Identifier
-
Mp00178:
Binary words
—to composition⟶
Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤ
Values
101 => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
110 => [1,1,2] => [2,1] => ([(0,2),(1,2)],3) => 2
0101 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 2
0110 => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1001 => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1011 => [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
1100 => [1,1,3] => [2,1] => ([(0,2),(1,2)],3) => 2
1101 => [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1110 => [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
00101 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00110 => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01001 => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01011 => [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
01100 => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01101 => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01110 => [2,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
10001 => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10010 => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10011 => [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
10100 => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10101 => [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
10110 => [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
11000 => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 2
11001 => [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11010 => [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
11011 => [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11100 => [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
11101 => [1,1,1,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11110 => [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
000101 => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000110 => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
001001 => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
001011 => [3,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
001100 => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
001101 => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001110 => [3,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
010001 => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
010010 => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
010011 => [2,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
010100 => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
010101 => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
010110 => [2,2,1,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
011000 => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
011001 => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
011010 => [2,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
011011 => [2,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
011100 => [2,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
011101 => [2,1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
011110 => [2,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
100001 => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100010 => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100011 => [1,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
100101 => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100110 => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
101000 => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
101001 => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
101011 => [1,2,2,1,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
101100 => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
101101 => [1,2,1,2,1] => [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) => 3
101110 => [1,2,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110000 => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
110001 => [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110010 => [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110011 => [1,1,3,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110100 => [1,1,2,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110101 => [1,1,2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110110 => [1,1,2,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
111000 => [1,1,1,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
111001 => [1,1,1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
111010 => [1,1,1,2,2] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
111011 => [1,1,1,2,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111100 => [1,1,1,1,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
111101 => [1,1,1,1,2,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
111110 => [1,1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
0000101 => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0000110 => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0001001 => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0001011 => [4,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
0001100 => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0001101 => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0001110 => [4,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0010001 => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0010010 => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
0010011 => [3,3,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
0010100 => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0010101 => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0010110 => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0011000 => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0011001 => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0011010 => [3,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
0011011 => [3,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
0011100 => [3,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0011101 => [3,1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0011110 => [3,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
0100001 => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0100010 => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0100011 => [2,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
0100101 => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0100110 => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0101000 => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
0101001 => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
>>> Load all 939 entries. <<<0101011 => [2,2,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
0101100 => [2,2,1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0101101 => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0101110 => [2,2,1,1,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0110000 => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0110001 => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0110010 => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0110011 => [2,1,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
0110100 => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0110101 => [2,1,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0110110 => [2,1,2,1,2] => [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) => 3
0111000 => [2,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0111001 => [2,1,1,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0111010 => [2,1,1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
0111011 => [2,1,1,2,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0111100 => [2,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
0111101 => [2,1,1,1,2,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0111110 => [2,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
1000001 => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1000010 => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1000011 => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
1000100 => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1000101 => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1000110 => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1001000 => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1001001 => [1,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1001010 => [1,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
1001011 => [1,3,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
1001100 => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1001101 => [1,3,1,2,1] => [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) => 3
1001110 => [1,3,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1010000 => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1010001 => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1010010 => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1010011 => [1,2,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
1010100 => [1,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1010101 => [1,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
1010110 => [1,2,2,1,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1011000 => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1011001 => [1,2,1,3,1] => [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) => 3
1011010 => [1,2,1,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
1011011 => [1,2,1,2,1,1] => [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) => 3
1011100 => [1,2,1,1,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1011101 => [1,2,1,1,2,1] => [1,1,2,1,1] => ([(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) => 2
1011110 => [1,2,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1100000 => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
1100001 => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1100010 => [1,1,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1100011 => [1,1,4,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1100100 => [1,1,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
1100101 => [1,1,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1100110 => [1,1,3,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1101000 => [1,1,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1101001 => [1,1,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1101011 => [1,1,2,2,1,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1101100 => [1,1,2,1,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1101101 => [1,1,2,1,2,1] => [2,1,1,1,1] => ([(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) => 2
1101110 => [1,1,2,1,1,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1110000 => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
1110001 => [1,1,1,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1110010 => [1,1,1,3,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1110011 => [1,1,1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1110100 => [1,1,1,2,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1110101 => [1,1,1,2,2,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1111000 => [1,1,1,1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
1111001 => [1,1,1,1,3,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
1111010 => [1,1,1,1,2,2] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
1111100 => [1,1,1,1,1,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
00000101 => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00000110 => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00001001 => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00001011 => [5,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
00001100 => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00001101 => [5,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00001110 => [5,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00010001 => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
00010010 => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00010011 => [4,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
00010100 => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00010101 => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00010110 => [4,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00011000 => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00011001 => [4,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00011010 => [4,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
00011011 => [4,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
00011100 => [4,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00011101 => [4,1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00011110 => [4,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
00100001 => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00100010 => [3,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00100011 => [3,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
00100101 => [3,3,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00100110 => [3,3,1,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00101000 => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00101001 => [3,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00101011 => [3,2,2,1,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
00101100 => [3,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00101101 => [3,2,1,2,1] => [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) => 3
00101110 => [3,2,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00110000 => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00110001 => [3,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00110010 => [3,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00110011 => [3,1,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
00110100 => [3,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00110101 => [3,1,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00110110 => [3,1,2,1,2] => [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) => 3
00111000 => [3,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00111001 => [3,1,1,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00111010 => [3,1,1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
00111011 => [3,1,1,2,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
00111100 => [3,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
00111101 => [3,1,1,1,2,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
00111110 => [3,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
01000001 => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01000010 => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01000011 => [2,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
01000100 => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01000101 => [2,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01000110 => [2,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01001000 => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01001001 => [2,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
01001010 => [2,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
01001011 => [2,3,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
01001100 => [2,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01001101 => [2,3,1,2,1] => [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) => 3
01001110 => [2,3,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01010000 => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
01010001 => [2,2,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01010010 => [2,2,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01010011 => [2,2,3,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01010100 => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
01010101 => [2,2,2,2,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
01010110 => [2,2,2,1,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01011000 => [2,2,1,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01011001 => [2,2,1,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01011010 => [2,2,1,2,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01011011 => [2,2,1,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01011100 => [2,2,1,1,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01011101 => [2,2,1,1,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01011110 => [2,2,1,1,1,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01100000 => [2,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01100001 => [2,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01100010 => [2,1,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01100011 => [2,1,4,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
01100100 => [2,1,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
01100101 => [2,1,3,2,1] => [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) => 3
01100110 => [2,1,3,1,2] => [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) => 3
01101000 => [2,1,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01101001 => [2,1,2,3,1] => [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) => 3
01101011 => [2,1,2,2,1,1] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01101100 => [2,1,2,1,3] => [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) => 3
01101101 => [2,1,2,1,2,1] => [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) => 2
01101110 => [2,1,2,1,1,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01110000 => [2,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
01110001 => [2,1,1,4,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01110010 => [2,1,1,3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01110011 => [2,1,1,3,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01110100 => [2,1,1,2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01110101 => [2,1,1,2,2,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01111000 => [2,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
01111001 => [2,1,1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01111010 => [2,1,1,1,2,2] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
01111100 => [2,1,1,1,1,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
10000001 => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10000010 => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10000011 => [1,6,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
10000100 => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10000101 => [1,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10000110 => [1,5,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10001001 => [1,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10001010 => [1,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
10001011 => [1,4,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
10001100 => [1,4,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10001101 => [1,4,1,2,1] => [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) => 3
10001110 => [1,4,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10010000 => [1,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10010001 => [1,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10010010 => [1,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
10010011 => [1,3,3,1,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
10010100 => [1,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10010101 => [1,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10010110 => [1,3,2,1,2] => [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) => 3
10011000 => [1,3,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10011001 => [1,3,1,3,1] => [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) => 3
10011010 => [1,3,1,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
10011011 => [1,3,1,2,1,1] => [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) => 3
10011100 => [1,3,1,1,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10011101 => [1,3,1,1,2,1] => [1,1,2,1,1] => ([(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) => 2
10011110 => [1,3,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10100000 => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10100001 => [1,2,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10100010 => [1,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10100011 => [1,2,4,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
10100100 => [1,2,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
10100101 => [1,2,3,2,1] => [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) => 3
10100110 => [1,2,3,1,2] => [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) => 3
10101000 => [1,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
10101001 => [1,2,2,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10101011 => [1,2,2,2,1,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
10101100 => [1,2,2,1,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10101110 => [1,2,2,1,1,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10110000 => [1,2,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10110001 => [1,2,1,4,1] => [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) => 3
10110010 => [1,2,1,3,2] => [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) => 3
10110011 => [1,2,1,3,1,1] => [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) => 3
10110100 => [1,2,1,2,3] => [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) => 3
10110101 => [1,2,1,2,2,1] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10110110 => [1,2,1,2,1,2] => [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) => 2
10111000 => [1,2,1,1,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10111001 => [1,2,1,1,3,1] => [1,1,2,1,1] => ([(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) => 2
10111010 => [1,2,1,1,2,2] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10111100 => [1,2,1,1,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11000000 => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
11000001 => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11000010 => [1,1,5,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11000011 => [1,1,5,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11000100 => [1,1,4,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11000101 => [1,1,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11000110 => [1,1,4,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11001000 => [1,1,3,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11001001 => [1,1,3,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11001010 => [1,1,3,2,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11001011 => [1,1,3,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11001100 => [1,1,3,1,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11001101 => [1,1,3,1,2,1] => [2,1,1,1,1] => ([(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) => 2
11001110 => [1,1,3,1,1,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11010000 => [1,1,2,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11010001 => [1,1,2,4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11010010 => [1,1,2,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11010011 => [1,1,2,3,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11010100 => [1,1,2,2,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11010101 => [1,1,2,2,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11010110 => [1,1,2,2,1,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11011000 => [1,1,2,1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11011001 => [1,1,2,1,3,1] => [2,1,1,1,1] => ([(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) => 2
11011010 => [1,1,2,1,2,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11011100 => [1,1,2,1,1,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11100000 => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
11100001 => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11100010 => [1,1,1,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11100011 => [1,1,1,4,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11100100 => [1,1,1,3,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
11101000 => [1,1,1,2,4] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11110000 => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
11110001 => [1,1,1,1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
11110010 => [1,1,1,1,3,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
11110100 => [1,1,1,1,2,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
11111000 => [1,1,1,1,1,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
000000101 => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000000110 => [7,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000001001 => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000001011 => [6,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
000001100 => [6,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000001101 => [6,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000001110 => [6,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000010001 => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000010010 => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000010011 => [5,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
000010100 => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000010101 => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000010110 => [5,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000011000 => [5,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000011001 => [5,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000011010 => [5,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
000011011 => [5,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
000011100 => [5,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000011101 => [5,1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
000011110 => [5,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
000100001 => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000100010 => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
000100011 => [4,4,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
000100101 => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000100110 => [4,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000101000 => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000101001 => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000101011 => [4,2,2,1,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
000101100 => [4,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000101101 => [4,2,1,2,1] => [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) => 3
000101110 => [4,2,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
000110000 => [4,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
000110001 => [4,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000110010 => [4,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000110011 => [4,1,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
000110100 => [4,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
000110101 => [4,1,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
000110110 => [4,1,2,1,2] => [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) => 3
000111000 => [4,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000111001 => [4,1,1,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
000111010 => [4,1,1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
000111011 => [4,1,1,2,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
000111100 => [4,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
000111101 => [4,1,1,1,2,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
000111110 => [4,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
001000001 => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
001000010 => [3,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
001000011 => [3,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
001000100 => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
001000101 => [3,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001000110 => [3,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001001000 => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
001001001 => [3,3,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
001001010 => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
001001011 => [3,3,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001001100 => [3,3,1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
001001101 => [3,3,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001001110 => [3,3,1,1,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001010000 => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
001010001 => [3,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001010010 => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001010011 => [3,2,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
001010100 => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
001010101 => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
001010110 => [3,2,2,1,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001011000 => [3,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001011001 => [3,2,1,3,1] => [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) => 3
001011010 => [3,2,1,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
001011011 => [3,2,1,2,1,1] => [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) => 3
001011100 => [3,2,1,1,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001011101 => [3,2,1,1,2,1] => [1,1,2,1,1] => ([(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) => 2
001011110 => [3,2,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
001100000 => [3,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
001100001 => [3,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001100010 => [3,1,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001100011 => [3,1,4,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
001100100 => [3,1,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
001100101 => [3,1,3,2,1] => [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) => 3
001100110 => [3,1,3,1,2] => [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) => 3
001101000 => [3,1,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
001101001 => [3,1,2,3,1] => [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) => 3
001101011 => [3,1,2,2,1,1] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
001101100 => [3,1,2,1,3] => [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) => 3
001101101 => [3,1,2,1,2,1] => [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) => 2
001101110 => [3,1,2,1,1,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
001110000 => [3,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
001110001 => [3,1,1,4,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001110010 => [3,1,1,3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001110011 => [3,1,1,3,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
001110100 => [3,1,1,2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001110101 => [3,1,1,2,2,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
001111000 => [3,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
001111001 => [3,1,1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
001111010 => [3,1,1,1,2,2] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
001111100 => [3,1,1,1,1,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
010000001 => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
010000010 => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
010000011 => [2,6,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
010000100 => [2,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
010000101 => [2,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
010000110 => [2,5,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
010001001 => [2,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
010001010 => [2,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
010001011 => [2,4,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
010001100 => [2,4,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
010001101 => [2,4,1,2,1] => [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) => 3
010001110 => [2,4,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010010000 => [2,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
010010001 => [2,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
010010010 => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
010010011 => [2,3,3,1,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
010010100 => [2,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
010010101 => [2,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010010110 => [2,3,2,1,2] => [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) => 3
010011000 => [2,3,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
010011001 => [2,3,1,3,1] => [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) => 3
010011010 => [2,3,1,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
010011011 => [2,3,1,2,1,1] => [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) => 3
010011100 => [2,3,1,1,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010011101 => [2,3,1,1,2,1] => [1,1,2,1,1] => ([(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) => 2
010011110 => [2,3,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010100000 => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
010100001 => [2,2,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010100010 => [2,2,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010100011 => [2,2,4,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010100100 => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
010100101 => [2,2,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010100110 => [2,2,3,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010101000 => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
010101001 => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010101011 => [2,2,2,2,1,1] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
010101100 => [2,2,2,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010101110 => [2,2,2,1,1,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010110000 => [2,2,1,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010110001 => [2,2,1,4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010110010 => [2,2,1,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010110011 => [2,2,1,3,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010110100 => [2,2,1,2,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010110101 => [2,2,1,2,2,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010110110 => [2,2,1,2,1,2] => [2,1,1,1,1] => ([(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) => 2
010111000 => [2,2,1,1,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010111001 => [2,2,1,1,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010111010 => [2,2,1,1,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010111100 => [2,2,1,1,1,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011000000 => [2,1,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
011000001 => [2,1,6,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
011000010 => [2,1,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
011000011 => [2,1,5,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
011000100 => [2,1,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
011000101 => [2,1,4,2,1] => [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) => 3
011000110 => [2,1,4,1,2] => [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) => 3
011001000 => [2,1,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
011001001 => [2,1,3,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
011001010 => [2,1,3,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
011001011 => [2,1,3,2,1,1] => [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) => 3
011001100 => [2,1,3,1,3] => [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) => 3
011001101 => [2,1,3,1,2,1] => [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) => 2
011001110 => [2,1,3,1,1,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011010000 => [2,1,2,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
011010001 => [2,1,2,4,1] => [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) => 3
011010010 => [2,1,2,3,2] => [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) => 3
011010011 => [2,1,2,3,1,1] => [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) => 3
011010100 => [2,1,2,2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
011010101 => [2,1,2,2,2,1] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011010110 => [2,1,2,2,1,2] => [1,1,2,1,1] => ([(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) => 2
011011000 => [2,1,2,1,4] => [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) => 3
011011001 => [2,1,2,1,3,1] => [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) => 2
011011010 => [2,1,2,1,2,2] => [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) => 3
011011100 => [2,1,2,1,1,3] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011100000 => [2,1,1,6] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
011100001 => [2,1,1,5,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
011100010 => [2,1,1,4,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
011100011 => [2,1,1,4,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011100100 => [2,1,1,3,3] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
011101000 => [2,1,1,2,4] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
011110000 => [2,1,1,1,5] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
011110001 => [2,1,1,1,4,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011110010 => [2,1,1,1,3,2] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011110100 => [2,1,1,1,2,3] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
011111000 => [2,1,1,1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
100000001 => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100000010 => [1,7,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100000011 => [1,7,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
100000100 => [1,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100000101 => [1,6,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100000110 => [1,6,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100001000 => [1,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100001001 => [1,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100001010 => [1,5,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
100001011 => [1,5,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
100001100 => [1,5,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100001101 => [1,5,1,2,1] => [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) => 3
100001110 => [1,5,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
100010000 => [1,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100010001 => [1,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
100010010 => [1,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100010011 => [1,4,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
100010100 => [1,4,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100010101 => [1,4,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
100010110 => [1,4,2,1,2] => [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) => 3
100011000 => [1,4,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100011001 => [1,4,1,3,1] => [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) => 3
100011010 => [1,4,1,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
100011011 => [1,4,1,2,1,1] => [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) => 3
100011100 => [1,4,1,1,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
100011101 => [1,4,1,1,2,1] => [1,1,2,1,1] => ([(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) => 2
100011110 => [1,4,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
100100000 => [1,3,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100100001 => [1,3,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100100010 => [1,3,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100100011 => [1,3,4,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
100100101 => [1,3,3,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
100100110 => [1,3,3,1,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
100101000 => [1,3,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100101001 => [1,3,2,3,1] => [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) => 3
100101011 => [1,3,2,2,1,1] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
100101100 => [1,3,2,1,3] => [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) => 3
100101101 => [1,3,2,1,2,1] => [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) => 2
100101110 => [1,3,2,1,1,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
100110000 => [1,3,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
100110001 => [1,3,1,4,1] => [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) => 3
100110010 => [1,3,1,3,2] => [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) => 3
100110011 => [1,3,1,3,1,1] => [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) => 3
100110100 => [1,3,1,2,3] => [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) => 3
100110101 => [1,3,1,2,2,1] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
100110110 => [1,3,1,2,1,2] => [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) => 2
100111000 => [1,3,1,1,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
100111001 => [1,3,1,1,3,1] => [1,1,2,1,1] => ([(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) => 2
100111010 => [1,3,1,1,2,2] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
100111100 => [1,3,1,1,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101000000 => [1,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
101000001 => [1,2,6,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
101000010 => [1,2,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
101000011 => [1,2,5,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
101000100 => [1,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
101000101 => [1,2,4,2,1] => [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) => 3
101000110 => [1,2,4,1,2] => [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) => 3
101001000 => [1,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
101001001 => [1,2,3,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101001010 => [1,2,3,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
101001011 => [1,2,3,2,1,1] => [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) => 3
101001100 => [1,2,3,1,3] => [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) => 3
101001101 => [1,2,3,1,2,1] => [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) => 2
101001110 => [1,2,3,1,1,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101010000 => [1,2,2,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
101010001 => [1,2,2,4,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101010010 => [1,2,2,3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101010011 => [1,2,2,3,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101010100 => [1,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
101010101 => [1,2,2,2,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
101010110 => [1,2,2,2,1,2] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101011000 => [1,2,2,1,4] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101011010 => [1,2,2,1,2,2] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101011100 => [1,2,2,1,1,3] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101100000 => [1,2,1,6] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
101100001 => [1,2,1,5,1] => [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) => 3
101100010 => [1,2,1,4,2] => [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) => 3
101100011 => [1,2,1,4,1,1] => [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) => 3
101100100 => [1,2,1,3,3] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
101100101 => [1,2,1,3,2,1] => [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) => 2
101100110 => [1,2,1,3,1,2] => [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) => 2
101101000 => [1,2,1,2,4] => [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) => 3
101101001 => [1,2,1,2,3,1] => [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) => 2
101101100 => [1,2,1,2,1,3] => [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) => 2
101110000 => [1,2,1,1,5] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101110001 => [1,2,1,1,4,1] => [1,1,2,1,1] => ([(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) => 2
101110010 => [1,2,1,1,3,2] => [1,1,2,1,1] => ([(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) => 2
101110100 => [1,2,1,1,2,3] => [1,1,2,1,1] => ([(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) => 2
101111000 => [1,2,1,1,1,4] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110000000 => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
110000001 => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110000010 => [1,1,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110000011 => [1,1,6,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110000100 => [1,1,5,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110000101 => [1,1,5,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110000110 => [1,1,5,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110001000 => [1,1,4,4] => [2,2] => ([(1,3),(2,3)],4) => 2
110001001 => [1,1,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110001010 => [1,1,4,2,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110001011 => [1,1,4,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110001100 => [1,1,4,1,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110001101 => [1,1,4,1,2,1] => [2,1,1,1,1] => ([(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) => 2
110001110 => [1,1,4,1,1,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110010000 => [1,1,3,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110010001 => [1,1,3,4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110010010 => [1,1,3,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110010011 => [1,1,3,3,1,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110010100 => [1,1,3,2,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110010101 => [1,1,3,2,2,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110010110 => [1,1,3,2,1,2] => [2,1,1,1,1] => ([(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) => 2
110011000 => [1,1,3,1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110011001 => [1,1,3,1,3,1] => [2,1,1,1,1] => ([(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) => 2
110011010 => [1,1,3,1,2,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110011100 => [1,1,3,1,1,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110100000 => [1,1,2,6] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110100001 => [1,1,2,5,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110100010 => [1,1,2,4,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110100011 => [1,1,2,4,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110100100 => [1,1,2,3,3] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110100101 => [1,1,2,3,2,1] => [2,1,1,1,1] => ([(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) => 2
110100110 => [1,1,2,3,1,2] => [2,1,1,1,1] => ([(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) => 2
110101000 => [1,1,2,2,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110101001 => [1,1,2,2,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110101100 => [1,1,2,2,1,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110110000 => [1,1,2,1,5] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110110001 => [1,1,2,1,4,1] => [2,1,1,1,1] => ([(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) => 2
110110010 => [1,1,2,1,3,2] => [2,1,1,1,1] => ([(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) => 2
110110100 => [1,1,2,1,2,3] => [2,1,1,1,1] => ([(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) => 2
110111000 => [1,1,2,1,1,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111000000 => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
111000001 => [1,1,1,6,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
111000010 => [1,1,1,5,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
111000011 => [1,1,1,5,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111000100 => [1,1,1,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
111001000 => [1,1,1,3,4] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
111001001 => [1,1,1,3,3,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111001010 => [1,1,1,3,2,2] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111010000 => [1,1,1,2,5] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
111010100 => [1,1,1,2,2,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111100000 => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
111100001 => [1,1,1,1,5,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
111100010 => [1,1,1,1,4,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
111100100 => [1,1,1,1,3,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
111101000 => [1,1,1,1,2,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
111110000 => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
1010101100 => [1,2,2,2,1,3] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1010111000 => [1,2,2,1,1,4] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1011001010 => [1,2,1,3,2,2] => [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) => 3
1011001100 => [1,2,1,3,1,3] => [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) => 2
1011010010 => [1,2,1,2,3,2] => [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) => 2
1011010100 => [1,2,1,2,2,3] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1011011000 => [1,2,1,2,1,4] => [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) => 2
1011100010 => [1,2,1,1,4,2] => [1,1,2,1,1] => ([(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) => 2
1011100100 => [1,2,1,1,3,3] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1011101000 => [1,2,1,1,2,4] => [1,1,2,1,1] => ([(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) => 2
1011110000 => [1,2,1,1,1,5] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1100101100 => [1,1,3,2,1,3] => [2,1,1,1,1] => ([(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) => 2
1100110010 => [1,1,3,1,3,2] => [2,1,1,1,1] => ([(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) => 2
1100110100 => [1,1,3,1,2,3] => [2,1,1,1,1] => ([(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) => 2
1100111000 => [1,1,3,1,1,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1101001010 => [1,1,2,3,2,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1101001100 => [1,1,2,3,1,3] => [2,1,1,1,1] => ([(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) => 2
1101010010 => [1,1,2,2,3,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1101010100 => [1,1,2,2,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1101011000 => [1,1,2,2,1,4] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1101100010 => [1,1,2,1,4,2] => [2,1,1,1,1] => ([(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) => 2
1101100100 => [1,1,2,1,3,3] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1101101000 => [1,1,2,1,2,4] => [2,1,1,1,1] => ([(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) => 2
1101110000 => [1,1,2,1,1,5] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1110001010 => [1,1,1,4,2,2] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1110010010 => [1,1,1,3,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1110100100 => [1,1,1,2,3,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1110101000 => [1,1,1,2,2,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1111000010 => [1,1,1,1,5,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
1111000100 => [1,1,1,1,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
1111001000 => [1,1,1,1,3,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
1111010000 => [1,1,1,1,2,5] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
1111100000 => [1,1,1,1,1,6] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
1110000001 => [1,1,1,7,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1101010001 => [1,1,2,2,4,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1101000011 => [1,1,2,5,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1100001011 => [1,1,5,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1100000001 => [1,1,8,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1100000000 => [1,1,9] => [2,1] => ([(0,2),(1,2)],3) => 2
1011000001 => [1,2,1,6,1] => [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) => 3
1010010001 => [1,2,3,4,1] => [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) => 3
1010000101 => [1,2,5,2,1] => [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) => 3
1010000001 => [1,2,7,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1010000000 => [1,2,8] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1001100001 => [1,3,1,5,1] => [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) => 3
1001000000 => [1,3,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1000110001 => [1,4,1,4,1] => [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) => 3
1000101110 => [1,4,2,1,1,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1000101011 => [1,4,2,2,1,1] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1000100101 => [1,4,3,2,1] => [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) => 3
1000100000 => [1,4,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1000011110 => [1,5,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1000011001 => [1,5,1,3,1] => [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) => 3
1000010110 => [1,5,2,1,2] => [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) => 3
1000001110 => [1,6,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1000001101 => [1,6,1,2,1] => [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) => 3
1000001010 => [1,6,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
1000001001 => [1,6,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1000000110 => [1,7,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1000000101 => [1,7,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
1000000100 => [1,7,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1000000011 => [1,8,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
1000000010 => [1,8,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
1000000001 => [1,9,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10000000010 => [1,9,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10000000110 => [1,8,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10000001110 => [1,7,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10000011110 => [1,6,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10000000100 => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10000010000 => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10000100010 => [1,5,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10001000010 => [1,4,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10000100100 => [1,5,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
10001001010 => [1,4,3,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
10001000100 => [1,4,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
10000101000 => [1,5,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10010001010 => [1,3,4,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
10001010010 => [1,4,2,3,2] => [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) => 3
10010000100 => [1,3,5,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10001001000 => [1,4,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10010010010 => [1,3,3,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
10001010100 => [1,4,2,2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10100000000 => [1,2,9] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10010001000 => [1,3,4,4] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
10100010010 => [1,2,4,3,2] => [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) => 3
10010100010 => [1,3,2,4,2] => [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) => 3
10010010100 => [1,3,3,2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0111100001 => [2,1,1,1,5,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0111000001 => [2,1,1,6,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0110000001 => [2,1,7,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0100000001 => [2,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01111000001 => [2,1,1,1,6,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0110100001 => [2,1,2,5,1] => [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) => 3
01110000001 => [2,1,1,7,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0101000001 => [2,2,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01100000001 => [2,1,8,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
0010000001 => [3,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01000000001 => [2,9,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
0101010101 => [2,2,2,2,2,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
0101010011 => [2,2,2,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0101001101 => [2,2,3,1,2,1] => [2,1,1,1,1] => ([(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) => 2
0101001011 => [2,2,3,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0100110101 => [2,3,1,2,2,1] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0100110011 => [2,3,1,3,1,1] => [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) => 3
0100101101 => [2,3,2,1,2,1] => [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) => 2
0100101011 => [2,3,2,2,1,1] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0100011101 => [2,4,1,1,2,1] => [1,1,2,1,1] => ([(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) => 2
0100011011 => [2,4,1,2,1,1] => [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) => 3
0011010101 => [3,1,2,2,2,1] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0011010011 => [3,1,2,3,1,1] => [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) => 3
0011001101 => [3,1,3,1,2,1] => [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) => 2
0011001011 => [3,1,3,2,1,1] => [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) => 3
0010110101 => [3,2,1,2,2,1] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0010110011 => [3,2,1,3,1,1] => [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) => 3
0010101011 => [3,2,2,2,1,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
0010011101 => [3,3,1,1,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0010011011 => [3,3,1,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0001110101 => [4,1,1,2,2,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0001110011 => [4,1,1,3,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0001101101 => [4,1,2,1,2,1] => [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) => 2
0001101011 => [4,1,2,2,1,1] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0001011101 => [4,2,1,1,2,1] => [1,1,2,1,1] => ([(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) => 2
0001011011 => [4,2,1,2,1,1] => [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) => 3
0000111101 => [5,1,1,1,2,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0000111011 => [5,1,1,2,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11010101000 => [1,1,2,2,2,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11010100100 => [1,1,2,2,3,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11010010100 => [1,1,2,3,2,3] => [2,1,1,1,1] => ([(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) => 2
11001010100 => [1,1,3,2,2,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10101010100 => [1,2,2,2,2,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
111000000001 => [1,1,1,9,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
100110000001 => [1,3,1,7,1] => [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) => 3
100001100001 => [1,5,1,5,1] => [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) => 3
100000011001 => [1,7,1,3,1] => [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) => 3
100000000001 => [1,11,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
100000001101 => [1,8,1,2,1] => [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) => 3
100000110001 => [1,6,1,4,1] => [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) => 3
100000100101 => [1,6,3,2,1] => [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) => 3
100011000001 => [1,4,1,6,1] => [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) => 3
100010010001 => [1,4,3,4,1] => [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) => 3
100010000101 => [1,4,5,2,1] => [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) => 3
101100000001 => [1,2,1,8,1] => [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) => 3
101001000001 => [1,2,3,6,1] => [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) => 3
101000010001 => [1,2,5,4,1] => [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) => 3
101000000101 => [1,2,7,2,1] => [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) => 3
00101010101 => [3,2,2,2,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
00101010011 => [3,2,2,3,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
00100101011 => [3,3,2,2,1,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0000111110 => [5,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
10101010010 => [1,2,2,2,3,2] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10101001001 => [1,2,2,3,3,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10101001010 => [1,2,2,3,2,2] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10101000100 => [1,2,2,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10100100101 => [1,2,3,3,2,1] => [1,1,2,1,1] => ([(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) => 2
10100100010 => [1,2,3,4,2] => [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) => 3
10100101001 => [1,2,3,2,3,1] => [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) => 2
10100010001 => [1,2,4,4,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10100010100 => [1,2,4,2,3] => [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) => 3
10100001000 => [1,2,5,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
10010010101 => [1,3,3,2,2,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10010001001 => [1,3,4,3,1] => [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) => 3
10010100101 => [1,3,2,3,2,1] => [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) => 2
10010101001 => [1,3,2,2,3,1] => [1,1,2,1,1] => ([(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) => 2
10010100100 => [1,3,2,3,3] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
10010010001 => [1,3,3,4,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10001000101 => [1,4,4,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10001001001 => [1,4,3,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10001010001 => [1,4,2,4,1] => [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) => 3
10000100001 => [1,5,5,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
01001010101 => [2,3,2,2,2,1] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01001010010 => [2,3,2,3,2] => [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) => 3
01001001001 => [2,3,3,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
01001001010 => [2,3,3,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
01001000100 => [2,3,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01000100101 => [2,4,3,2,1] => [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) => 3
01000100010 => [2,4,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
01000101001 => [2,4,2,3,1] => [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) => 3
01000100100 => [2,4,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
01000010001 => [2,5,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01000010010 => [2,5,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01000010100 => [2,5,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01000001000 => [2,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
01010010101 => [2,2,3,2,2,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01010010010 => [2,2,3,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01010001001 => [2,2,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01010001010 => [2,2,4,2,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01010000100 => [2,2,5,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01010100010 => [2,2,2,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01010101001 => [2,2,2,2,3,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
01010100100 => [2,2,2,3,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
01010010001 => [2,2,3,4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01010010100 => [2,2,3,2,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01010001000 => [2,2,4,4] => [2,2] => ([(1,3),(2,3)],4) => 2
01001000101 => [2,3,4,2,1] => [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) => 3
01001000010 => [2,3,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01001010001 => [2,3,2,4,1] => [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) => 3
01001010100 => [2,3,2,2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01001001000 => [2,3,3,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
01000100001 => [2,4,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
01000101000 => [2,4,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00100010101 => [3,4,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00100010010 => [3,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00100001001 => [3,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00100001010 => [3,5,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
00100000100 => [3,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00100100101 => [3,3,3,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00100100010 => [3,3,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00100101001 => [3,3,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00100010001 => [3,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00100010100 => [3,4,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00100001000 => [3,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00101000101 => [3,2,4,2,1] => [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) => 3
00101000010 => [3,2,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00101001001 => [3,2,3,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00101001010 => [3,2,3,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
00101000100 => [3,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00101010001 => [3,2,2,4,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00101010010 => [3,2,2,3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00101010100 => [3,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
00101001000 => [3,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00100100001 => [3,3,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00100101000 => [3,3,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00100010000 => [3,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00010000101 => [4,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00010000010 => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00010001001 => [4,4,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00010001010 => [4,4,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
00010000100 => [4,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00010010001 => [4,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00010010010 => [4,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00010010100 => [4,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00010100001 => [4,2,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00010100010 => [4,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
00010100100 => [4,2,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
00010101000 => [4,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00010010000 => [4,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00001000001 => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00001000010 => [5,5,2] => [2,1] => ([(0,2),(1,2)],3) => 2
00001000100 => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00001001000 => [5,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00001010000 => [5,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00000000101 => [9,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00100000001 => [3,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
10000000001 => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00000011011 => [7,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
10001010101 => [1,4,2,2,2,1] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10000010101 => [1,6,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0001000100 => [4,4,3] => [2,1] => ([(0,2),(1,2)],3) => 2
10000001011 => [1,7,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
11000000011 => [1,1,8,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00010010101 => [4,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00010100101 => [4,2,3,2,1] => [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) => 3
00010101001 => [4,2,2,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00000100010 => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
00001010101 => [5,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
10101010001 => [1,2,2,2,4,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01101010100 => [2,1,2,2,2,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01101001010 => [2,1,2,3,2,2] => [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) => 3
01010101000 => [2,2,2,2,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
11010000100 => [1,1,2,5,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11110001000 => [1,1,1,1,4,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
11000111000 => [1,1,4,1,1,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
11000100011 => [1,1,4,4,1,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
00011111000 => [4,1,1,1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
00011100011 => [4,1,1,4,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
search for individual values
searching the database for the individual values of this statistic
Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition C is the compositions composed of the lengths of consecutive runs of the same integer in C.
The delta morphism of a composition C is the compositions composed of the lengths of consecutive runs of the same integer in C.
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.
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.
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.
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