,7),(1,7),(2,7),(3,7),(5,6),(7,4),(7,5)],8)

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Created: Jan 11, 2022 at 19:47 by Martin Rubey

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Last Updated: Jan 11, 2022 at 19:47 by Martin Rubey