Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤ
Values
0 => [1] => [1] => ([],1) => 0
1 => [1] => [1] => ([],1) => 0
00 => [2] => [1] => ([],1) => 0
11 => [2] => [1] => ([],1) => 0
000 => [3] => [1] => ([],1) => 0
001 => [2,1] => [1,1] => ([(0,1)],2) => 1
011 => [1,2] => [1,1] => ([(0,1)],2) => 1
100 => [1,2] => [1,1] => ([(0,1)],2) => 1
110 => [2,1] => [1,1] => ([(0,1)],2) => 1
111 => [3] => [1] => ([],1) => 0
0000 => [4] => [1] => ([],1) => 0
0001 => [3,1] => [1,1] => ([(0,1)],2) => 1
0100 => [1,1,2] => [2,1] => ([(0,2),(1,2)],3) => 2
0110 => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0111 => [1,3] => [1,1] => ([(0,1)],2) => 1
1000 => [1,3] => [1,1] => ([(0,1)],2) => 1
1001 => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1011 => [1,1,2] => [2,1] => ([(0,2),(1,2)],3) => 2
1110 => [3,1] => [1,1] => ([(0,1)],2) => 1
1111 => [4] => [1] => ([],1) => 0
00000 => [5] => [1] => ([],1) => 0
00001 => [4,1] => [1,1] => ([(0,1)],2) => 1
00011 => [3,2] => [1,1] => ([(0,1)],2) => 1
00100 => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00110 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 2
00111 => [2,3] => [1,1] => ([(0,1)],2) => 1
01000 => [1,1,3] => [2,1] => ([(0,2),(1,2)],3) => 2
01001 => [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01011 => [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
01110 => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
01111 => [1,4] => [1,1] => ([(0,1)],2) => 1
10000 => [1,4] => [1,1] => ([(0,1)],2) => 1
10001 => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
10100 => [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
10110 => [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
10111 => [1,1,3] => [2,1] => ([(0,2),(1,2)],3) => 2
11000 => [2,3] => [1,1] => ([(0,1)],2) => 1
11001 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 2
11011 => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11100 => [3,2] => [1,1] => ([(0,1)],2) => 1
11110 => [4,1] => [1,1] => ([(0,1)],2) => 1
11111 => [5] => [1] => ([],1) => 0
000000 => [6] => [1] => ([],1) => 0
000001 => [5,1] => [1,1] => ([(0,1)],2) => 1
000011 => [4,2] => [1,1] => ([(0,1)],2) => 1
000100 => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000110 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001000 => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001001 => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001011 => [2,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
001110 => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001111 => [2,4] => [1,1] => ([(0,1)],2) => 1
010000 => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 2
010001 => [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010100 => [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
010110 => [1,1,1,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010111 => [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
011000 => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011001 => [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
011011 => [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011100 => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011110 => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011111 => [1,5] => [1,1] => ([(0,1)],2) => 1
100000 => [1,5] => [1,1] => ([(0,1)],2) => 1
100001 => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
100011 => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
100100 => [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100110 => [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
100111 => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
101000 => [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
101001 => [1,1,1,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101011 => [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
101110 => [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
101111 => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 2
110000 => [2,4] => [1,1] => ([(0,1)],2) => 1
110001 => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
110100 => [2,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
110110 => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110111 => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111001 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111011 => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111100 => [4,2] => [1,1] => ([(0,1)],2) => 1
111110 => [5,1] => [1,1] => ([(0,1)],2) => 1
111111 => [6] => [1] => ([],1) => 0
0000000 => [7] => [1] => ([],1) => 0
0000001 => [6,1] => [1,1] => ([(0,1)],2) => 1
0000011 => [5,2] => [1,1] => ([(0,1)],2) => 1
0000100 => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0000110 => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0000111 => [4,3] => [1,1] => ([(0,1)],2) => 1
0001000 => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0001001 => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0001011 => [3,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0001110 => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
0001111 => [3,4] => [1,1] => ([(0,1)],2) => 1
0010000 => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0010001 => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0010100 => [2,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
0010110 => [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
0010111 => [2,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0011000 => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
>>> Load all 1372 entries. <<<0011001 => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
0011011 => [2,2,1,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0011100 => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0011110 => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0011111 => [2,5] => [1,1] => ([(0,1)],2) => 1
0100000 => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
0100001 => [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0100011 => [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0100100 => [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
0100110 => [1,1,2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0100111 => [1,1,2,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0101000 => [1,1,1,1,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
0101001 => [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) => 2
0101011 => [1,1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
0101110 => [1,1,1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0101111 => [1,1,1,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
0110000 => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0110001 => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0110100 => [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
0110110 => [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) => 1
0110111 => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0111001 => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0111011 => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0111100 => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0111110 => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0111111 => [1,6] => [1,1] => ([(0,1)],2) => 1
1000000 => [1,6] => [1,1] => ([(0,1)],2) => 1
1000001 => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1000011 => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1000100 => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1000110 => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1001000 => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1001001 => [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) => 1
1001011 => [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
1001110 => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1001111 => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1010000 => [1,1,1,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
1010001 => [1,1,1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1010100 => [1,1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
1010110 => [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) => 2
1010111 => [1,1,1,1,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
1011000 => [1,1,2,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1011001 => [1,1,2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1011011 => [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
1011100 => [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1011110 => [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1011111 => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
1100000 => [2,5] => [1,1] => ([(0,1)],2) => 1
1100001 => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1100011 => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1100100 => [2,2,1,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1100110 => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
1100111 => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
1101000 => [2,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1101001 => [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
1101011 => [2,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
1101110 => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1101111 => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1110000 => [3,4] => [1,1] => ([(0,1)],2) => 1
1110001 => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
1110100 => [3,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1110110 => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1110111 => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111000 => [4,3] => [1,1] => ([(0,1)],2) => 1
1111001 => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111011 => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111100 => [5,2] => [1,1] => ([(0,1)],2) => 1
1111110 => [6,1] => [1,1] => ([(0,1)],2) => 1
1111111 => [7] => [1] => ([],1) => 0
00000000 => [8] => [1] => ([],1) => 0
00000001 => [7,1] => [1,1] => ([(0,1)],2) => 1
00000011 => [6,2] => [1,1] => ([(0,1)],2) => 1
00000100 => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00000110 => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00000111 => [5,3] => [1,1] => ([(0,1)],2) => 1
00001000 => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00001001 => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
00001011 => [4,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00001110 => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00010000 => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00010001 => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
00010100 => [3,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
00010110 => [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
00010111 => [3,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00011000 => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00011001 => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00011011 => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
00011100 => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
00011110 => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00011111 => [3,5] => [1,1] => ([(0,1)],2) => 1
00100000 => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00100001 => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
00100011 => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
00100100 => [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) => 1
00100110 => [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
00100111 => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
00101000 => [2,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
00101001 => [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
00101011 => [2,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
00101110 => [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
00101111 => [2,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00110000 => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
00110001 => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00110100 => [2,2,1,1,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00110110 => [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
00110111 => [2,2,1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00111001 => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
00111011 => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
00111100 => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00111110 => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00111111 => [2,6] => [1,1] => ([(0,1)],2) => 1
01000000 => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
01000001 => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01000011 => [1,1,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01000100 => [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
01000110 => [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
01001000 => [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
01001001 => [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
01001011 => [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
01001110 => [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
01001111 => [1,1,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
01010000 => [1,1,1,1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
01010001 => [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) => 2
01010100 => [1,1,1,1,1,1,2] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
01010110 => [1,1,1,1,1,2,1] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
01010111 => [1,1,1,1,1,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
01011000 => [1,1,1,2,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01011001 => [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
01011011 => [1,1,1,2,1,2] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
01011100 => [1,1,1,3,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01011110 => [1,1,1,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
01011111 => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
01100000 => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
01100001 => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
01100011 => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
01100100 => [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
01100110 => [1,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
01100111 => [1,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
01101000 => [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
01101001 => [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
01101011 => [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
01101110 => [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) => 1
01101111 => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
01110000 => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
01110001 => [1,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
01110100 => [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
01110110 => [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) => 1
01110111 => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
01111000 => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
01111001 => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
01111011 => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
01111100 => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
01111110 => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
01111111 => [1,7] => [1,1] => ([(0,1)],2) => 1
10000000 => [1,7] => [1,1] => ([(0,1)],2) => 1
10000001 => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
10000011 => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
10000100 => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10000110 => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10000111 => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
10001000 => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10001001 => [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) => 1
10001011 => [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
10001110 => [1,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
10001111 => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
10010000 => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10010001 => [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) => 1
10010100 => [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
10010110 => [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
10010111 => [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
10011000 => [1,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
10011001 => [1,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
10011011 => [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
10011100 => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10011110 => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10011111 => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
10100000 => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
10100001 => [1,1,1,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10100011 => [1,1,1,3,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10100100 => [1,1,1,2,1,2] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10100110 => [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
10100111 => [1,1,1,2,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10101000 => [1,1,1,1,1,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
10101001 => [1,1,1,1,1,2,1] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
10101011 => [1,1,1,1,1,1,2] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
10101110 => [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) => 2
10101111 => [1,1,1,1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
10110000 => [1,1,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
10110001 => [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
10110100 => [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
10110110 => [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
10110111 => [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
10111001 => [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
10111011 => [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
10111100 => [1,1,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
10111110 => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
10111111 => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
11000000 => [2,6] => [1,1] => ([(0,1)],2) => 1
11000001 => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11000011 => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11000100 => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11000110 => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11001000 => [2,2,1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11001001 => [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
11001011 => [2,2,1,1,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
11001110 => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11001111 => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
11010000 => [2,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
11010001 => [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
11010100 => [2,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
11010110 => [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
11010111 => [2,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
11011000 => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11011001 => [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
11011011 => [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) => 1
11011100 => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11011110 => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11011111 => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11100000 => [3,5] => [1,1] => ([(0,1)],2) => 1
11100001 => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11100011 => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
11100100 => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11100110 => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
11100111 => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11101000 => [3,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
11101001 => [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
11101011 => [3,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
11101110 => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11101111 => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11110001 => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11110100 => [4,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
11110110 => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11110111 => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11111000 => [5,3] => [1,1] => ([(0,1)],2) => 1
11111001 => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11111011 => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11111100 => [6,2] => [1,1] => ([(0,1)],2) => 1
11111110 => [7,1] => [1,1] => ([(0,1)],2) => 1
11111111 => [8] => [1] => ([],1) => 0
000000000 => [9] => [1] => ([],1) => 0
000000001 => [8,1] => [1,1] => ([(0,1)],2) => 1
000000011 => [7,2] => [1,1] => ([(0,1)],2) => 1
000000100 => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000000110 => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000000111 => [6,3] => [1,1] => ([(0,1)],2) => 1
000001000 => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000001001 => [5,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000001011 => [5,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000001110 => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000001111 => [5,4] => [1,1] => ([(0,1)],2) => 1
000010000 => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000010001 => [4,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000010100 => [4,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
000010110 => [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
000010111 => [4,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000011000 => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000011001 => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000011011 => [4,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000011100 => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000011110 => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
000011111 => [4,5] => [1,1] => ([(0,1)],2) => 1
000100000 => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000100001 => [3,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000100011 => [3,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000100100 => [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) => 1
000100110 => [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
000100111 => [3,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000101000 => [3,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
000101001 => [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
000101011 => [3,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
000101110 => [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
000101111 => [3,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000110000 => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000110001 => [3,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000110100 => [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
000110110 => [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) => 1
000110111 => [3,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000111001 => [3,3,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
000111011 => [3,3,1,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
000111100 => [3,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000111110 => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000111111 => [3,6] => [1,1] => ([(0,1)],2) => 1
001000000 => [2,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001000001 => [2,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001000011 => [2,1,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001000100 => [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) => 1
001000110 => [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) => 1
001001000 => [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) => 1
001001001 => [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) => 1
001001011 => [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
001001110 => [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) => 1
001001111 => [2,1,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001010000 => [2,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
001010001 => [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
001010100 => [2,1,1,1,1,1,2] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
001010110 => [2,1,1,1,1,2,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
001010111 => [2,1,1,1,1,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
001011000 => [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
001011001 => [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
001011011 => [2,1,1,2,1,2] => [1,2,1,1,1] => ([(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
001011100 => [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
001011110 => [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
001011111 => [2,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
001100000 => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
001100001 => [2,2,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
001100011 => [2,2,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
001100100 => [2,2,2,1,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001100110 => [2,2,2,2,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
001100111 => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
001101000 => [2,2,1,1,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
001101001 => [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
001101011 => [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
001101110 => [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
001101111 => [2,2,1,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
001110000 => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001110001 => [2,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
001110100 => [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
001110110 => [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) => 1
001110111 => [2,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001111000 => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001111001 => [2,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001111011 => [2,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001111100 => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001111110 => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001111111 => [2,7] => [1,1] => ([(0,1)],2) => 1
010000000 => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
010000001 => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010000011 => [1,1,5,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010000100 => [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
010000110 => [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
010000111 => [1,1,4,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010001000 => [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
010001001 => [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
010001011 => [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
010001110 => [1,1,3,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010001111 => [1,1,3,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010010000 => [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
010010001 => [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
010010100 => [1,1,2,1,1,1,2] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
010010110 => [1,1,2,1,1,2,1] => [2,1,2,1,1] => ([(0,5),(0,6),(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) => 2
010010111 => [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
010011000 => [1,1,2,2,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010011001 => [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
010011011 => [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
010011100 => [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
010011110 => [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
010011111 => [1,1,2,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
010100000 => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
010100001 => [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) => 2
010100011 => [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) => 2
010100100 => [1,1,1,1,2,1,2] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
010100110 => [1,1,1,1,2,2,1] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
010100111 => [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) => 2
010101000 => [1,1,1,1,1,1,3] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
010101110 => [1,1,1,1,1,3,1] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
010101111 => [1,1,1,1,1,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
010110000 => [1,1,1,2,4] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010110001 => [1,1,1,2,3,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010110100 => [1,1,1,2,1,1,2] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
010110110 => [1,1,1,2,1,2,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => 2
010110111 => [1,1,1,2,1,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010111001 => [1,1,1,3,2,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010111011 => [1,1,1,3,1,2] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
010111100 => [1,1,1,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010111110 => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010111111 => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
011000000 => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011000001 => [1,2,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011000011 => [1,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011000100 => [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) => 1
011000110 => [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) => 1
011001000 => [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
011001001 => [1,2,2,1,2,1] => [1,2,1,1,1] => ([(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
011001011 => [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
011001110 => [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
011001111 => [1,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
011010000 => [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
011010001 => [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
011010100 => [1,2,1,1,1,1,2] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
011010110 => [1,2,1,1,1,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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) => 2
011010111 => [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
011011000 => [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) => 1
011011001 => [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
011011011 => [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) => 1
011011100 => [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) => 1
011011110 => [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) => 1
011011111 => [1,2,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011100000 => [1,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011100001 => [1,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011100011 => [1,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
011100100 => [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) => 1
011100110 => [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
011100111 => [1,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011101000 => [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
011101001 => [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
011101011 => [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
011101110 => [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) => 1
011101111 => [1,3,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011110001 => [1,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011110100 => [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
011110110 => [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) => 1
011110111 => [1,4,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011111000 => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011111001 => [1,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011111011 => [1,5,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011111100 => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011111110 => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011111111 => [1,8] => [1,1] => ([(0,1)],2) => 1
100000000 => [1,8] => [1,1] => ([(0,1)],2) => 1
100000001 => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
100000011 => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
100000100 => [1,5,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100000110 => [1,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100000111 => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
100001000 => [1,4,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100001001 => [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) => 1
100001011 => [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
100001110 => [1,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100010000 => [1,3,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100010001 => [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) => 1
100010100 => [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
100010110 => [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
100010111 => [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
100011000 => [1,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100011001 => [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
100011011 => [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) => 1
100011100 => [1,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
100011110 => [1,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100011111 => [1,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
100100000 => [1,2,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100100001 => [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) => 1
100100011 => [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) => 1
100100100 => [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) => 1
100100110 => [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
100100111 => [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) => 1
100101000 => [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
100101001 => [1,2,1,1,1,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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) => 2
100101011 => [1,2,1,1,1,1,2] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
100101110 => [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
100101111 => [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
100110000 => [1,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
100110001 => [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
100110100 => [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
100110110 => [1,2,2,1,2,1] => [1,2,1,1,1] => ([(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
100110111 => [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
100111001 => [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) => 1
100111011 => [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) => 1
100111100 => [1,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100111110 => [1,2,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100111111 => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
101000000 => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
101000001 => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101000011 => [1,1,1,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101000100 => [1,1,1,3,1,2] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101000110 => [1,1,1,3,2,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101001000 => [1,1,1,2,1,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101001001 => [1,1,1,2,1,2,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => 2
101001011 => [1,1,1,2,1,1,2] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101001110 => [1,1,1,2,3,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
101001111 => [1,1,1,2,4] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101010000 => [1,1,1,1,1,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
101010001 => [1,1,1,1,1,3,1] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101010111 => [1,1,1,1,1,1,3] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
101011000 => [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) => 2
101011001 => [1,1,1,1,2,2,1] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101011011 => [1,1,1,1,2,1,2] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101011100 => [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) => 2
101011110 => [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) => 2
101011111 => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
101100000 => [1,1,2,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
101100001 => [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
101100011 => [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
101100100 => [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
101100110 => [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
101100111 => [1,1,2,2,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101101000 => [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
101101001 => [1,1,2,1,1,2,1] => [2,1,2,1,1] => ([(0,5),(0,6),(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) => 2
101101011 => [1,1,2,1,1,1,2] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101101110 => [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
101101111 => [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
101110000 => [1,1,3,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
101110001 => [1,1,3,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101110100 => [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
101110110 => [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
101110111 => [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
101111000 => [1,1,4,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
101111001 => [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
101111011 => [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
101111100 => [1,1,5,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
101111110 => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
101111111 => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
110000000 => [2,7] => [1,1] => ([(0,1)],2) => 1
110000001 => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
110000011 => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
110000100 => [2,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110000110 => [2,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110000111 => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
110001000 => [2,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110001001 => [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) => 1
110001011 => [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
110001110 => [2,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
110001111 => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
110010000 => [2,2,1,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110010001 => [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
110010100 => [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
110010110 => [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
110010111 => [2,2,1,1,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110011000 => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
110011001 => [2,2,2,2,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
110011011 => [2,2,2,1,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110011100 => [2,2,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110011110 => [2,2,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110011111 => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
110100000 => [2,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
110100001 => [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
110100011 => [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
110100100 => [2,1,1,2,1,2] => [1,2,1,1,1] => ([(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 => [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
110100111 => [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
110101000 => [2,1,1,1,1,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
110101001 => [2,1,1,1,1,2,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
110101011 => [2,1,1,1,1,1,2] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
110101110 => [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
110101111 => [2,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
110110000 => [2,1,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110110001 => [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) => 1
110110100 => [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
110110110 => [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) => 1
110110111 => [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) => 1
110111001 => [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) => 1
110111011 => [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) => 1
110111100 => [2,1,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110111110 => [2,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110111111 => [2,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111000000 => [3,6] => [1,1] => ([(0,1)],2) => 1
111000001 => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111000011 => [3,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111000100 => [3,3,1,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
111000110 => [3,3,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
111001000 => [3,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111001001 => [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) => 1
111001011 => [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
111001110 => [3,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111001111 => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111010000 => [3,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
111010001 => [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
111010100 => [3,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
111010110 => [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
111010111 => [3,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
111011000 => [3,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111011001 => [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
111011011 => [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) => 1
111011100 => [3,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111011110 => [3,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111011111 => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111100000 => [4,5] => [1,1] => ([(0,1)],2) => 1
111100001 => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
111100011 => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111100100 => [4,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111100110 => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
111100111 => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111101000 => [4,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
111101001 => [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
111101011 => [4,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
111101110 => [4,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111101111 => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111110000 => [5,4] => [1,1] => ([(0,1)],2) => 1
111110001 => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111110100 => [5,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
111110110 => [5,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111110111 => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111111000 => [6,3] => [1,1] => ([(0,1)],2) => 1
111111001 => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111111011 => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111111100 => [7,2] => [1,1] => ([(0,1)],2) => 1
111111110 => [8,1] => [1,1] => ([(0,1)],2) => 1
111111111 => [9] => [1] => ([],1) => 0
1011011000 => [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
1011100100 => [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
1011101000 => [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
1100110100 => [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
1101011000 => [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
1101100100 => [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
1101101000 => [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
1101110000 => [2,1,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1110010100 => [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
1110011000 => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1110100100 => [3,1,1,2,1,2] => [1,2,1,1,1] => ([(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
1110101000 => [3,1,1,1,1,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
1110110000 => [3,1,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1111000100 => [4,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1111001000 => [4,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1111010000 => [4,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
101101110000 => [1,1,2,1,3,4] => [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
101110011000 => [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
101110110000 => [1,1,3,1,2,4] => [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
101111000100 => [1,1,4,3,1,2] => [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
101111001000 => [1,1,4,2,1,3] => [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
101111010000 => [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
110011011000 => [2,2,2,1,2,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110011100100 => [2,2,3,2,1,2] => [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
110011101000 => [2,2,3,1,1,3] => [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
110101110000 => [2,1,1,1,3,4] => [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
110110011000 => [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
110110110000 => [2,1,2,1,2,4] => [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) => 1
110111000100 => [2,1,3,3,1,2] => [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
110111001000 => [2,1,3,2,1,3] => [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) => 1
110111010000 => [2,1,3,1,1,4] => [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
110111100000 => [2,1,4,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111000110100 => [3,3,2,1,1,2] => [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
111001011000 => [3,2,1,1,2,3] => [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
111001100100 => [3,2,2,2,1,2] => [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
111001101000 => [3,2,2,1,1,3] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111001110000 => [3,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111010011000 => [3,1,1,2,2,3] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111010110000 => [3,1,1,1,2,4] => [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
111011000100 => [3,1,2,3,1,2] => [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) => 1
111011001000 => [3,1,2,2,1,3] => [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
111011010000 => [3,1,2,1,1,4] => [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
111011100000 => [3,1,3,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111100010100 => [4,3,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111100011000 => [4,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111100100100 => [4,2,1,2,1,2] => [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) => 1
111100101000 => [4,2,1,1,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
111100110000 => [4,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
111101000100 => [4,1,1,3,1,2] => [1,2,1,1,1] => ([(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
111101001000 => [4,1,1,2,1,3] => [1,2,1,1,1] => ([(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
111101010000 => [4,1,1,1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
111101100000 => [4,1,2,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111110000100 => [5,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111110001000 => [5,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111110010000 => [5,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111110100000 => [5,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1111111111 => [10] => [1] => ([],1) => 0
1111111110 => [9,1] => [1,1] => ([(0,1)],2) => 1
1111111100 => [8,2] => [1,1] => ([(0,1)],2) => 1
1111111011 => [7,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111111001 => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111110110 => [6,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1111110001 => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111110000 => [6,4] => [1,1] => ([(0,1)],2) => 1
1111101001 => [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
1111101000 => [5,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1111100100 => [5,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1111100011 => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111100001 => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111011110 => [4,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1111011011 => [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) => 1
1111011000 => [4,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1111010111 => [4,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
1111010100 => [4,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
1111010001 => [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
1111001111 => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111001011 => [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
1111001001 => [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) => 1
1111000110 => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1111000011 => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
1111000001 => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1111000000 => [4,6] => [1,1] => ([(0,1)],2) => 1
1110111111 => [3,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1110111110 => [3,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1110111011 => [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) => 1
1110110100 => [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
1110110001 => [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) => 1
1110101111 => [3,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
1110101011 => [3,1,1,1,1,1,2] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
1110101001 => [3,1,1,1,1,2,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1110100011 => [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
1110100001 => [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
1110011111 => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1110011110 => [3,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1110011001 => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
1110010001 => [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) => 1
1110001001 => [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
1110000111 => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1110000011 => [3,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1110000001 => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1101111111 => [2,1,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1101111110 => [2,1,6,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1101111011 => [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) => 1
1101111001 => [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) => 1
1101111000 => [2,1,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1101110111 => [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) => 1
1101110001 => [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
1101101111 => [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) => 1
1101101001 => [2,1,2,1,1,2,1] => [1,1,1,2,1,1] => ([(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) => 2
1101100110 => [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
1101100011 => [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) => 1
1101100001 => [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) => 1
1101100000 => [2,1,2,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1101011111 => [2,1,1,1,5] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
1101011001 => [2,1,1,1,2,2,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1101010111 => [2,1,1,1,1,1,3] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
1101010001 => [2,1,1,1,1,3,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1101001111 => [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
1101001110 => [2,1,1,2,3,1] => [1,2,1,1,1] => ([(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
1101001011 => [2,1,1,2,1,1,2] => [1,2,1,2,1] => ([(0,6),(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) => 2
1101001001 => [2,1,1,2,1,2,1] => [1,2,1,1,1,1] => ([(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) => 2
1101001000 => [2,1,1,2,1,3] => [1,2,1,1,1] => ([(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
1101000011 => [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
1101000001 => [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
1100111111 => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
1100111100 => [2,2,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1100111001 => [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
1100110110 => [2,2,2,1,2,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
1100110001 => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1100110000 => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
1100101110 => [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
1100101011 => [2,2,1,1,1,1,2] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1100101001 => [2,2,1,1,1,2,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1100100111 => [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
1100100110 => [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
1100100011 => [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
1100011110 => [2,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1100011100 => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1100011011 => [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) => 1
1100011001 => [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
1100011000 => [2,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1100010111 => [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
1100001011 => [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
1100001000 => [2,4,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1100000111 => [2,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1100000110 => [2,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1100000011 => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1100000001 => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1100000000 => [2,8] => [1,1] => ([(0,1)],2) => 1
1011111111 => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
1011111110 => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1011111100 => [1,1,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1011111011 => [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
1011111000 => [1,1,5,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1011110111 => [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
1011110100 => [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
1011110001 => [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
1011100011 => [1,1,3,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1011100001 => [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
1011100000 => [1,1,3,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1011011001 => [1,1,2,1,2,2,1] => [2,1,1,2,1] => ([(0,6),(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) => 2
1011010111 => [1,1,2,1,1,1,3] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1011010001 => [1,1,2,1,1,3,1] => [2,1,2,1,1] => ([(0,5),(0,6),(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) => 2
1011010000 => [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
1011001011 => [1,1,2,2,1,1,2] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1011001001 => [1,1,2,2,1,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(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) => 2
1011001000 => [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
1011000100 => [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
1011000011 => [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
1011000000 => [1,1,2,6] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
1010111111 => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
1010111110 => [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) => 2
1010110111 => [1,1,1,1,2,1,3] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1010110001 => [1,1,1,1,2,3,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1010110000 => [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) => 2
1010101111 => [1,1,1,1,1,1,4] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
1010100111 => [1,1,1,1,1,2,3] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1010100011 => [1,1,1,1,1,3,2] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1010100000 => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
1010011011 => [1,1,1,2,2,1,2] => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1010011001 => [1,1,1,2,2,2,1] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1010011000 => [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
1010010111 => [1,1,1,2,1,1,3] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1010010001 => [1,1,1,2,1,3,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => 2
1010001111 => [1,1,1,3,4] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1010001110 => [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
1010001011 => [1,1,1,3,1,1,2] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1010000111 => [1,1,1,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1010000001 => [1,1,1,6,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
1010000000 => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
1001111110 => [1,2,6,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1001111000 => [1,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1001110100 => [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
1001110001 => [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
1001110000 => [1,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1001101011 => [1,2,2,1,1,1,2] => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1001101001 => [1,2,2,1,1,2,1] => [1,2,2,1,1] => ([(0,5),(0,6),(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) => 2
1001101000 => [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
1001100111 => [1,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
1001100110 => [1,2,2,2,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
1001100100 => [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
1001100011 => [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
1001011111 => [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
1001011110 => [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
1001011011 => [1,2,1,1,2,1,2] => [1,1,2,1,1,1] => ([(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) => 2
1001011001 => [1,2,1,1,2,2,1] => [1,1,2,2,1] => ([(0,6),(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) => 2
1001011000 => [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
1001010111 => [1,2,1,1,1,1,3] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1001001111 => [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) => 1
1001001110 => [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) => 1
1001001011 => [1,2,1,2,1,1,2] => [1,1,1,1,2,1] => ([(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) => 2
1001000000 => [1,2,1,6] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1000111110 => [1,3,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1000111100 => [1,3,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1000111011 => [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
1000111001 => [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
1000110111 => [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) => 1
1000110110 => [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) => 1
1000110100 => [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
1000110001 => [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) => 1
1000101111 => [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
1000101110 => [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
1000101011 => [1,3,1,1,1,1,2] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
1000100111 => [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) => 1
1000011111 => [1,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1000011110 => [1,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
1000011011 => [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) => 1
1000010111 => [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
1000010110 => [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
1000001111 => [1,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1000001110 => [1,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1000001011 => [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
1000001001 => [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) => 1
1000000110 => [1,6,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1000000100 => [1,6,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
1000000011 => [1,7,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1000000001 => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
1000000000 => [1,9] => [1,1] => ([(0,1)],2) => 1
10000000000 => [1,10] => [1,1] => ([(0,1)],2) => 1
10000000110 => [1,7,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10000001110 => [1,6,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10000011110 => [1,5,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10000111110 => [1,4,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10001111110 => [1,3,6,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10011111110 => [1,2,7,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10111111110 => [1,1,8,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
11111111110 => [10,1] => [1,1] => ([(0,1)],2) => 1
10000000100 => [1,7,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100000111110 => [1,5,5,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
11011111110 => [2,1,7,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11001111110 => [2,2,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110111111110 => [2,1,8,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100011001110 => [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
110000011110 => [2,5,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100001111100 => [1,4,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10010001000 => [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) => 1
100110001110 => [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
100011100110 => [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
0111111111 => [1,9] => [1,1] => ([(0,1)],2) => 1
0111111001 => [1,6,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0111110001 => [1,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0111100001 => [1,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0100000001 => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0000000001 => [9,1] => [1,1] => ([(0,1)],2) => 1
01111111111 => [1,10] => [1,1] => ([(0,1)],2) => 1
0111111011 => [1,6,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0111101001 => [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
0111010001 => [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
0110100001 => [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
0101000001 => [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) => 2
01000000001 => [1,1,8,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00000000001 => [10,1] => [1,1] => ([(0,1)],2) => 1
0100100111 => [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
0100011011 => [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
0100010111 => [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
0010010111 => [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
0010001111 => [2,1,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0001101011 => [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
0001100111 => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0001010111 => [3,1,1,1,1,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
0001001111 => [3,1,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0000110111 => [4,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0000101111 => [4,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
010010001111 => [1,1,2,1,3,4] => [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
010000111011 => [1,1,4,3,1,2] => [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
010000110111 => [1,1,4,2,1,3] => [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
010000101111 => [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
001100100111 => [2,2,2,1,2,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
001100011011 => [2,2,3,2,1,2] => [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
001100010111 => [2,2,3,1,1,3] => [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
001010001111 => [2,1,1,1,3,4] => [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
001000110111 => [2,1,3,2,1,3] => [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) => 1
001000101111 => [2,1,3,1,1,4] => [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
001000011111 => [2,1,4,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000111001011 => [3,3,2,1,1,2] => [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
000110011011 => [3,2,2,2,1,2] => [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
000110010111 => [3,2,2,1,1,3] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
000110001111 => [3,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000100111011 => [3,1,2,3,1,2] => [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) => 1
000100110111 => [3,1,2,2,1,3] => [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
000100101111 => [3,1,2,1,1,4] => [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
000100011111 => [3,1,3,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000011011011 => [4,2,1,2,1,2] => [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) => 1
000011010111 => [4,2,1,1,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
000011001111 => [4,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
000010110111 => [4,1,1,2,1,3] => [1,2,1,1,1] => ([(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
000010101111 => [4,1,1,1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
000010011111 => [4,1,2,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000001111011 => [5,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000001110111 => [5,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000001101111 => [5,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000001011111 => [5,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
111111111111 => [12] => [1] => ([],1) => 0
111110000001 => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111001100001 => [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
111000011001 => [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
111000000111 => [3,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111000110001 => [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
111011000001 => [3,1,2,5,1] => [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) => 1
111010010001 => [3,1,1,2,1,3,1] => [1,2,1,1,1,1] => ([(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) => 2
100111100001 => [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
100110011001 => [1,2,2,2,2,2,1] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
100110000111 => [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
100110110111 => [1,2,2,1,2,1,3] => [1,2,1,1,1,1] => ([(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) => 2
100110110001 => [1,2,2,1,2,3,1] => [1,2,1,1,1,1] => ([(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) => 2
100001111001 => [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
100001100111 => [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
100000011111 => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
100000110111 => [1,5,2,1,3] => [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) => 1
100000110001 => [1,5,2,3,1] => [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) => 1
100011011001 => [1,3,2,1,2,2,1] => [1,1,1,1,2,1] => ([(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) => 2
100011110001 => [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) => 1
100010010111 => [1,3,1,2,1,1,3] => [1,1,1,1,2,1] => ([(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) => 2
100010010001 => [1,3,1,2,1,3,1] => [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) => 1
101101111001 => [1,1,2,1,4,2,1] => [2,1,1,1,1,1] => ([(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) => 2
101101100111 => [1,1,2,1,2,2,3] => [2,1,1,2,1] => ([(0,6),(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) => 2
101101100001 => [1,1,2,1,2,4,1] => [2,1,1,1,1,1] => ([(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) => 2
101100011111 => [1,1,2,3,5] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101100011001 => [1,1,2,3,2,2,1] => [2,1,1,2,1] => ([(0,6),(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) => 2
101100000111 => [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
101100110111 => [1,1,2,2,2,1,3] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101100110001 => [1,1,2,2,2,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101111011001 => [1,1,4,1,2,2,1] => [2,1,1,2,1] => ([(0,6),(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) => 2
101111000001 => [1,1,4,5,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101111110001 => [1,1,6,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
101110010111 => [1,1,3,2,1,1,3] => [2,1,1,2,1] => ([(0,6),(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) => 2
101110010001 => [1,1,3,2,1,3,1] => [2,1,1,1,1,1] => ([(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) => 2
101001011111 => [1,1,1,2,1,1,5] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101001000001 => [1,1,1,2,1,5,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => 2
101001110111 => [1,1,1,2,3,1,3] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => 2
101001110001 => [1,1,1,2,3,3,1] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101000010111 => [1,1,1,4,1,1,3] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101000010001 => [1,1,1,4,1,3,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => 2
0000000000 => [10] => [1] => ([],1) => 0
0000000110 => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0000011000 => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0000011110 => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0001111110 => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0110011000 => [1,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
0111100000 => [1,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0111111110 => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0111001000 => [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) => 1
0100111110 => [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
0101101000 => [1,1,1,2,1,1,3] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
000000000000 => [12] => [1] => ([],1) => 0
000001111110 => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000110011110 => [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
000111100110 => [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
000111111000 => [3,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000111001110 => [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
000100111110 => [3,1,2,5,1] => [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) => 1
000101101110 => [3,1,1,2,1,3,1] => [1,2,1,1,1,1] => ([(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) => 2
011000011110 => [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
011001100110 => [1,2,2,2,2,2,1] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
011001111000 => [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
011001001110 => [1,2,2,1,2,3,1] => [1,2,1,1,1,1] => ([(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) => 2
011110000110 => [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
011110011000 => [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
011111100000 => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011111001000 => [1,5,2,1,3] => [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) => 1
011100100110 => [1,3,2,1,2,2,1] => [1,1,1,1,2,1] => ([(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) => 2
011101101000 => [1,3,1,2,1,1,3] => [1,1,1,1,2,1] => ([(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) => 2
010010011110 => [1,1,2,1,2,4,1] => [2,1,1,1,1,1] => ([(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) => 2
010011100110 => [1,1,2,3,2,2,1] => [2,1,1,2,1] => ([(0,6),(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) => 2
010011111000 => [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
010011001110 => [1,1,2,2,2,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
010000111110 => [1,1,4,5,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
010001101110 => [1,1,3,2,1,3,1] => [2,1,1,1,1,1] => ([(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) => 2
010110001110 => [1,1,1,2,3,3,1] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
010111101000 => [1,1,1,4,1,1,3] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0010110100 => [2,1,1,2,1,1,2] => [1,2,1,2,1] => ([(0,6),(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) => 2
0011010100 => [2,2,1,1,1,1,2] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0010101110 => [2,1,1,1,1,3,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0010111100 => [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
0011110100 => [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
0000010100 => [5,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
0111010100 => [1,3,1,1,1,1,2] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0000001110 => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0000111110 => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0011111110 => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00000000000 => [11] => [1] => ([],1) => 0
0000000100 => [7,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0000010110 => [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
0000101110 => [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
0001011110 => [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
0010111110 => [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
00011111110 => [3,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0101111110 => [1,1,1,6,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
00111111110 => [2,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
01111111110 => [1,9,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0011011000 => [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
0011100100 => [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) => 1
0011101000 => [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
0100110100 => [1,1,2,2,1,1,2] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0101011000 => [1,1,1,1,1,2,3] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0101100100 => [1,1,1,2,2,1,2] => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0101110000 => [1,1,1,3,4] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0110010100 => [1,2,2,1,1,1,2] => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0110100100 => [1,2,1,1,2,1,2] => [1,1,2,1,1,1] => ([(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) => 2
0110101000 => [1,2,1,1,1,1,3] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0110110000 => [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) => 1
0111000100 => [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
0111010000 => [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
001100110100 => [2,2,2,2,1,1,2] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
001101100100 => [2,2,1,2,2,1,2] => [2,1,2,1,1] => ([(0,5),(0,6),(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) => 2
001110011000 => [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
010011011000 => [1,1,2,2,1,2,3] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(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) => 2
010110011000 => [1,1,1,2,2,2,3] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
011001100100 => [1,2,2,2,2,1,2] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
011001110000 => [1,2,2,3,4] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
011100011000 => [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
011100110000 => [1,3,2,2,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
10100010001 => [1,1,1,3,1,3,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => 2
10100001000 => [1,1,1,4,1,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
10010001001 => [1,2,1,3,1,2,1] => [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) => 1
10010010001 => [1,2,1,2,1,3,1] => [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) => 1
10001001001 => [1,3,1,2,1,2,1] => [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) => 1
10001010001 => [1,3,1,1,1,3,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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) => 2
10000100001 => [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) => 1
00010001001 => [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) => 1
0100000000 => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
0100000011 => [1,1,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0100000111 => [1,1,5,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0100011111 => [1,1,3,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0100111111 => [1,1,2,6] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0101111111 => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
01000000000 => [1,1,9] => [2,1] => ([(0,2),(1,2)],3) => 2
0100001011 => [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
0100101111 => [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
0101011111 => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
0110111111 => [1,2,1,6] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0101011100 => [1,1,1,1,1,3,2] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0101100110 => [1,1,1,2,2,2,1] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0101110001 => [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
0101110100 => [1,1,1,3,1,1,2] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0101111000 => [1,1,1,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0110010110 => [1,2,2,1,1,2,1] => [1,2,2,1,1] => ([(0,5),(0,6),(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) => 2
0110011001 => [1,2,2,2,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
0110011100 => [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
0110100110 => [1,2,1,1,2,2,1] => [1,1,2,2,1] => ([(0,6),(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) => 2
0110110001 => [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) => 1
0110110100 => [1,2,1,2,1,1,2] => [1,1,1,1,2,1] => ([(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) => 2
0111000110 => [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
0111001001 => [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) => 1
0111011000 => [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) => 1
0111100100 => [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) => 1
0111101000 => [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
0111110000 => [1,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011001110001 => [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
011100010110 => [1,3,3,1,1,2,1] => [1,2,2,1,1] => ([(0,5),(0,6),(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) => 2
011100011001 => [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
011100011100 => [1,3,3,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
011100110001 => [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
011111000001 => [1,5,5,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0100000100 => [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
0011100110 => [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
0001101110 => [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) => 1
0010110110 => [2,1,1,2,1,2,1] => [1,2,1,1,1,1] => ([(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) => 2
0001110110 => [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
0011111000 => [2,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0100111100 => [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
0001111100 => [3,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001111000110 => [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) => 1
000111010110 => [3,3,1,1,1,2,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
001101100110 => [2,2,1,2,2,2,1] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
001001110110 => [2,1,2,3,1,2,1] => [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) => 1
000101110110 => [3,1,1,3,1,2,1] => [1,2,1,1,1,1] => ([(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) => 2
100111110000 => [1,2,5,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001111110000 => [2,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
110001111000 => [2,3,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100011111000 => [1,3,5,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000011111100 => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0000001001 => [6,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
100111001001 => [1,2,3,2,1,2,1] => [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) => 1
110001011001 => [2,3,1,1,2,2,1] => [1,1,2,2,1] => ([(0,6),(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) => 2
110001101001 => [2,3,2,1,1,2,1] => [1,1,1,2,1,1] => ([(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) => 2
110001110001 => [2,3,3,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
110010011001 => [2,2,1,2,2,2,1] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
110011001001 => [2,2,2,2,1,2,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
110011100001 => [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
110110001001 => [2,1,2,3,1,2,1] => [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) => 1
111000101001 => [3,3,1,1,1,2,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
111001001001 => [3,2,1,2,1,2,1] => [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) => 1
111010001001 => [3,1,1,3,1,2,1] => [1,2,1,1,1,1] => ([(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) => 2
0111000011 => [1,3,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0011110001 => [2,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110011000011 => [2,2,2,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110000111100 => [2,4,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
110000001111 => [2,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011100000111 => [1,3,5,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111000011100 => [3,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001111000011 => [2,4,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
011110000011 => [1,4,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111100000011 => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
000111110001 => [3,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001111100001 => [2,5,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0011011001 => [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
0010110001 => [2,1,1,2,3,1] => [1,2,1,1,1] => ([(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
0001000001 => [3,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0111011001 => [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
0111100011 => [1,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0011111001 => [2,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0000111111 => [4,6] => [1,1] => ([(0,1)],2) => 1
110011011001 => [2,2,2,1,2,2,1] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
110110011001 => [2,1,2,2,2,2,1] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
110011101001 => [2,2,3,1,1,2,1] => [2,1,2,1,1] => ([(0,5),(0,6),(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) => 2
110011100011 => [2,2,3,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
110111001001 => [2,1,3,2,1,2,1] => [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) => 1
110001111001 => [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) => 1
110011110001 => [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
011100111001 => [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) => 1
111001011001 => [3,2,1,1,2,2,1] => [1,1,2,2,1] => ([(0,6),(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) => 2
111010011001 => [3,1,1,2,2,2,1] => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
111001101001 => [3,2,2,1,1,2,1] => [1,2,2,1,1] => ([(0,5),(0,6),(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) => 2
111001100011 => [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
111011001001 => [3,1,2,2,1,2,1] => [1,1,2,1,1,1] => ([(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) => 2
111000111001 => [3,3,3,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
111001110001 => [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
111000001111 => [3,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
011110011001 => [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
011110000111 => [1,4,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
111100101001 => [4,2,1,1,1,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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) => 2
111101001001 => [4,1,1,2,1,2,1] => [1,2,1,1,1,1] => ([(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) => 2
111100011001 => [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
111100110001 => [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
111100000111 => [4,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
001111100011 => [2,5,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011111000011 => [1,5,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111110000011 => [5,5,2] => [2,1] => ([(0,2),(1,2)],3) => 2
111111000001 => [6,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
0011000110 => [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
0010001110 => [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
0110111001 => [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) => 1
0001101001 => [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
0000110001 => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0000010001 => [5,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
10000000001 => [1,9,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11000000001 => [2,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11100000001 => [3,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
11111111111 => [11] => [1] => ([],1) => 0
0100011001 => [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
0100111001 => [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
0101111001 => [1,1,1,4,2,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0110010001 => [1,2,2,1,3,1] => [1,2,1,1,1] => ([(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
0100010001 => [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
0100110001 => [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
0100100001 => [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
0101100001 => [1,1,1,2,4,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0110011011 => [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
0110111011 => [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) => 1
0100111011 => [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
0101111011 => [1,1,1,4,1,2] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0110100011 => [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
0100100011 => [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
0101100011 => [1,1,1,2,3,2] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0101000011 => [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) => 2
0110010111 => [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
0110110111 => [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) => 1
0100110111 => [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
0101110111 => [1,1,1,3,1,3] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0110100111 => [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
0101100111 => [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
0110101111 => [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
0101101111 => [1,1,1,2,1,4] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
0101001111 => [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) => 2
100110011011 => [1,2,2,2,2,1,2] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
101100100111 => [1,1,2,2,1,2,3] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(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) => 2
101001100111 => [1,1,1,2,2,2,3] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
100011101001 => [1,3,3,1,1,2,1] => [1,2,2,1,1] => ([(0,5),(0,6),(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) => 2
100011100011 => [1,3,3,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
0000011001 => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0011001111 => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
0110011111 => [1,2,2,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0000110100 => [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
0000000011 => [8,2] => [1,1] => ([(0,1)],2) => 1
0000011011 => [5,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0001101111 => [3,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0011011111 => [2,2,1,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
00000000011 => [9,2] => [1,1] => ([(0,1)],2) => 1
0011010111 => [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
0111001011 => [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
0111110111 => [1,5,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
11000000000 => [2,9] => [1,1] => ([(0,1)],2) => 1
0110001011 => [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
0110000111 => [1,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110000111001 => [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) => 1
001110000111 => [2,3,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011000001111 => [1,2,5,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0011010110 => [2,2,1,1,1,2,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0100110110 => [1,1,2,2,1,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(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) => 2
0110001110 => [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
0101001110 => [1,1,1,1,2,3,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
0011001110 => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0100101110 => [1,1,2,1,1,3,1] => [2,1,2,1,1] => ([(0,5),(0,6),(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) => 2
0100011110 => [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
0010011110 => [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) => 1
001110100110 => [2,3,1,1,2,2,1] => [1,1,2,2,1] => ([(0,6),(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) => 2
001110010110 => [2,3,2,1,1,2,1] => [1,1,1,2,1,1] => ([(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) => 2
011000110110 => [1,2,3,2,1,2,1] => [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) => 1
001100110110 => [2,2,2,2,1,2,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
000110110110 => [3,2,1,2,1,2,1] => [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) => 1
001110001110 => [2,3,3,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
001100011110 => [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
0101000000 => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
0001010000 => [3,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
0100010000 => [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
0001000100 => [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) => 1
0111011100 => [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) => 1
0110001001 => [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) => 1
0001001011 => [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
0001100011 => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0110000011 => [1,2,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0001110111 => [3,3,1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0111101111 => [1,4,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011000110000 => [1,2,3,2,4] => [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) => 1
000001100011 => [5,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000110000011 => [3,2,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011110001111 => [1,4,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
01111110000 => [1,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
110011001011 => [2,2,2,2,1,1,2] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
110010011011 => [2,2,1,2,2,1,2] => [2,1,2,1,1] => ([(0,5),(0,6),(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) => 2
110001100111 => [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
100011100111 => [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
100110001111 => [1,2,2,3,4] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
100011001111 => [1,3,2,2,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
0000000111 => [7,3] => [1,1] => ([(0,1)],2) => 1
0000001111 => [6,4] => [1,1] => ([(0,1)],2) => 1
0001111111 => [3,7] => [1,1] => ([(0,1)],2) => 1
0011111111 => [2,8] => [1,1] => ([(0,1)],2) => 1
0000001011 => [6,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0000010111 => [5,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0001011111 => [3,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
0010111111 => [2,1,1,6] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
00111111111 => [2,9] => [1,1] => ([(0,1)],2) => 1
10111111111 => [1,1,9] => [2,1] => ([(0,2),(1,2)],3) => 2
10000001011 => [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
0011011110 => [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
0011101110 => [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) => 1
0011110110 => [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) => 1
0011111100 => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
00101111110 => [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
000111100011 => [3,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
01111100100 => [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) => 1
111101101001 => [4,1,2,1,1,2,1] => [1,1,1,2,1,1] => ([(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) => 2
110001100000 => [2,3,2,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110000011000 => [2,5,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111100011110 => [4,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110011000110 => [2,2,2,3,2,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
110001100110 => [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
111100000110 => [4,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
011001100011 => [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
110001100011 => [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) => 1
0110001111 => [1,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0011000011 => [2,2,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
0011011011 => [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
0001111011 => [3,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111111001111 => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
111111000011 => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
110011001111 => [2,2,2,2,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
110011011011 => [2,2,2,1,2,1,2] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => 2
110110011011 => [2,1,2,2,2,1,2] => [1,1,3,1,1] => ([(0,5),(0,6),(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) => 2
001111001111 => [2,4,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
001100111111 => [2,2,2,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
001100000011 => [2,2,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
000011000011 => [4,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
000000000011 => [10,2] => [1,1] => ([(0,1)],2) => 1
011111111011 => [1,8,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111111111100 => [10,2] => [1,1] => ([(0,1)],2) => 1
111100111100 => [4,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
110011111100 => [2,2,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
110011000000 => [2,2,2,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
110000110000 => [2,4,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
0111011111 => [1,3,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
111100111001 => [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) => 1
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Generating function
$F_{1} = 2$
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
This is the greatest distance between any pair of vertices.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
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.
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