Identifier
Values
=>
Cc0020;cc-rep
[1]=>[1]=>([],1)=>1 [1,2]=>[2]=>([],2)=>1 [2,1]=>[2]=>([],2)=>1 [1,2,3]=>[3]=>([],3)=>1 [1,3,2]=>[1,2]=>([(1,2)],3)=>2 [2,1,3]=>[3]=>([],3)=>1 [2,3,1]=>[3]=>([],3)=>1 [3,1,2]=>[3]=>([],3)=>1 [3,2,1]=>[2,1]=>([(0,2),(1,2)],3)=>2 [1,2,3,4]=>[4]=>([],4)=>1 [1,2,4,3]=>[2,2]=>([(1,3),(2,3)],4)=>2 [1,3,2,4]=>[1,3]=>([(2,3)],4)=>2 [1,3,4,2]=>[1,3]=>([(2,3)],4)=>2 [1,4,2,3]=>[1,3]=>([(2,3)],4)=>2 [2,1,3,4]=>[4]=>([],4)=>1 [2,1,4,3]=>[2,2]=>([(1,3),(2,3)],4)=>2 [2,3,1,4]=>[4]=>([],4)=>1 [2,3,4,1]=>[4]=>([],4)=>1 [2,4,1,3]=>[4]=>([],4)=>1 [2,4,3,1]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2 [3,1,2,4]=>[4]=>([],4)=>1 [3,1,4,2]=>[2,2]=>([(1,3),(2,3)],4)=>2 [3,2,1,4]=>[2,2]=>([(1,3),(2,3)],4)=>2 [3,2,4,1]=>[2,2]=>([(1,3),(2,3)],4)=>2 [3,4,1,2]=>[4]=>([],4)=>1 [3,4,2,1]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2 [4,1,2,3]=>[4]=>([],4)=>1 [4,1,3,2]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2 [4,2,1,3]=>[2,2]=>([(1,3),(2,3)],4)=>2 [4,2,3,1]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2 [4,3,1,2]=>[1,3]=>([(2,3)],4)=>2 [1,2,3,4,5]=>[5]=>([],5)=>1 [1,2,3,5,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [1,2,4,3,5]=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,2,4,5,3]=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,2,5,3,4]=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,3,2,4,5]=>[1,4]=>([(3,4)],5)=>2 [1,3,4,2,5]=>[1,4]=>([(3,4)],5)=>2 [1,3,4,5,2]=>[1,4]=>([(3,4)],5)=>2 [1,3,5,2,4]=>[1,4]=>([(3,4)],5)=>2 [1,4,2,3,5]=>[1,4]=>([(3,4)],5)=>2 [1,4,5,2,3]=>[1,4]=>([(3,4)],5)=>2 [1,5,2,3,4]=>[1,4]=>([(3,4)],5)=>2 [1,5,4,2,3]=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [2,1,3,4,5]=>[5]=>([],5)=>1 [2,1,3,5,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [2,1,4,3,5]=>[2,3]=>([(2,4),(3,4)],5)=>2 [2,1,4,5,3]=>[2,3]=>([(2,4),(3,4)],5)=>2 [2,1,5,3,4]=>[2,3]=>([(2,4),(3,4)],5)=>2 [2,3,1,4,5]=>[5]=>([],5)=>1 [2,3,1,5,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [2,3,4,1,5]=>[5]=>([],5)=>1 [2,3,4,5,1]=>[5]=>([],5)=>1 [2,3,5,1,4]=>[5]=>([],5)=>1 [2,3,5,4,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [2,4,1,3,5]=>[5]=>([],5)=>1 [2,4,1,5,3]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [2,4,3,1,5]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [2,4,3,5,1]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [2,4,5,1,3]=>[5]=>([],5)=>1 [2,4,5,3,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [2,5,1,3,4]=>[5]=>([],5)=>1 [2,5,1,4,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [2,5,3,1,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [2,5,3,4,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [2,5,4,1,3]=>[2,3]=>([(2,4),(3,4)],5)=>2 [3,1,2,4,5]=>[5]=>([],5)=>1 [3,1,2,5,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [3,1,4,2,5]=>[2,3]=>([(2,4),(3,4)],5)=>2 [3,1,4,5,2]=>[2,3]=>([(2,4),(3,4)],5)=>2 [3,1,5,2,4]=>[2,3]=>([(2,4),(3,4)],5)=>2 [3,2,1,4,5]=>[2,3]=>([(2,4),(3,4)],5)=>2 [3,2,4,1,5]=>[2,3]=>([(2,4),(3,4)],5)=>2 [3,2,4,5,1]=>[2,3]=>([(2,4),(3,4)],5)=>2 [3,2,5,1,4]=>[2,3]=>([(2,4),(3,4)],5)=>2 [3,4,1,2,5]=>[5]=>([],5)=>1 [3,4,1,5,2]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [3,4,2,1,5]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [3,4,2,5,1]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [3,4,5,1,2]=>[5]=>([],5)=>1 [3,4,5,2,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [3,5,1,2,4]=>[5]=>([],5)=>1 [3,5,1,4,2]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [3,5,2,1,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [3,5,2,4,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [3,5,4,1,2]=>[2,3]=>([(2,4),(3,4)],5)=>2 [4,1,2,3,5]=>[5]=>([],5)=>1 [4,1,2,5,3]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [4,1,3,2,5]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [4,1,3,5,2]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [4,1,5,2,3]=>[2,3]=>([(2,4),(3,4)],5)=>2 [4,2,1,3,5]=>[2,3]=>([(2,4),(3,4)],5)=>2 [4,2,3,1,5]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [4,2,3,5,1]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [4,2,5,1,3]=>[2,3]=>([(2,4),(3,4)],5)=>2 [4,3,1,2,5]=>[1,4]=>([(3,4)],5)=>2 [4,3,5,1,2]=>[1,4]=>([(3,4)],5)=>2 [4,5,1,2,3]=>[5]=>([],5)=>1 [4,5,1,3,2]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [4,5,2,1,3]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [4,5,2,3,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [4,5,3,1,2]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [5,1,2,3,4]=>[5]=>([],5)=>1 [5,1,2,4,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,1,3,2,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [5,1,3,4,2]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,1,4,2,3]=>[2,3]=>([(2,4),(3,4)],5)=>2 [5,2,1,3,4]=>[2,3]=>([(2,4),(3,4)],5)=>2 [5,2,3,1,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [5,2,3,4,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,2,4,1,3]=>[2,3]=>([(2,4),(3,4)],5)=>2 [5,3,1,2,4]=>[1,4]=>([(3,4)],5)=>2 [5,3,4,1,2]=>[1,4]=>([(3,4)],5)=>2 [5,4,1,2,3]=>[1,4]=>([(3,4)],5)=>2 [1,2,3,4,5,6]=>[6]=>([],6)=>1 [1,2,3,4,6,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [1,2,3,5,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,3,5,6,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,3,6,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,4,3,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,2,4,5,3,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,2,4,5,6,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,2,4,6,3,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,2,5,3,4,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,2,5,6,3,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,2,6,3,4,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,3,2,4,5,6]=>[1,5]=>([(4,5)],6)=>2 [1,3,4,2,5,6]=>[1,5]=>([(4,5)],6)=>2 [1,3,4,5,2,6]=>[1,5]=>([(4,5)],6)=>2 [1,3,4,5,6,2]=>[1,5]=>([(4,5)],6)=>2 [1,3,4,6,2,5]=>[1,5]=>([(4,5)],6)=>2 [1,3,5,2,4,6]=>[1,5]=>([(4,5)],6)=>2 [1,3,5,6,2,4]=>[1,5]=>([(4,5)],6)=>2 [1,3,6,2,4,5]=>[1,5]=>([(4,5)],6)=>2 [1,4,2,3,5,6]=>[1,5]=>([(4,5)],6)=>2 [1,4,5,2,3,6]=>[1,5]=>([(4,5)],6)=>2 [1,4,5,6,2,3]=>[1,5]=>([(4,5)],6)=>2 [1,4,6,2,3,5]=>[1,5]=>([(4,5)],6)=>2 [1,5,2,3,4,6]=>[1,5]=>([(4,5)],6)=>2 [1,5,4,2,3,6]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [1,5,4,6,2,3]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [1,5,6,2,3,4]=>[1,5]=>([(4,5)],6)=>2 [1,6,2,3,4,5]=>[1,5]=>([(4,5)],6)=>2 [1,6,4,2,3,5]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [1,6,4,5,2,3]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [1,6,5,2,3,4]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [2,1,3,4,5,6]=>[6]=>([],6)=>1 [2,1,3,4,6,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,1,3,5,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,1,3,5,6,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,1,3,6,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,1,4,3,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,1,4,5,3,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,1,4,5,6,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,1,4,6,3,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,1,5,3,4,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,1,5,6,3,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,1,6,3,4,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,3,1,4,5,6]=>[6]=>([],6)=>1 [2,3,1,4,6,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,1,5,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,3,1,5,6,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,3,1,6,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,3,4,1,5,6]=>[6]=>([],6)=>1 [2,3,4,1,6,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,4,5,1,6]=>[6]=>([],6)=>1 [2,3,4,5,6,1]=>[6]=>([],6)=>1 [2,3,4,6,1,5]=>[6]=>([],6)=>1 [2,3,4,6,5,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,5,1,4,6]=>[6]=>([],6)=>1 [2,3,5,1,6,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,5,4,1,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,5,4,6,1]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,5,6,1,4]=>[6]=>([],6)=>1 [2,3,5,6,4,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,6,1,4,5]=>[6]=>([],6)=>1 [2,3,6,1,5,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,6,4,1,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,6,4,5,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,3,6,5,1,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,4,1,3,5,6]=>[6]=>([],6)=>1 [2,4,1,3,6,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,4,1,5,3,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,4,1,5,6,3]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,4,1,6,3,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,4,3,1,5,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,4,3,5,1,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,4,3,5,6,1]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,4,3,6,1,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,4,5,1,3,6]=>[6]=>([],6)=>1 [2,4,5,1,6,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,4,5,3,1,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,4,5,3,6,1]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,4,5,6,1,3]=>[6]=>([],6)=>1 [2,4,5,6,3,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,4,6,1,3,5]=>[6]=>([],6)=>1 [2,4,6,1,5,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,4,6,3,1,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,4,6,3,5,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,4,6,5,1,3]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,5,1,3,4,6]=>[6]=>([],6)=>1 [2,5,1,3,6,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,5,1,4,3,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,5,1,4,6,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,5,1,6,3,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,5,3,1,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,5,3,4,1,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,5,3,4,6,1]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,5,3,6,1,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,5,4,1,3,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,5,4,6,1,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,5,6,1,3,4]=>[6]=>([],6)=>1 [2,5,6,1,4,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,5,6,3,1,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,5,6,3,4,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,5,6,4,1,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,6,1,3,4,5]=>[6]=>([],6)=>1 [2,6,1,3,5,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,6,1,4,3,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,6,1,4,5,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,6,1,5,3,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,6,3,1,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,6,3,4,1,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,6,3,4,5,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,6,3,5,1,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [2,6,4,1,3,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,6,4,5,1,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,6,5,1,3,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,1,2,4,5,6]=>[6]=>([],6)=>1 [3,1,2,4,6,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,1,2,5,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,1,2,5,6,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,1,2,6,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,1,4,2,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,1,4,5,2,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,1,4,5,6,2]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,1,4,6,2,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,1,5,2,4,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,1,5,6,2,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,1,6,2,4,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,2,1,4,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,2,4,1,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,2,4,5,1,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,2,4,5,6,1]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,2,4,6,1,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,2,5,1,4,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,2,5,6,1,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,2,6,1,4,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,4,1,2,5,6]=>[6]=>([],6)=>1 [3,4,1,2,6,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,4,1,5,2,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,4,1,5,6,2]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,4,1,6,2,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,4,2,1,5,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,4,2,5,1,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,4,2,5,6,1]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,4,2,6,1,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,4,5,1,2,6]=>[6]=>([],6)=>1 [3,4,5,1,6,2]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,4,5,2,1,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,4,5,2,6,1]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,4,5,6,1,2]=>[6]=>([],6)=>1 [3,4,5,6,2,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,4,6,1,2,5]=>[6]=>([],6)=>1 [3,4,6,1,5,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,4,6,2,1,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,4,6,2,5,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,4,6,5,1,2]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,5,1,2,4,6]=>[6]=>([],6)=>1 [3,5,1,2,6,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,5,1,4,2,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,5,1,4,6,2]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,5,1,6,2,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,5,2,1,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,5,2,4,1,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,5,2,4,6,1]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,5,2,6,1,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,5,4,1,2,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,5,4,6,1,2]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,5,6,1,2,4]=>[6]=>([],6)=>1 [3,5,6,1,4,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,5,6,2,1,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,5,6,2,4,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,5,6,4,1,2]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,6,1,2,4,5]=>[6]=>([],6)=>1 [3,6,1,2,5,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,6,1,4,2,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,6,1,4,5,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,6,1,5,2,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,6,2,1,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,6,2,4,1,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,6,2,4,5,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,6,2,5,1,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [3,6,4,1,2,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,6,4,5,1,2]=>[2,4]=>([(3,5),(4,5)],6)=>2 [3,6,5,1,2,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [4,1,2,3,5,6]=>[6]=>([],6)=>1 [4,1,2,3,6,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,1,2,5,3,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,1,2,5,6,3]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,1,2,6,3,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,1,3,2,5,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,1,3,5,2,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,1,3,5,6,2]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,1,3,6,2,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,1,5,2,3,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [4,1,5,6,2,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [4,1,6,2,3,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [4,2,1,3,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [4,2,3,1,5,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,2,3,5,1,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,2,3,5,6,1]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,2,3,6,1,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,2,5,1,3,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [4,2,5,6,1,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [4,2,6,1,3,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [4,3,1,2,5,6]=>[1,5]=>([(4,5)],6)=>2 [4,3,5,1,2,6]=>[1,5]=>([(4,5)],6)=>2 [4,3,5,6,1,2]=>[1,5]=>([(4,5)],6)=>2 [4,3,6,1,2,5]=>[1,5]=>([(4,5)],6)=>2 [4,5,1,2,3,6]=>[6]=>([],6)=>1 [4,5,1,2,6,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,5,1,3,2,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,5,1,3,6,2]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,5,1,6,2,3]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,5,2,1,3,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,5,2,3,1,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,5,2,3,6,1]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,5,2,6,1,3]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,5,3,1,2,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,5,3,6,1,2]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,5,6,1,2,3]=>[6]=>([],6)=>1 [4,5,6,1,3,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,5,6,2,1,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,5,6,2,3,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,5,6,3,1,2]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,6,1,2,3,5]=>[6]=>([],6)=>1 [4,6,1,2,5,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,6,1,3,2,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,6,1,3,5,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,6,1,5,2,3]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,6,2,1,3,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,6,2,3,1,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,6,2,3,5,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,6,2,5,1,3]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,6,3,1,2,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,6,3,5,1,2]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [4,6,5,1,2,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [5,1,2,3,4,6]=>[6]=>([],6)=>1 [5,1,2,3,6,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,2,4,3,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,2,4,6,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,2,6,3,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [5,1,3,2,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [5,1,3,4,2,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,3,4,6,2]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,3,6,2,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [5,1,4,2,3,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [5,1,4,6,2,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [5,1,6,2,3,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [5,2,1,3,4,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [5,2,3,1,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [5,2,3,4,1,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,2,3,4,6,1]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,2,3,6,1,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [5,2,4,1,3,6]=>[2,4]=>([(3,5),(4,5)],6)=>2 [5,2,4,6,1,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [5,2,6,1,3,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [5,3,1,2,4,6]=>[1,5]=>([(4,5)],6)=>2 [5,3,4,1,2,6]=>[1,5]=>([(4,5)],6)=>2 [5,3,4,6,1,2]=>[1,5]=>([(4,5)],6)=>2 [5,3,6,1,2,4]=>[1,5]=>([(4,5)],6)=>2 [5,4,1,2,3,6]=>[1,5]=>([(4,5)],6)=>2 [5,4,6,1,2,3]=>[1,5]=>([(4,5)],6)=>2 [5,6,1,2,3,4]=>[6]=>([],6)=>1 [5,6,1,2,4,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,6,1,3,2,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,6,1,3,4,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,6,1,4,2,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,6,2,1,3,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [5,6,2,3,1,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,6,2,3,4,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,6,2,4,1,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,6,3,1,2,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [5,6,3,4,1,2]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,6,4,1,2,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [6,1,2,3,4,5]=>[6]=>([],6)=>1 [6,1,2,3,5,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [6,1,2,4,3,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [6,1,2,4,5,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [6,1,2,5,3,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [6,1,3,2,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [6,1,3,4,2,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [6,1,3,4,5,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [6,1,3,5,2,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [6,1,4,2,3,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [6,1,4,5,2,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [6,1,5,2,3,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [6,2,1,3,4,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [6,2,3,1,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [6,2,3,4,1,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [6,2,3,4,5,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [6,2,3,5,1,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [6,2,4,1,3,5]=>[2,4]=>([(3,5),(4,5)],6)=>2 [6,2,4,5,1,3]=>[2,4]=>([(3,5),(4,5)],6)=>2 [6,2,5,1,3,4]=>[2,4]=>([(3,5),(4,5)],6)=>2 [6,3,1,2,4,5]=>[1,5]=>([(4,5)],6)=>2 [6,3,4,1,2,5]=>[1,5]=>([(4,5)],6)=>2 [6,3,4,5,1,2]=>[1,5]=>([(4,5)],6)=>2 [6,3,5,1,2,4]=>[1,5]=>([(4,5)],6)=>2 [6,4,1,2,3,5]=>[1,5]=>([(4,5)],6)=>2 [6,4,5,1,2,3]=>[1,5]=>([(4,5)],6)=>2 [6,5,1,2,3,4]=>[1,5]=>([(4,5)],6)=>2 [6,5,4,1,2,3]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [2,3,4,5,7,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,4,6,7,5,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,4,7,1,6,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,4,7,5,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,5,6,7,4,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,5,7,1,6,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,5,7,4,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,6,7,1,5,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,6,7,4,5,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,7,1,4,6,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,7,1,5,6,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,3,7,4,5,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,4,5,6,7,3,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,4,5,7,1,6,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,4,5,7,3,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,4,6,7,1,5,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,4,6,7,3,5,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,4,7,1,3,6,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,4,7,1,5,6,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,4,7,3,5,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,5,6,7,1,4,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,5,6,7,3,4,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,5,7,1,3,6,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,5,7,1,4,6,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,5,7,3,4,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,6,7,1,3,5,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,6,7,1,4,5,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,6,7,3,4,5,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,7,1,3,4,6,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,7,1,3,5,6,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,7,1,4,5,6,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [2,7,3,4,5,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,4,5,6,7,2,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,4,5,7,1,6,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,4,5,7,2,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,4,6,7,1,5,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,4,6,7,2,5,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,4,7,1,2,6,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,4,7,1,5,6,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,4,7,2,5,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,5,6,7,1,4,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,5,6,7,2,4,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,5,7,1,2,6,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,5,7,1,4,6,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,5,7,2,4,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,6,7,1,2,5,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,6,7,1,4,5,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,6,7,2,4,5,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,7,1,2,4,6,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,7,1,2,5,6,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,7,1,4,5,6,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [3,7,2,4,5,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,5,6,7,1,3,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,5,6,7,2,3,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,5,7,1,2,6,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,5,7,1,3,6,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,5,7,2,3,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,6,7,1,2,5,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,6,7,1,3,5,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,6,7,2,3,5,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,7,1,2,3,6,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,7,1,2,5,6,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,7,1,3,5,6,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,7,2,3,5,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [5,6,7,1,2,4,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [5,6,7,1,3,4,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [5,6,7,2,3,4,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [5,7,1,2,3,6,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [5,7,1,2,4,6,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [5,7,1,3,4,6,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [5,7,2,3,4,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [6,7,1,2,3,5,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [6,7,1,2,4,5,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [6,7,1,3,4,5,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [6,7,2,3,4,5,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [7,1,2,3,4,6,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [7,1,2,3,5,6,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [7,1,2,4,5,6,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [7,1,3,4,5,6,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [7,2,3,4,5,6,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [4,5,6,7,8,2,3,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [5,6,7,8,2,3,4,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,5,6,7,8,4,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,4,5,6,8,7,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,4,8,5,6,7,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,8,3,4,5,6,7,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [5,6,7,8,1,3,4,2]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [5,6,7,8,1,2,4,3]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [3,5,6,7,8,2,4,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,4,8,3,5,6,7,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,8,1,5,6,7,4]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [4,8,2,3,5,6,7,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,8,1,3,5,6,7,4]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [8,1,2,3,5,6,7,4]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [4,8,1,2,5,6,7,3]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [3,4,8,1,5,6,7,2]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,8,1,4,6,7,5]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,8,1,3,4,5,7,6]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [6,7,8,1,3,4,5,2]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [6,7,8,1,2,4,5,3]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [6,7,8,1,2,3,5,4]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [3,4,5,8,1,2,7,6]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,7,8,3,4,5,6,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,5,6,7,8,3,4,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [3,5,6,7,8,1,4,2]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [6,8,1,2,3,4,7,5]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,5,7,8,1,4,6,3]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,4,5,6,8,1,7,3]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,8,1,4,5,7,6]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [7,8,1,2,3,5,6,4]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [8,1,2,3,4,5,7,6]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [8,1,3,4,5,6,7,2]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [4,5,6,7,8,1,3,2]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,6,8,4,5,7,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [4,8,1,3,5,6,7,2]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [3,8,1,2,5,6,7,4]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,4,8,1,5,6,7,3]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [3,4,8,2,5,6,7,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,4,6,8,1,5,7,3]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,4,6,8,3,5,7,1]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,4,6,8,1,3,7,5]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,4,8,1,6,7,5]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,3,4,8,1,5,7,6]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 [2,5,6,7,8,1,4,3]=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
DEX composition
Description
The DEX composition of a permutation.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.