Identifier
Values
=>
Cc0020;cc-rep
[+]=>[1]=>[1]=>([],1)=>0 [-]=>[1]=>[1]=>([],1)=>0 [+,+]=>[1,2]=>[1,2]=>([],2)=>0 [-,+]=>[2,1]=>[2,1]=>([(0,1)],2)=>1 [+,-]=>[1,2]=>[1,2]=>([],2)=>0 [-,-]=>[1,2]=>[1,2]=>([],2)=>0 [2,1]=>[2,1]=>[2,1]=>([(0,1)],2)=>1 [+,+,+]=>[1,2,3]=>[1,2,3]=>([],3)=>0 [+,-,+]=>[1,3,2]=>[1,3,2]=>([(1,2)],3)=>1 [+,+,-]=>[1,2,3]=>[1,2,3]=>([],3)=>0 [-,-,+]=>[3,1,2]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>2 [-,+,-]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)=>1 [+,-,-]=>[1,2,3]=>[1,2,3]=>([],3)=>0 [-,-,-]=>[1,2,3]=>[1,2,3]=>([],3)=>0 [+,3,2]=>[1,3,2]=>[1,3,2]=>([(1,2)],3)=>1 [-,3,2]=>[3,1,2]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>2 [2,1,-]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)=>1 [2,3,1]=>[3,1,2]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>2 [3,-,1]=>[3,1,2]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>2 [+,+,+,+]=>[1,2,3,4]=>[1,2,3,4]=>([],4)=>0 [+,+,-,+]=>[1,2,4,3]=>[1,2,4,3]=>([(2,3)],4)=>1 [+,+,+,-]=>[1,2,3,4]=>[1,2,3,4]=>([],4)=>0 [+,-,-,+]=>[1,4,2,3]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)=>2 [+,-,+,-]=>[1,3,2,4]=>[1,3,2,4]=>([(2,3)],4)=>1 [+,+,-,-]=>[1,2,3,4]=>[1,2,3,4]=>([],4)=>0 [-,-,-,+]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [-,-,+,-]=>[3,1,2,4]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>2 [-,+,-,-]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)=>1 [+,-,-,-]=>[1,2,3,4]=>[1,2,3,4]=>([],4)=>0 [-,-,-,-]=>[1,2,3,4]=>[1,2,3,4]=>([],4)=>0 [+,+,4,3]=>[1,2,4,3]=>[1,2,4,3]=>([(2,3)],4)=>1 [+,-,4,3]=>[1,4,2,3]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)=>2 [-,-,4,3]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [+,3,2,-]=>[1,3,2,4]=>[1,3,2,4]=>([(2,3)],4)=>1 [-,3,2,-]=>[3,1,2,4]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>2 [+,3,4,2]=>[1,4,2,3]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)=>2 [-,3,4,2]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [+,4,-,2]=>[1,4,2,3]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)=>2 [-,4,-,2]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [2,1,-,-]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)=>1 [2,3,1,-]=>[3,1,2,4]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>2 [2,3,4,1]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [2,4,-,1]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [3,-,1,-]=>[3,1,2,4]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>2 [3,-,4,1]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [4,-,-,1]=>[4,1,2,3]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 [+,+,+,+,+]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)=>0 [-,+,+,+,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [+,+,+,-,+]=>[1,2,3,5,4]=>[1,2,3,5,4]=>([(3,4)],5)=>1 [+,+,+,+,-]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)=>0 [-,+,+,-,+]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [+,+,-,-,+]=>[1,2,5,3,4]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)=>2 [+,+,-,+,-]=>[1,2,4,3,5]=>[1,2,4,3,5]=>([(3,4)],5)=>1 [+,+,+,-,-]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)=>0 [+,-,-,-,+]=>[1,5,2,3,4]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [+,-,-,+,-]=>[1,4,2,3,5]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5)=>2 [+,-,+,-,-]=>[1,3,2,4,5]=>[1,3,2,4,5]=>([(3,4)],5)=>1 [+,+,-,-,-]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)=>0 [-,-,-,-,+]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [-,-,-,+,-]=>[4,1,2,3,5]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,-,+,-,-]=>[3,1,2,4,5]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>2 [-,+,-,-,-]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)=>1 [+,-,-,-,-]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)=>0 [-,-,-,-,-]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)=>0 [+,+,+,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>([(3,4)],5)=>1 [-,+,+,5,4]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [+,+,-,5,4]=>[1,2,5,3,4]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)=>2 [+,-,-,5,4]=>[1,5,2,3,4]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,-,-,5,4]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [+,+,4,3,-]=>[1,2,4,3,5]=>[1,2,4,3,5]=>([(3,4)],5)=>1 [+,-,4,3,-]=>[1,4,2,3,5]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5)=>2 [-,-,4,3,-]=>[4,1,2,3,5]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [+,+,4,5,3]=>[1,2,5,3,4]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)=>2 [+,-,4,5,3]=>[1,5,2,3,4]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,-,4,5,3]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [+,+,5,-,3]=>[1,2,5,3,4]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)=>2 [+,-,5,-,3]=>[1,5,2,3,4]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,-,5,-,3]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [+,3,2,-,-]=>[1,3,2,4,5]=>[1,3,2,4,5]=>([(3,4)],5)=>1 [-,3,2,-,-]=>[3,1,2,4,5]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>2 [+,3,4,2,-]=>[1,4,2,3,5]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5)=>2 [-,3,4,2,-]=>[4,1,2,3,5]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [+,3,4,5,2]=>[1,5,2,3,4]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,3,4,5,2]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [+,3,5,-,2]=>[1,5,2,3,4]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,3,5,-,2]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [+,4,-,2,-]=>[1,4,2,3,5]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5)=>2 [-,4,-,2,-]=>[4,1,2,3,5]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [+,4,-,5,2]=>[1,5,2,3,4]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,4,-,5,2]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [+,5,-,-,2]=>[1,5,2,3,4]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [-,5,-,-,2]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [2,1,+,+,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [2,1,+,-,+]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [2,1,-,-,-]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)=>1 [2,1,+,5,4]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [2,3,1,-,-]=>[3,1,2,4,5]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>2 [2,3,4,1,-]=>[4,1,2,3,5]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [2,3,4,5,1]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [2,3,5,-,1]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [2,4,-,1,-]=>[4,1,2,3,5]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [2,4,-,5,1]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [2,5,-,-,1]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [3,1,2,+,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [3,1,2,-,+]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [3,1,2,5,4]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [3,+,1,+,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [3,+,1,-,+]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [3,-,1,-,-]=>[3,1,2,4,5]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>2 [3,+,1,5,4]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [3,-,4,1,-]=>[4,1,2,3,5]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [3,-,4,5,1]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [3,-,5,-,1]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [4,1,2,3,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [4,1,2,5,3]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [4,1,+,2,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [4,1,+,5,2]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [4,+,1,3,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [4,+,1,5,3]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [4,+,+,1,+]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [4,-,-,1,-]=>[4,1,2,3,5]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [4,+,+,5,1]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [4,-,-,5,1]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,1,2,3,4]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,1,2,+,3]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,1,2,-,3]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [5,1,+,2,4]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,1,+,+,2]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,1,+,-,2]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [5,+,1,3,4]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,+,1,+,3]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,+,1,-,3]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [5,+,+,1,4]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,+,+,+,1]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [5,+,+,-,1]=>[2,3,5,1,4]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 [5,-,-,-,1]=>[5,1,2,3,4]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [+,+,+,+,+,+]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>0 [+,-,+,+,+,+]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,+,+,+,-,+]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>([(4,5)],6)=>1 [+,+,+,+,+,-]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>0 [-,+,+,+,+,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,-,+,+,-,+]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,+,+,-,-,+]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)=>2 [+,+,+,-,+,-]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>([(4,5)],6)=>1 [+,+,+,+,-,-]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>0 [-,+,+,-,+,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,+,-,-,-,+]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,+,-,-,+,-]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6)=>2 [+,+,-,+,-,-]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>([(4,5)],6)=>1 [+,+,+,-,-,-]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>0 [+,-,-,-,-,+]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [+,-,-,-,+,-]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,-,-,+,-,-]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6)=>2 [+,-,+,-,-,-]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>([(4,5)],6)=>1 [+,+,-,-,-,-]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>0 [-,-,-,-,-,+]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [-,-,-,-,+,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,-,+,-,-]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,+,-,-,-]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>2 [-,+,-,-,-,-]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)=>1 [+,-,-,-,-,-]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>0 [-,-,-,-,-,-]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>0 [+,+,+,+,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>([(4,5)],6)=>1 [+,-,+,+,6,5]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,+,+,-,6,5]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)=>2 [+,+,-,-,6,5]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,-,-,-,6,5]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,-,-,6,5]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,+,+,5,4,-]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>([(4,5)],6)=>1 [-,+,+,5,4,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,+,-,5,4,-]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6)=>2 [+,-,-,5,4,-]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,-,5,4,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [+,+,+,5,6,4]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)=>2 [+,+,-,5,6,4]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,-,-,5,6,4]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,-,5,6,4]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,+,+,6,-,4]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)=>2 [+,+,-,6,-,4]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,-,-,6,-,4]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,-,6,-,4]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,+,4,3,-,-]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>([(4,5)],6)=>1 [+,-,4,3,-,-]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6)=>2 [-,-,4,3,-,-]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,+,4,5,3,-]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6)=>2 [+,-,4,5,3,-]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,4,5,3,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [+,+,4,5,6,3]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,-,4,5,6,3]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,4,5,6,3]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,+,4,6,-,3]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,-,4,6,-,3]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,4,6,-,3]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,+,5,-,3,-]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6)=>2 [+,-,5,-,3,-]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,-,5,-,3,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [+,+,5,-,6,3]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,-,5,-,6,3]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,5,-,6,3]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,+,6,-,-,3]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,-,6,-,-,3]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,-,6,-,-,3]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,3,2,+,+,+]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,3,2,+,-,+]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,3,2,-,-,-]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>([(4,5)],6)=>1 [-,3,2,-,-,-]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>2 [+,3,2,+,6,5]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,3,4,2,-,-]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6)=>2 [-,3,4,2,-,-]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,3,4,5,2,-]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,3,4,5,2,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [+,3,4,5,6,2]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,3,4,5,6,2]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,3,4,6,-,2]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,3,4,6,-,2]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,3,5,-,2,-]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,3,5,-,2,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [+,3,5,-,6,2]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,3,5,-,6,2]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,3,6,-,-,2]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,3,6,-,-,2]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,4,2,3,+,+]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,4,2,3,-,+]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,4,2,3,6,5]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,4,+,2,+,+]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,4,+,2,-,+]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,4,-,2,-,-]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6)=>2 [-,4,-,2,-,-]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,4,+,2,6,5]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,4,-,5,2,-]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,4,-,5,2,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [+,4,-,5,6,2]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,4,-,5,6,2]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,4,-,6,-,2]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,4,-,6,-,2]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,5,2,3,4,+]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,5,2,3,6,4]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,5,2,+,3,+]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,5,2,+,6,3]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,5,+,2,4,+]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,5,+,2,6,4]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,5,+,+,2,+]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,5,-,-,2,-]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [-,5,-,-,2,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [+,5,+,+,6,2]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,5,-,-,6,2]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,5,-,-,6,2]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [+,6,2,3,4,5]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,6,2,3,+,4]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,6,2,3,-,4]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,6,2,+,3,5]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,6,2,+,+,3]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,6,2,+,-,3]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,6,+,2,4,5]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,6,+,2,+,4]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,6,+,2,-,4]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,6,+,+,2,5]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,6,+,+,+,2]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [+,6,+,+,-,2]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [+,6,-,-,-,2]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [-,6,-,-,-,2]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [2,1,+,+,+,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [2,1,+,-,+,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [2,1,-,-,-,-]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)=>1 [2,1,+,5,4,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [2,3,1,-,-,-]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>2 [2,3,4,1,-,-]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [2,3,4,5,1,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [2,3,4,6,-,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [2,3,5,-,1,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [2,3,5,-,6,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [2,3,6,-,-,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [2,4,-,1,-,-]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [2,4,-,5,1,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [2,4,-,5,6,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [2,4,-,6,-,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [2,5,-,-,1,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [2,5,-,-,6,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [2,6,-,-,-,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [3,1,2,+,+,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,1,2,-,+,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [3,1,2,5,4,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [3,+,1,+,+,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [3,+,1,-,+,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [3,-,1,-,-,-]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>2 [3,+,1,5,4,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [3,-,4,1,-,-]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [3,-,4,5,1,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [3,-,4,5,6,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [3,-,4,6,-,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [3,-,5,-,1,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [3,-,5,-,6,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [3,-,6,-,-,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [4,1,2,3,+,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,1,2,5,3,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [4,1,+,2,+,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,1,+,5,2,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [4,+,1,3,+,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,+,1,5,3,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [4,+,+,1,+,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [4,-,-,1,-,-]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [4,+,+,5,1,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [4,-,-,5,1,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,-,-,5,6,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [4,-,-,6,-,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,1,2,3,4,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,2,+,3,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,2,-,3,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [5,1,+,2,4,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,+,+,2,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,1,+,-,2,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [5,+,1,3,4,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,+,1,+,3,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,+,1,-,3,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [5,+,+,1,4,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,+,+,+,1,-]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [5,+,+,-,1,-]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 [5,-,-,-,1,-]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,-,-,-,6,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,-,-,-,-,1]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
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 largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
upper permutation
Description
The upper bound in the Grassmann interval corresponding to the decorated permutation.
Let $I$ be the anti-exceedance set of a decorated permutation $w$. Let $v$ be the $k$-Grassmannian permutation determined by $v[k] = w^{-1}(I)$ and let $u$ be the permutation satisfying $u = wv$. Then $[u, v]$ is the Grassmann interval corresponding to $w$.
This map returns $v$.