Identifier
Values
=>
Cc0002;cc-rep-0 Cc0005;cc-rep
[1]=>[1,0,1,0]=>0 [2]=>[1,1,0,0,1,0]=>0 [1,1]=>[1,0,1,1,0,0]=>1 [3]=>[1,1,1,0,0,0,1,0]=>1 [2,1]=>[1,0,1,0,1,0]=>0 [1,1,1]=>[1,0,1,1,1,0,0,0]=>2 [4]=>[1,1,1,1,0,0,0,0,1,0]=>2 [3,1]=>[1,1,0,1,0,0,1,0]=>0 [2,2]=>[1,1,0,0,1,1,0,0]=>1 [2,1,1]=>[1,0,1,1,0,1,0,0]=>2 [1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0]=>3 [5]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>3 [4,1]=>[1,1,1,0,1,0,0,0,1,0]=>2 [3,2]=>[1,1,0,0,1,0,1,0]=>0 [3,1,1]=>[1,0,1,1,0,0,1,0]=>1 [2,2,1]=>[1,0,1,0,1,1,0,0]=>2 [2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0]=>3 [1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>4 [6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>4 [5,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>3 [4,2]=>[1,1,1,0,0,1,0,0,1,0]=>1 [4,1,1]=>[1,1,0,1,1,0,0,0,1,0]=>2 [3,3]=>[1,1,1,0,0,0,1,1,0,0]=>2 [3,2,1]=>[1,0,1,0,1,0,1,0]=>0 [3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0]=>3 [2,2,2]=>[1,1,0,0,1,1,1,0,0,0]=>3 [2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0]=>4 [2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>4 [1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>5 [6,1]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4 [5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>3 [5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>4 [4,3]=>[1,1,1,0,0,0,1,0,1,0]=>2 [4,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>0 [4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0]=>3 [3,3,1]=>[1,1,0,1,0,0,1,1,0,0]=>1 [3,2,2]=>[1,1,0,0,1,1,0,1,0,0]=>2 [3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0]=>3 [3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4 [2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0]=>4 [2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>5 [2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5 [1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6 [6,2]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>4 [6,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>5 [5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>3 [5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>3 [5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>4 [4,4]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4 [4,3,1]=>[1,1,0,1,0,0,1,0,1,0]=>0 [4,2,2]=>[1,1,0,0,1,1,0,0,1,0]=>1 [4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0]=>2 [4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5 [3,3,2]=>[1,1,0,0,1,0,1,1,0,0]=>2 [3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0]=>3 [3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0]=>4 [3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>4 [3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5 [2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>5 [2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>6 [2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>6 [2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6 [6,3]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>5 [6,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4 [6,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>6 [5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>4 [5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2 [5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>3 [5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>4 [5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5 [4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>3 [4,3,2]=>[1,1,0,0,1,0,1,0,1,0]=>0 [4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>1 [4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>2 [4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>4 [4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>6 [3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>4 [3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0]=>3 [3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>5 [3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>5 [3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>6 [3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>5 [3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6 [2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>6 [2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>7 [2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>7 [6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5 [6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4 [6,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>5 [6,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>6 [6,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>6 [5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>6 [5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>4 [5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1 [5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>2 [5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>3 [5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>5 [5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>7 [4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>2 [4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>3 [4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>3 [4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>0 [4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>4 [4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>4 [4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>5 [4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>5 [4,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>7 [3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>4 [3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>5 [3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>6 [3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>6 [3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>6 [3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>7 [3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>6 [2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>7 [2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>8 [2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>8 [6,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>6 [6,4,1]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>5 [6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4 [6,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>5 [6,2,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>6 [6,2,1,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>6 [6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>7 [5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>6 [5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2 [5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>3 [5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3 [5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>0 [5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>4 [5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4 [5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>5 [5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>7 [5,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>8 [4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>4 [4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>1 [4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5 [4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2 [4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>3 [4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>4 [4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>5 [4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>6 [4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>6 [4,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>6 [3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>5 [3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>6 [3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>7 [3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>7 [3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>7 [3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>7 [3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>8 [3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>8 [2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>8 [2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>9 [6,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>6 [6,4,2]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4 [6,4,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>5 [6,3,3]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5 [6,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>4 [6,3,1,1,1]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>6 [6,2,2,2]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>6 [6,2,2,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>7 [6,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>7 [6,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>9 [5,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>5 [5,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>6 [5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>3 [5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>0 [5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>4 [5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>1 [5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2 [5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>3 [5,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>6 [5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>5 [5,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>7 [5,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>8 [4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>6 [4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2 [4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>3 [4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>4 [4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>7 [4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>4 [4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>5 [4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>6 [4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>5 [4,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>6 [4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>7 [4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>8 [4,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>7 [3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>7 [3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>6 [3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>8 [3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>8 [3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>9 [3,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>8 [3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>8 [3,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>9 [2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>9 [2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>10 [7,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>9 [6,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>6 [6,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>7 [6,4,3]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4 [6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3 [6,4,1,1,1]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>5 [6,3,3,1]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4 [6,3,2,2]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>5 [6,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>6 [6,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>7 [6,2,2,2,1]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>6 [6,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>8 [6,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>9 [5,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5 [5,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>4 [5,5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>6 [5,4,4]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>6 [5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>0 [5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>1 [5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>2 [5,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>7 [5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>2 [5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>3 [5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>4 [5,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5 [5,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>7 [5,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>7 [5,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>8 [5,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>8 [4,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>5 [4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>3 [4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>4 [4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>5 [4,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>6 [4,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>8 [4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>6 [4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>6 [4,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>7 [4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>7 [4,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>8 [4,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>6 [4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>8 [4,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>9 [3,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>7 [3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>8 [3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>9 [3,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>9 [3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>9 [3,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>10 [3,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>9 [3,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>10 [2,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>10 [7,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>9 [6,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>5 [6,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6 [6,5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>6 [6,4,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>6 [6,4,3,1]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2 [6,4,2,2]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3 [6,4,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>4 [6,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>7 [6,3,3,2]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4 [6,3,3,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>5 [6,3,2,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>6 [6,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7 [6,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>9 [6,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>7 [6,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>8 [6,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>10 [5,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>7 [5,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3 [5,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>4 [5,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>5 [5,5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>8 [5,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4 [5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>0 [5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1 [5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>2 [5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>5 [5,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>8 [5,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5 [5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>3 [5,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>6 [5,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>6 [5,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>7 [5,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>6 [5,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>9 [5,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>9 [4,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>5 [4,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>6 [4,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>6 [4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>4 [4,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>7 [4,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>7 [4,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>8 [4,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>7 [4,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>7 [4,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>8 [4,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>9 [4,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>8 [4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>8 [4,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>9 [4,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>9 [4,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>10 [3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>8 [3,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>9 [3,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>10 [3,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>10 [3,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>10 [3,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>11 [3,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>10 [7,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>9 [7,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>10 [6,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>6 [6,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>4 [6,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>5 [6,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6 [6,5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>7 [6,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>5 [6,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1 [6,4,3,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2 [6,4,2,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3 [6,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6 [6,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>9 [6,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>6 [6,3,3,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>4 [6,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>7 [6,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>7 [6,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>8 [6,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>9 [6,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>8 [6,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>10 [5,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>6 [5,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2 [5,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3 [5,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>4 [5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>7 [5,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>10 [5,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3 [5,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>4 [5,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>4 [5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0 [5,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5 [5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>5 [5,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6 [5,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>6 [5,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>5 [5,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>6 [5,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>7 [5,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>7 [5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>8 [5,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>8 [5,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>10 [5,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>11 [4,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>7 [4,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>5 [4,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>8 [4,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>6 [4,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>7 [4,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>8 [4,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>8 [4,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>9 [4,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>9 [4,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>8 [4,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>9 [4,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>10 [4,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>10 [4,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>9 [4,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>10 [4,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>10 [3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>9 [3,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>11 [3,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>11 [3,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>12 [3,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>11 [7,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>10 [7,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>9 [7,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>11 [6,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>6 [6,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2 [6,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3 [6,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>4 [6,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>7 [6,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>10 [6,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3 [6,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4 [6,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4 [6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>0 [6,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5 [6,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5 [6,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>6 [6,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>8 [6,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>5 [6,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>6 [6,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>7 [6,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>9 [6,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>8 [6,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>10 [6,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>10 [6,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>11 [5,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4 [5,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>5 [5,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5 [5,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1 [5,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>6 [5,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>6 [5,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>7 [5,5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>9 [5,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>6 [5,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2 [5,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>7 [5,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3 [5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>4 [5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5 [5,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>6 [5,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>8 [5,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>7 [5,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>7 [5,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>8 [5,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>9 [5,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>8 [5,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>9 [5,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>10 [5,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>11 [4,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>6 [4,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>7 [4,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>8 [4,4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>10 [4,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>8 [4,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>9 [4,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>10 [4,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>9 [4,4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>10 [4,4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>11 [4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>9 [4,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>11 [4,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>11 [4,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>12 [4,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>10 [3,3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>11 [3,3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>12 [3,3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>12 [7,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>10 [7,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>9 [7,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>10 [7,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>11 [7,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>10 [7,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>11 [6,6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>11 [6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3 [6,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4 [6,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4 [6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>0 [6,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>5 [6,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>5 [6,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>6 [6,5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>10 [6,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>5 [6,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1 [6,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>6 [6,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2 [6,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3 [6,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4 [6,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>7 [6,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>7 [6,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>8 [6,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>6 [6,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>7 [6,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>8 [6,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>9 [6,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>10 [6,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>11 [6,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>12 [5,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>6 [5,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2 [5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>7 [5,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3 [5,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4 [5,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>5 [5,5,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>8 [5,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>8 [5,5,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>9 [5,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4 [5,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>5 [5,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>6 [5,4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>9 [5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>6 [5,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>7 [5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>8 [5,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>6 [5,4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>9 [5,4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>10 [5,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>9 [5,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>10 [5,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>10 [5,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>11 [5,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>10 [4,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>7 [4,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>8 [4,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>9 [4,4,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>10 [4,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>10 [4,4,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>11 [4,4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>11 [4,4,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>12 [4,4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>11 [4,3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>11 [4,3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>12 [4,3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>12 [3,3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>11 [3,3,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>12 [3,3,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>13 [6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0 [5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5 [6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4 [5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8 [4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>8 [6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3 [5,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>7 [6,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>6 [5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>9 [6,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>7 [6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2 [5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>6 [6,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>5 [5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>8 [6,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4 [5,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>7 [6,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>6 [6,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>6 [6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1 [5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>5 [6,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>4 [5,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>7 [6,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3 [5,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>6 [6,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>5 [6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2 [5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>5 [6,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4 [6,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3 [6,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5 [6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>0 [5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4 [6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3 [5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6 [6,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2 [5,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>5 [6,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4 [6,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1 [5,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>4 [6,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3 [6,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2 [6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>0 [5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3 [6,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2 [6,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1 [6,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>0 [6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>4 [7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0 [6,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6 [7,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>5 [6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>10 [5,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>10 [7,6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4 [6,6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>9 [7,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>8 [6,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>12 [5,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>13 [7,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>9 [6,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>12 [5,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>12 [4,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>12 [6,6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>8 [6,5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>12 [6,5,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>12 [6,4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>12 [5,4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>12 [6,3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>13 [3,3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>12 [6,6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>7 [6,5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>10 [6,5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>11 [6,5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>10 [5,5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>13 [7,6,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>7 [6,5,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>10 [6,5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>10 [6,4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>10 [5,4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>10 [6,5,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>12 [7,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>11 [7,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1 [6,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>6 [6,5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>9 [6,6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>6 [6,5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>8 [4,4,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>12 [6,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6 [5,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>10 [7,6,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>6 [6,5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>10 [6,5,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6 [7,6,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>9 [5,5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>10 [7,5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>7 [6,5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>6 [7,6,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>10 [7,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>9 [6,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>6 [6,5,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>9 [6,6,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>11 [7,6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>10 [7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0 [6,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5 [7,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4 [6,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8 [5,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>9 [7,6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3 [6,5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>9 [6,5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>8 [5,4,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>11 [4,3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>11 [6,5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5 [4,4,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>11 [7,6,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>6 [6,5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6 [5,4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>9 [6,6,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>10 [7,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>0 [6,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4 [6,5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6 [4,4,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>10
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Description
The dinv deficit of a Dyck path.
For a Dyck path $D$ of semilength $n$, this is defined as
$$\binom{n}{2} - \operatorname{area}(D) - \operatorname{dinv}(D).$$
In other words, this is the number of boxes in the partition traced out by $D$ for which the leg-length minus the arm-length is not in $\{0,1\}$.
See also St000376The bounce deficit of a Dyck path. for the bounce deficit.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.