Identifier
Values
=>
Cc0020;cc-rep
[1]=>=>[1]=>([],1)=>1 [1,2]=>0=>[2]=>([],2)=>1 [2,1]=>1=>[1,1]=>([(0,1)],2)=>2 [1,2,3]=>00=>[3]=>([],3)=>1 [1,3,2]=>01=>[2,1]=>([(0,2),(1,2)],3)=>2 [2,1,3]=>10=>[1,2]=>([(1,2)],3)=>2 [2,3,1]=>10=>[1,2]=>([(1,2)],3)=>2 [3,1,2]=>10=>[1,2]=>([(1,2)],3)=>2 [3,2,1]=>11=>[1,1,1]=>([(0,1),(0,2),(1,2)],3)=>3 [1,2,3,4]=>000=>[4]=>([],4)=>1 [1,2,4,3]=>001=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2 [1,3,2,4]=>010=>[2,2]=>([(1,3),(2,3)],4)=>2 [1,3,4,2]=>010=>[2,2]=>([(1,3),(2,3)],4)=>2 [1,4,2,3]=>010=>[2,2]=>([(1,3),(2,3)],4)=>2 [2,1,3,4]=>100=>[1,3]=>([(2,3)],4)=>2 [2,3,1,4]=>100=>[1,3]=>([(2,3)],4)=>2 [2,3,4,1]=>100=>[1,3]=>([(2,3)],4)=>2 [2,4,1,3]=>100=>[1,3]=>([(2,3)],4)=>2 [3,1,2,4]=>100=>[1,3]=>([(2,3)],4)=>2 [3,1,4,2]=>110=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>3 [3,2,1,4]=>110=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>3 [3,2,4,1]=>110=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>3 [3,4,1,2]=>100=>[1,3]=>([(2,3)],4)=>2 [3,4,2,1]=>110=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>3 [4,1,2,3]=>100=>[1,3]=>([(2,3)],4)=>2 [4,1,3,2]=>110=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>3 [4,2,1,3]=>110=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>3 [4,2,3,1]=>110=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>3 [4,3,2,1]=>111=>[1,1,1,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>4 [1,2,3,4,5]=>0000=>[5]=>([],5)=>1 [1,2,3,5,4]=>0001=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>2 [1,2,4,3,5]=>0010=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [1,2,4,5,3]=>0010=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [1,2,5,3,4]=>0010=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>2 [1,3,2,4,5]=>0100=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,3,4,2,5]=>0100=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,3,4,5,2]=>0100=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,3,5,2,4]=>0100=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,4,2,3,5]=>0100=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,4,5,2,3]=>0100=>[2,3]=>([(2,4),(3,4)],5)=>2 [1,5,2,3,4]=>0100=>[2,3]=>([(2,4),(3,4)],5)=>2 [2,1,3,4,5]=>1000=>[1,4]=>([(3,4)],5)=>2 [2,3,1,4,5]=>1000=>[1,4]=>([(3,4)],5)=>2 [2,3,4,1,5]=>1000=>[1,4]=>([(3,4)],5)=>2 [2,3,4,5,1]=>1000=>[1,4]=>([(3,4)],5)=>2 [2,3,5,1,4]=>1000=>[1,4]=>([(3,4)],5)=>2 [2,4,1,3,5]=>1000=>[1,4]=>([(3,4)],5)=>2 [2,4,5,1,3]=>1000=>[1,4]=>([(3,4)],5)=>2 [2,5,1,3,4]=>1000=>[1,4]=>([(3,4)],5)=>2 [3,1,2,4,5]=>1000=>[1,4]=>([(3,4)],5)=>2 [3,1,4,2,5]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,1,4,5,2]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,1,5,2,4]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,2,1,4,5]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,2,4,1,5]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,2,4,5,1]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,2,5,1,4]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,4,1,2,5]=>1000=>[1,4]=>([(3,4)],5)=>2 [3,4,1,5,2]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,4,2,1,5]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,4,2,5,1]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,4,5,1,2]=>1000=>[1,4]=>([(3,4)],5)=>2 [3,4,5,2,1]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,5,1,2,4]=>1000=>[1,4]=>([(3,4)],5)=>2 [3,5,1,4,2]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,5,2,1,4]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [3,5,2,4,1]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,1,2,3,5]=>1000=>[1,4]=>([(3,4)],5)=>2 [4,1,3,2,5]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,1,3,5,2]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,1,5,2,3]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,1,5,3,2]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [4,2,1,3,5]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,2,1,5,3]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [4,2,3,1,5]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,2,3,5,1]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,2,5,1,3]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,2,5,3,1]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [4,3,1,5,2]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [4,3,2,1,5]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [4,3,2,5,1]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [4,3,5,2,1]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [4,5,1,2,3]=>1000=>[1,4]=>([(3,4)],5)=>2 [4,5,1,3,2]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,5,2,1,3]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,5,2,3,1]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [4,5,3,2,1]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,1,2,3,4]=>1000=>[1,4]=>([(3,4)],5)=>2 [5,1,3,2,4]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [5,1,3,4,2]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [5,1,4,2,3]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [5,1,4,3,2]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,2,1,3,4]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [5,2,1,4,3]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,2,3,1,4]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [5,2,3,4,1]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [5,2,4,1,3]=>1100=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>3 [5,2,4,3,1]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,3,1,4,2]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,3,2,1,4]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,3,2,4,1]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,3,4,2,1]=>1110=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 [5,4,3,2,1]=>1111=>[1,1,1,1,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5 [1,2,3,4,5,6]=>00000=>[6]=>([],6)=>1 [1,2,3,4,6,5]=>00001=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 [1,2,3,5,4,6]=>00010=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [1,2,3,5,6,4]=>00010=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [1,2,3,6,4,5]=>00010=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2 [1,2,4,3,5,6]=>00100=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,4,5,3,6]=>00100=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,4,5,6,3]=>00100=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,4,6,3,5]=>00100=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,5,3,4,6]=>00100=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,5,6,3,4]=>00100=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,2,6,3,4,5]=>00100=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>2 [1,3,2,4,5,6]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,3,4,2,5,6]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,3,4,5,2,6]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,3,4,5,6,2]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,3,4,6,2,5]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,3,5,2,4,6]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,3,5,6,2,4]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,3,6,2,4,5]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,4,2,3,5,6]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,4,5,2,3,6]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,4,5,6,2,3]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,4,6,2,3,5]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,5,2,3,4,6]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,5,6,2,3,4]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [1,6,2,3,4,5]=>01000=>[2,4]=>([(3,5),(4,5)],6)=>2 [2,1,3,4,5,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,3,1,4,5,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,3,4,1,5,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,3,4,5,1,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,3,4,5,6,1]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,3,4,6,1,5]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,3,5,1,4,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,3,5,6,1,4]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,3,6,1,4,5]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,4,1,3,5,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,4,5,1,3,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,4,5,6,1,3]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,4,6,1,3,5]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,5,1,3,4,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,5,6,1,3,4]=>10000=>[1,5]=>([(4,5)],6)=>2 [2,6,1,3,4,5]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,1,2,4,5,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,1,4,2,5,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,1,4,5,2,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,1,4,5,6,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,1,4,6,2,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,1,5,2,4,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,1,5,6,2,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,1,6,2,4,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,2,1,4,5,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,2,4,1,5,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,2,4,5,1,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,2,4,5,6,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,2,4,6,1,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,2,5,1,4,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,2,5,6,1,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,2,6,1,4,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,1,2,5,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,4,1,5,2,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,1,5,6,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,1,6,2,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,2,1,5,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,2,5,1,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,2,5,6,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,2,6,1,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,5,1,2,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,4,5,1,6,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,5,2,1,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,5,2,6,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,5,6,1,2]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,4,5,6,2,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,6,1,2,5]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,4,6,1,5,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,6,2,1,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,4,6,2,5,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,1,2,4,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,5,1,4,2,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,1,4,6,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,1,6,2,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,2,1,4,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,2,4,1,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,2,4,6,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,2,6,1,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,6,1,2,4]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,5,6,1,4,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,6,2,1,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,5,6,2,4,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,6,1,2,4,5]=>10000=>[1,5]=>([(4,5)],6)=>2 [3,6,1,4,2,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,6,1,4,5,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,6,1,5,2,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,6,2,1,4,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,6,2,4,1,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,6,2,4,5,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [3,6,2,5,1,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,1,2,3,5,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [4,1,3,2,5,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,1,3,5,2,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,1,3,5,6,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,1,3,6,2,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,1,5,2,3,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,1,5,2,6,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,1,5,3,2,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,1,5,3,6,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,1,5,6,2,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,1,5,6,3,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,1,6,2,3,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,1,6,2,5,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,1,6,3,2,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,1,6,3,5,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,1,3,5,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,2,1,5,3,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,1,5,6,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,1,6,3,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,3,1,5,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,2,3,5,1,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,2,3,5,6,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,2,3,6,1,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,2,5,1,3,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,2,5,1,6,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,5,3,1,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,5,3,6,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,5,6,1,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,2,5,6,3,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,6,1,3,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,2,6,1,5,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,6,3,1,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,2,6,3,5,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,1,5,2,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,1,5,6,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,1,6,2,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,2,1,5,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,2,5,1,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,2,5,6,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,2,6,1,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,5,1,6,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,5,2,1,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,5,2,6,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,5,6,2,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,6,1,5,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,6,2,1,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,3,6,2,5,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,5,1,2,3,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [4,5,1,3,2,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,1,3,6,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,1,6,2,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,1,6,3,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,5,2,1,3,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,2,1,6,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,5,2,3,1,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,2,3,6,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,2,6,1,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,2,6,3,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,5,3,1,6,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,5,3,2,1,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,5,3,2,6,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,5,3,6,2,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,5,6,1,2,3]=>10000=>[1,5]=>([(4,5)],6)=>2 [4,5,6,1,3,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,6,2,1,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,6,2,3,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,5,6,3,2,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,6,1,2,3,5]=>10000=>[1,5]=>([(4,5)],6)=>2 [4,6,1,3,2,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,6,1,3,5,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,6,1,5,2,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,6,1,5,3,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,6,2,1,3,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,6,2,1,5,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,6,2,3,1,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,6,2,3,5,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,6,2,5,1,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [4,6,2,5,3,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,6,3,1,5,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,6,3,2,1,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,6,3,2,5,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [4,6,3,5,2,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,1,2,3,4,6]=>10000=>[1,5]=>([(4,5)],6)=>2 [5,1,3,2,4,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,1,3,4,2,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,1,3,4,6,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,1,3,6,2,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,1,4,2,3,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,1,4,2,6,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,1,4,3,2,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,1,4,3,6,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,1,4,6,2,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,1,4,6,3,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,1,6,2,3,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,1,6,2,4,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,1,6,3,2,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,1,6,3,4,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,1,6,4,3,2]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,2,1,3,4,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,2,1,4,3,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,1,4,6,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,1,6,3,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,1,6,4,3]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,2,3,1,4,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,2,3,4,1,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,2,3,4,6,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,2,3,6,1,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,2,4,1,3,6]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,2,4,1,6,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,4,3,1,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,4,3,6,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,4,6,1,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,2,4,6,3,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,6,1,3,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,2,6,1,4,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,6,3,1,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,6,3,4,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,2,6,4,3,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,3,1,4,2,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,1,4,6,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,1,6,2,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,1,6,4,2]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,3,2,1,4,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,2,1,6,4]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,3,2,4,1,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,2,4,6,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,2,6,1,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,2,6,4,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,3,4,1,6,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,4,2,1,6]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,4,2,6,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,4,6,2,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,6,1,4,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,6,2,1,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,6,2,4,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,3,6,4,2,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,4,1,6,3,2]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,4,2,1,6,3]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,4,2,6,3,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,4,3,1,6,2]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,4,3,2,1,6]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,4,3,2,6,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,4,3,6,2,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,4,6,3,2,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [5,6,1,2,3,4]=>10000=>[1,5]=>([(4,5)],6)=>2 [5,6,1,3,2,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,6,1,3,4,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,6,1,4,2,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,6,1,4,3,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,6,2,1,3,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,6,2,1,4,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,6,2,3,1,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,6,2,3,4,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,6,2,4,1,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [5,6,2,4,3,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,6,3,1,4,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,6,3,2,1,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,6,3,2,4,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,6,3,4,2,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [5,6,4,3,2,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,1,2,3,4,5]=>10000=>[1,5]=>([(4,5)],6)=>2 [6,1,3,2,4,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,1,3,4,2,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,1,3,4,5,2]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,1,3,5,2,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,1,4,2,3,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,1,4,2,5,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,1,4,3,2,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,1,4,3,5,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,1,4,5,2,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,1,4,5,3,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,1,5,2,3,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,1,5,2,4,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,1,5,3,2,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,1,5,3,4,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,1,5,4,3,2]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,2,1,3,4,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,2,1,4,3,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,1,4,5,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,1,5,3,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,1,5,4,3]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,2,3,1,4,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,2,3,4,1,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,2,3,4,5,1]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,2,3,5,1,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,2,4,1,3,5]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,2,4,1,5,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,4,3,1,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,4,3,5,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,4,5,1,3]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,2,4,5,3,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,5,1,3,4]=>11000=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>3 [6,2,5,1,4,3]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,5,3,1,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,5,3,4,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,2,5,4,3,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,3,1,4,2,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,1,4,5,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,1,5,2,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,1,5,4,2]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,3,2,1,4,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,2,1,5,4]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,3,2,4,1,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,2,4,5,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,2,5,1,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,2,5,4,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,3,4,1,5,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,4,2,1,5]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,4,2,5,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,4,5,2,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,5,1,4,2]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,5,2,1,4]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,5,2,4,1]=>11100=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 [6,3,5,4,2,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,4,1,5,3,2]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,4,2,1,5,3]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,4,2,5,3,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,4,3,1,5,2]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,4,3,2,1,5]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,4,3,2,5,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,4,3,5,2,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,4,5,3,2,1]=>11110=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 [6,5,4,3,2,1]=>11111=>[1,1,1,1,1,1]=>([(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)=>6 [1,2,3,4,5,7,6]=>000001=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2 [6,1,7,5,4,3,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,2,1,7,5,4,3]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,2,7,5,4,3,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,3,1,7,5,4,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,3,2,1,7,5,4]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,3,2,7,5,4,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,3,7,5,4,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,4,1,7,5,3,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,4,2,1,7,5,3]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,4,2,7,5,3,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,4,3,1,7,5,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,4,3,2,1,7,5]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,4,3,2,7,5,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,4,3,7,5,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,4,7,5,3,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,1,7,4,3,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,2,1,7,4,3]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,2,7,4,3,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,3,1,7,4,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,3,2,1,7,4]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,3,2,7,4,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,3,7,4,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,4,1,7,3,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,4,2,1,7,3]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,4,2,7,3,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,4,3,1,7,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,4,3,2,1,7]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,4,3,2,7,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,4,3,7,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,4,7,3,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,5,7,4,3,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [6,7,5,4,3,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,1,6,5,4,3,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,2,1,6,5,4,3]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,2,6,5,4,3,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,3,1,6,5,4,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,3,2,1,6,5,4]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,3,2,6,5,4,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,3,6,5,4,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,4,1,6,5,3,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,4,2,1,6,5,3]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,4,2,6,5,3,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,4,3,1,6,5,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,4,3,2,1,6,5]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,4,3,2,6,5,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,4,3,6,5,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,4,6,5,3,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,1,6,4,3,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,2,1,6,4,3]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,2,6,4,3,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,3,1,6,4,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,3,2,1,6,4]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,3,2,6,4,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,3,6,4,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,4,1,6,3,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,4,2,1,6,3]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,4,2,6,3,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,4,3,1,6,2]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,4,3,2,1,6]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,4,3,2,6,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,4,3,6,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,4,6,3,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,5,6,4,3,2,1]=>111110=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6 [7,6,5,4,3,2,1]=>111111=>[1,1,1,1,1,1,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>7 [8,7,6,5,4,3,2,1]=>1111111=>[1,1,1,1,1,1,1,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>8 [1,2,3,4,5,6,8,7]=>0000001=>[7,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>2 []=>=>[1]=>([],1)=>1
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
click to show known generating functions       
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
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.