=>

[1,0]=>[2,1]=>[2] [1,0,1,0]=>[3,1,2]=>[3] [1,1,0,0]=>[2,3,1]=>[3] [1,0,1,0,1,0]=>[4,1,2,3]=>[4] [1,0,1,1,0,0]=>[3,1,4,2]=>[4] [1,1,0,0,1,0]=>[2,4,1,3]=>[4] [1,1,0,1,0,0]=>[4,3,1,2]=>[4] [1,1,1,0,0,0]=>[2,3,4,1]=>[4] [1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[5] [1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[5] [1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[5] [1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>[5] [1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[5] [1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[5] [1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[5] [1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>[5] [1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>[3,2] [1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>[5] [1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[5] [1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>[5] [1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>[5] [1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5] [1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[6] [1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[6] [1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[6] [1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>[6] [1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[6] [1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[6] [1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6] [1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>[6] [1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>[4,2] [1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>[6] [1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[6] [1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>[6] [1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>[6] [1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[6] [1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[6] [1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[6] [1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[6] [1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>[6] [1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6] [1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>[6] [1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>[6] [1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[4,2] [1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>[3,3] [1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>[4,2] [1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>[6] [1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>[6] [1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>[3,3] [1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>[6] [1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[6] [1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[6] [1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>[6] [1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>[4,2] [1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>[6] [1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[6] [1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>[3,3] [1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>[4,2] [1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>[6] [1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[6] [1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>[6] [1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>[6] [1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>[6] [1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6] [1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[7] [1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[7] [1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[7] [1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>[7] [1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[7] [1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[7] [1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7] [1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>[7] [1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>[5,2] [1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>[7] [1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[7] [1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>[7] [1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>[7] [1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[7] [1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[7] [1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[7] [1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7] [1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>[7] [1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7] [1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>[7] [1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>[7] [1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>[5,2] [1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>[4,3] [1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>[5,2] [1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>[7] [1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>[7] [1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>[4,3] [1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>[7] [1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[7] [1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7] [1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>[7] [1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>[5,2] [1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>[7] [1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>[7] [1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>[4,3] [1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>[5,2] [1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>[7] [1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[7] [1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>[7] [1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>[7] [1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>[7] [1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[7] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[7] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[7] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[7] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>[7] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[7] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[7] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>[7] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>[5,2] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>[7] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>[7] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>[7] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7] [1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>[7] [1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>[7] [1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>[7] [1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>[7] [1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>[7] [1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>[5,2] [1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>[5,2] [1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>[4,3] [1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>[4,3] [1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>[4,3] [1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>[5,2] [1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>[5,2] [1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>[4,3] [1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>[5,2] [1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>[7] [1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>[7] [1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>[7] [1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>[5,2] [1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>[7] [1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>[4,3] [1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>[7] [1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>[4,3] [1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>[4,3] [1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>[7] [1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>[7] [1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>[7] [1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>[4,3] [1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>[7] [1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[7] [1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[7] [1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[7] [1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>[7] [1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7] [1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>[7] [1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>[7] [1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>[5,2] [1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>[4,3] [1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>[5,2] [1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>[7] [1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>[7] [1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>[4,3] [1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>[7] [1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>[7] [1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>[7] [1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>[4,3] [1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>[4,3] [1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>[4,3] [1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>[5,2] [1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>[4,3] [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>[7] [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>[5,2] [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>[7] [1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>[7] [1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>[4,3] [1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>[4,3] [1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>[7] [1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[7] [1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[7] [1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>[7] [1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>[5,2] [1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>[7] [1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>[7] [1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>[4,3] [1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>[5,2] [1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>[7] [1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[7] [1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>[4,3] [1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>[4,3] [1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>[5,2] [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>[7] [1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[7] [1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>[7] [1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>[7] [1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>[7] [1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>[7] [1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]=>[8] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[8] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[8] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,1,2,3,7,4,5,6]=>[6,2] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[8] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[8] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>[8] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[8] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[8] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,1,2,5,3,4,6,7]=>[8] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]=>[5,3] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,1,2,5,3,8,4,7]=>[8] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,1,2,6,3,7,4,5]=>[5,3] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>[6,2] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,1,2,7,6,3,8,5]=>[8] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,1,2,5,6,3,4,7]=>[8] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[8,1,2,7,6,3,4,5]=>[6,2] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[7,1,2,5,6,3,8,4]=>[8] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[8] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,8,7,3,6]=>[8] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[8] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[8] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>[8] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[8] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>[8] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,8,2,6,7,4,5]=>[8] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,1,4,2,3,5,6,7]=>[8] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,1,4,2,3,5,8,6]=>[8] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>[8] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,1,5,2,3,4,8,6]=>[6,2] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,1,8,2,3,4,5,7]=>[4,4] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>[6,2] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,1,8,2,3,7,4,5]=>[5,3] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,5,2,3,7,8,4]=>[6,2] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,4,2,8,3,6,7]=>[8] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>[8] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,1,4,2,6,3,5,7]=>[8] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>[8] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,1,5,2,6,3,4,7]=>[5,3] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>[8] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[7,1,8,2,6,3,4,5]=>[4,4] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]=>[5,3] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,1,4,2,8,7,3,6]=>[8] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[8,1,4,2,6,7,3,5]=>[8] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[8,1,5,2,6,7,3,4]=>[4,4] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[5,1,4,2,6,7,8,3]=>[8] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>[8] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>[6,2] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,6,5,2,8,4,7]=>[8] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,8,5,2,7,4,6]=>[8] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,8,6,2,7,4,5]=>[5,3] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,1,4,5,2,3,6,7]=>[8] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,1,8,5,2,3,4,6]=>[5,3] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]=>[8] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[7,1,6,5,2,3,8,4]=>[6,2] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,8,6,2,5,7]=>[8] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,8,5,7,2,4,6]=>[5,3] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,7,5,6,2,8,4]=>[8] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[8,1,4,5,7,2,3,6]=>[4,4] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[8,1,4,7,6,2,3,5]=>[5,3] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,8,5,6,7,2,4]=>[8] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>[8] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>[8] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,8,1,3,7,4,5,6]=>[6,2] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>[8] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,8,1,3,6,7,4,5]=>[8] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[8] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>[8] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>[8] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,7,5,6]=>[8] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>[5,3] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,6,1,5,3,8,4,7]=>[8] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1,8,6,3,5,7]=>[8] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,8,1,7,6,3,4,5]=>[6,2] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,3,1,2,4,5,6,7]=>[8] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,3,1,2,4,5,8,6]=>[8] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,3,1,2,4,8,5,7]=>[8] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,3,1,2,4,7,8,5]=>[8] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,3,1,2,8,4,6,7]=>[8] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,3,1,2,6,4,5,7]=>[8] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[8,3,1,2,7,4,5,6]=>[6,2] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[7,3,1,2,6,4,8,5]=>[8] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,1,2,8,7,4,6]=>[8] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,3,1,2,6,7,8,4]=>[8] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[8,4,1,2,3,7,5,6]=>[6,2] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,6,1,2,3,4,8,5]=>[5,3] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>[5,3] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,6,1,2,3,7,4,5]=>[4,4] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,1,2,3,7,8,4]=>[5,3] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>[6,2] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7,4,1,2,6,3,8,5]=>[6,2] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]=>[8] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,1,2,6,3,4,5]=>[5,3] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,7,1,2,6,3,8,4]=>[4,4] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8,4,1,2,6,7,3,5]=>[6,2] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,8,1,2,6,7,3,4]=>[5,3] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,1,2,6,7,8,3]=>[6,2] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,3,1,8,2,5,6,7]=>[8] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,3,1,7,2,5,8,6]=>[8] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,3,1,6,2,8,5,7]=>[8] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,3,1,5,2,4,6,7]=>[8] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,3,1,6,2,4,5,7]=>[6,2] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7,3,1,6,2,4,8,5]=>[6,2] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>[8] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8,3,1,6,2,7,4,5]=>[5,3] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>[5,3] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>[8] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>[8] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7,4,1,6,2,3,8,5]=>[8] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>[8] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,4,1,5,2,8,3,7]=>[5,3] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8,4,1,6,2,7,3,5]=>[8] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,8,1,5,2,7,3,4]=>[4,4] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[6,4,1,5,2,7,8,3]=>[5,3] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,1,8,7,2,5,6]=>[6,2] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,1,7,6,2,8,5]=>[8] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>[8] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>[5,3] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>[6,2] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7,8,1,5,6,2,3,4]=>[5,3] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,2]=>[8] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>[8] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>[8] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[8] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,7,1,6,4,8,5]=>[8] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]=>[8] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,8,4,1,3,5,6,7]=>[8] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]=>[8] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]=>[8] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[4,4] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]=>[6,2] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,8,4,1,7,3,5,6]=>[6,2] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,7,4,1,6,3,8,5]=>[8] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,8,5,1,7,3,4,6]=>[8] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,7,5,1,6,3,8,4]=>[5,3] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,5,4,1,6,7,8,3]=>[8] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,3,4,1,2,5,6,7]=>[8] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,3,5,1,2,4,6,7]=>[5,3] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>[5,3] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8,3,5,1,2,7,4,6]=>[5,3] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>[4,4] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]=>[8] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>[8] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[8] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>[6,2] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,8,4,1,2,7,3,5]=>[5,3] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,8,5,1,2,7,3,4]=>[8] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,3,4,1,7,2,5,6]=>[6,2] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7,3,4,1,6,2,8,5]=>[8] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,3,5,1,6,2,4,7]=>[4,4] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,3,8,1,6,2,4,5]=>[5,3] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,3,5,1,6,2,8,4]=>[4,4] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,5,4,1,6,2,3,7]=>[5,3] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>[4,4] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,8,5,1,6,2,3,4]=>[8] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,5,4,1,6,2,8,3]=>[5,3] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,2]=>[8] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>[8] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>[8] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[8] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,8,1,7,5,6]=>[8] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,6,5,1,8,4,7]=>[8] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,6,5,1,7,8,4]=>[8] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,7,4,8,1,3,5,6]=>[4,4] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,7,4,6,1,3,8,5]=>[5,3] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,8,6,5,1,3,4,7]=>[6,2] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,7,8,5,1,3,4,6]=>[5,3] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,7,6,5,1,3,8,4]=>[6,2] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,3,8,5,1,2,4,6]=>[4,4] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,4,6,1,2,3,5]=>[8] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>[8] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8,6,4,5,1,7,2,3]=>[5,3] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>[8] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,3,4,8,6,1,5,7]=>[8] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,4,8,7,1,5,6]=>[6,2] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,4,7,6,1,8,5]=>[8] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,8,5,7,1,4,6]=>[5,3] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,7,5,6,1,8,4]=>[8] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,8,4,7,6,1,3,5]=>[5,3] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,8,7,5,6,1,3,4]=>[6,2] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[8] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,3,7,5,6,1,2,4]=>[5,3] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,4,5,8,7,1,6]=>[8] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,8,6,7,1,5]=>[8] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,4,5,6,7,1,3]=>[8] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8]