Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Images
=>
Cc0005;cc-rep-1
[1]=>[1,0]=>[1]=>[1] [1,1]=>[1,0,1,0]=>[2,1]=>[2,1] [2]=>[1,1,0,0]=>[1,2]=>[1,2] [1,1,1]=>[1,0,1,0,1,0]=>[3,2,1]=>[3,2,1] [1,2]=>[1,0,1,1,0,0]=>[2,3,1]=>[3,1,2] [2,1]=>[1,1,0,0,1,0]=>[3,1,2]=>[2,3,1] [3]=>[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3] [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1] [1,1,2]=>[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[4,3,1,2] [1,2,1]=>[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[4,2,3,1] [1,3]=>[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,1,2,3] [2,1,1]=>[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[3,4,2,1] [2,2]=>[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[3,4,1,2] [3,1]=>[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[2,3,4,1] [4]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4] [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[5,4,3,2,1] [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2] [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[5,4,2,3,1] [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3] [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[5,3,4,2,1] [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[5,3,4,1,2] [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[5,2,3,4,1] [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4] [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[4,5,3,2,1] [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[4,5,3,1,2] [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[4,5,2,3,1] [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[4,5,1,2,3] [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,4,5,2,1] [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,4,5,1,2] [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[2,3,4,5,1] [5]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5] [1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1] [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2] [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1] [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3] [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1] [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2] [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[6,5,2,3,4,1] [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4] [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1] [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2] [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1] [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[6,4,5,1,2,3] [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[6,3,4,5,2,1] [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[6,3,4,5,1,2] [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[6,2,3,4,5,1] [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5] [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1] [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2] [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[5,6,4,2,3,1] [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[5,6,4,1,2,3] [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[5,6,3,4,2,1] [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2] [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[5,6,2,3,4,1] [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[5,6,1,2,3,4] [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1] [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[4,5,6,3,1,2] [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[4,5,6,2,3,1] [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3] [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1] [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[3,4,5,6,1,2] [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1] [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6] [1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1] [1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2] [1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1] [1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3] [1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1] [1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2] [1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[7,6,5,2,3,4,1] [1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4] [1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1] [1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2] [1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1] [1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[7,6,4,5,1,2,3] [1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[7,6,3,4,5,2,1] [1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[7,6,3,4,5,1,2] [1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[7,6,2,3,4,5,1] [1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5] [1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1] [1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2] [1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1] [1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[7,5,6,4,1,2,3] [1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1] [1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2] [1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[7,5,6,2,3,4,1] [1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[7,5,6,1,2,3,4] [1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[7,4,5,6,3,2,1] [1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[7,4,5,6,3,1,2] [1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[7,4,5,6,2,3,1] [1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[7,4,5,6,1,2,3] [1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[7,3,4,5,6,2,1] [1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[7,3,4,5,6,1,2] [1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[7,2,3,4,5,6,1] [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6] [2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1] [2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2] [2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[6,7,5,4,2,3,1] [2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[6,7,5,4,1,2,3] [2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[6,7,5,3,4,2,1] [2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[6,7,5,3,4,1,2] [2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[6,7,5,2,3,4,1] [2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[6,7,5,1,2,3,4] [2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[6,7,4,5,3,2,1] [2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[6,7,4,5,3,1,2] [2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[6,7,4,5,2,3,1] [2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[6,7,4,5,1,2,3] [2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[6,7,3,4,5,2,1] [2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[6,7,3,4,5,1,2] [2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[6,7,2,3,4,5,1] [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[6,7,1,2,3,4,5] [3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1] [3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[5,6,7,4,3,1,2] [3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[5,6,7,4,2,3,1] [3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[5,6,7,4,1,2,3] [3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[5,6,7,3,4,2,1] [3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[5,6,7,3,4,1,2] [3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[5,6,7,2,3,4,1] [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[5,6,7,1,2,3,4] [4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1] [4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[4,5,6,7,3,1,2] [4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[4,5,6,7,2,3,1] [4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[4,5,6,7,1,2,3] [5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1] [5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[3,4,5,6,7,1,2] [6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1] [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7] [1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1] [1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2] [1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1] [1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3] [1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1] [1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2] [1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,2,3,4,1] [1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4] [1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1] [1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[8,7,6,4,5,3,1,2] [1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1] [1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,2,1]=>[8,7,6,4,5,1,2,3] [1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,2,1]=>[8,7,6,3,4,5,2,1] [1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,2,1]=>[8,7,6,3,4,5,1,2] [1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,2,1]=>[8,7,6,2,3,4,5,1] [1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5] [1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1] [1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2] [1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[8,7,5,6,4,2,3,1] [1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,2,1]=>[8,7,5,6,4,1,2,3] [1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1] [1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2] [1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[8,7,5,6,2,3,4,1] [1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[8,7,5,6,1,2,3,4] [1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[8,7,4,5,6,3,2,1] [1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>[8,7,4,5,6,3,1,2] [1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[8,7,4,5,6,2,3,1] [1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[8,7,4,5,6,1,2,3] [1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[8,7,3,4,5,6,2,1] [1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,2,1]=>[8,7,3,4,5,6,1,2] [1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[8,7,2,3,4,5,6,1] [1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6] [1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1] [1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[8,6,7,5,4,3,1,2] [1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1] [1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,3,1]=>[8,6,7,5,4,1,2,3] [1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[8,6,7,5,3,4,2,1] [1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,3,1]=>[8,6,7,5,3,4,1,2] [1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[8,6,7,5,2,3,4,1] [1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[8,6,7,5,1,2,3,4] [1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1] [1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,2,3,1]=>[8,6,7,4,5,3,1,2] [1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1] [1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[8,6,7,4,5,1,2,3] [1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[8,6,7,3,4,5,2,1] [1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[8,6,7,3,4,5,1,2] [1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,3,1]=>[8,6,7,2,3,4,5,1] [1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[8,6,7,1,2,3,4,5] [1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[8,5,6,7,4,3,2,1] [1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,4,1]=>[8,5,6,7,4,3,1,2] [1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[8,5,6,7,4,2,3,1] [1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[8,5,6,7,4,1,2,3] [1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[8,5,6,7,3,4,2,1] [1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[8,5,6,7,3,4,1,2] [1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[8,5,6,7,2,3,4,1] [1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[8,5,6,7,1,2,3,4] [1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[8,4,5,6,7,3,2,1] [1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>[8,4,5,6,7,3,1,2] [1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[8,4,5,6,7,2,3,1] [1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[8,4,5,6,7,1,2,3] [1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[8,3,4,5,6,7,2,1] [1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[8,3,4,5,6,7,1,2] [1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[8,2,3,4,5,6,7,1] [1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7] [2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1] [2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2] [2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[7,8,6,5,4,2,3,1] [2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[7,8,6,5,4,1,2,3] [2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[7,8,6,5,3,4,2,1] [2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[7,8,6,5,3,4,1,2] [2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,1,2]=>[7,8,6,5,2,3,4,1] [2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[7,8,6,5,1,2,3,4] [2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[7,8,6,4,5,3,2,1] [2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2] [2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[7,8,6,4,5,2,3,1] [2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,1,2]=>[7,8,6,4,5,1,2,3] [2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,1,2]=>[7,8,6,3,4,5,2,1] [2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[7,8,6,3,4,5,1,2] [2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,1,2]=>[7,8,6,2,3,4,5,1] [2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[7,8,6,1,2,3,4,5] [2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[7,8,5,6,4,3,2,1] [2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[7,8,5,6,4,3,1,2] [2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,1,2]=>[7,8,5,6,4,2,3,1] [2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[7,8,5,6,4,1,2,3] [2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[7,8,5,6,3,4,2,1] [2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2] [2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[7,8,5,6,2,3,4,1] [2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[7,8,5,6,1,2,3,4] [2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[7,8,4,5,6,3,2,1] [2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[7,8,4,5,6,3,1,2] [2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[7,8,4,5,6,2,3,1] [2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,1,2]=>[7,8,4,5,6,1,2,3] [2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,1,2]=>[7,8,3,4,5,6,2,1] [2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[7,8,3,4,5,6,1,2] [2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[7,8,2,3,4,5,6,1] [2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[7,8,1,2,3,4,5,6] [3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1] [3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[6,7,8,5,4,3,1,2] [3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,1,2,3]=>[6,7,8,5,4,2,3,1] [3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[6,7,8,5,4,1,2,3] [3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,1,2,3]=>[6,7,8,5,3,4,2,1] [3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[6,7,8,5,3,4,1,2] [3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[6,7,8,5,2,3,4,1] [3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[6,7,8,5,1,2,3,4] [3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,1,2,3]=>[6,7,8,4,5,3,2,1] [3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,1,2,3]=>[6,7,8,4,5,3,1,2] [3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[6,7,8,4,5,2,3,1] [3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,1,2,3]=>[6,7,8,4,5,1,2,3] [3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[6,7,8,3,4,5,2,1] [3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,1,2,3]=>[6,7,8,3,4,5,1,2] [3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[6,7,8,2,3,4,5,1] [3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[6,7,8,1,2,3,4,5] [4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1] [4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[5,6,7,8,4,3,1,2] [4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[5,6,7,8,4,2,3,1] [4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[5,6,7,8,4,1,2,3] [4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[5,6,7,8,3,4,2,1] [4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[5,6,7,8,3,4,1,2] [4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[5,6,7,8,2,3,4,1] [4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4] [5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1] [5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[4,5,6,7,8,3,1,2] [5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[4,5,6,7,8,2,3,1] [5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[4,5,6,7,8,1,2,3] [6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[3,4,5,6,7,8,2,1] [6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[3,4,5,6,7,8,1,2] [7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1] [8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8] [1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1] [1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2] [1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,3,1] [1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3] [1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,2,1] [1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,1,2] [1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,5,4,3,2,1]=>[9,8,7,6,5,2,3,4,1] [1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4] [1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,4,5,3,2,1] [1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[8,9,7,5,6,4,3,2,1]=>[9,8,7,6,4,5,3,1,2] [1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,4,3,2,1]=>[9,8,7,6,4,5,2,3,1] [1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,6,4,3,2,1]=>[9,8,7,6,4,5,1,2,3] [1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[9,8,5,6,7,4,3,2,1]=>[9,8,7,6,3,4,5,2,1] [1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5] [1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,5,6,4,3,2,1] [1,1,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,4,5,3,2,1]=>[9,8,7,5,6,1,2,3,4] [1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,5,6,3,2,1] [1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6] [1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,2,1]=>[9,8,6,7,5,4,3,2,1] [1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,3,4,2,1]=>[9,8,6,7,5,4,3,1,2] [1,1,2,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,3,4,2,1]=>[9,8,6,7,5,4,1,2,3] [1,1,2,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,3,4,2,1]=>[9,8,6,7,4,5,3,2,1] [1,1,2,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,3,4,2,1]=>[9,8,6,7,4,5,2,3,1] [1,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,4,2,1]=>[9,8,6,7,1,2,3,4,5] [1,1,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,4,5,2,1]=>[9,8,5,6,7,4,3,2,1] [1,1,4,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,3,4,5,6,2,1]=>[9,8,4,5,6,7,3,2,1] [1,1,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,3,4,5,6,2,1]=>[9,8,4,5,6,7,1,2,3] [1,1,5,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[9,8,3,4,5,6,7,2,1]=>[9,8,3,4,5,6,7,2,1] [1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,2,1]=>[9,8,2,3,4,5,6,7,1] [1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7] [1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,2,1] [1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,1,2] [1,2,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,2,3,1]=>[9,7,8,6,5,4,2,3,1] [1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,2,3,1]=>[9,7,8,6,5,4,1,2,3] [1,2,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,4,5,2,3,1]=>[9,7,8,5,6,3,4,2,1] [1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,2,3,1]=>[9,7,8,5,6,3,4,1,2] [1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[9,7,8,1,2,3,4,5,6] [1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,4,1]=>[9,6,7,8,5,4,3,2,1] [1,3,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,4,1]=>[9,6,7,8,1,2,3,4,5] [1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,3,4,5,1]=>[9,5,6,7,8,1,2,3,4] [1,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,3,4,5,6,1]=>[9,4,5,6,7,8,1,2,3] [1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,3,4,5,6,7,1]=>[9,3,4,5,6,7,8,2,1] [1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[9,3,4,5,6,7,8,1,2] [1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[9,2,3,4,5,6,7,8,1] [1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8] [2,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,2,1] [2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2] [2,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,1,2]=>[8,9,7,6,5,4,2,3,1] [2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,1,2]=>[8,9,7,6,5,4,1,2,3] [2,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,5,4,3,1,2]=>[8,9,7,6,5,3,4,2,1] [2,1,1,2,1,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,1,2]=>[8,9,7,6,4,5,3,2,1] [2,1,2,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,1,2]=>[8,9,7,5,6,4,3,2,1] [2,1,3,3]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[7,8,9,4,5,6,3,1,2]=>[8,9,7,4,5,6,1,2,3] [2,1,6]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,1,2]=>[8,9,7,1,2,3,4,5,6] [2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,1,2]=>[8,9,6,7,5,4,3,2,1] [2,2,1,4]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,3,4,1,2]=>[8,9,6,7,5,1,2,3,4] [2,2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,3,4,1,2]=>[8,9,6,7,4,5,3,2,1] [2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,3,4,1,2]=>[8,9,6,7,4,5,2,3,1] [2,2,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,4,1,2]=>[8,9,6,7,1,2,3,4,5] [2,4,1,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,3,4,5,6,1,2]=>[8,9,4,5,6,7,3,2,1] [2,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,3,4,5,6,1,2]=>[8,9,4,5,6,7,1,2,3] [2,5,1,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[9,8,3,4,5,6,7,1,2]=>[8,9,3,4,5,6,7,2,1] [2,5,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[8,9,3,4,5,6,7,1,2]=>[8,9,3,4,5,6,7,1,2] [2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[8,9,2,3,4,5,6,7,1] [2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[8,9,1,2,3,4,5,6,7] [3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[7,8,9,6,5,4,3,2,1] [3,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,1,2,3]=>[7,8,9,6,5,4,3,1,2] [3,2,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,1,2,3]=>[7,8,9,5,6,4,3,2,1] [3,2,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,1,2,3]=>[7,8,9,5,6,3,4,1,2] [3,3,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,6,1,2,3]=>[7,8,9,4,5,6,3,2,1] [3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[7,8,9,4,5,6,1,2,3]=>[7,8,9,4,5,6,1,2,3] [3,4,2]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[8,9,4,5,6,7,1,2,3]=>[7,8,9,3,4,5,6,1,2] [3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[7,8,9,1,2,3,4,5,6] [4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[6,7,8,9,5,4,3,2,1] [4,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,1,2,3,4]=>[6,7,8,9,5,1,2,3,4] [4,2,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,1,2,3,4]=>[6,7,8,9,4,5,3,2,1] [4,2,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,1,2,3,4]=>[6,7,8,9,4,5,2,3,1] [4,3,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[9,8,5,6,7,1,2,3,4]=>[6,7,8,9,3,4,5,2,1] [4,3,2]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[8,9,5,6,7,1,2,3,4]=>[6,7,8,9,3,4,5,1,2] [4,4,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,6,7,8,1,2,3,4]=>[6,7,8,9,2,3,4,5,1] [4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[6,7,8,9,1,2,3,4,5] [5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[5,6,7,8,9,4,3,2,1] [5,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,1,2,3,4,5]=>[5,6,7,8,9,4,1,2,3] [5,2,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,1,2,3,4,5]=>[5,6,7,8,9,3,4,2,1] [5,3,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,1,2,3,4,5]=>[5,6,7,8,9,2,3,4,1] [5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[5,6,7,8,9,1,2,3,4] [6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[4,5,6,7,8,9,3,2,1] [6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,8,1,2,3,4,5,6]=>[4,5,6,7,8,9,2,3,1] [6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,1,2,3] [7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,2,1] [7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,1,2] [8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1] [9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9] [1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1] [1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2] [1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,3,1] [1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3] [1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,4,2,1] [1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,4,1,2] [1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4] [1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,4,5,3,2,1] [1,1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,5,4,3,2,1]=>[10,9,8,7,6,4,5,2,3,1] [1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5] [1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1] [1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6] [1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,3,2,1]=>[10,9,8,6,7,5,4,3,2,1] [1,1,1,2,1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,4,5,3,2,1]=>[10,9,8,6,7,5,4,3,1,2] [1,1,1,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,4,5,3,2,1]=>[10,9,8,6,7,4,5,3,2,1] [1,1,1,2,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,3,2,1]=>[10,9,8,6,7,4,5,2,3,1] [1,1,1,3,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,4,5,6,3,2,1]=>[10,9,8,5,6,7,4,3,2,1] [1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7] [1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,4,2,1]=>[10,9,7,8,6,5,4,3,2,1] [1,1,2,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,2,1]=>[10,9,7,8,5,6,3,4,1,2] [1,1,5,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,3,4,5,6,7,2,1]=>[10,9,4,5,6,7,8,3,2,1] [1,1,7,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,9,2,1]=>[10,9,2,3,4,5,6,7,8,1] [1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8] [1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[10,8,9,7,6,5,4,3,2,1] [1,2,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,2,3,1]=>[10,8,9,7,6,5,4,3,1,2] [1,2,1,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,2,3,1]=>[10,8,9,7,6,5,4,2,3,1] [1,2,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,2,3,1]=>[10,8,9,6,7,5,4,3,2,1] [1,2,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,4,5,2,3,1]=>[10,8,9,6,7,4,5,3,2,1] [1,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[10,8,9,6,7,4,5,2,3,1] [1,2,3,4]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,4,5,6,2,3,1]=>[10,8,9,5,6,7,1,2,3,4] [1,2,7]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,2,3,1]=>[10,8,9,1,2,3,4,5,6,7] [1,3,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[8,9,10,5,6,7,2,3,4,1]=>[10,7,8,9,4,5,6,1,2,3] [1,3,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,2,3,4,1]=>[10,7,8,9,1,2,3,4,5,6] [1,4,5]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,2,3,4,5,1]=>[10,6,7,8,9,1,2,3,4,5] [1,7,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,2,3,4,5,6,7,8,1]=>[10,3,4,5,6,7,8,9,2,1] [1,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,2,3,4,5,6,7,8,1]=>[10,3,4,5,6,7,8,9,1,2] [1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,3,4,5,6,7,8,9,1] [1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9] [2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,2,1] [2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2] [2,1,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,2,3,1] [2,1,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,6,5,4,3,1,2]=>[9,10,8,7,6,5,3,4,2,1] [2,1,2,1,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,3,1,2]=>[9,10,8,6,7,5,4,3,2,1] [2,2,1,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,4,1,2]=>[9,10,7,8,6,5,4,3,2,1] [2,2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,3,4,1,2]=>[9,10,7,8,5,6,4,3,2,1] [2,2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,2,1] [2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,1,2] [2,6,1,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[10,9,3,4,5,6,7,8,1,2]=>[9,10,3,4,5,6,7,8,2,1] [2,6,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[9,10,3,4,5,6,7,8,1,2]=>[9,10,3,4,5,6,7,8,1,2] [2,7,1]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,9,1,2]=>[9,10,2,3,4,5,6,7,8,1] [2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[9,10,1,2,3,4,5,6,7,8] [3,1,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[8,9,10,7,6,5,4,3,2,1] [3,2,1,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,1,2,3]=>[8,9,10,6,7,5,4,3,2,1] [3,2,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,1,2,3]=>[8,9,10,6,7,4,5,2,3,1] [3,3,2,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,4,5,6,1,2,3]=>[8,9,10,5,6,7,3,4,1,2] [3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[8,9,10,1,2,3,4,5,6,7] [4,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[7,8,9,10,6,5,4,3,2,1] [4,2,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,1,2,3,4]=>[7,8,9,10,5,6,3,4,1,2] [4,3,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[8,9,10,5,6,7,1,2,3,4]=>[7,8,9,10,4,5,6,1,2,3] [4,4,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[10,9,5,6,7,8,1,2,3,4]=>[7,8,9,10,3,4,5,6,2,1] [4,4,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[9,10,5,6,7,8,1,2,3,4]=>[7,8,9,10,3,4,5,6,1,2] [4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[7,8,9,10,1,2,3,4,5,6] [5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[6,7,8,9,10,5,4,3,2,1] [5,1,4]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,1,2,3,4,5]=>[6,7,8,9,10,5,1,2,3,4] [5,2,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,1,2,3,4,5]=>[6,7,8,9,10,4,5,2,3,1] [5,4,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[10,6,7,8,9,1,2,3,4,5]=>[6,7,8,9,10,2,3,4,5,1] [5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[6,7,8,9,10,1,2,3,4,5] [6,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[5,6,7,8,9,10,4,3,2,1] [6,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[10,7,8,9,1,2,3,4,5,6]=>[5,6,7,8,9,10,2,3,4,1] [6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[5,6,7,8,9,10,1,2,3,4] [7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,3,2,1] [7,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[10,8,9,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,2,3,1] [7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,1,2,3] [8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,2,1] [8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,1,2] [9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1] [10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10] [1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10] [10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1] [2,2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[11,12,9,10,7,8,5,6,3,4,1,2] [1,2,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[12,10,11,8,9,6,7,4,5,2,3,1]=>[12,10,11,8,9,6,7,4,5,2,3,1] [1,8,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,2,3,4,5,6,7,8,9,1]=>[11,3,4,5,6,7,8,9,10,1,2] [1,1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2] [1,2,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[10,11,8,9,6,7,4,5,2,3,1]=>[11,9,10,7,8,5,6,3,4,1,2]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
inverse
Description
Sends a permutation to its inverse.