Identifier
Mp00199: prime Dyck pathDyck paths
Mp00031: to 312-avoiding permutationPermutations
Mp00088: Permutations Kreweras complementPermutations
Mp00068: Permutations Simion-Schmidt mapPermutations
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,1,0,0]=>[2,1]=>[1,2]=>[1,2] [1,0,1,0]=>[1,1,0,1,0,0]=>[2,3,1]=>[1,2,3]=>[1,3,2] [1,1,0,0]=>[1,1,1,0,0,0]=>[3,2,1]=>[1,3,2]=>[1,3,2] [1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,2,3,4]=>[1,4,3,2] [1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[1,2,4,3]=>[1,4,3,2] [1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[1,3,2,4]=>[1,4,3,2] [1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[1,4,2,3]=>[1,4,3,2] [1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,4,3,2]=>[1,4,3,2] [1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,2,3,4,5]=>[1,5,4,3,2] [1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[1,2,3,5,4]=>[1,5,4,3,2] [1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[1,2,4,3,5]=>[1,5,4,3,2] [1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[1,2,5,3,4]=>[1,5,4,3,2] [1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[1,2,5,4,3]=>[1,5,4,3,2] [1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[1,3,2,4,5]=>[1,5,4,3,2] [1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[1,3,2,5,4]=>[1,5,4,3,2] [1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[1,4,2,3,5]=>[1,5,4,3,2] [1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[1,5,2,3,4]=>[1,5,4,3,2] [1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[1,5,2,4,3]=>[1,5,4,3,2] [1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[1,4,3,2,5]=>[1,5,4,3,2] [1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[1,5,3,2,4]=>[1,5,4,3,2] [1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[1,5,4,2,3]=>[1,5,4,3,2] [1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,5,4,3,2]=>[1,5,4,3,2] [1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>[1,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[1,2,3,4,6,5]=>[1,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[1,2,3,5,4,6]=>[1,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[1,2,3,6,4,5]=>[1,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[1,2,3,6,5,4]=>[1,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[1,2,4,3,5,6]=>[1,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[1,2,4,3,6,5]=>[1,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[1,2,5,3,4,6]=>[1,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[1,2,6,3,4,5]=>[1,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[1,2,6,3,5,4]=>[1,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[1,2,5,4,3,6]=>[1,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[1,2,6,4,3,5]=>[1,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[1,2,6,5,3,4]=>[1,6,5,4,3,2] [1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[1,2,6,5,4,3]=>[1,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[1,3,2,4,5,6]=>[1,6,5,4,3,2] [1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[1,3,2,4,6,5]=>[1,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[1,3,2,5,4,6]=>[1,6,5,4,3,2] [1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[1,3,2,6,4,5]=>[1,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[1,3,2,6,5,4]=>[1,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[1,4,2,3,5,6]=>[1,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[1,4,2,3,6,5]=>[1,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[1,5,2,3,4,6]=>[1,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2] [1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[1,6,2,3,5,4]=>[1,6,5,4,3,2] [1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[1,5,2,4,3,6]=>[1,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[1,6,2,4,3,5]=>[1,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[1,6,2,5,3,4]=>[1,6,5,4,3,2] [1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[1,6,2,5,4,3]=>[1,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[1,4,3,2,5,6]=>[1,6,5,4,3,2] [1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[1,4,3,2,6,5]=>[1,6,5,4,3,2] [1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[1,5,3,2,4,6]=>[1,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,6,3,2,4,5]=>[1,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[1,6,3,2,5,4]=>[1,6,5,4,3,2] [1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[1,5,4,2,3,6]=>[1,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[1,6,4,2,3,5]=>[1,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[1,6,5,2,3,4]=>[1,6,5,4,3,2] [1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[1,6,5,2,4,3]=>[1,6,5,4,3,2] [1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[1,5,4,3,2,6]=>[1,6,5,4,3,2] [1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[1,6,4,3,2,5]=>[1,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[1,6,5,3,2,4]=>[1,6,5,4,3,2] [1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[1,6,5,4,2,3]=>[1,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[1,2,3,4,5,7,6]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[1,2,3,4,6,5,7]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[1,2,3,4,7,5,6]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[1,2,3,4,7,6,5]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[1,2,3,5,4,6,7]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[1,2,3,5,4,7,6]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[1,2,3,6,4,5,7]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[1,2,3,7,4,5,6]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[1,2,3,7,4,6,5]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[1,2,3,6,5,4,7]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[1,2,3,7,5,4,6]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[1,2,3,7,6,4,5]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[1,2,3,7,6,5,4]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[1,2,4,3,5,6,7]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[1,2,4,3,5,7,6]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[1,2,4,3,6,5,7]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[1,2,4,3,7,5,6]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[1,2,4,3,7,6,5]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[1,2,5,3,4,6,7]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[1,2,5,3,4,7,6]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[1,2,6,3,4,5,7]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[1,2,7,3,4,5,6]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[1,2,7,3,4,6,5]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[1,2,6,3,5,4,7]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[1,2,7,3,5,4,6]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[1,2,7,3,6,4,5]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[1,2,7,3,6,5,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[1,2,5,4,3,6,7]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[1,2,5,4,3,7,6]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[1,2,6,4,3,5,7]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[1,2,7,4,3,5,6]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[1,2,7,4,3,6,5]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[1,2,6,5,3,4,7]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[1,2,7,5,3,4,6]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[1,2,7,6,3,4,5]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[1,2,7,6,3,5,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[1,2,6,5,4,3,7]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[1,2,7,5,4,3,6]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[1,2,7,6,4,3,5]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[1,2,7,6,5,3,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[1,2,7,6,5,4,3]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[1,3,2,4,5,6,7]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[1,3,2,4,5,7,6]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[1,3,2,4,6,5,7]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[1,3,2,4,7,5,6]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[1,3,2,4,7,6,5]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[1,3,2,5,4,6,7]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[1,3,2,5,4,7,6]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[1,3,2,6,4,5,7]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[1,3,2,7,4,5,6]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[1,3,2,7,4,6,5]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[1,3,2,6,5,4,7]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[1,3,2,7,5,4,6]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[1,3,2,7,6,4,5]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[1,3,2,7,6,5,4]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[1,4,2,3,5,6,7]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[1,4,2,3,5,7,6]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[1,4,2,3,6,5,7]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[1,4,2,3,7,5,6]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[1,4,2,3,7,6,5]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[1,5,2,3,4,6,7]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[1,5,2,3,4,7,6]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[1,6,2,3,4,5,7]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[1,7,2,3,4,6,5]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[1,6,2,3,5,4,7]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[1,7,2,3,5,4,6]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[1,7,2,3,6,4,5]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[1,7,2,3,6,5,4]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[1,5,2,4,3,6,7]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[1,5,2,4,3,7,6]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[1,6,2,4,3,5,7]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[1,7,2,4,3,5,6]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[1,7,2,4,3,6,5]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[1,6,2,5,3,4,7]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[1,7,2,5,3,4,6]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[1,7,2,6,3,4,5]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[1,7,2,6,3,5,4]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[1,6,2,5,4,3,7]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[1,7,2,5,4,3,6]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[1,7,2,6,4,3,5]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[1,7,2,6,5,3,4]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[1,7,2,6,5,4,3]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[1,4,3,2,5,6,7]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[1,4,3,2,5,7,6]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[1,4,3,2,6,5,7]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[1,4,3,2,7,5,6]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[1,4,3,2,7,6,5]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[1,5,3,2,4,6,7]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[1,5,3,2,4,7,6]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[1,6,3,2,4,5,7]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[1,7,3,2,4,5,6]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[1,7,3,2,4,6,5]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[1,6,3,2,5,4,7]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[1,7,3,2,5,4,6]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[1,7,3,2,6,4,5]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[1,7,3,2,6,5,4]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[1,5,4,2,3,6,7]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[1,5,4,2,3,7,6]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[1,6,4,2,3,5,7]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[1,7,4,2,3,5,6]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[1,7,4,2,3,6,5]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[1,6,5,2,3,4,7]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[1,7,5,2,3,4,6]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,7,6,2,3,4,5]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[1,7,6,2,3,5,4]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[1,6,5,2,4,3,7]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[1,7,5,2,4,3,6]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[1,7,6,2,4,3,5]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[1,7,6,2,5,3,4]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[1,7,6,2,5,4,3]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[1,5,4,3,2,6,7]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[1,5,4,3,2,7,6]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[1,6,4,3,2,5,7]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,7,4,3,2,5,6]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[1,7,4,3,2,6,5]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[1,6,5,3,2,4,7]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,7,5,3,2,4,6]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[1,7,6,3,2,4,5]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[1,7,6,3,2,5,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[1,6,5,4,2,3,7]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,7,5,4,2,3,6]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[1,7,6,4,2,3,5]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[1,7,6,5,2,3,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[1,7,6,5,2,4,3]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,6,5,4,3,2,7]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[1,7,5,4,3,2,6]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[1,7,6,4,3,2,5]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[1,7,6,5,3,2,4]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[1,7,6,5,4,2,3]=>[1,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[1,2,3,4,5,6,8,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[1,2,3,4,5,7,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>[1,2,3,4,5,8,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[1,2,3,4,5,8,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>[1,2,3,4,6,5,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>[1,2,3,4,6,5,8,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]=>[1,2,3,4,7,5,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>[1,2,3,4,8,5,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,8,7,5,1]=>[1,2,3,4,8,5,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[1,2,3,4,7,6,5,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,6,8,5,1]=>[1,2,3,4,8,6,5,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,6,5,1]=>[1,2,3,4,8,7,5,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[1,2,3,5,4,6,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[1,2,3,5,4,7,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]=>[1,2,3,5,4,8,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>[1,2,3,5,4,8,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>[1,2,3,6,4,5,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,4,8,7,1]=>[1,2,3,6,4,5,8,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]=>[1,2,3,7,4,5,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[1,2,3,8,4,5,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[1,2,3,8,4,5,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,6,4,8,1]=>[1,2,3,7,4,6,5,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]=>[1,2,3,8,4,6,5,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>[1,2,3,8,4,7,5,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,7,6,4,1]=>[1,2,3,8,4,7,6,5]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,4,1]=>[1,2,3,8,5,4,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]=>[1,2,3,8,5,4,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,6,7,5,4,8,1]=>[1,2,3,7,6,4,5,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,5,8,4,1]=>[1,2,3,8,6,4,5,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]=>[1,2,3,8,7,4,5,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,6,8,7,5,4,1]=>[1,2,3,8,7,4,6,5]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]=>[1,2,3,8,6,5,4,7]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,7,6,8,5,4,1]=>[1,2,3,8,7,5,4,6]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,7,8,6,5,4,1]=>[1,2,3,8,7,6,4,5]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>[1,2,4,3,5,6,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[1,2,4,3,5,6,8,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>[1,2,4,3,5,7,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,7,8,6,1]=>[1,2,4,3,5,8,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,3,5,8,7,6,1]=>[1,2,4,3,5,8,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[1,2,4,3,6,5,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[1,2,4,3,6,5,8,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,6,7,5,8,1]=>[1,2,4,3,7,5,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,6,7,8,5,1]=>[1,2,4,3,8,5,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>[1,2,4,3,8,5,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,4,3,7,6,8,5,1]=>[1,2,4,3,8,6,5,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,4,3,7,8,6,5,1]=>[1,2,4,3,8,7,5,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>[1,2,5,3,4,6,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,3,6,8,7,1]=>[1,2,5,3,4,6,8,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,3,8,7,6,1]=>[1,2,5,3,4,8,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,1]=>[1,2,6,3,4,5,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]=>[1,2,7,3,4,5,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>[1,2,8,3,4,5,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,7,3,1]=>[1,2,8,3,4,5,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,6,3,8,1]=>[1,2,7,3,4,6,5,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,5,3,7,8,1]=>[1,2,6,3,5,4,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>[1,2,7,3,5,4,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]=>[1,2,8,3,5,4,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>[1,2,8,3,5,4,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,5,3,8,1]=>[1,2,7,3,6,4,5,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>[1,2,8,3,7,4,5,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[1,2,8,3,7,6,4,5]=>[1,8,7,6,5,4,3,2] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[1,2,8,3,7,6,5,4]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[1,2,5,4,3,6,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[1,2,5,4,3,8,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[1,2,7,4,3,5,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]=>[1,2,8,4,3,5,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>[1,2,8,4,3,7,5,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]=>[1,2,8,4,3,7,6,5]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,4,3,7,8,1]=>[1,2,6,5,3,4,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,5,6,4,7,3,8,1]=>[1,2,7,5,3,4,6,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,3,1]=>[1,2,8,5,3,4,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]=>[1,2,7,6,3,4,5,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,4,8,3,1]=>[1,2,8,6,3,4,5,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[1,2,8,7,3,4,5,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,5,6,8,7,4,3,1]=>[1,2,8,7,3,4,6,5]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,5,7,6,8,4,3,1]=>[1,2,8,7,3,5,4,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,5,8,7,6,4,3,1]=>[1,2,8,7,3,6,5,4]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>[1,2,8,5,4,3,6,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,5,7,4,8,3,1]=>[1,2,8,6,4,3,5,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,6,5,8,7,4,3,1]=>[1,2,8,7,4,3,6,5]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]=>[1,2,8,7,6,3,4,5]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[1,2,8,7,6,3,5,4]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[1,2,8,6,5,4,3,7]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,6,5,8,4,3,1]=>[1,2,8,7,5,4,3,6]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]=>[1,2,8,7,6,4,3,5]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[1,2,8,7,6,5,3,4]=>[1,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[1,3,2,4,5,6,7,8]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]=>[1,3,2,4,5,6,8,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[1,3,2,4,5,7,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,7,8,6,1]=>[1,3,2,4,5,8,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,4,6,7,8,5,1]=>[1,3,2,4,8,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,2,4,7,6,8,5,1]=>[1,3,2,4,8,6,5,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[1,3,2,4,8,7,6,5]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]=>[1,3,2,5,4,6,7,8]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[1,3,2,5,4,7,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>[1,3,2,8,4,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]=>[1,3,2,8,4,6,5,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>[1,3,2,6,5,4,8,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[1,3,2,7,5,4,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,2,6,5,7,8,4,1]=>[1,3,2,8,5,4,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,2,6,5,8,7,4,1]=>[1,3,2,8,5,4,7,6]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>[1,3,2,8,7,4,6,5]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,2,7,6,5,8,4,1]=>[1,3,2,8,6,5,4,7]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>[1,3,2,8,7,6,4,5]=>[1,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[1,4,2,3,5,6,7,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[1,4,2,3,5,8,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,8,7,1]=>[1,4,2,3,6,5,8,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[1,4,2,3,7,5,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,4,2,6,7,8,5,1]=>[1,4,2,3,8,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,6,8,7,5,1]=>[1,4,2,3,8,5,7,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,4,2,7,6,8,5,1]=>[1,4,2,3,8,6,5,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]=>[1,4,2,3,8,7,5,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[1,4,2,3,8,7,6,5]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[1,5,2,3,4,6,7,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>[1,5,2,3,4,7,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,2,7,8,6,1]=>[1,5,2,3,4,8,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,2,8,7,6,1]=>[1,5,2,3,4,8,7,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>[1,6,2,3,4,5,7,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]=>[1,6,2,3,4,5,8,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>[1,7,2,3,4,5,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,2,1]=>[1,8,2,3,4,5,7,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,6,2,8,1]=>[1,7,2,3,4,6,5,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>[1,8,2,3,4,6,5,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>[1,8,2,3,4,7,5,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[1,8,2,3,4,7,6,5]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>[1,7,2,3,5,4,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]=>[1,8,2,3,5,4,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,5,2,8,1]=>[1,7,2,3,6,4,5,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,5,8,2,1]=>[1,8,2,3,6,4,5,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]=>[1,8,2,3,6,5,4,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,4,7,6,8,5,2,1]=>[1,8,2,3,7,5,4,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[1,8,2,3,7,6,5,4]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,4,6,2,8,7,1]=>[1,6,2,4,3,5,8,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]=>[1,7,2,4,3,5,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,2,1]=>[1,8,2,4,3,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]=>[1,7,2,4,3,6,5,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>[1,8,2,4,3,6,5,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,4,7,8,6,2,1]=>[1,8,2,4,3,7,5,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,5,4,8,7,6,2,1]=>[1,8,2,4,3,7,6,5]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,1]=>[1,6,2,5,3,4,7,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]=>[1,6,2,5,3,4,8,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>[1,7,2,5,3,4,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,2,1]=>[1,8,2,5,3,4,6,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[1,7,2,6,3,4,5,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[1,8,2,7,3,4,5,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>[1,7,2,6,3,5,4,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,5,7,6,4,8,2,1]=>[1,8,2,6,3,5,4,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,6,8,4,2,1]=>[1,8,2,7,3,5,4,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>[1,8,2,7,3,6,4,5]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[1,8,2,7,3,6,5,4]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>[1,7,2,5,4,3,6,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,6,5,7,4,2,8,1]=>[1,7,2,6,4,3,5,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,5,7,4,8,2,1]=>[1,8,2,6,4,3,5,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,5,7,8,4,2,1]=>[1,8,2,7,4,3,5,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,6,5,8,7,4,2,1]=>[1,8,2,7,4,3,6,5]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,5,4,8,2,1]=>[1,8,2,6,5,3,4,7]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,5,8,4,2,1]=>[1,8,2,7,5,3,4,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,5,4,2,1]=>[1,8,2,7,6,3,4,5]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]=>[1,8,2,7,6,3,5,4]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,7,6,5,4,2,8,1]=>[1,7,2,6,5,4,3,8]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>[1,8,2,7,5,4,3,6]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[1,8,2,7,6,4,3,5]=>[1,8,7,6,5,4,3,2] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>[1,8,2,7,6,5,4,3]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[1,4,3,2,5,6,7,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,2,5,7,8,6,1]=>[1,4,3,2,5,8,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,6,7,8,5,1]=>[1,4,3,2,8,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[1,4,3,2,7,6,5,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[1,5,3,2,4,7,6,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]=>[1,5,3,2,4,8,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>[1,6,3,2,4,5,7,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>[1,8,3,2,4,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]=>[1,8,3,2,4,5,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,3,5,7,6,2,8,1]=>[1,7,3,2,4,6,5,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>[1,8,3,2,4,7,5,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[1,7,3,2,5,4,6,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>[1,8,3,2,5,4,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[1,8,3,2,5,4,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,3,6,7,5,8,2,1]=>[1,8,3,2,6,4,5,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,7,6,8,5,2,1]=>[1,8,3,2,7,5,4,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>[1,8,3,2,7,6,4,5]=>[1,8,7,6,5,4,3,2] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]=>[1,8,3,2,7,6,5,4]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,1]=>[1,5,4,2,3,6,7,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]=>[1,5,4,2,3,8,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,5,3,6,2,7,8,1]=>[1,6,4,2,3,5,7,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>[1,6,4,2,3,5,8,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,2,8,1]=>[1,7,4,2,3,5,6,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,3,6,7,8,2,1]=>[1,8,4,2,3,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>[1,8,4,2,3,5,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>[1,8,4,2,3,6,5,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>[1,8,4,2,3,7,5,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,3,8,7,6,2,1]=>[1,8,4,2,3,7,6,5]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>[1,6,5,2,3,4,8,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[1,7,5,2,3,4,6,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>[1,8,5,2,3,4,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[1,7,6,2,3,4,5,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[1,8,6,2,3,4,5,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>[1,8,7,2,3,5,4,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>[1,8,7,2,3,6,4,5]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>[1,8,7,2,3,6,5,4]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]=>[1,7,6,2,4,3,5,8]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,6,5,7,3,8,2,1]=>[1,8,6,2,4,3,5,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,6,7,5,3,8,2,1]=>[1,8,6,2,5,3,4,7]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>[1,8,7,2,5,3,4,6]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>[1,8,7,2,6,3,4,5]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[1,8,7,2,6,3,5,4]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>[1,8,7,2,6,5,3,4]=>[1,8,7,6,5,4,3,2] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[1,8,7,2,6,5,4,3]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]=>[1,8,4,3,2,5,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]=>[1,8,4,3,2,7,5,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]=>[1,6,5,3,2,4,7,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]=>[1,6,5,3,2,4,8,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[1,7,5,3,2,4,6,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,6,3,7,8,2,1]=>[1,8,5,3,2,4,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,4,6,3,8,7,2,1]=>[1,8,5,3,2,4,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,4,6,7,3,2,8,1]=>[1,7,6,3,2,4,5,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[1,8,6,3,2,4,5,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[1,8,7,3,2,4,5,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,4,6,8,7,3,2,1]=>[1,8,7,3,2,4,6,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,4,7,6,3,2,8,1]=>[1,7,6,3,2,5,4,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,4,7,6,3,8,2,1]=>[1,8,6,3,2,5,4,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>[1,8,7,3,2,5,4,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,4,7,8,6,3,2,1]=>[1,8,7,3,2,6,4,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,6,4,3,7,8,2,1]=>[1,8,5,4,2,3,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,4,3,8,7,2,1]=>[1,8,5,4,2,3,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,6,4,7,3,8,2,1]=>[1,8,6,4,2,3,5,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[1,8,7,4,2,3,5,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]=>[1,8,7,4,2,3,6,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[1,8,7,5,2,3,4,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[1,8,7,6,2,3,4,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]=>[1,7,6,5,2,4,3,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[1,8,7,6,2,4,3,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[1,8,7,6,2,5,4,3]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[1,7,5,4,3,2,6,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[1,8,5,4,3,2,6,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,5,4,3,8,7,2,1]=>[1,8,5,4,3,2,7,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>[1,8,7,4,3,2,5,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]=>[1,8,7,4,3,2,6,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[1,7,6,5,3,2,4,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[1,8,6,5,3,2,4,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[1,8,7,5,3,2,4,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[1,8,7,6,3,2,4,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[1,8,7,6,3,2,5,4]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[1,7,6,5,4,2,3,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[1,8,6,5,4,2,3,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[1,8,7,6,4,2,3,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[1,8,7,6,5,2,3,4]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[1,8,7,6,5,2,4,3]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[1,8,6,5,4,3,2,7]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[1,8,7,5,4,3,2,6]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[1,8,7,6,4,3,2,5]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[1,8,7,6,5,3,2,4]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[1,8,7,6,5,4,2,3]=>[1,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]=>[1,2,3,4,5,6,7,9,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,8,7,9,1]=>[1,2,3,4,5,6,8,7,9]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,7,1]=>[1,2,3,4,5,6,9,7,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,9,8,7,1]=>[1,2,3,4,5,6,9,8,7]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,1]=>[1,2,3,4,5,7,6,8,9]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,6,1]=>[1,2,3,4,5,9,6,7,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,5,7,9,8,6,1]=>[1,2,3,4,5,9,6,8,7]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,8,7,9,6,1]=>[1,2,3,4,5,9,7,6,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,9,8,7,6,1]=>[1,2,3,4,5,9,8,7,6]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,1]=>[1,2,3,4,6,5,7,8,9]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,5,1]=>[1,2,3,4,9,5,6,7,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,7,6,8,9,5,1]=>[1,2,3,4,9,6,5,7,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,7,8,6,9,5,1]=>[1,2,3,4,9,7,5,6,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,4,1]=>[1,2,3,9,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,9,4,1]=>[1,2,3,9,5,4,6,7,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,8,7,6,5,4,1]=>[1,2,3,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,9,1]=>[1,2,4,3,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,8,7,9,1]=>[1,2,4,3,6,5,8,7,9]=>[1,9,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,6,5,9,8,7,1]=>[1,2,4,3,6,5,9,8,7]=>[1,9,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,3,1]=>[1,2,9,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,9,3,1]=>[1,2,9,4,3,5,6,7,8]=>[1,9,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,8,7,6,5,4,3,1]=>[1,2,9,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>[1,3,2,4,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,9,8,1]=>[1,3,2,5,4,7,6,9,8]=>[1,9,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,9,8,7,6,5,4,1]=>[1,3,2,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]=>[1,4,2,3,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,1]=>[1,7,2,3,4,5,6,8,9]=>[1,9,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,2,9,1]=>[1,8,2,3,4,5,6,7,9]=>[1,9,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2] [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,9,8,7,6,5,4,2,1]=>[1,9,2,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,1]=>[1,4,3,2,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,9,2,1]=>[1,9,3,2,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,7,3,9,8,2,1]=>[1,9,6,2,3,4,5,8,7]=>[1,9,8,7,6,5,4,3,2] [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,9,8,7,6,5,3,2,1]=>[1,9,8,2,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,9,8,7,6,1]=>[1,5,4,3,2,9,8,7,6]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,9,8,7,5,4,3,2,1]=>[1,9,8,7,6,2,5,4,3]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,6,5,4,3,2,9,8,1]=>[1,7,6,5,4,3,2,9,8]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,6,9,8,5,4,3,2,1]=>[1,9,8,7,6,3,2,5,4]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[1,9,8,7,6,5,2,3,4]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,8,6,5,4,3,2,1]=>[1,9,8,7,6,5,2,4,3]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[1,8,7,6,5,4,3,2,9]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>[1,9,7,6,5,4,3,2,8]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]=>[1,9,8,6,5,4,3,2,7]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>[1,9,8,7,5,4,3,2,6]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]=>[1,9,8,7,6,4,3,2,5]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>[1,9,8,7,6,5,3,2,4]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>[1,9,8,7,6,5,4,2,3]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[1,9,8,7,6,5,4,3,2,10]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,9,8,7,6,5,4,3,1]=>[1,2,10,9,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,11,10,9,8,7,6,5,4,3,1]=>[1,2,11,10,9,8,7,6,5,4,3]=>[1,11,10,9,8,7,6,5,4,3,2] [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,2,10,9,8,7,6,5,4,1]=>[1,3,2,10,9,8,7,6,5,4]=>[1,10,9,8,7,6,5,4,3,2] []=>[1,0]=>[1]=>[1]=>[1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,10,9,8,7,6,5,3,2,1]=>[1,10,9,2,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,9,8,7,6,4,3,2,1]=>[1,10,9,8,2,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[1,10,9,8,7,2,3,4,5,6]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,10,9,8,6,5,4,3,2,1]=>[1,10,9,8,7,6,2,5,4,3]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,10,9,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,2,4,3]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[1,10,8,7,6,5,4,3,2,9]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[1,10,9,7,6,5,4,3,2,8]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[1,10,9,8,6,5,4,3,2,7]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[1,10,9,8,7,5,4,3,2,6]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[1,10,9,8,7,6,4,3,2,5]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,3,2,4]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,4,2,3]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,9,10]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]=>[1,2,3,4,5,6,7,8,10,9]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,9,10,8,1]=>[1,2,3,4,5,6,7,10,8,9]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,10,7,1]=>[1,2,3,4,5,6,10,7,8,9]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,10,6,1]=>[1,2,3,4,5,10,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,10,5,1]=>[1,2,3,4,10,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,10,4,1]=>[1,2,3,10,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,3,1]=>[1,2,10,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,11,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,10,1]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,11,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,10,9,8,1]=>[1,2,3,4,5,6,7,10,9,8]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,8,10,11,9,1]=>[1,2,3,4,5,6,7,8,11,9,10]=>[1,11,10,9,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,10,1]=>[1,2,3,4,5,7,6,8,9,10]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,10,1]=>[1,2,3,4,6,5,7,8,9,10]=>[1,10,9,8,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,10,9,1]=>[1,2,4,3,6,5,8,7,10,9]=>[1,10,9,8,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[1,3,2,4,5,6,7,8,9,10]=>[1,10,9,8,7,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,10,1]=>[1,3,2,5,4,7,6,9,8,10]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,10,9,8,1]=>[1,4,3,2,7,6,5,10,9,8]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,2,10,1]=>[1,9,2,3,4,5,6,7,8,10]=>[1,10,9,8,7,6,5,4,3,2] [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[9,11,10,8,7,6,5,4,3,2,1]=>[1,11,10,9,8,7,6,5,2,4,3]=>[1,11,10,9,8,7,6,5,4,3,2]
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].