Identifier
Values
=>
[1]=>[1]=>0 [1,2]=>[1,2]=>0 [2,1]=>[2,1]=>1 [1,2,3]=>[1,2,3]=>0 [1,3,2]=>[1,3,2]=>2 [2,1,3]=>[2,1,3]=>1 [2,3,1]=>[1,3,2]=>2 [3,1,2]=>[3,1,2]=>1 [3,2,1]=>[3,2,1]=>2 [1,2,3,4]=>[1,2,3,4]=>0 [1,2,4,3]=>[1,2,4,3]=>3 [1,3,2,4]=>[1,3,2,4]=>2 [1,3,4,2]=>[1,2,4,3]=>3 [1,4,2,3]=>[1,4,2,3]=>2 [1,4,3,2]=>[1,4,3,2]=>3 [2,1,3,4]=>[2,1,3,4]=>1 [2,1,4,3]=>[2,1,4,3]=>4 [2,3,1,4]=>[1,3,2,4]=>2 [2,3,4,1]=>[1,2,4,3]=>3 [2,4,1,3]=>[2,4,1,3]=>3 [2,4,3,1]=>[1,4,3,2]=>3 [3,1,2,4]=>[3,1,2,4]=>1 [3,1,4,2]=>[2,1,4,3]=>4 [3,2,1,4]=>[3,2,1,4]=>2 [3,2,4,1]=>[2,1,4,3]=>4 [3,4,1,2]=>[2,4,1,3]=>3 [3,4,2,1]=>[1,4,3,2]=>3 [4,1,2,3]=>[4,1,2,3]=>1 [4,1,3,2]=>[4,1,3,2]=>2 [4,2,1,3]=>[4,2,1,3]=>2 [4,2,3,1]=>[4,1,3,2]=>2 [4,3,1,2]=>[4,3,1,2]=>4 [4,3,2,1]=>[4,3,2,1]=>5 [1,2,3,4,5]=>[1,2,3,4,5]=>0 [1,2,3,5,4]=>[1,2,3,5,4]=>4 [1,2,4,3,5]=>[1,2,4,3,5]=>3 [1,2,4,5,3]=>[1,2,3,5,4]=>4 [1,2,5,3,4]=>[1,2,5,3,4]=>3 [1,2,5,4,3]=>[1,2,5,4,3]=>4 [1,3,2,4,5]=>[1,3,2,4,5]=>2 [1,3,2,5,4]=>[1,3,2,5,4]=>6 [1,3,4,2,5]=>[1,2,4,3,5]=>3 [1,3,4,5,2]=>[1,2,3,5,4]=>4 [1,3,5,2,4]=>[1,3,5,2,4]=>5 [1,3,5,4,2]=>[1,2,5,4,3]=>4 [1,4,2,3,5]=>[1,4,2,3,5]=>2 [1,4,2,5,3]=>[1,3,2,5,4]=>6 [1,4,3,2,5]=>[1,4,3,2,5]=>3 [1,4,3,5,2]=>[1,3,2,5,4]=>6 [1,4,5,2,3]=>[1,3,5,2,4]=>5 [1,4,5,3,2]=>[1,2,5,4,3]=>4 [1,5,2,3,4]=>[1,5,2,3,4]=>2 [1,5,2,4,3]=>[1,5,2,4,3]=>3 [1,5,3,2,4]=>[1,5,3,2,4]=>3 [1,5,3,4,2]=>[1,5,2,4,3]=>3 [1,5,4,2,3]=>[1,5,4,2,3]=>6 [1,5,4,3,2]=>[1,5,4,3,2]=>7 [2,1,3,4,5]=>[2,1,3,4,5]=>1 [2,1,3,5,4]=>[2,1,3,5,4]=>5 [2,1,4,3,5]=>[2,1,4,3,5]=>4 [2,1,4,5,3]=>[2,1,3,5,4]=>5 [2,1,5,3,4]=>[2,1,5,3,4]=>4 [2,1,5,4,3]=>[2,1,5,4,3]=>5 [2,3,1,4,5]=>[1,3,2,4,5]=>2 [2,3,1,5,4]=>[1,3,2,5,4]=>6 [2,3,4,1,5]=>[1,2,4,3,5]=>3 [2,3,4,5,1]=>[1,2,3,5,4]=>4 [2,3,5,1,4]=>[1,3,5,2,4]=>5 [2,3,5,4,1]=>[1,2,5,4,3]=>4 [2,4,1,3,5]=>[2,4,1,3,5]=>3 [2,4,1,5,3]=>[1,3,2,5,4]=>6 [2,4,3,1,5]=>[1,4,3,2,5]=>3 [2,4,3,5,1]=>[1,3,2,5,4]=>6 [2,4,5,1,3]=>[1,3,5,2,4]=>5 [2,4,5,3,1]=>[1,2,5,4,3]=>4 [2,5,1,3,4]=>[2,5,1,3,4]=>3 [2,5,1,4,3]=>[2,5,1,4,3]=>4 [2,5,3,1,4]=>[1,5,3,2,4]=>3 [2,5,3,4,1]=>[1,5,2,4,3]=>3 [2,5,4,1,3]=>[2,5,4,1,3]=>7 [2,5,4,3,1]=>[1,5,4,3,2]=>7 [3,1,2,4,5]=>[3,1,2,4,5]=>1 [3,1,2,5,4]=>[3,1,2,5,4]=>5 [3,1,4,2,5]=>[2,1,4,3,5]=>4 [3,1,4,5,2]=>[2,1,3,5,4]=>5 [3,1,5,2,4]=>[3,1,5,2,4]=>4 [3,1,5,4,2]=>[2,1,5,4,3]=>5 [3,2,1,4,5]=>[3,2,1,4,5]=>2 [3,2,1,5,4]=>[3,2,1,5,4]=>6 [3,2,4,1,5]=>[2,1,4,3,5]=>4 [3,2,4,5,1]=>[2,1,3,5,4]=>5 [3,2,5,1,4]=>[3,2,5,1,4]=>5 [3,2,5,4,1]=>[2,1,5,4,3]=>5 [3,4,1,2,5]=>[2,4,1,3,5]=>3 [3,4,1,5,2]=>[1,3,2,5,4]=>6 [3,4,2,1,5]=>[1,4,3,2,5]=>3 [3,4,2,5,1]=>[1,3,2,5,4]=>6 [3,4,5,1,2]=>[1,3,5,2,4]=>5 [3,4,5,2,1]=>[1,2,5,4,3]=>4 [3,5,1,2,4]=>[3,5,1,2,4]=>3 [3,5,1,4,2]=>[2,5,1,4,3]=>4 [3,5,2,1,4]=>[3,5,2,1,4]=>4 [3,5,2,4,1]=>[2,5,1,4,3]=>4 [3,5,4,1,2]=>[2,5,4,1,3]=>7 [3,5,4,2,1]=>[1,5,4,3,2]=>7 [4,1,2,3,5]=>[4,1,2,3,5]=>1 [4,1,2,5,3]=>[3,1,2,5,4]=>5 [4,1,3,2,5]=>[4,1,3,2,5]=>2 [4,1,3,5,2]=>[3,1,2,5,4]=>5 [4,1,5,2,3]=>[3,1,5,2,4]=>4 [4,1,5,3,2]=>[2,1,5,4,3]=>5 [4,2,1,3,5]=>[4,2,1,3,5]=>2 [4,2,1,5,3]=>[3,2,1,5,4]=>6 [4,2,3,1,5]=>[4,1,3,2,5]=>2 [4,2,3,5,1]=>[3,1,2,5,4]=>5 [4,2,5,1,3]=>[3,2,5,1,4]=>5 [4,2,5,3,1]=>[2,1,5,4,3]=>5 [4,3,1,2,5]=>[4,3,1,2,5]=>4 [4,3,1,5,2]=>[3,2,1,5,4]=>6 [4,3,2,1,5]=>[4,3,2,1,5]=>5 [4,3,2,5,1]=>[3,2,1,5,4]=>6 [4,3,5,1,2]=>[3,2,5,1,4]=>5 [4,3,5,2,1]=>[2,1,5,4,3]=>5 [4,5,1,2,3]=>[3,5,1,2,4]=>3 [4,5,1,3,2]=>[2,5,1,4,3]=>4 [4,5,2,1,3]=>[3,5,2,1,4]=>4 [4,5,2,3,1]=>[2,5,1,4,3]=>4 [4,5,3,1,2]=>[2,5,4,1,3]=>7 [4,5,3,2,1]=>[1,5,4,3,2]=>7 [5,1,2,3,4]=>[5,1,2,3,4]=>1 [5,1,2,4,3]=>[5,1,2,4,3]=>2 [5,1,3,2,4]=>[5,1,3,2,4]=>2 [5,1,3,4,2]=>[5,1,2,4,3]=>2 [5,1,4,2,3]=>[5,1,4,2,3]=>5 [5,1,4,3,2]=>[5,1,4,3,2]=>6 [5,2,1,3,4]=>[5,2,1,3,4]=>2 [5,2,1,4,3]=>[5,2,1,4,3]=>3 [5,2,3,1,4]=>[5,1,3,2,4]=>2 [5,2,3,4,1]=>[5,1,2,4,3]=>2 [5,2,4,1,3]=>[5,2,4,1,3]=>6 [5,2,4,3,1]=>[5,1,4,3,2]=>6 [5,3,1,2,4]=>[5,3,1,2,4]=>4 [5,3,1,4,2]=>[5,2,1,4,3]=>3 [5,3,2,1,4]=>[5,3,2,1,4]=>5 [5,3,2,4,1]=>[5,2,1,4,3]=>3 [5,3,4,1,2]=>[5,2,4,1,3]=>6 [5,3,4,2,1]=>[5,1,4,3,2]=>6 [5,4,1,2,3]=>[5,4,1,2,3]=>4 [5,4,1,3,2]=>[5,4,1,3,2]=>5 [5,4,2,1,3]=>[5,4,2,1,3]=>5 [5,4,2,3,1]=>[5,4,1,3,2]=>5 [5,4,3,1,2]=>[5,4,3,1,2]=>6 [5,4,3,2,1]=>[5,4,3,2,1]=>7 [1,2,3,4,5,6]=>[1,2,3,4,5,6]=>0 [1,2,3,4,6,5]=>[1,2,3,4,6,5]=>5 [1,2,3,5,4,6]=>[1,2,3,5,4,6]=>4 [1,2,3,5,6,4]=>[1,2,3,4,6,5]=>5 [1,2,3,6,4,5]=>[1,2,3,6,4,5]=>4 [1,2,3,6,5,4]=>[1,2,3,6,5,4]=>5 [1,2,4,3,5,6]=>[1,2,4,3,5,6]=>3 [1,2,4,3,6,5]=>[1,2,4,3,6,5]=>8 [1,2,4,5,3,6]=>[1,2,3,5,4,6]=>4 [1,2,4,5,6,3]=>[1,2,3,4,6,5]=>5 [1,2,4,6,3,5]=>[1,2,4,6,3,5]=>7 [1,2,4,6,5,3]=>[1,2,3,6,5,4]=>5 [1,2,5,3,4,6]=>[1,2,5,3,4,6]=>3 [1,2,5,3,6,4]=>[1,2,4,3,6,5]=>8 [1,2,5,4,3,6]=>[1,2,5,4,3,6]=>4 [1,2,5,4,6,3]=>[1,2,4,3,6,5]=>8 [1,2,5,6,3,4]=>[1,2,4,6,3,5]=>7 [1,2,5,6,4,3]=>[1,2,3,6,5,4]=>5 [1,2,6,3,4,5]=>[1,2,6,3,4,5]=>3 [1,2,6,3,5,4]=>[1,2,6,3,5,4]=>4 [1,2,6,4,3,5]=>[1,2,6,4,3,5]=>4 [1,2,6,4,5,3]=>[1,2,6,3,5,4]=>4 [1,2,6,5,3,4]=>[1,2,6,5,3,4]=>8 [1,2,6,5,4,3]=>[1,2,6,5,4,3]=>9 [1,3,2,4,5,6]=>[1,3,2,4,5,6]=>2 [1,3,2,4,6,5]=>[1,3,2,4,6,5]=>7 [1,3,2,5,4,6]=>[1,3,2,5,4,6]=>6 [1,3,2,5,6,4]=>[1,3,2,4,6,5]=>7 [1,3,2,6,4,5]=>[1,3,2,6,4,5]=>6 [1,3,2,6,5,4]=>[1,3,2,6,5,4]=>7 [1,3,4,2,5,6]=>[1,2,4,3,5,6]=>3 [1,3,4,2,6,5]=>[1,2,4,3,6,5]=>8 [1,3,4,5,2,6]=>[1,2,3,5,4,6]=>4 [1,3,4,5,6,2]=>[1,2,3,4,6,5]=>5 [1,3,4,6,2,5]=>[1,2,4,6,3,5]=>7 [1,3,4,6,5,2]=>[1,2,3,6,5,4]=>5 [1,3,5,2,4,6]=>[1,3,5,2,4,6]=>5 [1,3,5,2,6,4]=>[1,2,4,3,6,5]=>8 [1,3,5,4,2,6]=>[1,2,5,4,3,6]=>4 [1,3,5,4,6,2]=>[1,2,4,3,6,5]=>8 [1,3,5,6,2,4]=>[1,2,4,6,3,5]=>7 [1,3,5,6,4,2]=>[1,2,3,6,5,4]=>5 [1,3,6,2,4,5]=>[1,3,6,2,4,5]=>5 [1,3,6,2,5,4]=>[1,3,6,2,5,4]=>6 [1,3,6,4,2,5]=>[1,2,6,4,3,5]=>4 [1,3,6,4,5,2]=>[1,2,6,3,5,4]=>4 [1,3,6,5,2,4]=>[1,3,6,5,2,4]=>10 [1,3,6,5,4,2]=>[1,2,6,5,4,3]=>9 [1,4,2,3,5,6]=>[1,4,2,3,5,6]=>2 [1,4,2,3,6,5]=>[1,4,2,3,6,5]=>7 [1,4,2,5,3,6]=>[1,3,2,5,4,6]=>6 [1,4,2,5,6,3]=>[1,3,2,4,6,5]=>7 [1,4,2,6,3,5]=>[1,4,2,6,3,5]=>6 [1,4,2,6,5,3]=>[1,3,2,6,5,4]=>7 [1,4,3,2,5,6]=>[1,4,3,2,5,6]=>3 [1,4,3,2,6,5]=>[1,4,3,2,6,5]=>8 [1,4,3,5,2,6]=>[1,3,2,5,4,6]=>6 [1,4,3,5,6,2]=>[1,3,2,4,6,5]=>7 [1,4,3,6,2,5]=>[1,4,3,6,2,5]=>7 [1,4,3,6,5,2]=>[1,3,2,6,5,4]=>7 [1,4,5,2,3,6]=>[1,3,5,2,4,6]=>5 [1,4,5,2,6,3]=>[1,2,4,3,6,5]=>8 [1,4,5,3,2,6]=>[1,2,5,4,3,6]=>4 [1,4,5,3,6,2]=>[1,2,4,3,6,5]=>8 [1,4,5,6,2,3]=>[1,2,4,6,3,5]=>7 [1,4,5,6,3,2]=>[1,2,3,6,5,4]=>5 [1,4,6,2,3,5]=>[1,4,6,2,3,5]=>5 [1,4,6,2,5,3]=>[1,3,6,2,5,4]=>6 [1,4,6,3,2,5]=>[1,4,6,3,2,5]=>6 [1,4,6,3,5,2]=>[1,3,6,2,5,4]=>6 [1,4,6,5,2,3]=>[1,3,6,5,2,4]=>10 [1,4,6,5,3,2]=>[1,2,6,5,4,3]=>9 [1,5,2,3,4,6]=>[1,5,2,3,4,6]=>2 [1,5,2,3,6,4]=>[1,4,2,3,6,5]=>7 [1,5,2,4,3,6]=>[1,5,2,4,3,6]=>3 [1,5,2,4,6,3]=>[1,4,2,3,6,5]=>7 [1,5,2,6,3,4]=>[1,4,2,6,3,5]=>6 [1,5,2,6,4,3]=>[1,3,2,6,5,4]=>7 [1,5,3,2,4,6]=>[1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>[1,4,3,2,6,5]=>8 [1,5,3,4,2,6]=>[1,5,2,4,3,6]=>3 [1,5,3,4,6,2]=>[1,4,2,3,6,5]=>7 [1,5,3,6,2,4]=>[1,4,3,6,2,5]=>7 [1,5,3,6,4,2]=>[1,3,2,6,5,4]=>7 [1,5,4,2,3,6]=>[1,5,4,2,3,6]=>6 [1,5,4,2,6,3]=>[1,4,3,2,6,5]=>8 [1,5,4,3,2,6]=>[1,5,4,3,2,6]=>7 [1,5,4,3,6,2]=>[1,4,3,2,6,5]=>8 [1,5,4,6,2,3]=>[1,4,3,6,2,5]=>7 [1,5,4,6,3,2]=>[1,3,2,6,5,4]=>7 [1,5,6,2,3,4]=>[1,4,6,2,3,5]=>5 [1,5,6,2,4,3]=>[1,3,6,2,5,4]=>6 [1,5,6,3,2,4]=>[1,4,6,3,2,5]=>6 [1,5,6,3,4,2]=>[1,3,6,2,5,4]=>6 [1,5,6,4,2,3]=>[1,3,6,5,2,4]=>10 [1,5,6,4,3,2]=>[1,2,6,5,4,3]=>9 [1,6,2,3,4,5]=>[1,6,2,3,4,5]=>2 [1,6,2,3,5,4]=>[1,6,2,3,5,4]=>3 [1,6,2,4,3,5]=>[1,6,2,4,3,5]=>3 [1,6,2,4,5,3]=>[1,6,2,3,5,4]=>3 [1,6,2,5,3,4]=>[1,6,2,5,3,4]=>7 [1,6,2,5,4,3]=>[1,6,2,5,4,3]=>8 [1,6,3,2,4,5]=>[1,6,3,2,4,5]=>3 [1,6,3,2,5,4]=>[1,6,3,2,5,4]=>4 [1,6,3,4,2,5]=>[1,6,2,4,3,5]=>3 [1,6,3,4,5,2]=>[1,6,2,3,5,4]=>3 [1,6,3,5,2,4]=>[1,6,3,5,2,4]=>8 [1,6,3,5,4,2]=>[1,6,2,5,4,3]=>8 [1,6,4,2,3,5]=>[1,6,4,2,3,5]=>6 [1,6,4,2,5,3]=>[1,6,3,2,5,4]=>4 [1,6,4,3,2,5]=>[1,6,4,3,2,5]=>7 [1,6,4,3,5,2]=>[1,6,3,2,5,4]=>4 [1,6,4,5,2,3]=>[1,6,3,5,2,4]=>8 [1,6,4,5,3,2]=>[1,6,2,5,4,3]=>8 [1,6,5,2,3,4]=>[1,6,5,2,3,4]=>6 [1,6,5,2,4,3]=>[1,6,5,2,4,3]=>7 [1,6,5,3,2,4]=>[1,6,5,3,2,4]=>7 [1,6,5,3,4,2]=>[1,6,5,2,4,3]=>7 [1,6,5,4,2,3]=>[1,6,5,4,2,3]=>8 [1,6,5,4,3,2]=>[1,6,5,4,3,2]=>9 [2,1,3,4,5,6]=>[2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>[2,1,3,4,6,5]=>6 [2,1,3,5,4,6]=>[2,1,3,5,4,6]=>5 [2,1,3,5,6,4]=>[2,1,3,4,6,5]=>6 [2,1,3,6,4,5]=>[2,1,3,6,4,5]=>5 [2,1,3,6,5,4]=>[2,1,3,6,5,4]=>6 [2,1,4,3,5,6]=>[2,1,4,3,5,6]=>4 [2,1,4,3,6,5]=>[2,1,4,3,6,5]=>9 [2,1,4,5,3,6]=>[2,1,3,5,4,6]=>5 [2,1,4,5,6,3]=>[2,1,3,4,6,5]=>6 [2,1,4,6,3,5]=>[2,1,4,6,3,5]=>8 [2,1,4,6,5,3]=>[2,1,3,6,5,4]=>6 [2,1,5,3,4,6]=>[2,1,5,3,4,6]=>4 [2,1,5,3,6,4]=>[2,1,4,3,6,5]=>9 [2,1,5,4,3,6]=>[2,1,5,4,3,6]=>5 [2,1,5,4,6,3]=>[2,1,4,3,6,5]=>9 [2,1,5,6,3,4]=>[2,1,4,6,3,5]=>8 [2,1,5,6,4,3]=>[2,1,3,6,5,4]=>6 [2,1,6,3,4,5]=>[2,1,6,3,4,5]=>4 [2,1,6,3,5,4]=>[2,1,6,3,5,4]=>5 [2,1,6,4,3,5]=>[2,1,6,4,3,5]=>5 [2,1,6,4,5,3]=>[2,1,6,3,5,4]=>5 [2,1,6,5,3,4]=>[2,1,6,5,3,4]=>9 [2,1,6,5,4,3]=>[2,1,6,5,4,3]=>10 [2,3,1,4,5,6]=>[1,3,2,4,5,6]=>2 [2,3,1,4,6,5]=>[1,3,2,4,6,5]=>7 [2,3,1,5,4,6]=>[1,3,2,5,4,6]=>6 [2,3,1,5,6,4]=>[1,3,2,4,6,5]=>7 [2,3,1,6,4,5]=>[1,3,2,6,4,5]=>6 [2,3,1,6,5,4]=>[1,3,2,6,5,4]=>7 [2,3,4,1,5,6]=>[1,2,4,3,5,6]=>3 [2,3,4,1,6,5]=>[1,2,4,3,6,5]=>8 [2,3,4,5,1,6]=>[1,2,3,5,4,6]=>4 [2,3,4,5,6,1]=>[1,2,3,4,6,5]=>5 [2,3,4,6,1,5]=>[1,2,4,6,3,5]=>7 [2,3,4,6,5,1]=>[1,2,3,6,5,4]=>5 [2,3,5,1,4,6]=>[1,3,5,2,4,6]=>5 [2,3,5,1,6,4]=>[1,2,4,3,6,5]=>8 [2,3,5,4,1,6]=>[1,2,5,4,3,6]=>4 [2,3,5,4,6,1]=>[1,2,4,3,6,5]=>8 [2,3,5,6,1,4]=>[1,2,4,6,3,5]=>7 [2,3,5,6,4,1]=>[1,2,3,6,5,4]=>5 [2,3,6,1,4,5]=>[1,3,6,2,4,5]=>5 [2,3,6,1,5,4]=>[1,3,6,2,5,4]=>6 [2,3,6,4,1,5]=>[1,2,6,4,3,5]=>4 [2,3,6,4,5,1]=>[1,2,6,3,5,4]=>4 [2,3,6,5,1,4]=>[1,3,6,5,2,4]=>10 [2,3,6,5,4,1]=>[1,2,6,5,4,3]=>9 [2,4,1,3,5,6]=>[2,4,1,3,5,6]=>3 [2,4,1,3,6,5]=>[2,4,1,3,6,5]=>8 [2,4,1,5,3,6]=>[1,3,2,5,4,6]=>6 [2,4,1,5,6,3]=>[1,3,2,4,6,5]=>7 [2,4,1,6,3,5]=>[2,4,1,6,3,5]=>7 [2,4,1,6,5,3]=>[1,3,2,6,5,4]=>7 [2,4,3,1,5,6]=>[1,4,3,2,5,6]=>3 [2,4,3,1,6,5]=>[1,4,3,2,6,5]=>8 [2,4,3,5,1,6]=>[1,3,2,5,4,6]=>6 [2,4,3,5,6,1]=>[1,3,2,4,6,5]=>7 [2,4,3,6,1,5]=>[1,4,3,6,2,5]=>7 [2,4,3,6,5,1]=>[1,3,2,6,5,4]=>7 [2,4,5,1,3,6]=>[1,3,5,2,4,6]=>5 [2,4,5,1,6,3]=>[1,2,4,3,6,5]=>8 [2,4,5,3,1,6]=>[1,2,5,4,3,6]=>4 [2,4,5,3,6,1]=>[1,2,4,3,6,5]=>8 [2,4,5,6,1,3]=>[1,2,4,6,3,5]=>7 [2,4,5,6,3,1]=>[1,2,3,6,5,4]=>5 [2,4,6,1,3,5]=>[2,4,6,1,3,5]=>6 [2,4,6,1,5,3]=>[1,3,6,2,5,4]=>6 [2,4,6,3,1,5]=>[1,4,6,3,2,5]=>6 [2,4,6,3,5,1]=>[1,3,6,2,5,4]=>6 [2,4,6,5,1,3]=>[1,3,6,5,2,4]=>10 [2,4,6,5,3,1]=>[1,2,6,5,4,3]=>9 [2,5,1,3,4,6]=>[2,5,1,3,4,6]=>3 [2,5,1,3,6,4]=>[2,4,1,3,6,5]=>8 [2,5,1,4,3,6]=>[2,5,1,4,3,6]=>4 [2,5,1,4,6,3]=>[2,4,1,3,6,5]=>8 [2,5,1,6,3,4]=>[2,4,1,6,3,5]=>7 [2,5,1,6,4,3]=>[1,3,2,6,5,4]=>7 [2,5,3,1,4,6]=>[1,5,3,2,4,6]=>3 [2,5,3,1,6,4]=>[1,4,3,2,6,5]=>8 [2,5,3,4,1,6]=>[1,5,2,4,3,6]=>3 [2,5,3,4,6,1]=>[1,4,2,3,6,5]=>7 [2,5,3,6,1,4]=>[1,4,3,6,2,5]=>7 [2,5,3,6,4,1]=>[1,3,2,6,5,4]=>7 [2,5,4,1,3,6]=>[2,5,4,1,3,6]=>7 [2,5,4,1,6,3]=>[1,4,3,2,6,5]=>8 [2,5,4,3,1,6]=>[1,5,4,3,2,6]=>7 [2,5,4,3,6,1]=>[1,4,3,2,6,5]=>8 [2,5,4,6,1,3]=>[1,4,3,6,2,5]=>7 [2,5,4,6,3,1]=>[1,3,2,6,5,4]=>7 [2,5,6,1,3,4]=>[2,4,6,1,3,5]=>6 [2,5,6,1,4,3]=>[1,3,6,2,5,4]=>6 [2,5,6,3,1,4]=>[1,4,6,3,2,5]=>6 [2,5,6,3,4,1]=>[1,3,6,2,5,4]=>6 [2,5,6,4,1,3]=>[1,3,6,5,2,4]=>10 [2,5,6,4,3,1]=>[1,2,6,5,4,3]=>9 [2,6,1,3,4,5]=>[2,6,1,3,4,5]=>3 [2,6,1,3,5,4]=>[2,6,1,3,5,4]=>4 [2,6,1,4,3,5]=>[2,6,1,4,3,5]=>4 [2,6,1,4,5,3]=>[2,6,1,3,5,4]=>4 [2,6,1,5,3,4]=>[2,6,1,5,3,4]=>8 [2,6,1,5,4,3]=>[2,6,1,5,4,3]=>9 [2,6,3,1,4,5]=>[1,6,3,2,4,5]=>3 [2,6,3,1,5,4]=>[1,6,3,2,5,4]=>4 [2,6,3,4,1,5]=>[1,6,2,4,3,5]=>3 [2,6,3,4,5,1]=>[1,6,2,3,5,4]=>3 [2,6,3,5,1,4]=>[1,6,3,5,2,4]=>8 [2,6,3,5,4,1]=>[1,6,2,5,4,3]=>8 [2,6,4,1,3,5]=>[2,6,4,1,3,5]=>7 [2,6,4,1,5,3]=>[1,6,3,2,5,4]=>4 [2,6,4,3,1,5]=>[1,6,4,3,2,5]=>7 [2,6,4,3,5,1]=>[1,6,3,2,5,4]=>4 [2,6,4,5,1,3]=>[1,6,3,5,2,4]=>8 [2,6,4,5,3,1]=>[1,6,2,5,4,3]=>8 [2,6,5,1,3,4]=>[2,6,5,1,3,4]=>7 [2,6,5,1,4,3]=>[2,6,5,1,4,3]=>8 [2,6,5,3,1,4]=>[1,6,5,3,2,4]=>7 [2,6,5,3,4,1]=>[1,6,5,2,4,3]=>7 [2,6,5,4,1,3]=>[2,6,5,4,1,3]=>9 [2,6,5,4,3,1]=>[1,6,5,4,3,2]=>9 [3,1,2,4,5,6]=>[3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>[3,1,2,4,6,5]=>6 [3,1,2,5,4,6]=>[3,1,2,5,4,6]=>5 [3,1,2,5,6,4]=>[3,1,2,4,6,5]=>6 [3,1,2,6,4,5]=>[3,1,2,6,4,5]=>5 [3,1,2,6,5,4]=>[3,1,2,6,5,4]=>6 [3,1,4,2,5,6]=>[2,1,4,3,5,6]=>4 [3,1,4,2,6,5]=>[2,1,4,3,6,5]=>9 [3,1,4,5,2,6]=>[2,1,3,5,4,6]=>5 [3,1,4,5,6,2]=>[2,1,3,4,6,5]=>6 [3,1,4,6,2,5]=>[2,1,4,6,3,5]=>8 [3,1,4,6,5,2]=>[2,1,3,6,5,4]=>6 [3,1,5,2,4,6]=>[3,1,5,2,4,6]=>4 [3,1,5,2,6,4]=>[2,1,4,3,6,5]=>9 [3,1,5,4,2,6]=>[2,1,5,4,3,6]=>5 [3,1,5,4,6,2]=>[2,1,4,3,6,5]=>9 [3,1,5,6,2,4]=>[2,1,4,6,3,5]=>8 [3,1,5,6,4,2]=>[2,1,3,6,5,4]=>6 [3,1,6,2,4,5]=>[3,1,6,2,4,5]=>4 [3,1,6,2,5,4]=>[3,1,6,2,5,4]=>5 [3,1,6,4,2,5]=>[2,1,6,4,3,5]=>5 [3,1,6,4,5,2]=>[2,1,6,3,5,4]=>5 [3,1,6,5,2,4]=>[3,1,6,5,2,4]=>9 [3,1,6,5,4,2]=>[2,1,6,5,4,3]=>10 [3,2,1,4,5,6]=>[3,2,1,4,5,6]=>2 [3,2,1,4,6,5]=>[3,2,1,4,6,5]=>7 [3,2,1,5,4,6]=>[3,2,1,5,4,6]=>6 [3,2,1,5,6,4]=>[3,2,1,4,6,5]=>7 [3,2,1,6,4,5]=>[3,2,1,6,4,5]=>6 [3,2,1,6,5,4]=>[3,2,1,6,5,4]=>7 [3,2,4,1,5,6]=>[2,1,4,3,5,6]=>4 [3,2,4,1,6,5]=>[2,1,4,3,6,5]=>9 [3,2,4,5,1,6]=>[2,1,3,5,4,6]=>5 [3,2,4,5,6,1]=>[2,1,3,4,6,5]=>6 [3,2,4,6,1,5]=>[2,1,4,6,3,5]=>8 [3,2,4,6,5,1]=>[2,1,3,6,5,4]=>6 [3,2,5,1,4,6]=>[3,2,5,1,4,6]=>5 [3,2,5,1,6,4]=>[2,1,4,3,6,5]=>9 [3,2,5,4,1,6]=>[2,1,5,4,3,6]=>5 [3,2,5,4,6,1]=>[2,1,4,3,6,5]=>9 [3,2,5,6,1,4]=>[2,1,4,6,3,5]=>8 [3,2,5,6,4,1]=>[2,1,3,6,5,4]=>6 [3,2,6,1,4,5]=>[3,2,6,1,4,5]=>5 [3,2,6,1,5,4]=>[3,2,6,1,5,4]=>6 [3,2,6,4,1,5]=>[2,1,6,4,3,5]=>5 [3,2,6,4,5,1]=>[2,1,6,3,5,4]=>5 [3,2,6,5,1,4]=>[3,2,6,5,1,4]=>10 [3,2,6,5,4,1]=>[2,1,6,5,4,3]=>10 [3,4,1,2,5,6]=>[2,4,1,3,5,6]=>3 [3,4,1,2,6,5]=>[2,4,1,3,6,5]=>8 [3,4,1,5,2,6]=>[1,3,2,5,4,6]=>6 [3,4,1,5,6,2]=>[1,3,2,4,6,5]=>7 [3,4,1,6,2,5]=>[2,4,1,6,3,5]=>7 [3,4,1,6,5,2]=>[1,3,2,6,5,4]=>7 [3,4,2,1,5,6]=>[1,4,3,2,5,6]=>3 [3,4,2,1,6,5]=>[1,4,3,2,6,5]=>8 [3,4,2,5,1,6]=>[1,3,2,5,4,6]=>6 [3,4,2,5,6,1]=>[1,3,2,4,6,5]=>7 [3,4,2,6,1,5]=>[1,4,3,6,2,5]=>7 [3,4,2,6,5,1]=>[1,3,2,6,5,4]=>7 [3,4,5,1,2,6]=>[1,3,5,2,4,6]=>5 [3,4,5,1,6,2]=>[1,2,4,3,6,5]=>8 [3,4,5,2,1,6]=>[1,2,5,4,3,6]=>4 [3,4,5,2,6,1]=>[1,2,4,3,6,5]=>8 [3,4,5,6,1,2]=>[1,2,4,6,3,5]=>7 [3,4,5,6,2,1]=>[1,2,3,6,5,4]=>5 [3,4,6,1,2,5]=>[2,4,6,1,3,5]=>6 [3,4,6,1,5,2]=>[1,3,6,2,5,4]=>6 [3,4,6,2,1,5]=>[1,4,6,3,2,5]=>6 [3,4,6,2,5,1]=>[1,3,6,2,5,4]=>6 [3,4,6,5,1,2]=>[1,3,6,5,2,4]=>10 [3,4,6,5,2,1]=>[1,2,6,5,4,3]=>9 [3,5,1,2,4,6]=>[3,5,1,2,4,6]=>3 [3,5,1,2,6,4]=>[2,4,1,3,6,5]=>8 [3,5,1,4,2,6]=>[2,5,1,4,3,6]=>4 [3,5,1,4,6,2]=>[2,4,1,3,6,5]=>8 [3,5,1,6,2,4]=>[2,4,1,6,3,5]=>7 [3,5,1,6,4,2]=>[1,3,2,6,5,4]=>7 [3,5,2,1,4,6]=>[3,5,2,1,4,6]=>4 [3,5,2,1,6,4]=>[1,4,3,2,6,5]=>8 [3,5,2,4,1,6]=>[2,5,1,4,3,6]=>4 [3,5,2,4,6,1]=>[2,4,1,3,6,5]=>8 [3,5,2,6,1,4]=>[1,4,3,6,2,5]=>7 [3,5,2,6,4,1]=>[1,3,2,6,5,4]=>7 [3,5,4,1,2,6]=>[2,5,4,1,3,6]=>7 [3,5,4,1,6,2]=>[1,4,3,2,6,5]=>8 [3,5,4,2,1,6]=>[1,5,4,3,2,6]=>7 [3,5,4,2,6,1]=>[1,4,3,2,6,5]=>8 [3,5,4,6,1,2]=>[1,4,3,6,2,5]=>7 [3,5,4,6,2,1]=>[1,3,2,6,5,4]=>7 [3,5,6,1,2,4]=>[2,4,6,1,3,5]=>6 [3,5,6,1,4,2]=>[1,3,6,2,5,4]=>6 [3,5,6,2,1,4]=>[1,4,6,3,2,5]=>6 [3,5,6,2,4,1]=>[1,3,6,2,5,4]=>6 [3,5,6,4,1,2]=>[1,3,6,5,2,4]=>10 [3,5,6,4,2,1]=>[1,2,6,5,4,3]=>9 [3,6,1,2,4,5]=>[3,6,1,2,4,5]=>3 [3,6,1,2,5,4]=>[3,6,1,2,5,4]=>4 [3,6,1,4,2,5]=>[2,6,1,4,3,5]=>4 [3,6,1,4,5,2]=>[2,6,1,3,5,4]=>4 [3,6,1,5,2,4]=>[3,6,1,5,2,4]=>8 [3,6,1,5,4,2]=>[2,6,1,5,4,3]=>9 [3,6,2,1,4,5]=>[3,6,2,1,4,5]=>4 [3,6,2,1,5,4]=>[3,6,2,1,5,4]=>5 [3,6,2,4,1,5]=>[2,6,1,4,3,5]=>4 [3,6,2,4,5,1]=>[2,6,1,3,5,4]=>4 [3,6,2,5,1,4]=>[3,6,2,5,1,4]=>9 [3,6,2,5,4,1]=>[2,6,1,5,4,3]=>9 [3,6,4,1,2,5]=>[2,6,4,1,3,5]=>7 [3,6,4,1,5,2]=>[1,6,3,2,5,4]=>4 [3,6,4,2,1,5]=>[1,6,4,3,2,5]=>7 [3,6,4,2,5,1]=>[1,6,3,2,5,4]=>4 [3,6,4,5,1,2]=>[1,6,3,5,2,4]=>8 [3,6,4,5,2,1]=>[1,6,2,5,4,3]=>8 [3,6,5,1,2,4]=>[3,6,5,1,2,4]=>7 [3,6,5,1,4,2]=>[2,6,5,1,4,3]=>8 [3,6,5,2,1,4]=>[3,6,5,2,1,4]=>8 [3,6,5,2,4,1]=>[2,6,5,1,4,3]=>8 [3,6,5,4,1,2]=>[2,6,5,4,1,3]=>9 [3,6,5,4,2,1]=>[1,6,5,4,3,2]=>9 [4,1,2,3,5,6]=>[4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>[4,1,2,3,6,5]=>6 [4,1,2,5,3,6]=>[3,1,2,5,4,6]=>5 [4,1,2,5,6,3]=>[3,1,2,4,6,5]=>6 [4,1,2,6,3,5]=>[4,1,2,6,3,5]=>5 [4,1,2,6,5,3]=>[3,1,2,6,5,4]=>6 [4,1,3,2,5,6]=>[4,1,3,2,5,6]=>2 [4,1,3,2,6,5]=>[4,1,3,2,6,5]=>7 [4,1,3,5,2,6]=>[3,1,2,5,4,6]=>5 [4,1,3,5,6,2]=>[3,1,2,4,6,5]=>6 [4,1,3,6,2,5]=>[4,1,3,6,2,5]=>6 [4,1,3,6,5,2]=>[3,1,2,6,5,4]=>6 [4,1,5,2,3,6]=>[3,1,5,2,4,6]=>4 [4,1,5,2,6,3]=>[2,1,4,3,6,5]=>9 [4,1,5,3,2,6]=>[2,1,5,4,3,6]=>5 [4,1,5,3,6,2]=>[2,1,4,3,6,5]=>9 [4,1,5,6,2,3]=>[2,1,4,6,3,5]=>8 [4,1,5,6,3,2]=>[2,1,3,6,5,4]=>6 [4,1,6,2,3,5]=>[4,1,6,2,3,5]=>4 [4,1,6,2,5,3]=>[3,1,6,2,5,4]=>5 [4,1,6,3,2,5]=>[4,1,6,3,2,5]=>5 [4,1,6,3,5,2]=>[3,1,6,2,5,4]=>5 [4,1,6,5,2,3]=>[3,1,6,5,2,4]=>9 [4,1,6,5,3,2]=>[2,1,6,5,4,3]=>10 [4,2,1,3,5,6]=>[4,2,1,3,5,6]=>2 [4,2,1,3,6,5]=>[4,2,1,3,6,5]=>7 [4,2,1,5,3,6]=>[3,2,1,5,4,6]=>6 [4,2,1,5,6,3]=>[3,2,1,4,6,5]=>7 [4,2,1,6,3,5]=>[4,2,1,6,3,5]=>6 [4,2,1,6,5,3]=>[3,2,1,6,5,4]=>7 [4,2,3,1,5,6]=>[4,1,3,2,5,6]=>2 [4,2,3,1,6,5]=>[4,1,3,2,6,5]=>7 [4,2,3,5,1,6]=>[3,1,2,5,4,6]=>5 [4,2,3,5,6,1]=>[3,1,2,4,6,5]=>6 [4,2,3,6,1,5]=>[4,1,3,6,2,5]=>6 [4,2,3,6,5,1]=>[3,1,2,6,5,4]=>6 [4,2,5,1,3,6]=>[3,2,5,1,4,6]=>5 [4,2,5,1,6,3]=>[2,1,4,3,6,5]=>9 [4,2,5,3,1,6]=>[2,1,5,4,3,6]=>5 [4,2,5,3,6,1]=>[2,1,4,3,6,5]=>9 [4,2,5,6,1,3]=>[2,1,4,6,3,5]=>8 [4,2,5,6,3,1]=>[2,1,3,6,5,4]=>6 [4,2,6,1,3,5]=>[4,2,6,1,3,5]=>5 [4,2,6,1,5,3]=>[3,2,6,1,5,4]=>6 [4,2,6,3,1,5]=>[4,1,6,3,2,5]=>5 [4,2,6,3,5,1]=>[3,1,6,2,5,4]=>5 [4,2,6,5,1,3]=>[3,2,6,5,1,4]=>10 [4,2,6,5,3,1]=>[2,1,6,5,4,3]=>10 [4,3,1,2,5,6]=>[4,3,1,2,5,6]=>4 [4,3,1,2,6,5]=>[4,3,1,2,6,5]=>9 [4,3,1,5,2,6]=>[3,2,1,5,4,6]=>6 [4,3,1,5,6,2]=>[3,2,1,4,6,5]=>7 [4,3,1,6,2,5]=>[4,3,1,6,2,5]=>8 [4,3,1,6,5,2]=>[3,2,1,6,5,4]=>7 [4,3,2,1,5,6]=>[4,3,2,1,5,6]=>5 [4,3,2,1,6,5]=>[4,3,2,1,6,5]=>10 [4,3,2,5,1,6]=>[3,2,1,5,4,6]=>6 [4,3,2,5,6,1]=>[3,2,1,4,6,5]=>7 [4,3,2,6,1,5]=>[4,3,2,6,1,5]=>9 [4,3,2,6,5,1]=>[3,2,1,6,5,4]=>7 [4,3,5,1,2,6]=>[3,2,5,1,4,6]=>5 [4,3,5,1,6,2]=>[2,1,4,3,6,5]=>9 [4,3,5,2,1,6]=>[2,1,5,4,3,6]=>5 [4,3,5,2,6,1]=>[2,1,4,3,6,5]=>9 [4,3,5,6,1,2]=>[2,1,4,6,3,5]=>8 [4,3,5,6,2,1]=>[2,1,3,6,5,4]=>6 [4,3,6,1,2,5]=>[4,3,6,1,2,5]=>7 [4,3,6,1,5,2]=>[3,2,6,1,5,4]=>6 [4,3,6,2,1,5]=>[4,3,6,2,1,5]=>8 [4,3,6,2,5,1]=>[3,2,6,1,5,4]=>6 [4,3,6,5,1,2]=>[3,2,6,5,1,4]=>10 [4,3,6,5,2,1]=>[2,1,6,5,4,3]=>10 [4,5,1,2,3,6]=>[3,5,1,2,4,6]=>3 [4,5,1,2,6,3]=>[2,4,1,3,6,5]=>8 [4,5,1,3,2,6]=>[2,5,1,4,3,6]=>4 [4,5,1,3,6,2]=>[2,4,1,3,6,5]=>8 [4,5,1,6,2,3]=>[2,4,1,6,3,5]=>7 [4,5,1,6,3,2]=>[1,3,2,6,5,4]=>7 [4,5,2,1,3,6]=>[3,5,2,1,4,6]=>4 [4,5,2,1,6,3]=>[1,4,3,2,6,5]=>8 [4,5,2,3,1,6]=>[2,5,1,4,3,6]=>4 [4,5,2,3,6,1]=>[2,4,1,3,6,5]=>8 [4,5,2,6,1,3]=>[1,4,3,6,2,5]=>7 [4,5,2,6,3,1]=>[1,3,2,6,5,4]=>7 [4,5,3,1,2,6]=>[2,5,4,1,3,6]=>7 [4,5,3,1,6,2]=>[1,4,3,2,6,5]=>8 [4,5,3,2,1,6]=>[1,5,4,3,2,6]=>7 [4,5,3,2,6,1]=>[1,4,3,2,6,5]=>8 [4,5,3,6,1,2]=>[1,4,3,6,2,5]=>7 [4,5,3,6,2,1]=>[1,3,2,6,5,4]=>7 [4,5,6,1,2,3]=>[2,4,6,1,3,5]=>6 [4,5,6,1,3,2]=>[1,3,6,2,5,4]=>6 [4,5,6,2,1,3]=>[1,4,6,3,2,5]=>6 [4,5,6,2,3,1]=>[1,3,6,2,5,4]=>6 [4,5,6,3,1,2]=>[1,3,6,5,2,4]=>10 [4,5,6,3,2,1]=>[1,2,6,5,4,3]=>9 [4,6,1,2,3,5]=>[4,6,1,2,3,5]=>3 [4,6,1,2,5,3]=>[3,6,1,2,5,4]=>4 [4,6,1,3,2,5]=>[4,6,1,3,2,5]=>4 [4,6,1,3,5,2]=>[3,6,1,2,5,4]=>4 [4,6,1,5,2,3]=>[3,6,1,5,2,4]=>8 [4,6,1,5,3,2]=>[2,6,1,5,4,3]=>9 [4,6,2,1,3,5]=>[4,6,2,1,3,5]=>4 [4,6,2,1,5,3]=>[3,6,2,1,5,4]=>5 [4,6,2,3,1,5]=>[4,6,1,3,2,5]=>4 [4,6,2,3,5,1]=>[3,6,1,2,5,4]=>4 [4,6,2,5,1,3]=>[3,6,2,5,1,4]=>9 [4,6,2,5,3,1]=>[2,6,1,5,4,3]=>9 [4,6,3,1,2,5]=>[4,6,3,1,2,5]=>5 [4,6,3,1,5,2]=>[3,6,2,1,5,4]=>5 [4,6,3,2,1,5]=>[4,6,3,2,1,5]=>6 [4,6,3,2,5,1]=>[3,6,2,1,5,4]=>5 [4,6,3,5,1,2]=>[3,6,2,5,1,4]=>9 [4,6,3,5,2,1]=>[2,6,1,5,4,3]=>9 [4,6,5,1,2,3]=>[3,6,5,1,2,4]=>7 [4,6,5,1,3,2]=>[2,6,5,1,4,3]=>8 [4,6,5,2,1,3]=>[3,6,5,2,1,4]=>8 [4,6,5,2,3,1]=>[2,6,5,1,4,3]=>8 [4,6,5,3,1,2]=>[2,6,5,4,1,3]=>9 [4,6,5,3,2,1]=>[1,6,5,4,3,2]=>9 [5,1,2,3,4,6]=>[5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>[4,1,2,3,6,5]=>6 [5,1,2,4,3,6]=>[5,1,2,4,3,6]=>2 [5,1,2,4,6,3]=>[4,1,2,3,6,5]=>6 [5,1,2,6,3,4]=>[4,1,2,6,3,5]=>5 [5,1,2,6,4,3]=>[3,1,2,6,5,4]=>6 [5,1,3,2,4,6]=>[5,1,3,2,4,6]=>2 [5,1,3,2,6,4]=>[4,1,3,2,6,5]=>7 [5,1,3,4,2,6]=>[5,1,2,4,3,6]=>2 [5,1,3,4,6,2]=>[4,1,2,3,6,5]=>6 [5,1,3,6,2,4]=>[4,1,3,6,2,5]=>6 [5,1,3,6,4,2]=>[3,1,2,6,5,4]=>6 [5,1,4,2,3,6]=>[5,1,4,2,3,6]=>5 [5,1,4,2,6,3]=>[4,1,3,2,6,5]=>7 [5,1,4,3,2,6]=>[5,1,4,3,2,6]=>6 [5,1,4,3,6,2]=>[4,1,3,2,6,5]=>7 [5,1,4,6,2,3]=>[4,1,3,6,2,5]=>6 [5,1,4,6,3,2]=>[3,1,2,6,5,4]=>6 [5,1,6,2,3,4]=>[4,1,6,2,3,5]=>4 [5,1,6,2,4,3]=>[3,1,6,2,5,4]=>5 [5,1,6,3,2,4]=>[4,1,6,3,2,5]=>5 [5,1,6,3,4,2]=>[3,1,6,2,5,4]=>5 [5,1,6,4,2,3]=>[3,1,6,5,2,4]=>9 [5,1,6,4,3,2]=>[2,1,6,5,4,3]=>10 [5,2,1,3,4,6]=>[5,2,1,3,4,6]=>2 [5,2,1,3,6,4]=>[4,2,1,3,6,5]=>7 [5,2,1,4,3,6]=>[5,2,1,4,3,6]=>3 [5,2,1,4,6,3]=>[4,2,1,3,6,5]=>7 [5,2,1,6,3,4]=>[4,2,1,6,3,5]=>6 [5,2,1,6,4,3]=>[3,2,1,6,5,4]=>7 [5,2,3,1,4,6]=>[5,1,3,2,4,6]=>2 [5,2,3,1,6,4]=>[4,1,3,2,6,5]=>7 [5,2,3,4,1,6]=>[5,1,2,4,3,6]=>2 [5,2,3,4,6,1]=>[4,1,2,3,6,5]=>6 [5,2,3,6,1,4]=>[4,1,3,6,2,5]=>6 [5,2,3,6,4,1]=>[3,1,2,6,5,4]=>6 [5,2,4,1,3,6]=>[5,2,4,1,3,6]=>6 [5,2,4,1,6,3]=>[4,1,3,2,6,5]=>7 [5,2,4,3,1,6]=>[5,1,4,3,2,6]=>6 [5,2,4,3,6,1]=>[4,1,3,2,6,5]=>7 [5,2,4,6,1,3]=>[4,1,3,6,2,5]=>6 [5,2,4,6,3,1]=>[3,1,2,6,5,4]=>6 [5,2,6,1,3,4]=>[4,2,6,1,3,5]=>5 [5,2,6,1,4,3]=>[3,2,6,1,5,4]=>6 [5,2,6,3,1,4]=>[4,1,6,3,2,5]=>5 [5,2,6,3,4,1]=>[3,1,6,2,5,4]=>5 [5,2,6,4,1,3]=>[3,2,6,5,1,4]=>10 [5,2,6,4,3,1]=>[2,1,6,5,4,3]=>10 [5,3,1,2,4,6]=>[5,3,1,2,4,6]=>4 [5,3,1,2,6,4]=>[4,3,1,2,6,5]=>9 [5,3,1,4,2,6]=>[5,2,1,4,3,6]=>3 [5,3,1,4,6,2]=>[4,2,1,3,6,5]=>7 [5,3,1,6,2,4]=>[4,3,1,6,2,5]=>8 [5,3,1,6,4,2]=>[3,2,1,6,5,4]=>7 [5,3,2,1,4,6]=>[5,3,2,1,4,6]=>5 [5,3,2,1,6,4]=>[4,3,2,1,6,5]=>10 [5,3,2,4,1,6]=>[5,2,1,4,3,6]=>3 [5,3,2,4,6,1]=>[4,2,1,3,6,5]=>7 [5,3,2,6,1,4]=>[4,3,2,6,1,5]=>9 [5,3,2,6,4,1]=>[3,2,1,6,5,4]=>7 [5,3,4,1,2,6]=>[5,2,4,1,3,6]=>6 [5,3,4,1,6,2]=>[4,1,3,2,6,5]=>7 [5,3,4,2,1,6]=>[5,1,4,3,2,6]=>6 [5,3,4,2,6,1]=>[4,1,3,2,6,5]=>7 [5,3,4,6,1,2]=>[4,1,3,6,2,5]=>6 [5,3,4,6,2,1]=>[3,1,2,6,5,4]=>6 [5,3,6,1,2,4]=>[4,3,6,1,2,5]=>7 [5,3,6,1,4,2]=>[3,2,6,1,5,4]=>6 [5,3,6,2,1,4]=>[4,3,6,2,1,5]=>8 [5,3,6,2,4,1]=>[3,2,6,1,5,4]=>6 [5,3,6,4,1,2]=>[3,2,6,5,1,4]=>10 [5,3,6,4,2,1]=>[2,1,6,5,4,3]=>10 [5,4,1,2,3,6]=>[5,4,1,2,3,6]=>4 [5,4,1,2,6,3]=>[4,3,1,2,6,5]=>9 [5,4,1,3,2,6]=>[5,4,1,3,2,6]=>5 [5,4,1,3,6,2]=>[4,3,1,2,6,5]=>9 [5,4,1,6,2,3]=>[4,3,1,6,2,5]=>8 [5,4,1,6,3,2]=>[3,2,1,6,5,4]=>7 [5,4,2,1,3,6]=>[5,4,2,1,3,6]=>5 [5,4,2,1,6,3]=>[4,3,2,1,6,5]=>10 [5,4,2,3,1,6]=>[5,4,1,3,2,6]=>5 [5,4,2,3,6,1]=>[4,3,1,2,6,5]=>9 [5,4,2,6,1,3]=>[4,3,2,6,1,5]=>9 [5,4,2,6,3,1]=>[3,2,1,6,5,4]=>7 [5,4,3,1,2,6]=>[5,4,3,1,2,6]=>6 [5,4,3,1,6,2]=>[4,3,2,1,6,5]=>10 [5,4,3,2,1,6]=>[5,4,3,2,1,6]=>7 [5,4,3,2,6,1]=>[4,3,2,1,6,5]=>10 [5,4,3,6,1,2]=>[4,3,2,6,1,5]=>9 [5,4,3,6,2,1]=>[3,2,1,6,5,4]=>7 [5,4,6,1,2,3]=>[4,3,6,1,2,5]=>7 [5,4,6,1,3,2]=>[3,2,6,1,5,4]=>6 [5,4,6,2,1,3]=>[4,3,6,2,1,5]=>8 [5,4,6,2,3,1]=>[3,2,6,1,5,4]=>6 [5,4,6,3,1,2]=>[3,2,6,5,1,4]=>10 [5,4,6,3,2,1]=>[2,1,6,5,4,3]=>10 [5,6,1,2,3,4]=>[4,6,1,2,3,5]=>3 [5,6,1,2,4,3]=>[3,6,1,2,5,4]=>4 [5,6,1,3,2,4]=>[4,6,1,3,2,5]=>4 [5,6,1,3,4,2]=>[3,6,1,2,5,4]=>4 [5,6,1,4,2,3]=>[3,6,1,5,2,4]=>8 [5,6,1,4,3,2]=>[2,6,1,5,4,3]=>9 [5,6,2,1,3,4]=>[4,6,2,1,3,5]=>4 [5,6,2,1,4,3]=>[3,6,2,1,5,4]=>5 [5,6,2,3,1,4]=>[4,6,1,3,2,5]=>4 [5,6,2,3,4,1]=>[3,6,1,2,5,4]=>4 [5,6,2,4,1,3]=>[3,6,2,5,1,4]=>9 [5,6,2,4,3,1]=>[2,6,1,5,4,3]=>9 [5,6,3,1,2,4]=>[4,6,3,1,2,5]=>5 [5,6,3,1,4,2]=>[3,6,2,1,5,4]=>5 [5,6,3,2,1,4]=>[4,6,3,2,1,5]=>6 [5,6,3,2,4,1]=>[3,6,2,1,5,4]=>5 [5,6,3,4,1,2]=>[3,6,2,5,1,4]=>9 [5,6,3,4,2,1]=>[2,6,1,5,4,3]=>9 [5,6,4,1,2,3]=>[3,6,5,1,2,4]=>7 [5,6,4,1,3,2]=>[2,6,5,1,4,3]=>8 [5,6,4,2,1,3]=>[3,6,5,2,1,4]=>8 [5,6,4,2,3,1]=>[2,6,5,1,4,3]=>8 [5,6,4,3,1,2]=>[2,6,5,4,1,3]=>9 [5,6,4,3,2,1]=>[1,6,5,4,3,2]=>9 [6,1,2,3,4,5]=>[6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>[6,1,2,3,5,4]=>2 [6,1,2,4,3,5]=>[6,1,2,4,3,5]=>2 [6,1,2,4,5,3]=>[6,1,2,3,5,4]=>2 [6,1,2,5,3,4]=>[6,1,2,5,3,4]=>6 [6,1,2,5,4,3]=>[6,1,2,5,4,3]=>7 [6,1,3,2,4,5]=>[6,1,3,2,4,5]=>2 [6,1,3,2,5,4]=>[6,1,3,2,5,4]=>3 [6,1,3,4,2,5]=>[6,1,2,4,3,5]=>2 [6,1,3,4,5,2]=>[6,1,2,3,5,4]=>2 [6,1,3,5,2,4]=>[6,1,3,5,2,4]=>7 [6,1,3,5,4,2]=>[6,1,2,5,4,3]=>7 [6,1,4,2,3,5]=>[6,1,4,2,3,5]=>5 [6,1,4,2,5,3]=>[6,1,3,2,5,4]=>3 [6,1,4,3,2,5]=>[6,1,4,3,2,5]=>6 [6,1,4,3,5,2]=>[6,1,3,2,5,4]=>3 [6,1,4,5,2,3]=>[6,1,3,5,2,4]=>7 [6,1,4,5,3,2]=>[6,1,2,5,4,3]=>7 [6,1,5,2,3,4]=>[6,1,5,2,3,4]=>5 [6,1,5,2,4,3]=>[6,1,5,2,4,3]=>6 [6,1,5,3,2,4]=>[6,1,5,3,2,4]=>6 [6,1,5,3,4,2]=>[6,1,5,2,4,3]=>6 [6,1,5,4,2,3]=>[6,1,5,4,2,3]=>7 [6,1,5,4,3,2]=>[6,1,5,4,3,2]=>8 [6,2,1,3,4,5]=>[6,2,1,3,4,5]=>2 [6,2,1,3,5,4]=>[6,2,1,3,5,4]=>3 [6,2,1,4,3,5]=>[6,2,1,4,3,5]=>3 [6,2,1,4,5,3]=>[6,2,1,3,5,4]=>3 [6,2,1,5,3,4]=>[6,2,1,5,3,4]=>7 [6,2,1,5,4,3]=>[6,2,1,5,4,3]=>8 [6,2,3,1,4,5]=>[6,1,3,2,4,5]=>2 [6,2,3,1,5,4]=>[6,1,3,2,5,4]=>3 [6,2,3,4,1,5]=>[6,1,2,4,3,5]=>2 [6,2,3,4,5,1]=>[6,1,2,3,5,4]=>2 [6,2,3,5,1,4]=>[6,1,3,5,2,4]=>7 [6,2,3,5,4,1]=>[6,1,2,5,4,3]=>7 [6,2,4,1,3,5]=>[6,2,4,1,3,5]=>6 [6,2,4,1,5,3]=>[6,1,3,2,5,4]=>3 [6,2,4,3,1,5]=>[6,1,4,3,2,5]=>6 [6,2,4,3,5,1]=>[6,1,3,2,5,4]=>3 [6,2,4,5,1,3]=>[6,1,3,5,2,4]=>7 [6,2,4,5,3,1]=>[6,1,2,5,4,3]=>7 [6,2,5,1,3,4]=>[6,2,5,1,3,4]=>6 [6,2,5,1,4,3]=>[6,2,5,1,4,3]=>7 [6,2,5,3,1,4]=>[6,1,5,3,2,4]=>6 [6,2,5,3,4,1]=>[6,1,5,2,4,3]=>6 [6,2,5,4,1,3]=>[6,2,5,4,1,3]=>8 [6,2,5,4,3,1]=>[6,1,5,4,3,2]=>8 [6,3,1,2,4,5]=>[6,3,1,2,4,5]=>4 [6,3,1,2,5,4]=>[6,3,1,2,5,4]=>5 [6,3,1,4,2,5]=>[6,2,1,4,3,5]=>3 [6,3,1,4,5,2]=>[6,2,1,3,5,4]=>3 [6,3,1,5,2,4]=>[6,3,1,5,2,4]=>9 [6,3,1,5,4,2]=>[6,2,1,5,4,3]=>8 [6,3,2,1,4,5]=>[6,3,2,1,4,5]=>5 [6,3,2,1,5,4]=>[6,3,2,1,5,4]=>6 [6,3,2,4,1,5]=>[6,2,1,4,3,5]=>3 [6,3,2,4,5,1]=>[6,2,1,3,5,4]=>3 [6,3,2,5,1,4]=>[6,3,2,5,1,4]=>10 [6,3,2,5,4,1]=>[6,2,1,5,4,3]=>8 [6,3,4,1,2,5]=>[6,2,4,1,3,5]=>6 [6,3,4,1,5,2]=>[6,1,3,2,5,4]=>3 [6,3,4,2,1,5]=>[6,1,4,3,2,5]=>6 [6,3,4,2,5,1]=>[6,1,3,2,5,4]=>3 [6,3,4,5,1,2]=>[6,1,3,5,2,4]=>7 [6,3,4,5,2,1]=>[6,1,2,5,4,3]=>7 [6,3,5,1,2,4]=>[6,3,5,1,2,4]=>8 [6,3,5,1,4,2]=>[6,2,5,1,4,3]=>7 [6,3,5,2,1,4]=>[6,3,5,2,1,4]=>9 [6,3,5,2,4,1]=>[6,2,5,1,4,3]=>7 [6,3,5,4,1,2]=>[6,2,5,4,1,3]=>8 [6,3,5,4,2,1]=>[6,1,5,4,3,2]=>8 [6,4,1,2,3,5]=>[6,4,1,2,3,5]=>4 [6,4,1,2,5,3]=>[6,3,1,2,5,4]=>5 [6,4,1,3,2,5]=>[6,4,1,3,2,5]=>5 [6,4,1,3,5,2]=>[6,3,1,2,5,4]=>5 [6,4,1,5,2,3]=>[6,3,1,5,2,4]=>9 [6,4,1,5,3,2]=>[6,2,1,5,4,3]=>8 [6,4,2,1,3,5]=>[6,4,2,1,3,5]=>5 [6,4,2,1,5,3]=>[6,3,2,1,5,4]=>6 [6,4,2,3,1,5]=>[6,4,1,3,2,5]=>5 [6,4,2,3,5,1]=>[6,3,1,2,5,4]=>5 [6,4,2,5,1,3]=>[6,3,2,5,1,4]=>10 [6,4,2,5,3,1]=>[6,2,1,5,4,3]=>8 [6,4,3,1,2,5]=>[6,4,3,1,2,5]=>6 [6,4,3,1,5,2]=>[6,3,2,1,5,4]=>6 [6,4,3,2,1,5]=>[6,4,3,2,1,5]=>7 [6,4,3,2,5,1]=>[6,3,2,1,5,4]=>6 [6,4,3,5,1,2]=>[6,3,2,5,1,4]=>10 [6,4,3,5,2,1]=>[6,2,1,5,4,3]=>8 [6,4,5,1,2,3]=>[6,3,5,1,2,4]=>8 [6,4,5,1,3,2]=>[6,2,5,1,4,3]=>7 [6,4,5,2,1,3]=>[6,3,5,2,1,4]=>9 [6,4,5,2,3,1]=>[6,2,5,1,4,3]=>7 [6,4,5,3,1,2]=>[6,2,5,4,1,3]=>8 [6,4,5,3,2,1]=>[6,1,5,4,3,2]=>8 [6,5,1,2,3,4]=>[6,5,1,2,3,4]=>4 [6,5,1,2,4,3]=>[6,5,1,2,4,3]=>5 [6,5,1,3,2,4]=>[6,5,1,3,2,4]=>5 [6,5,1,3,4,2]=>[6,5,1,2,4,3]=>5 [6,5,1,4,2,3]=>[6,5,1,4,2,3]=>6 [6,5,1,4,3,2]=>[6,5,1,4,3,2]=>7 [6,5,2,1,3,4]=>[6,5,2,1,3,4]=>5 [6,5,2,1,4,3]=>[6,5,2,1,4,3]=>6 [6,5,2,3,1,4]=>[6,5,1,3,2,4]=>5 [6,5,2,3,4,1]=>[6,5,1,2,4,3]=>5 [6,5,2,4,1,3]=>[6,5,2,4,1,3]=>7 [6,5,2,4,3,1]=>[6,5,1,4,3,2]=>7 [6,5,3,1,2,4]=>[6,5,3,1,2,4]=>6 [6,5,3,1,4,2]=>[6,5,2,1,4,3]=>6 [6,5,3,2,1,4]=>[6,5,3,2,1,4]=>7 [6,5,3,2,4,1]=>[6,5,2,1,4,3]=>6 [6,5,3,4,1,2]=>[6,5,2,4,1,3]=>7 [6,5,3,4,2,1]=>[6,5,1,4,3,2]=>7 [6,5,4,1,2,3]=>[6,5,4,1,2,3]=>9 [6,5,4,1,3,2]=>[6,5,4,1,3,2]=>10 [6,5,4,2,1,3]=>[6,5,4,2,1,3]=>10 [6,5,4,2,3,1]=>[6,5,4,1,3,2]=>10 [6,5,4,3,1,2]=>[6,5,4,3,1,2]=>11 [6,5,4,3,2,1]=>[6,5,4,3,2,1]=>12
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Description
The Denert index of a permutation.
It is defined as
$$ \begin{align*} den(\sigma) &= \#\{ 1\leq l < k \leq n : \sigma(k) < \sigma(l) \leq k \} \\ &+ \#\{ 1\leq l < k \leq n : \sigma(l) \leq k < \sigma(k) \} \\ &+ \#\{ 1\leq l < k \leq n : k < \sigma(k) < \sigma(l) \} \end{align*} $$
where $n$ is the size of $\sigma$. It was studied by Denert in [1], and it was shown by Foata and Zeilberger in [2] that the bistatistic $(exc,den)$ is Euler-Mahonian. Here, $exc$ is the number of weak exceedences, see St000155The number of exceedances (also excedences) of a permutation..
Map
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..