Identifier
Mp00098:
Alternating sign matrices
—link pattern⟶
Perfect matchings
Mp00116: Perfect matchings —Kasraoui-Zeng⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00116: Perfect matchings —Kasraoui-Zeng⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
=>
Cc0017;cc-rep-0Cc0012;cc-rep-1Cc0012;cc-rep-2Cc0002;cc-rep-4
[[1]]=>[(1,2)]=>[(1,2)]=>[2,1]=>[1,1]
[[1,0],[0,1]]=>[(1,4),(2,3)]=>[(1,3),(2,4)]=>[3,4,1,2]=>[2,2]
[[0,1],[1,0]]=>[(1,2),(3,4)]=>[(1,2),(3,4)]=>[2,1,4,3]=>[2,2]
[[1,0,0],[0,1,0],[0,0,1]]=>[(1,6),(2,5),(3,4)]=>[(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[3,3]
[[0,1,0],[1,0,0],[0,0,1]]=>[(1,2),(3,4),(5,6)]=>[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[3,3]
[[1,0,0],[0,0,1],[0,1,0]]=>[(1,6),(2,3),(4,5)]=>[(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[3,3]
[[0,1,0],[1,-1,1],[0,1,0]]=>[(1,2),(3,6),(4,5)]=>[(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[3,3]
[[0,0,1],[1,0,0],[0,1,0]]=>[(1,6),(2,3),(4,5)]=>[(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[3,3]
[[0,1,0],[0,0,1],[1,0,0]]=>[(1,2),(3,4),(5,6)]=>[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[3,3]
[[0,0,1],[0,1,0],[1,0,0]]=>[(1,4),(2,3),(5,6)]=>[(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[3,3]
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]=>[(1,8),(2,7),(3,6),(4,5)]=>[(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[4,4]
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]=>[(1,2),(3,6),(4,5),(7,8)]=>[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[4,4]
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]=>[(1,8),(2,3),(4,5),(6,7)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[4,4]
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]=>[(1,2),(3,8),(4,5),(6,7)]=>[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[4,4]
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]=>[(1,8),(2,3),(4,5),(6,7)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[4,4]
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]=>[(1,2),(3,6),(4,5),(7,8)]=>[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[4,4]
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]=>[(1,6),(2,3),(4,5),(7,8)]=>[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[4,4]
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]=>[(1,8),(2,7),(3,4),(5,6)]=>[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[4,4]
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[4,4]
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]=>[(1,8),(2,3),(4,7),(5,6)]=>[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[4,4]
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]=>[(1,2),(3,8),(4,7),(5,6)]=>[(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[4,4]
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]=>[(1,8),(2,3),(4,7),(5,6)]=>[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[4,4]
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[4,4]
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]=>[(1,4),(2,3),(5,6),(7,8)]=>[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[4,4]
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]=>[(1,8),(2,7),(3,4),(5,6)]=>[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[4,4]
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[4,4]
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]=>[(1,8),(2,7),(3,4),(5,6)]=>[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[4,4]
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]=>[(1,8),(2,3),(4,7),(5,6)]=>[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[4,4]
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[4,4]
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[4,4]
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]=>[(1,4),(2,3),(5,6),(7,8)]=>[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[4,4]
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]=>[(1,8),(2,3),(4,5),(6,7)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[4,4]
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]=>[(1,2),(3,8),(4,5),(6,7)]=>[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[4,4]
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]=>[(1,8),(2,3),(4,5),(6,7)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[4,4]
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]=>[(1,2),(3,6),(4,5),(7,8)]=>[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[4,4]
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]=>[(1,6),(2,3),(4,5),(7,8)]=>[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[4,4]
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]=>[(1,8),(2,5),(3,4),(6,7)]=>[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[4,4]
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]=>[(1,2),(3,4),(5,8),(6,7)]=>[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[4,4]
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]=>[(1,8),(2,5),(3,4),(6,7)]=>[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[4,4]
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]=>[(1,8),(2,3),(4,5),(6,7)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[4,4]
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[4,4]
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]=>[(1,6),(2,5),(3,4),(7,8)]=>[(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[4,4]
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]=>[(1,6),(2,3),(4,5),(7,8)]=>[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[4,4]
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[4,4]
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]=>[(1,4),(2,3),(5,6),(7,8)]=>[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[4,4]
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]=>[(1,2),(3,8),(4,5),(6,7)]=>[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[4,4]
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]=>[(1,8),(2,3),(4,5),(6,7)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[4,4]
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]=>[(1,2),(3,4),(5,8),(6,7)]=>[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[4,4]
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]=>[(1,8),(2,5),(3,4),(6,7)]=>[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[4,4]
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]=>[(1,8),(2,3),(4,5),(6,7)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[4,4]
[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]=>[(1,2),(3,4),(5,8),(6,7)]=>[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[4,4]
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]=>[(1,4),(2,3),(5,8),(6,7)]=>[(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[4,4]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,0,0,1],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,-1,0,1],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,1,-1,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[1,-1,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,0,1],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,0,0,1],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,-1,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,-1,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,-1,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,-1,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,-1,1],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,-1,1],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,-1,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,-1,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,-1,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[1,-1,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,-1,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,-1,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,-1,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,-1,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,-1,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,-1,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,-1,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,-1,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,-1,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,-1,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,-1,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,-1,1],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,-1,1],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,-1,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,-1,1],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,0,0,1],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,-1,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,-1,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,-1,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,0,0,1],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,-1,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
Map
link pattern
Description
Sends an alternating sign matrix to the link pattern of the corresponding fully packed loop configuration.
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution for perfect matchings.
This yields the perfect matching with the number of nestings and crossings exchanged.
This yields the perfect matching with the number of nestings and crossings exchanged.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
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