************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2013 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be *
* useful, but WITHOUT ANY WARRANTY; without even the implied *
* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
************************************************************************
------------------------------------------------------------------------
Map identifier: Mp00201
------------------------------------------------------------------------
Map name: Ringel
------------------------------------------------------------------------
Domain: Dyck paths
------------------------------------------------------------------------
Codomain: Permutations
------------------------------------------------------------------------
Description: The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
------------------------------------------------------------------------
References: [1] Ringel, C. M. The finitistic dimension of a Nakayama algebra [[arXiv:2008.10044]]
------------------------------------------------------------------------
Code:
def to_matrix(D):
D = DyckWord(D)
N = zero_matrix(D.semilength()+1)
N[0, 0] = 1
i, j = 0, 0
for p in range(len(D)):
if D[p] == 1:
i += 1
else:
j += 1
N[j, i] = 1
return N
def is_projective(N, i, j):
return N[i, j] == 1 and (j+1 == N.ncols() or N[i, j+1] == 0)
def to_projective(N, i, j):
n = N.ncols()
while j < n and N[i, j] != 1:
j += 1
while j < n and N[i, j] != 0:
j += 1
return j-1
def to_injective(N, i, j):
while i >= 0 and N[i, j] != 1:
i -= 1
while i >= 0 and N[i, j] != 0:
i -= 1
return i+1
def to_top(N, i, j):
return i
def omega(N, i, j):
return (j+1, to_projective(N, i, j))
def Ringel_matrix(N, i):
S = (i, i)
IS = (to_injective(N, *S), i)
while True:
if is_projective(N, *IS):
return to_top(N, *IS)
IS = omega(N, *IS)
IS = omega(N, *IS)
S = omega(N, *S)
if is_projective(N, *S):
return to_top(N, *S)
S = omega(N, *S)
def mapping(D):
N = to_matrix(D)
return Permutation([Ringel_matrix(N, i)+1 for i in range(N.nrows())])
------------------------------------------------------------------------
Map images:
[1,0] => [2,1]
[1,0,1,0] => [3,1,2]
[1,1,0,0] => [2,3,1]
[1,0,1,0,1,0] => [4,1,2,3]
[1,0,1,1,0,0] => [3,1,4,2]
[1,1,0,0,1,0] => [2,4,1,3]
[1,1,0,1,0,0] => [4,3,1,2]
[1,1,1,0,0,0] => [2,3,4,1]
[1,0,1,0,1,0,1,0] => [5,1,2,3,4]
[1,0,1,0,1,1,0,0] => [4,1,2,5,3]
[1,0,1,1,0,0,1,0] => [3,1,5,2,4]
[1,0,1,1,0,1,0,0] => [5,1,4,2,3]
[1,0,1,1,1,0,0,0] => [3,1,4,5,2]
[1,1,0,0,1,0,1,0] => [2,5,1,3,4]
[1,1,0,0,1,1,0,0] => [2,4,1,5,3]
[1,1,0,1,0,0,1,0] => [5,3,1,2,4]
[1,1,0,1,0,1,0,0] => [5,4,1,2,3]
[1,1,0,1,1,0,0,0] => [4,3,1,5,2]
[1,1,1,0,0,0,1,0] => [2,3,5,1,4]
[1,1,1,0,0,1,0,0] => [2,5,4,1,3]
[1,1,1,0,1,0,0,0] => [5,3,4,1,2]
[1,1,1,1,0,0,0,0] => [2,3,4,5,1]
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4]
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5]
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4]
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3]
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5]
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4]
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5]
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4]
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3]
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5]
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4]
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3]
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2]
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5]
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4]
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5]
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4]
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3]
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5]
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4]
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5]
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4]
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3]
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5]
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4]
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3]
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2]
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5]
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4]
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5]
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4]
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3]
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5]
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4]
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3]
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2]
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5]
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4]
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3]
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2]
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5]
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6]
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5]
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4]
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5]
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6]
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5]
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4]
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5]
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4]
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3]
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6]
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5]
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5]
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4]
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6]
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5]
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6]
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5]
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4]
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5]
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4]
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3]
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5]
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6]
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5]
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4]
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5]
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4]
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3]
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5]
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4]
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3]
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3]
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6]
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5]
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6]
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5]
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4]
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6]
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5]
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6]
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4]
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5]
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4]
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3]
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5]
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6]
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5]
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4]
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5]
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4]
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3]
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5]
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4]
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3]
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2]
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5]
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5]
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4]
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5]
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5]
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4]
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5]
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4]
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3]
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5]
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6]
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5]
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4]
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5]
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4]
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3]
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5]
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4]
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2]
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5]
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5]
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4]
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5]
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4]
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3]
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5]
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3]
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2]
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5]
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4]
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3]
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,1,4,2,3,7,8,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,1,5,2,3,4,8,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [8,1,5,2,3,7,4,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,1,5,2,6,3,4,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,4,2,6,8,3,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,1,4,2,8,7,3,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,4,8,2,7,5,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,8,5,2,4,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,7,6,2,4,8,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,5,2,7,8,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,1,4,6,2,3,5,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [7,1,4,6,2,3,8,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,1,4,5,2,8,3,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [8,1,4,6,2,7,3,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,8,6,2,5,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,7,1,3,6,4,8,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,3,8,7,4,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,8,1,3,6,7,4,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,6,1,5,3,8,4,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,8,1,6,3,7,4,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,6,1,5,3,7,8,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,7,1,5,6,3,8,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,8,7,3,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,8,1,5,6,7,3,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,3,1,2,4,8,5,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,3,1,2,4,7,8,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,3,1,2,7,4,5,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1,2,6,8,4,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,4,1,2,3,7,8,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,4,1,2,6,3,5,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,3,1,7,2,5,8,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3,1,6,2,7,8,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,1,5,2,8,4,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [4,3,1,5,7,2,8,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,3,8,1,4,7,5,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,3,8,1,6,4,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,3,5,1,8,7,4,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,5,4,1,7,3,8,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3,4,1,2,7,8,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,3,5,1,6,2,4,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,1,2,3,4,8,5,9,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,1,2,3,4,7,5,6,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,1,2,3,4,8,5,6,7]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [8,1,2,3,4,7,5,9,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,1,2,3,4,9,8,5,7]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [9,1,2,3,4,7,8,5,6]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,1,2,3,8,4,6,9,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [5,1,2,3,7,4,9,6,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [5,1,2,3,9,4,8,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,1,2,3,7,4,8,9,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [9,1,2,3,6,4,5,7,8]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [8,1,2,3,6,4,5,9,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [9,1,2,3,7,4,5,6,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [8,1,2,3,7,4,5,9,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,1,2,3,6,4,9,5,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [9,1,2,3,6,4,8,5,7]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [9,1,2,3,7,4,8,5,6]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [7,1,2,3,6,4,8,9,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [5,1,2,3,6,9,4,7,8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,1,2,3,6,8,4,9,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [5,1,2,3,9,7,4,6,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,1,2,3,9,8,4,6,7]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,1,2,3,8,7,4,9,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [9,1,2,3,6,7,4,5,8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [9,1,2,3,6,8,4,5,7]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [9,1,2,3,8,7,4,5,6]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [8,1,2,3,6,7,4,9,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,9,4,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,1,2,3,6,9,8,4,7]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,1,2,3,9,7,8,4,6]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [9,1,2,3,6,7,8,4,5]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [4,1,2,9,3,5,6,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [4,1,2,8,3,5,6,9,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,7,3,5,9,6,8]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [4,1,2,9,3,5,8,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,1,2,7,3,5,8,9,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [4,1,2,6,3,9,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,8,5,9,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [4,1,2,9,3,7,5,6,8]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [4,1,2,9,3,8,5,6,7]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,1,2,8,3,7,5,9,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [4,1,2,6,3,7,9,5,8]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,1,2,6,3,9,8,5,7]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,1,2,9,3,7,8,5,6]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,1,2,6,3,7,8,9,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,1,2,5,3,4,6,7,8]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [8,1,2,5,3,4,6,9,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,1,2,5,3,4,9,6,8]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [9,1,2,5,3,4,8,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [7,1,2,5,3,4,8,9,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [9,1,2,6,3,4,5,7,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [8,1,2,6,3,4,5,9,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,1,2,9,3,4,5,6,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,1,2,8,3,4,5,6,7]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [7,1,2,8,3,4,5,9,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,1,2,6,3,4,9,5,8]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [9,1,2,6,3,4,8,5,7]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [7,1,2,9,3,4,8,5,6]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [7,1,2,6,3,4,8,9,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,1,2,5,3,9,4,7,8]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,1,2,5,3,8,4,9,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [9,1,2,5,3,7,4,6,8]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [9,1,2,5,3,8,4,6,7]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [8,1,2,5,3,7,4,9,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [9,1,2,6,3,7,4,5,8]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [9,1,2,6,3,8,4,5,7]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [8,1,2,9,3,7,4,5,6]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [8,1,2,6,3,7,4,9,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,1,2,5,3,7,9,4,8]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,1,2,5,3,9,8,4,7]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [9,1,2,5,3,7,8,4,6]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [9,1,2,6,3,7,8,4,5]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [6,1,2,5,3,7,8,9,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,8,3,6,9,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,7,3,9,6,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,9,3,8,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,7,3,8,9,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,2,9,6,3,5,7,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,1,2,8,6,3,5,9,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,9,7,3,5,6,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [4,1,2,8,9,3,5,6,7]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,1,2,8,7,3,5,9,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,7,6,3,9,5,8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [4,1,2,9,6,3,8,5,7]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,1,2,9,7,3,8,5,6]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,1,2,7,6,3,8,9,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [9,1,2,5,6,3,4,7,8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [8,1,2,5,6,3,4,9,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [9,1,2,5,7,3,4,6,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [8,1,2,5,9,3,4,6,7]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [8,1,2,5,7,3,4,9,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [9,1,2,7,6,3,4,5,8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [8,1,2,9,6,3,4,5,7]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [8,1,2,9,7,3,4,5,6]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [8,1,2,7,6,3,4,9,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,1,2,5,6,3,9,4,8]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [9,1,2,5,6,3,8,4,7]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [9,1,2,5,7,3,8,4,6]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [9,1,2,7,6,3,8,4,5]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [7,1,2,5,6,3,8,9,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,5,6,9,3,7,8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,5,6,8,3,9,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,9,7,3,6,8]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,9,8,3,6,7]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,5,8,7,3,9,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,2,9,6,7,3,5,8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,2,9,6,8,3,5,7]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,2,9,8,7,3,5,6]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,2,8,6,7,3,9,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [9,1,2,5,6,7,3,4,8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [9,1,2,5,6,8,3,4,7]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [9,1,2,5,8,7,3,4,6]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [9,1,2,8,6,7,3,4,5]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [8,1,2,5,6,7,3,9,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,9,3,8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [4,1,2,5,6,9,8,3,7]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,5,9,7,8,3,6]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,1,2,9,6,7,8,3,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [9,1,2,5,6,7,8,3,4]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,8,2,4,5,6,9,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,7,2,4,5,9,6,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,9,2,4,5,8,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,7,2,4,5,8,9,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,9,5,7,8]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,6,2,4,8,5,9,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,9,2,4,7,5,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,9,2,4,8,5,6,7]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,8,2,4,7,5,9,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,6,2,4,7,9,5,8]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,6,2,4,9,8,5,7]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,9,2,4,7,8,5,6]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,6,2,4,7,8,9,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,5,2,9,4,6,7,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,5,2,8,4,6,9,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,9,6,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,5,2,9,4,8,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,7,4,8,9,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,9,2,6,4,5,7,8]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,1,8,2,6,4,5,9,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,9,2,7,4,5,6,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,8,2,9,4,5,6,7]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,1,8,2,7,4,5,9,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,7,2,6,4,9,5,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,9,2,6,4,8,5,7]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,9,2,7,4,8,5,6]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,7,2,6,4,8,9,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,5,2,6,9,4,7,8]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,5,2,6,8,4,9,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,5,2,9,7,4,6,8]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,5,2,9,8,4,6,7]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,8,7,4,9,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,9,2,6,7,4,5,8]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,9,2,6,8,4,5,7]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,9,2,8,7,4,5,6]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,8,2,6,7,4,9,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,5,2,6,7,9,4,8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,5,2,6,9,8,4,7]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,5,2,9,7,8,4,6]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,9,2,6,7,8,4,5]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5,2,6,7,8,9,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,1,4,2,3,5,6,7,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,1,4,2,3,5,6,9,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,1,4,2,3,5,9,6,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [9,1,4,2,3,5,8,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [7,1,4,2,3,5,8,9,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [6,1,4,2,3,9,5,7,8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,1,4,2,3,8,5,9,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [9,1,4,2,3,7,5,6,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [9,1,4,2,3,8,5,6,7]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [8,1,4,2,3,7,5,9,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,1,4,2,3,7,9,5,8]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,1,4,2,3,9,8,5,7]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [9,1,4,2,3,7,8,5,6]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,1,4,2,3,7,8,9,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,1,5,2,3,4,6,7,8]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [8,1,5,2,3,4,6,9,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,1,5,2,3,4,9,6,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [9,1,5,2,3,4,8,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [7,1,5,2,3,4,8,9,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,9,2,3,4,5,7,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,1,8,2,3,4,5,9,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1,7,2,3,4,5,6,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,8,2,3,4,5,6,7]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,1,7,2,3,4,5,9,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1,7,2,3,4,9,5,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,1,9,2,3,4,8,5,7]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,1,7,2,3,4,8,5,6]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,1,7,2,3,4,8,9,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,5,2,3,9,4,7,8]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,1,5,2,3,8,4,9,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [9,1,5,2,3,7,4,6,8]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [9,1,5,2,3,8,4,6,7]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [8,1,5,2,3,7,4,9,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1,9,2,3,7,4,5,8]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,1,9,2,3,8,4,5,7]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,1,8,2,3,7,4,5,6]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [6,1,8,2,3,7,4,9,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1,5,2,3,7,9,4,8]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,1,5,2,3,9,8,4,7]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [9,1,5,2,3,7,8,4,6]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [6,1,9,2,3,7,8,4,5]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [6,1,5,2,3,7,8,9,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,4,2,9,3,6,7,8]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,4,2,8,3,6,9,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [5,1,4,2,7,3,9,6,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,1,4,2,9,3,8,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,1,4,2,7,3,8,9,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [9,1,4,2,6,3,5,7,8]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [8,1,4,2,6,3,5,9,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [9,1,4,2,7,3,5,6,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,1,4,2,9,3,5,6,7]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [8,1,4,2,7,3,5,9,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1,4,2,6,3,9,5,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [9,1,4,2,6,3,8,5,7]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [9,1,4,2,7,3,8,5,6]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7,1,4,2,6,3,8,9,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [9,1,5,2,6,3,4,7,8]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [8,1,5,2,6,3,4,9,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [9,1,5,2,7,3,4,6,8]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,1,5,2,9,3,4,6,7]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [8,1,5,2,7,3,4,9,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1,9,2,6,3,4,5,8]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [9,1,8,2,6,3,4,5,7]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [9,1,8,2,7,3,4,5,6]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7,1,8,2,6,3,4,9,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1,5,2,6,3,9,4,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [9,1,5,2,6,3,8,4,7]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [9,1,5,2,7,3,8,4,6]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7,1,9,2,6,3,8,4,5]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7,1,5,2,6,3,8,9,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,4,2,6,9,3,7,8]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,1,4,2,6,8,3,9,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [5,1,4,2,9,7,3,6,8]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,1,4,2,9,8,3,6,7]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,1,4,2,8,7,3,9,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [9,1,4,2,6,7,3,5,8]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [9,1,4,2,6,8,3,5,7]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [9,1,4,2,8,7,3,5,6]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [8,1,4,2,6,7,3,9,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [9,1,5,2,6,7,3,4,8]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [9,1,5,2,6,8,3,4,7]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [9,1,5,2,8,7,3,4,6]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [8,1,9,2,6,7,3,4,5]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [8,1,5,2,6,7,3,9,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [5,1,4,2,6,7,9,3,8]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,4,2,6,9,8,3,7]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,1,4,2,9,7,8,3,6]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [9,1,4,2,6,7,8,3,5]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [9,1,5,2,6,7,8,3,4]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [5,1,4,2,6,7,8,9,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,4,8,2,5,6,9,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,4,7,2,5,9,6,8]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,4,9,2,5,8,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,4,7,2,5,8,9,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,4,6,2,9,5,7,8]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,4,6,2,8,5,9,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,4,9,2,7,5,6,8]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,4,9,2,8,5,6,7]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,4,8,2,7,5,9,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,7,9,5,8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,4,6,2,9,8,5,7]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,4,9,2,7,8,5,6]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4,6,2,7,8,9,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,9,5,2,4,6,7,8]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,8,5,2,4,6,9,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,7,5,2,4,9,6,8]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,9,5,2,4,8,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,7,5,2,4,8,9,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,9,6,2,4,5,7,8]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,8,6,2,4,5,9,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,7,9,2,4,5,6,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,9,8,2,4,5,6,7]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,7,8,2,4,5,9,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,7,6,2,4,9,5,8]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,9,6,2,4,8,5,7]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,7,9,2,4,8,5,6]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,7,6,2,4,8,9,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,6,5,2,9,4,7,8]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,6,5,2,8,4,9,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,9,5,2,7,4,6,8]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,9,5,2,8,4,6,7]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,8,5,2,7,4,9,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,9,6,2,7,4,5,8]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,9,6,2,8,4,5,7]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,8,9,2,7,4,5,6]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,8,6,2,7,4,9,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,5,2,7,9,4,8]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,5,2,9,8,4,7]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,9,5,2,7,8,4,6]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,9,6,2,7,8,4,5]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,6,5,2,7,8,9,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [9,1,4,5,2,3,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [8,1,4,5,2,3,6,9,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,1,4,5,2,3,9,6,8]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [9,1,4,5,2,3,8,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [7,1,4,5,2,3,8,9,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [9,1,4,6,2,3,5,7,8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [8,1,4,6,2,3,5,9,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1,4,9,2,3,5,6,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9,1,4,8,2,3,5,6,7]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7,1,4,8,2,3,5,9,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1,4,6,2,3,9,5,8]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [9,1,4,6,2,3,8,5,7]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7,1,4,9,2,3,8,5,6]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7,1,4,6,2,3,8,9,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [9,1,6,5,2,3,4,7,8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [8,1,6,5,2,3,4,9,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1,9,5,2,3,4,6,8]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [9,1,8,5,2,3,4,6,7]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7,1,8,5,2,3,4,9,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1,9,6,2,3,4,5,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [9,1,8,6,2,3,4,5,7]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,1,8,9,2,3,4,5,6]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,1,8,6,2,3,4,9,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1,6,5,2,3,9,4,8]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [9,1,6,5,2,3,8,4,7]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,1,9,5,2,3,8,4,6]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,1,9,6,2,3,8,4,5]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,1,6,5,2,3,8,9,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,4,5,2,9,3,7,8]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,1,4,5,2,8,3,9,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [9,1,4,5,2,7,3,6,8]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [9,1,4,5,2,8,3,6,7]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [8,1,4,5,2,7,3,9,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [9,1,4,6,2,7,3,5,8]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [9,1,4,6,2,8,3,5,7]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [8,1,4,9,2,7,3,5,6]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [8,1,4,6,2,7,3,9,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1,6,5,2,7,3,4,8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [9,1,6,5,2,8,3,4,7]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [8,1,9,5,2,7,3,4,6]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [8,1,9,6,2,7,3,4,5]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [8,1,6,5,2,7,3,9,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,4,5,2,7,9,3,8]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,1,4,5,2,9,8,3,7]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [9,1,4,5,2,7,8,3,6]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [9,1,4,6,2,7,8,3,5]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [9,1,6,5,2,7,8,3,4]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [6,1,4,5,2,7,8,9,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,4,5,9,2,6,7,8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,1,4,5,8,2,6,9,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,4,5,7,2,9,6,8]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,4,5,9,2,8,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,1,4,5,7,2,8,9,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,4,9,6,2,5,7,8]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,1,4,8,6,2,5,9,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,4,9,7,2,5,6,8]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,4,8,9,2,5,6,7]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [3,1,4,8,7,2,5,9,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,4,7,6,2,9,5,8]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [3,1,4,9,6,2,8,5,7]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [3,1,4,9,7,2,8,5,6]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,1,4,7,6,2,8,9,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,9,5,6,2,4,7,8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,1,8,5,6,2,4,9,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,9,5,7,2,4,6,8]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [3,1,8,5,9,2,4,6,7]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [3,1,8,5,7,2,4,9,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [3,1,9,7,6,2,4,5,8]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,8,9,6,2,4,5,7]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [3,1,8,9,7,2,4,5,6]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,8,7,6,2,4,9,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,7,5,6,2,9,4,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,9,5,6,2,8,4,7]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [3,1,9,5,7,2,8,4,6]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,9,7,6,2,8,4,5]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,7,5,6,2,8,9,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [9,1,4,5,6,2,3,7,8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [8,1,4,5,6,2,3,9,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [9,1,4,5,7,2,3,6,8]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [8,1,4,5,9,2,3,6,7]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [8,1,4,5,7,2,3,9,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [9,1,4,7,6,2,3,5,8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [8,1,4,9,6,2,3,5,7]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8,1,4,9,7,2,3,5,6]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [8,1,4,7,6,2,3,9,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [9,1,7,5,6,2,3,4,8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8,1,9,5,6,2,3,4,7]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [8,1,9,5,7,2,3,4,6]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,7,6,2,3,4,5]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [8,1,7,5,6,2,3,9,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1,4,5,6,2,9,3,8]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [9,1,4,5,6,2,8,3,7]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [9,1,4,5,7,2,8,3,6]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [9,1,4,7,6,2,8,3,5]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [9,1,7,5,6,2,8,3,4]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,1,4,5,6,2,8,9,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,5,6,9,2,7,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,8,2,9,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,4,5,9,7,2,6,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,4,5,9,8,2,6,7]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,4,5,8,7,2,9,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,4,9,6,7,2,5,8]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,4,9,6,8,2,5,7]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,4,9,8,7,2,5,6]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,4,8,6,7,2,9,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,9,5,6,7,2,4,8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [3,1,9,5,6,8,2,4,7]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,9,5,8,7,2,4,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,9,8,6,7,2,4,5]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,8,5,6,7,2,9,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [9,1,4,5,6,7,2,3,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [9,1,4,5,6,8,2,3,7]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [9,1,4,5,8,7,2,3,6]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [9,1,4,8,6,7,2,3,5]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [9,1,8,5,6,7,2,3,4]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8,1,4,5,6,7,2,9,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,9,2,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,4,5,6,9,8,2,7]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,4,5,9,7,8,2,6]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,4,9,6,7,8,2,5]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,9,5,6,7,8,2,4]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,8,1,3,4,5,6,9,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,7,1,3,4,5,9,6,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,9,1,3,4,5,8,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,7,1,3,4,5,8,9,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,6,1,3,4,9,5,7,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,6,1,3,4,8,5,9,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,9,1,3,4,7,5,6,8]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,9,1,3,4,8,5,6,7]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,8,1,3,4,7,5,9,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,6,1,3,4,7,9,5,8]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,6,1,3,4,9,8,5,7]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,9,1,3,4,7,8,5,6]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,6,1,3,4,7,8,9,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,5,1,3,9,4,6,7,8]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,8,4,6,9,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,5,1,3,7,4,9,6,8]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,3,9,4,8,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,1,3,7,4,8,9,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,9,1,3,6,4,5,7,8]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,8,1,3,6,4,5,9,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,9,1,3,7,4,5,6,8]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,8,1,3,9,4,5,6,7]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,8,1,3,7,4,5,9,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,7,1,3,6,4,9,5,8]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,9,1,3,6,4,8,5,7]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,9,1,3,7,4,8,5,6]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,7,1,3,6,4,8,9,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,5,1,3,6,9,4,7,8]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,5,1,3,6,8,4,9,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,5,1,3,9,7,4,6,8]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,5,1,3,9,8,4,6,7]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,5,1,3,8,7,4,9,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,9,1,3,6,7,4,5,8]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,9,1,3,6,8,4,5,7]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,9,1,3,8,7,4,5,6]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,8,1,3,6,7,4,9,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,5,1,3,6,7,9,4,8]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,9,8,4,7]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,5,1,3,9,7,8,4,6]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,9,1,3,6,7,8,4,5]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,9,3,5,6,7,8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,8,3,5,6,9,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,7,3,5,9,6,8]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,9,3,5,8,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,7,3,5,8,9,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,6,3,9,5,7,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,9,3,7,5,6,8]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,9,3,8,5,6,7]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,1,8,3,7,5,9,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,6,3,7,9,5,8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,6,3,9,8,5,7]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,9,3,7,8,5,6]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,6,3,7,8,9,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,9,1,5,3,4,6,7,8]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,8,1,5,3,4,6,9,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,7,1,5,3,4,9,6,8]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,9,1,5,3,4,8,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,7,1,5,3,4,8,9,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,9,1,6,3,4,5,7,8]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,8,1,6,3,4,5,9,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,7,1,9,3,4,5,6,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,9,1,8,3,4,5,6,7]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,7,1,8,3,4,5,9,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,7,1,6,3,4,9,5,8]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,9,1,6,3,4,8,5,7]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,7,1,9,3,4,8,5,6]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,7,1,6,3,4,8,9,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,6,1,5,3,9,4,7,8]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,6,1,5,3,8,4,9,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,9,1,5,3,7,4,6,8]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,9,1,5,3,8,4,6,7]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,8,1,5,3,7,4,9,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,9,1,6,3,7,4,5,8]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,9,1,6,3,8,4,5,7]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,8,1,9,3,7,4,5,6]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,8,1,6,3,7,4,9,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,6,1,5,3,7,9,4,8]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,6,1,5,3,9,8,4,7]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,9,1,5,3,7,8,4,6]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,9,1,6,3,7,8,4,5]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,5,3,7,8,9,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,5,9,3,6,7,8]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,5,8,3,6,9,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,5,7,3,9,6,8]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,5,9,3,8,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,5,7,3,8,9,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,9,6,3,5,7,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,8,6,3,5,9,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,9,7,3,5,6,8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,8,9,3,5,6,7]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,8,7,3,5,9,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,7,6,3,9,5,8]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,9,6,3,8,5,7]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,9,7,3,8,5,6]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,6,3,8,9,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,9,1,5,6,3,4,7,8]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,8,1,5,6,3,4,9,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,9,1,5,7,3,4,6,8]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,8,1,5,9,3,4,6,7]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,8,1,5,7,3,4,9,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,9,1,7,6,3,4,5,8]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,8,1,9,6,3,4,5,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,8,1,9,7,3,4,5,6]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,8,1,7,6,3,4,9,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,7,1,5,6,3,9,4,8]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,9,1,5,6,3,8,4,7]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,9,1,5,7,3,8,4,6]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,9,1,7,6,3,8,4,5]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,7,1,5,6,3,8,9,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,5,6,9,3,7,8]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,5,6,8,3,9,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,5,9,7,3,6,8]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,5,9,8,3,6,7]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,1,5,8,7,3,9,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,9,6,7,3,5,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,9,6,8,3,5,7]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,9,8,7,3,5,6]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,1,8,6,7,3,9,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,9,1,5,6,7,3,4,8]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,9,1,5,6,8,3,4,7]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,9,1,5,8,7,3,4,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,9,1,8,6,7,3,4,5]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,8,1,5,6,7,3,9,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1,5,6,7,9,3,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,9,8,3,7]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,5,9,7,8,3,6]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,9,6,7,8,3,5]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,9,1,5,6,7,8,3,4]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [8,3,1,2,4,5,6,9,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,3,1,2,4,5,9,6,8]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [9,3,1,2,4,5,8,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [7,3,1,2,4,5,8,9,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,3,1,2,4,9,5,7,8]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,3,1,2,4,8,5,9,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [9,3,1,2,4,7,5,6,8]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [9,3,1,2,4,8,5,6,7]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [8,3,1,2,4,7,5,9,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,1,2,4,7,9,5,8]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,3,1,2,4,9,8,5,7]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [9,3,1,2,4,7,8,5,6]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [6,3,1,2,4,7,8,9,5]
-----------------------------------------------------------------------------
Created: Dec 10, 2020 at 20:42 by Martin Rubey
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Last Updated: Dec 10, 2020 at 20:42 by Martin Rubey