Identifier
-
Mp00262:
Binary words
—poset of factors⟶
Posets
St000069: Posets ⟶ ℤ
Values
0 => ([(0,1)],2) => 1
1 => ([(0,1)],2) => 1
00 => ([(0,2),(2,1)],3) => 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
11 => ([(0,2),(2,1)],3) => 1
000 => ([(0,3),(2,1),(3,2)],4) => 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
111 => ([(0,3),(2,1),(3,2)],4) => 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9) => 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9) => 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12) => 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12) => 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12) => 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13) => 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12) => 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12) => 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) => 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12) => 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13) => 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12) => 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12) => 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12) => 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12) => 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13) => 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12) => 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) => 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12) => 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12) => 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13) => 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12) => 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12) => 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12) => 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => 1
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15) => 1
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15) => 1
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16) => 1
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16) => 1
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17) => 1
000111 => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16) => 1
001000 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16) => 1
001001 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15) => 1
001010 => ([(0,2),(0,3),(1,9),(2,12),(2,14),(3,1),(3,12),(3,14),(5,7),(6,8),(7,4),(8,4),(9,5),(10,6),(10,11),(11,7),(11,8),(12,10),(12,13),(13,5),(13,6),(13,11),(14,9),(14,10),(14,13)],15) => 1
001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17) => 1
001100 => ([(0,3),(0,4),(1,15),(1,16),(2,10),(2,11),(3,1),(3,13),(3,14),(4,2),(4,13),(4,14),(6,9),(7,8),(8,5),(9,5),(10,7),(11,6),(12,8),(12,9),(13,10),(13,15),(14,11),(14,16),(15,7),(15,12),(16,6),(16,12)],17) => 1
001101 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17) => 1
001110 => ([(0,4),(0,5),(1,12),(2,3),(2,13),(2,16),(3,8),(3,14),(4,1),(4,9),(4,15),(5,2),(5,9),(5,15),(7,10),(8,11),(9,13),(10,6),(11,6),(12,7),(13,8),(14,10),(14,11),(15,12),(15,16),(16,7),(16,14)],17) => 1
001111 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15) => 1
010000 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15) => 1
010001 => ([(0,3),(0,4),(1,2),(1,11),(1,15),(2,7),(2,12),(3,13),(3,14),(4,1),(4,13),(4,14),(6,9),(7,10),(8,6),(9,5),(10,5),(11,7),(12,9),(12,10),(13,8),(13,15),(14,8),(14,11),(15,6),(15,12)],16) => 1
010010 => ([(0,2),(0,3),(1,10),(1,11),(2,13),(2,14),(3,1),(3,13),(3,14),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9),(12,5),(12,6),(13,10),(13,12),(14,11),(14,12)],15) => 1
010011 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17) => 1
010100 => ([(0,2),(0,3),(1,9),(2,12),(2,14),(3,1),(3,12),(3,14),(5,7),(6,8),(7,4),(8,4),(9,5),(10,6),(10,11),(11,7),(11,8),(12,10),(12,13),(13,5),(13,6),(13,11),(14,9),(14,10),(14,13)],15) => 1
010101 => ([(0,1),(0,2),(1,10),(1,11),(2,10),(2,11),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12) => 1
010110 => ([(0,2),(0,3),(1,6),(1,11),(2,14),(2,15),(3,1),(3,14),(3,15),(5,8),(6,7),(7,9),(8,10),(9,4),(10,4),(11,7),(11,13),(12,8),(12,13),(13,9),(13,10),(14,5),(14,6),(14,12),(15,5),(15,11),(15,12)],16) => 1
010111 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16) => 1
011000 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17) => 1
011001 => ([(0,3),(0,4),(1,11),(1,16),(2,10),(2,15),(3,2),(3,13),(3,14),(4,1),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,15),(13,16),(14,10),(14,11),(15,6),(15,12),(16,7),(16,12)],17) => 1
011010 => ([(0,2),(0,3),(1,6),(1,11),(2,14),(2,15),(3,1),(3,14),(3,15),(5,8),(6,7),(7,9),(8,10),(9,4),(10,4),(11,7),(11,13),(12,8),(12,13),(13,9),(13,10),(14,5),(14,6),(14,12),(15,5),(15,11),(15,12)],16) => 1
011011 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15) => 1
011100 => ([(0,4),(0,5),(1,12),(2,3),(2,13),(2,16),(3,8),(3,14),(4,1),(4,9),(4,15),(5,2),(5,9),(5,15),(7,10),(8,11),(9,13),(10,6),(11,6),(12,7),(13,8),(14,10),(14,11),(15,12),(15,16),(16,7),(16,14)],17) => 1
011101 => ([(0,3),(0,4),(1,2),(1,11),(1,15),(2,7),(2,12),(3,13),(3,14),(4,1),(4,13),(4,14),(6,9),(7,10),(8,6),(9,5),(10,5),(11,7),(12,9),(12,10),(13,8),(13,15),(14,8),(14,11),(15,6),(15,12)],16) => 1
011110 => ([(0,4),(0,5),(1,3),(1,7),(1,8),(2,13),(2,14),(3,2),(3,11),(3,12),(4,9),(4,10),(5,1),(5,9),(5,10),(7,12),(8,11),(9,8),(10,7),(11,13),(12,14),(13,6),(14,6)],15) => 1
011111 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => 1
100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => 1
100001 => ([(0,4),(0,5),(1,3),(1,7),(1,8),(2,13),(2,14),(3,2),(3,11),(3,12),(4,9),(4,10),(5,1),(5,9),(5,10),(7,12),(8,11),(9,8),(10,7),(11,13),(12,14),(13,6),(14,6)],15) => 1
100010 => ([(0,3),(0,4),(1,2),(1,11),(1,15),(2,7),(2,12),(3,13),(3,14),(4,1),(4,13),(4,14),(6,9),(7,10),(8,6),(9,5),(10,5),(11,7),(12,9),(12,10),(13,8),(13,15),(14,8),(14,11),(15,6),(15,12)],16) => 1
100011 => ([(0,4),(0,5),(1,12),(2,3),(2,13),(2,16),(3,8),(3,14),(4,1),(4,9),(4,15),(5,2),(5,9),(5,15),(7,10),(8,11),(9,13),(10,6),(11,6),(12,7),(13,8),(14,10),(14,11),(15,12),(15,16),(16,7),(16,14)],17) => 1
100100 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15) => 1
100101 => ([(0,2),(0,3),(1,6),(1,11),(2,14),(2,15),(3,1),(3,14),(3,15),(5,8),(6,7),(7,9),(8,10),(9,4),(10,4),(11,7),(11,13),(12,8),(12,13),(13,9),(13,10),(14,5),(14,6),(14,12),(15,5),(15,11),(15,12)],16) => 1
100110 => ([(0,3),(0,4),(1,11),(1,16),(2,10),(2,15),(3,2),(3,13),(3,14),(4,1),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,15),(13,16),(14,10),(14,11),(15,6),(15,12),(16,7),(16,12)],17) => 1
>>> Load all 411 entries. <<<100111 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17) => 1
101000 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16) => 1
101001 => ([(0,2),(0,3),(1,6),(1,11),(2,14),(2,15),(3,1),(3,14),(3,15),(5,8),(6,7),(7,9),(8,10),(9,4),(10,4),(11,7),(11,13),(12,8),(12,13),(13,9),(13,10),(14,5),(14,6),(14,12),(15,5),(15,11),(15,12)],16) => 1
101010 => ([(0,1),(0,2),(1,10),(1,11),(2,10),(2,11),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12) => 1
101011 => ([(0,2),(0,3),(1,9),(2,12),(2,14),(3,1),(3,12),(3,14),(5,7),(6,8),(7,4),(8,4),(9,5),(10,6),(10,11),(11,7),(11,8),(12,10),(12,13),(13,5),(13,6),(13,11),(14,9),(14,10),(14,13)],15) => 1
101100 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17) => 1
101101 => ([(0,2),(0,3),(1,10),(1,11),(2,13),(2,14),(3,1),(3,13),(3,14),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9),(12,5),(12,6),(13,10),(13,12),(14,11),(14,12)],15) => 1
101110 => ([(0,3),(0,4),(1,2),(1,11),(1,15),(2,7),(2,12),(3,13),(3,14),(4,1),(4,13),(4,14),(6,9),(7,10),(8,6),(9,5),(10,5),(11,7),(12,9),(12,10),(13,8),(13,15),(14,8),(14,11),(15,6),(15,12)],16) => 1
101111 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15) => 1
110000 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15) => 1
110001 => ([(0,4),(0,5),(1,12),(2,3),(2,13),(2,16),(3,8),(3,14),(4,1),(4,9),(4,15),(5,2),(5,9),(5,15),(7,10),(8,11),(9,13),(10,6),(11,6),(12,7),(13,8),(14,10),(14,11),(15,12),(15,16),(16,7),(16,14)],17) => 1
110010 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17) => 1
110011 => ([(0,3),(0,4),(1,15),(1,16),(2,10),(2,11),(3,1),(3,13),(3,14),(4,2),(4,13),(4,14),(6,9),(7,8),(8,5),(9,5),(10,7),(11,6),(12,8),(12,9),(13,10),(13,15),(14,11),(14,16),(15,7),(15,12),(16,6),(16,12)],17) => 1
110100 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17) => 1
110101 => ([(0,2),(0,3),(1,9),(2,12),(2,14),(3,1),(3,12),(3,14),(5,7),(6,8),(7,4),(8,4),(9,5),(10,6),(10,11),(11,7),(11,8),(12,10),(12,13),(13,5),(13,6),(13,11),(14,9),(14,10),(14,13)],15) => 1
110110 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15) => 1
110111 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16) => 1
111000 => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16) => 1
111001 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17) => 1
111010 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16) => 1
111011 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16) => 1
111100 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15) => 1
111101 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15) => 1
111110 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
0000001 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14) => 1
0000010 => ([(0,5),(0,6),(1,4),(1,14),(2,13),(3,2),(3,16),(4,3),(4,17),(5,12),(5,15),(6,1),(6,12),(6,15),(8,11),(9,10),(10,8),(11,7),(12,9),(13,7),(14,10),(14,17),(15,9),(15,14),(16,11),(16,13),(17,8),(17,16)],18) => 1
0000011 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18) => 1
0000100 => ([(0,4),(0,5),(1,2),(1,17),(2,7),(3,1),(3,8),(3,16),(4,18),(4,19),(5,3),(5,18),(5,19),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,10),(13,14),(14,11),(14,12),(15,9),(15,13),(16,13),(16,17),(17,7),(17,14),(18,15),(18,16),(19,8),(19,15)],20) => 1
0000101 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20) => 1
0000110 => ([(0,5),(0,6),(1,3),(1,15),(2,14),(3,2),(3,20),(4,8),(4,16),(5,1),(5,13),(5,19),(6,4),(6,13),(6,19),(8,9),(9,10),(10,11),(11,7),(12,7),(13,8),(14,12),(15,18),(15,20),(16,9),(16,18),(17,11),(17,12),(18,10),(18,17),(19,15),(19,16),(20,14),(20,17)],21) => 1
0000111 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20) => 1
0001000 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,6),(2,7),(3,16),(3,17),(4,1),(4,16),(4,17),(6,9),(7,8),(8,10),(9,11),(10,5),(11,5),(12,14),(12,15),(13,10),(13,11),(14,8),(14,13),(15,9),(15,13),(16,12),(16,18),(17,12),(17,19),(18,7),(18,14),(19,6),(19,15)],20) => 1
0001001 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20) => 1
0001010 => ([(0,3),(0,4),(1,2),(1,17),(2,6),(3,16),(3,19),(4,1),(4,16),(4,19),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,9),(12,14),(13,8),(13,15),(14,7),(14,15),(15,10),(15,11),(16,12),(16,18),(17,6),(17,13),(18,9),(18,13),(18,14),(19,12),(19,17),(19,18)],20) => 1
0001011 => ([(0,4),(0,5),(1,13),(2,3),(2,20),(3,7),(4,1),(4,19),(4,21),(5,2),(5,19),(5,21),(7,9),(8,11),(9,12),(10,8),(11,6),(12,6),(13,10),(14,10),(14,17),(15,16),(15,17),(16,9),(16,18),(17,8),(17,18),(18,11),(18,12),(19,14),(19,15),(20,7),(20,16),(21,13),(21,14),(21,15),(21,20)],22) => 1
0001100 => ([(0,4),(0,5),(1,12),(2,19),(2,21),(3,1),(3,13),(3,20),(4,2),(4,16),(4,17),(5,3),(5,16),(5,17),(7,11),(8,9),(9,10),(10,6),(11,6),(12,7),(13,8),(14,10),(14,11),(15,9),(15,14),(16,19),(16,20),(17,13),(17,21),(18,7),(18,14),(19,15),(19,18),(20,12),(20,18),(21,8),(21,15)],22) => 1
0001101 => ([(0,4),(0,5),(1,13),(2,1),(2,15),(3,14),(3,16),(4,2),(4,20),(4,21),(5,3),(5,20),(5,21),(7,8),(8,9),(9,11),(10,12),(11,6),(12,6),(13,10),(14,8),(14,18),(15,13),(15,17),(16,17),(16,18),(17,10),(17,19),(18,9),(18,19),(19,11),(19,12),(20,7),(20,14),(21,7),(21,15),(21,16)],22) => 1
0001110 => ([(0,5),(0,6),(1,2),(1,20),(2,8),(3,4),(3,15),(3,21),(4,9),(4,17),(5,1),(5,10),(5,18),(6,3),(6,10),(6,18),(8,11),(9,12),(10,15),(11,13),(12,14),(13,7),(14,7),(15,9),(16,11),(16,19),(17,12),(17,19),(18,20),(18,21),(19,13),(19,14),(20,8),(20,16),(21,16),(21,17)],22) => 1
0001111 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20) => 1
0010000 => ([(0,4),(0,5),(1,2),(1,17),(2,7),(3,1),(3,8),(3,16),(4,18),(4,19),(5,3),(5,18),(5,19),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,10),(13,14),(14,11),(14,12),(15,9),(15,13),(16,13),(16,17),(17,7),(17,14),(18,15),(18,16),(19,8),(19,15)],20) => 1
0010001 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,7),(2,14),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,17),(15,19),(16,17),(16,18),(17,6),(17,13),(18,13),(18,14),(19,6),(19,7)],20) => 1
0010010 => ([(0,2),(0,3),(1,11),(1,12),(2,16),(2,17),(3,1),(3,16),(3,17),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,13),(10,15),(11,14),(11,15),(12,13),(12,14),(13,5),(13,9),(14,6),(14,9),(15,5),(15,6),(16,10),(16,12),(17,10),(17,11)],18) => 1
0010011 => ([(0,3),(0,4),(1,12),(2,14),(2,19),(3,2),(3,18),(3,20),(4,1),(4,18),(4,20),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,6),(13,9),(13,16),(14,15),(14,16),(15,8),(15,17),(16,7),(16,17),(17,10),(17,11),(18,13),(18,14),(19,6),(19,9),(19,15),(20,12),(20,13),(20,19)],21) => 1
0010100 => ([(0,2),(0,3),(1,7),(1,8),(2,17),(2,18),(3,1),(3,17),(3,18),(5,10),(6,9),(7,6),(8,5),(9,11),(10,12),(11,4),(12,4),(13,14),(13,15),(14,9),(14,16),(15,10),(15,16),(16,11),(16,12),(17,7),(17,13),(17,19),(18,8),(18,13),(18,19),(19,5),(19,6),(19,14),(19,15)],20) => 1
0010101 => ([(0,2),(0,3),(1,10),(2,14),(2,17),(3,1),(3,14),(3,17),(5,8),(6,5),(7,9),(8,4),(9,4),(10,6),(11,13),(11,16),(12,8),(12,9),(13,7),(13,12),(14,11),(14,15),(15,6),(15,13),(15,16),(16,5),(16,7),(16,12),(17,10),(17,11),(17,15)],18) => 1
0010110 => ([(0,3),(0,4),(1,13),(2,6),(2,14),(3,2),(3,20),(3,21),(4,1),(4,20),(4,21),(6,7),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,10),(14,7),(14,18),(15,10),(15,17),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,11),(19,12),(20,6),(20,15),(20,16),(21,13),(21,14),(21,15),(21,16)],22) => 1
0010111 => ([(0,4),(0,5),(1,13),(2,3),(2,20),(3,7),(4,1),(4,19),(4,21),(5,2),(5,19),(5,21),(7,9),(8,11),(9,12),(10,8),(11,6),(12,6),(13,10),(14,10),(14,17),(15,16),(15,17),(16,9),(16,18),(17,8),(17,18),(18,11),(18,12),(19,14),(19,15),(20,7),(20,16),(21,13),(21,14),(21,15),(21,20)],22) => 1
0011000 => ([(0,4),(0,5),(1,12),(2,19),(2,21),(3,1),(3,13),(3,20),(4,2),(4,16),(4,17),(5,3),(5,16),(5,17),(7,11),(8,9),(9,10),(10,6),(11,6),(12,7),(13,8),(14,10),(14,11),(15,9),(15,14),(16,19),(16,20),(17,13),(17,21),(18,7),(18,14),(19,15),(19,18),(20,12),(20,18),(21,8),(21,15)],22) => 1
0011001 => ([(0,3),(0,4),(1,18),(1,20),(2,17),(2,19),(3,1),(3,15),(3,16),(4,2),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,19),(15,20),(16,17),(16,18),(17,13),(17,14),(18,6),(18,13),(19,7),(19,14),(20,6),(20,7)],21) => 1
0011010 => ([(0,3),(0,4),(1,13),(2,14),(2,15),(3,2),(3,20),(3,21),(4,1),(4,20),(4,21),(6,7),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,10),(14,10),(14,18),(15,17),(15,18),(16,7),(16,17),(17,8),(17,19),(18,9),(18,19),(19,11),(19,12),(20,6),(20,15),(20,16),(21,6),(21,13),(21,14),(21,16)],22) => 1
0011011 => ([(0,3),(0,4),(1,12),(2,14),(2,19),(3,2),(3,18),(3,20),(4,1),(4,18),(4,20),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,6),(13,9),(13,16),(14,15),(14,16),(15,8),(15,17),(16,7),(16,17),(17,10),(17,11),(18,13),(18,14),(19,6),(19,9),(19,15),(20,12),(20,13),(20,19)],21) => 1
0011100 => ([(0,4),(0,5),(1,13),(1,14),(2,3),(2,20),(2,21),(3,15),(3,16),(4,1),(4,17),(4,18),(5,2),(5,17),(5,18),(7,10),(8,9),(9,11),(10,12),(11,6),(12,6),(13,8),(14,7),(15,9),(15,19),(16,10),(16,19),(17,13),(17,20),(18,14),(18,21),(19,11),(19,12),(20,8),(20,15),(21,7),(21,16)],22) => 1
0011101 => ([(0,4),(0,5),(1,14),(2,3),(2,19),(2,20),(3,15),(3,16),(4,1),(4,17),(4,21),(5,2),(5,17),(5,21),(7,10),(8,9),(9,12),(10,13),(11,7),(12,6),(13,6),(14,8),(15,10),(15,18),(16,9),(16,18),(17,11),(17,20),(18,12),(18,13),(19,8),(19,16),(20,7),(20,15),(21,11),(21,14),(21,19)],22) => 1
0011110 => ([(0,5),(0,6),(1,14),(2,4),(2,9),(2,18),(3,16),(3,20),(4,3),(4,15),(4,19),(5,2),(5,10),(5,17),(6,1),(6,10),(6,17),(8,12),(9,15),(10,9),(11,8),(12,7),(13,7),(14,11),(15,16),(16,13),(17,14),(17,18),(18,11),(18,19),(19,8),(19,20),(20,12),(20,13)],21) => 1
0011111 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18) => 1
0100000 => ([(0,5),(0,6),(1,4),(1,14),(2,13),(3,2),(3,16),(4,3),(4,17),(5,12),(5,15),(6,1),(6,12),(6,15),(8,11),(9,10),(10,8),(11,7),(12,9),(13,7),(14,10),(14,17),(15,9),(15,14),(16,11),(16,13),(17,8),(17,16)],18) => 1
0100001 => ([(0,4),(0,5),(1,3),(1,9),(1,17),(2,14),(2,19),(3,2),(3,13),(3,18),(4,15),(4,16),(5,1),(5,15),(5,16),(7,11),(8,7),(9,13),(10,8),(11,6),(12,6),(13,14),(14,12),(15,9),(15,10),(16,10),(16,17),(17,8),(17,18),(18,7),(18,19),(19,11),(19,12)],20) => 1
0100010 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,13),(2,14),(3,15),(3,16),(4,1),(4,15),(4,16),(6,9),(7,8),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,17),(15,18),(16,17),(16,19),(17,6),(17,7),(18,7),(18,13),(19,6),(19,14)],20) => 1
0100011 => ([(0,4),(0,5),(1,14),(2,3),(2,19),(2,20),(3,15),(3,16),(4,1),(4,17),(4,21),(5,2),(5,17),(5,21),(7,10),(8,9),(9,12),(10,13),(11,7),(12,6),(13,6),(14,8),(15,10),(15,18),(16,9),(16,18),(17,11),(17,20),(18,12),(18,13),(19,8),(19,16),(20,7),(20,15),(21,11),(21,14),(21,19)],22) => 1
0100100 => ([(0,2),(0,3),(1,11),(1,12),(2,16),(2,17),(3,1),(3,16),(3,17),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,13),(10,15),(11,14),(11,15),(12,13),(12,14),(13,5),(13,9),(14,6),(14,9),(15,5),(15,6),(16,10),(16,12),(17,10),(17,11)],18) => 1
0100101 => ([(0,2),(0,3),(1,12),(1,13),(2,18),(2,19),(3,1),(3,18),(3,19),(5,8),(6,5),(7,10),(8,11),(9,7),(10,4),(11,4),(12,9),(12,15),(13,14),(13,15),(14,8),(14,16),(15,7),(15,16),(16,10),(16,11),(17,5),(17,9),(17,14),(18,6),(18,12),(18,17),(19,6),(19,13),(19,17)],20) => 1
0100110 => ([(0,3),(0,4),(1,17),(1,19),(2,13),(2,18),(3,1),(3,20),(3,21),(4,2),(4,20),(4,21),(6,9),(7,10),(8,6),(9,11),(10,12),(11,5),(12,5),(13,7),(14,9),(14,16),(15,10),(15,16),(16,11),(16,12),(17,6),(17,14),(18,7),(18,15),(19,14),(19,15),(20,8),(20,18),(20,19),(21,8),(21,13),(21,17)],22) => 1
0100111 => ([(0,4),(0,5),(1,13),(2,1),(2,15),(3,14),(3,16),(4,2),(4,20),(4,21),(5,3),(5,20),(5,21),(7,8),(8,9),(9,11),(10,12),(11,6),(12,6),(13,10),(14,8),(14,18),(15,13),(15,17),(16,17),(16,18),(17,10),(17,19),(18,9),(18,19),(19,11),(19,12),(20,7),(20,14),(21,7),(21,15),(21,16)],22) => 1
0101000 => ([(0,3),(0,4),(1,2),(1,17),(2,6),(3,16),(3,19),(4,1),(4,16),(4,19),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,9),(12,14),(13,8),(13,15),(14,7),(14,15),(15,10),(15,11),(16,12),(16,18),(17,6),(17,13),(18,9),(18,13),(18,14),(19,12),(19,17),(19,18)],20) => 1
0101001 => ([(0,2),(0,3),(1,5),(1,12),(2,18),(2,19),(3,1),(3,18),(3,19),(5,6),(6,7),(7,10),(8,11),(9,8),(10,4),(11,4),(12,6),(12,14),(13,9),(13,15),(14,7),(14,16),(15,8),(15,16),(16,10),(16,11),(17,9),(17,14),(17,15),(18,5),(18,13),(18,17),(19,12),(19,13),(19,17)],20) => 1
0101010 => ([(0,1),(0,2),(1,12),(1,13),(2,12),(2,13),(4,3),(5,3),(6,10),(6,11),(7,10),(7,11),(8,6),(8,7),(9,6),(9,7),(10,4),(10,5),(11,4),(11,5),(12,8),(12,9),(13,8),(13,9)],14) => 1
0101011 => ([(0,2),(0,3),(1,10),(2,14),(2,17),(3,1),(3,14),(3,17),(5,8),(6,5),(7,9),(8,4),(9,4),(10,6),(11,13),(11,16),(12,8),(12,9),(13,7),(13,12),(14,11),(14,15),(15,6),(15,13),(15,16),(16,5),(16,7),(16,12),(17,10),(17,11),(17,15)],18) => 1
0101100 => ([(0,3),(0,4),(1,13),(2,14),(2,15),(3,2),(3,20),(3,21),(4,1),(4,20),(4,21),(6,7),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,10),(14,10),(14,18),(15,17),(15,18),(16,7),(16,17),(17,8),(17,19),(18,9),(18,19),(19,11),(19,12),(20,6),(20,15),(20,16),(21,6),(21,13),(21,14),(21,16)],22) => 1
0101101 => ([(0,2),(0,3),(1,12),(1,13),(2,18),(2,19),(3,1),(3,18),(3,19),(5,8),(6,5),(7,10),(8,11),(9,7),(10,4),(11,4),(12,9),(12,15),(13,14),(13,15),(14,8),(14,16),(15,7),(15,16),(16,10),(16,11),(17,5),(17,9),(17,14),(18,6),(18,12),(18,17),(19,6),(19,13),(19,17)],20) => 1
0101110 => ([(0,3),(0,4),(1,2),(1,13),(1,18),(2,6),(2,14),(3,19),(3,20),(4,1),(4,19),(4,20),(6,10),(7,8),(8,9),(9,11),(10,12),(11,5),(12,5),(13,6),(14,10),(14,17),(15,8),(15,16),(16,9),(16,17),(17,11),(17,12),(18,14),(18,16),(19,7),(19,15),(19,18),(20,7),(20,13),(20,15)],21) => 1
0101111 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20) => 1
0110000 => ([(0,5),(0,6),(1,3),(1,15),(2,14),(3,2),(3,20),(4,8),(4,16),(5,1),(5,13),(5,19),(6,4),(6,13),(6,19),(8,9),(9,10),(10,11),(11,7),(12,7),(13,8),(14,12),(15,18),(15,20),(16,9),(16,18),(17,11),(17,12),(18,10),(18,17),(19,15),(19,16),(20,14),(20,17)],21) => 1
0110001 => ([(0,4),(0,5),(1,13),(1,20),(2,3),(2,14),(2,21),(3,8),(3,16),(4,1),(4,17),(4,18),(5,2),(5,17),(5,18),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,19),(16,10),(16,19),(17,20),(17,21),(18,13),(18,14),(19,11),(19,12),(20,7),(20,15),(21,15),(21,16)],22) => 1
0110010 => ([(0,3),(0,4),(1,17),(1,19),(2,13),(2,18),(3,1),(3,20),(3,21),(4,2),(4,20),(4,21),(6,9),(7,10),(8,6),(9,11),(10,12),(11,5),(12,5),(13,7),(14,9),(14,16),(15,10),(15,16),(16,11),(16,12),(17,6),(17,14),(18,7),(18,15),(19,14),(19,15),(20,8),(20,18),(20,19),(21,8),(21,13),(21,17)],22) => 1
0110011 => ([(0,3),(0,4),(1,18),(1,20),(2,17),(2,19),(3,1),(3,15),(3,16),(4,2),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,19),(15,20),(16,17),(16,18),(17,13),(17,14),(18,6),(18,13),(19,7),(19,14),(20,6),(20,7)],21) => 1
0110100 => ([(0,3),(0,4),(1,13),(2,6),(2,14),(3,2),(3,20),(3,21),(4,1),(4,20),(4,21),(6,7),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,10),(14,7),(14,18),(15,10),(15,17),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,11),(19,12),(20,6),(20,15),(20,16),(21,13),(21,14),(21,15),(21,16)],22) => 1
0110101 => ([(0,2),(0,3),(1,5),(1,12),(2,18),(2,19),(3,1),(3,18),(3,19),(5,6),(6,7),(7,10),(8,11),(9,8),(10,4),(11,4),(12,6),(12,14),(13,9),(13,15),(14,7),(14,16),(15,8),(15,16),(16,10),(16,11),(17,9),(17,14),(17,15),(18,5),(18,13),(18,17),(19,12),(19,13),(19,17)],20) => 1
0110110 => ([(0,2),(0,3),(1,11),(1,12),(2,16),(2,17),(3,1),(3,16),(3,17),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,6),(13,9),(14,5),(14,9),(15,5),(15,6),(16,10),(16,11),(17,10),(17,12)],18) => 1
0110111 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20) => 1
0111000 => ([(0,5),(0,6),(1,2),(1,20),(2,8),(3,4),(3,15),(3,21),(4,9),(4,17),(5,1),(5,10),(5,18),(6,3),(6,10),(6,18),(8,11),(9,12),(10,15),(11,13),(12,14),(13,7),(14,7),(15,9),(16,11),(16,19),(17,12),(17,19),(18,20),(18,21),(19,13),(19,14),(20,8),(20,16),(21,16),(21,17)],22) => 1
0111001 => ([(0,4),(0,5),(1,13),(1,20),(2,3),(2,14),(2,21),(3,8),(3,16),(4,1),(4,17),(4,18),(5,2),(5,17),(5,18),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,19),(16,10),(16,19),(17,20),(17,21),(18,13),(18,14),(19,11),(19,12),(20,7),(20,15),(21,15),(21,16)],22) => 1
0111010 => ([(0,3),(0,4),(1,2),(1,13),(1,18),(2,6),(2,14),(3,19),(3,20),(4,1),(4,19),(4,20),(6,10),(7,8),(8,9),(9,11),(10,12),(11,5),(12,5),(13,6),(14,10),(14,17),(15,8),(15,16),(16,9),(16,17),(17,11),(17,12),(18,14),(18,16),(19,7),(19,15),(19,18),(20,7),(20,13),(20,15)],21) => 1
0111011 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,7),(2,14),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,17),(15,19),(16,17),(16,18),(17,6),(17,13),(18,13),(18,14),(19,6),(19,7)],20) => 1
0111100 => ([(0,5),(0,6),(1,14),(2,4),(2,9),(2,18),(3,16),(3,20),(4,3),(4,15),(4,19),(5,2),(5,10),(5,17),(6,1),(6,10),(6,17),(8,12),(9,15),(10,9),(11,8),(12,7),(13,7),(14,11),(15,16),(16,13),(17,14),(17,18),(18,11),(18,19),(19,8),(19,20),(20,12),(20,13)],21) => 1
0111101 => ([(0,4),(0,5),(1,3),(1,9),(1,17),(2,14),(2,19),(3,2),(3,13),(3,18),(4,15),(4,16),(5,1),(5,15),(5,16),(7,11),(8,7),(9,13),(10,8),(11,6),(12,6),(13,14),(14,12),(15,9),(15,10),(16,10),(16,17),(17,8),(17,18),(18,7),(18,19),(19,11),(19,12)],20) => 1
0111110 => ([(0,5),(0,6),(1,4),(1,8),(1,9),(2,16),(2,17),(3,2),(3,12),(3,13),(4,3),(4,14),(4,15),(5,10),(5,11),(6,1),(6,10),(6,11),(8,15),(9,14),(10,9),(11,8),(12,16),(13,17),(14,12),(15,13),(16,7),(17,7)],18) => 1
0111111 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14) => 1
1000000 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14) => 1
1000001 => ([(0,5),(0,6),(1,4),(1,8),(1,9),(2,16),(2,17),(3,2),(3,12),(3,13),(4,3),(4,14),(4,15),(5,10),(5,11),(6,1),(6,10),(6,11),(8,15),(9,14),(10,9),(11,8),(12,16),(13,17),(14,12),(15,13),(16,7),(17,7)],18) => 1
1000010 => ([(0,4),(0,5),(1,3),(1,9),(1,17),(2,14),(2,19),(3,2),(3,13),(3,18),(4,15),(4,16),(5,1),(5,15),(5,16),(7,11),(8,7),(9,13),(10,8),(11,6),(12,6),(13,14),(14,12),(15,9),(15,10),(16,10),(16,17),(17,8),(17,18),(18,7),(18,19),(19,11),(19,12)],20) => 1
1000011 => ([(0,5),(0,6),(1,14),(2,4),(2,9),(2,18),(3,16),(3,20),(4,3),(4,15),(4,19),(5,2),(5,10),(5,17),(6,1),(6,10),(6,17),(8,12),(9,15),(10,9),(11,8),(12,7),(13,7),(14,11),(15,16),(16,13),(17,14),(17,18),(18,11),(18,19),(19,8),(19,20),(20,12),(20,13)],21) => 1
1000100 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,7),(2,14),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,17),(15,19),(16,17),(16,18),(17,6),(17,13),(18,13),(18,14),(19,6),(19,7)],20) => 1
1000101 => ([(0,3),(0,4),(1,2),(1,13),(1,18),(2,6),(2,14),(3,19),(3,20),(4,1),(4,19),(4,20),(6,10),(7,8),(8,9),(9,11),(10,12),(11,5),(12,5),(13,6),(14,10),(14,17),(15,8),(15,16),(16,9),(16,17),(17,11),(17,12),(18,14),(18,16),(19,7),(19,15),(19,18),(20,7),(20,13),(20,15)],21) => 1
1000110 => ([(0,4),(0,5),(1,13),(1,20),(2,3),(2,14),(2,21),(3,8),(3,16),(4,1),(4,17),(4,18),(5,2),(5,17),(5,18),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,19),(16,10),(16,19),(17,20),(17,21),(18,13),(18,14),(19,11),(19,12),(20,7),(20,15),(21,15),(21,16)],22) => 1
1000111 => ([(0,5),(0,6),(1,2),(1,20),(2,8),(3,4),(3,15),(3,21),(4,9),(4,17),(5,1),(5,10),(5,18),(6,3),(6,10),(6,18),(8,11),(9,12),(10,15),(11,13),(12,14),(13,7),(14,7),(15,9),(16,11),(16,19),(17,12),(17,19),(18,20),(18,21),(19,13),(19,14),(20,8),(20,16),(21,16),(21,17)],22) => 1
1001000 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20) => 1
1001001 => ([(0,2),(0,3),(1,11),(1,12),(2,16),(2,17),(3,1),(3,16),(3,17),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,6),(13,9),(14,5),(14,9),(15,5),(15,6),(16,10),(16,11),(17,10),(17,12)],18) => 1
1001010 => ([(0,2),(0,3),(1,5),(1,12),(2,18),(2,19),(3,1),(3,18),(3,19),(5,6),(6,7),(7,10),(8,11),(9,8),(10,4),(11,4),(12,6),(12,14),(13,9),(13,15),(14,7),(14,16),(15,8),(15,16),(16,10),(16,11),(17,9),(17,14),(17,15),(18,5),(18,13),(18,17),(19,12),(19,13),(19,17)],20) => 1
1001011 => ([(0,3),(0,4),(1,13),(2,6),(2,14),(3,2),(3,20),(3,21),(4,1),(4,20),(4,21),(6,7),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,10),(14,7),(14,18),(15,10),(15,17),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,11),(19,12),(20,6),(20,15),(20,16),(21,13),(21,14),(21,15),(21,16)],22) => 1
1001100 => ([(0,3),(0,4),(1,18),(1,20),(2,17),(2,19),(3,1),(3,15),(3,16),(4,2),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,19),(15,20),(16,17),(16,18),(17,13),(17,14),(18,6),(18,13),(19,7),(19,14),(20,6),(20,7)],21) => 1
1001101 => ([(0,3),(0,4),(1,17),(1,19),(2,13),(2,18),(3,1),(3,20),(3,21),(4,2),(4,20),(4,21),(6,9),(7,10),(8,6),(9,11),(10,12),(11,5),(12,5),(13,7),(14,9),(14,16),(15,10),(15,16),(16,11),(16,12),(17,6),(17,14),(18,7),(18,15),(19,14),(19,15),(20,8),(20,18),(20,19),(21,8),(21,13),(21,17)],22) => 1
1001110 => ([(0,4),(0,5),(1,13),(1,20),(2,3),(2,14),(2,21),(3,8),(3,16),(4,1),(4,17),(4,18),(5,2),(5,17),(5,18),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,19),(16,10),(16,19),(17,20),(17,21),(18,13),(18,14),(19,11),(19,12),(20,7),(20,15),(21,15),(21,16)],22) => 1
1001111 => ([(0,5),(0,6),(1,3),(1,15),(2,14),(3,2),(3,20),(4,8),(4,16),(5,1),(5,13),(5,19),(6,4),(6,13),(6,19),(8,9),(9,10),(10,11),(11,7),(12,7),(13,8),(14,12),(15,18),(15,20),(16,9),(16,18),(17,11),(17,12),(18,10),(18,17),(19,15),(19,16),(20,14),(20,17)],21) => 1
1010000 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20) => 1
1010001 => ([(0,3),(0,4),(1,2),(1,13),(1,18),(2,6),(2,14),(3,19),(3,20),(4,1),(4,19),(4,20),(6,10),(7,8),(8,9),(9,11),(10,12),(11,5),(12,5),(13,6),(14,10),(14,17),(15,8),(15,16),(16,9),(16,17),(17,11),(17,12),(18,14),(18,16),(19,7),(19,15),(19,18),(20,7),(20,13),(20,15)],21) => 1
1010010 => ([(0,2),(0,3),(1,12),(1,13),(2,18),(2,19),(3,1),(3,18),(3,19),(5,8),(6,5),(7,10),(8,11),(9,7),(10,4),(11,4),(12,9),(12,15),(13,14),(13,15),(14,8),(14,16),(15,7),(15,16),(16,10),(16,11),(17,5),(17,9),(17,14),(18,6),(18,12),(18,17),(19,6),(19,13),(19,17)],20) => 1
1010011 => ([(0,3),(0,4),(1,13),(2,14),(2,15),(3,2),(3,20),(3,21),(4,1),(4,20),(4,21),(6,7),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,10),(14,10),(14,18),(15,17),(15,18),(16,7),(16,17),(17,8),(17,19),(18,9),(18,19),(19,11),(19,12),(20,6),(20,15),(20,16),(21,6),(21,13),(21,14),(21,16)],22) => 1
1010100 => ([(0,2),(0,3),(1,10),(2,14),(2,17),(3,1),(3,14),(3,17),(5,8),(6,5),(7,9),(8,4),(9,4),(10,6),(11,13),(11,16),(12,8),(12,9),(13,7),(13,12),(14,11),(14,15),(15,6),(15,13),(15,16),(16,5),(16,7),(16,12),(17,10),(17,11),(17,15)],18) => 1
1010101 => ([(0,1),(0,2),(1,12),(1,13),(2,12),(2,13),(4,3),(5,3),(6,10),(6,11),(7,10),(7,11),(8,6),(8,7),(9,6),(9,7),(10,4),(10,5),(11,4),(11,5),(12,8),(12,9),(13,8),(13,9)],14) => 1
1010110 => ([(0,2),(0,3),(1,5),(1,12),(2,18),(2,19),(3,1),(3,18),(3,19),(5,6),(6,7),(7,10),(8,11),(9,8),(10,4),(11,4),(12,6),(12,14),(13,9),(13,15),(14,7),(14,16),(15,8),(15,16),(16,10),(16,11),(17,9),(17,14),(17,15),(18,5),(18,13),(18,17),(19,12),(19,13),(19,17)],20) => 1
1010111 => ([(0,3),(0,4),(1,2),(1,17),(2,6),(3,16),(3,19),(4,1),(4,16),(4,19),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,9),(12,14),(13,8),(13,15),(14,7),(14,15),(15,10),(15,11),(16,12),(16,18),(17,6),(17,13),(18,9),(18,13),(18,14),(19,12),(19,17),(19,18)],20) => 1
1011000 => ([(0,4),(0,5),(1,13),(2,1),(2,15),(3,14),(3,16),(4,2),(4,20),(4,21),(5,3),(5,20),(5,21),(7,8),(8,9),(9,11),(10,12),(11,6),(12,6),(13,10),(14,8),(14,18),(15,13),(15,17),(16,17),(16,18),(17,10),(17,19),(18,9),(18,19),(19,11),(19,12),(20,7),(20,14),(21,7),(21,15),(21,16)],22) => 1
1011001 => ([(0,3),(0,4),(1,17),(1,19),(2,13),(2,18),(3,1),(3,20),(3,21),(4,2),(4,20),(4,21),(6,9),(7,10),(8,6),(9,11),(10,12),(11,5),(12,5),(13,7),(14,9),(14,16),(15,10),(15,16),(16,11),(16,12),(17,6),(17,14),(18,7),(18,15),(19,14),(19,15),(20,8),(20,18),(20,19),(21,8),(21,13),(21,17)],22) => 1
1011010 => ([(0,2),(0,3),(1,12),(1,13),(2,18),(2,19),(3,1),(3,18),(3,19),(5,8),(6,5),(7,10),(8,11),(9,7),(10,4),(11,4),(12,9),(12,15),(13,14),(13,15),(14,8),(14,16),(15,7),(15,16),(16,10),(16,11),(17,5),(17,9),(17,14),(18,6),(18,12),(18,17),(19,6),(19,13),(19,17)],20) => 1
1011011 => ([(0,2),(0,3),(1,11),(1,12),(2,16),(2,17),(3,1),(3,16),(3,17),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,13),(10,15),(11,14),(11,15),(12,13),(12,14),(13,5),(13,9),(14,6),(14,9),(15,5),(15,6),(16,10),(16,12),(17,10),(17,11)],18) => 1
1011100 => ([(0,4),(0,5),(1,14),(2,3),(2,19),(2,20),(3,15),(3,16),(4,1),(4,17),(4,21),(5,2),(5,17),(5,21),(7,10),(8,9),(9,12),(10,13),(11,7),(12,6),(13,6),(14,8),(15,10),(15,18),(16,9),(16,18),(17,11),(17,20),(18,12),(18,13),(19,8),(19,16),(20,7),(20,15),(21,11),(21,14),(21,19)],22) => 1
1011101 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,13),(2,14),(3,15),(3,16),(4,1),(4,15),(4,16),(6,9),(7,8),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,17),(15,18),(16,17),(16,19),(17,6),(17,7),(18,7),(18,13),(19,6),(19,14)],20) => 1
1011110 => ([(0,4),(0,5),(1,3),(1,9),(1,17),(2,14),(2,19),(3,2),(3,13),(3,18),(4,15),(4,16),(5,1),(5,15),(5,16),(7,11),(8,7),(9,13),(10,8),(11,6),(12,6),(13,14),(14,12),(15,9),(15,10),(16,10),(16,17),(17,8),(17,18),(18,7),(18,19),(19,11),(19,12)],20) => 1
1011111 => ([(0,5),(0,6),(1,4),(1,14),(2,13),(3,2),(3,16),(4,3),(4,17),(5,12),(5,15),(6,1),(6,12),(6,15),(8,11),(9,10),(10,8),(11,7),(12,9),(13,7),(14,10),(14,17),(15,9),(15,14),(16,11),(16,13),(17,8),(17,16)],18) => 1
1100000 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18) => 1
1100001 => ([(0,5),(0,6),(1,14),(2,4),(2,9),(2,18),(3,16),(3,20),(4,3),(4,15),(4,19),(5,2),(5,10),(5,17),(6,1),(6,10),(6,17),(8,12),(9,15),(10,9),(11,8),(12,7),(13,7),(14,11),(15,16),(16,13),(17,14),(17,18),(18,11),(18,19),(19,8),(19,20),(20,12),(20,13)],21) => 1
1100010 => ([(0,4),(0,5),(1,14),(2,3),(2,19),(2,20),(3,15),(3,16),(4,1),(4,17),(4,21),(5,2),(5,17),(5,21),(7,10),(8,9),(9,12),(10,13),(11,7),(12,6),(13,6),(14,8),(15,10),(15,18),(16,9),(16,18),(17,11),(17,20),(18,12),(18,13),(19,8),(19,16),(20,7),(20,15),(21,11),(21,14),(21,19)],22) => 1
1100011 => ([(0,4),(0,5),(1,13),(1,14),(2,3),(2,20),(2,21),(3,15),(3,16),(4,1),(4,17),(4,18),(5,2),(5,17),(5,18),(7,10),(8,9),(9,11),(10,12),(11,6),(12,6),(13,8),(14,7),(15,9),(15,19),(16,10),(16,19),(17,13),(17,20),(18,14),(18,21),(19,11),(19,12),(20,8),(20,15),(21,7),(21,16)],22) => 1
1100100 => ([(0,3),(0,4),(1,12),(2,14),(2,19),(3,2),(3,18),(3,20),(4,1),(4,18),(4,20),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,6),(13,9),(13,16),(14,15),(14,16),(15,8),(15,17),(16,7),(16,17),(17,10),(17,11),(18,13),(18,14),(19,6),(19,9),(19,15),(20,12),(20,13),(20,19)],21) => 1
1100101 => ([(0,3),(0,4),(1,13),(2,14),(2,15),(3,2),(3,20),(3,21),(4,1),(4,20),(4,21),(6,7),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,10),(14,10),(14,18),(15,17),(15,18),(16,7),(16,17),(17,8),(17,19),(18,9),(18,19),(19,11),(19,12),(20,6),(20,15),(20,16),(21,6),(21,13),(21,14),(21,16)],22) => 1
1100110 => ([(0,3),(0,4),(1,18),(1,20),(2,17),(2,19),(3,1),(3,15),(3,16),(4,2),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,19),(15,20),(16,17),(16,18),(17,13),(17,14),(18,6),(18,13),(19,7),(19,14),(20,6),(20,7)],21) => 1
1100111 => ([(0,4),(0,5),(1,12),(2,19),(2,21),(3,1),(3,13),(3,20),(4,2),(4,16),(4,17),(5,3),(5,16),(5,17),(7,11),(8,9),(9,10),(10,6),(11,6),(12,7),(13,8),(14,10),(14,11),(15,9),(15,14),(16,19),(16,20),(17,13),(17,21),(18,7),(18,14),(19,15),(19,18),(20,12),(20,18),(21,8),(21,15)],22) => 1
1101000 => ([(0,4),(0,5),(1,13),(2,3),(2,20),(3,7),(4,1),(4,19),(4,21),(5,2),(5,19),(5,21),(7,9),(8,11),(9,12),(10,8),(11,6),(12,6),(13,10),(14,10),(14,17),(15,16),(15,17),(16,9),(16,18),(17,8),(17,18),(18,11),(18,12),(19,14),(19,15),(20,7),(20,16),(21,13),(21,14),(21,15),(21,20)],22) => 1
1101001 => ([(0,3),(0,4),(1,13),(2,6),(2,14),(3,2),(3,20),(3,21),(4,1),(4,20),(4,21),(6,7),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,10),(14,7),(14,18),(15,10),(15,17),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,11),(19,12),(20,6),(20,15),(20,16),(21,13),(21,14),(21,15),(21,16)],22) => 1
1101010 => ([(0,2),(0,3),(1,10),(2,14),(2,17),(3,1),(3,14),(3,17),(5,8),(6,5),(7,9),(8,4),(9,4),(10,6),(11,13),(11,16),(12,8),(12,9),(13,7),(13,12),(14,11),(14,15),(15,6),(15,13),(15,16),(16,5),(16,7),(16,12),(17,10),(17,11),(17,15)],18) => 1
1101011 => ([(0,2),(0,3),(1,7),(1,8),(2,17),(2,18),(3,1),(3,17),(3,18),(5,10),(6,9),(7,6),(8,5),(9,11),(10,12),(11,4),(12,4),(13,14),(13,15),(14,9),(14,16),(15,10),(15,16),(16,11),(16,12),(17,7),(17,13),(17,19),(18,8),(18,13),(18,19),(19,5),(19,6),(19,14),(19,15)],20) => 1
1101100 => ([(0,3),(0,4),(1,12),(2,14),(2,19),(3,2),(3,18),(3,20),(4,1),(4,18),(4,20),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,6),(13,9),(13,16),(14,15),(14,16),(15,8),(15,17),(16,7),(16,17),(17,10),(17,11),(18,13),(18,14),(19,6),(19,9),(19,15),(20,12),(20,13),(20,19)],21) => 1
1101101 => ([(0,2),(0,3),(1,11),(1,12),(2,16),(2,17),(3,1),(3,16),(3,17),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,13),(10,15),(11,14),(11,15),(12,13),(12,14),(13,5),(13,9),(14,6),(14,9),(15,5),(15,6),(16,10),(16,12),(17,10),(17,11)],18) => 1
1101110 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,7),(2,14),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,17),(15,19),(16,17),(16,18),(17,6),(17,13),(18,13),(18,14),(19,6),(19,7)],20) => 1
1101111 => ([(0,4),(0,5),(1,2),(1,17),(2,7),(3,1),(3,8),(3,16),(4,18),(4,19),(5,3),(5,18),(5,19),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,10),(13,14),(14,11),(14,12),(15,9),(15,13),(16,13),(16,17),(17,7),(17,14),(18,15),(18,16),(19,8),(19,15)],20) => 1
1110000 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20) => 1
1110001 => ([(0,5),(0,6),(1,2),(1,20),(2,8),(3,4),(3,15),(3,21),(4,9),(4,17),(5,1),(5,10),(5,18),(6,3),(6,10),(6,18),(8,11),(9,12),(10,15),(11,13),(12,14),(13,7),(14,7),(15,9),(16,11),(16,19),(17,12),(17,19),(18,20),(18,21),(19,13),(19,14),(20,8),(20,16),(21,16),(21,17)],22) => 1
1110010 => ([(0,4),(0,5),(1,13),(2,1),(2,15),(3,14),(3,16),(4,2),(4,20),(4,21),(5,3),(5,20),(5,21),(7,8),(8,9),(9,11),(10,12),(11,6),(12,6),(13,10),(14,8),(14,18),(15,13),(15,17),(16,17),(16,18),(17,10),(17,19),(18,9),(18,19),(19,11),(19,12),(20,7),(20,14),(21,7),(21,15),(21,16)],22) => 1
1110011 => ([(0,4),(0,5),(1,12),(2,19),(2,21),(3,1),(3,13),(3,20),(4,2),(4,16),(4,17),(5,3),(5,16),(5,17),(7,11),(8,9),(9,10),(10,6),(11,6),(12,7),(13,8),(14,10),(14,11),(15,9),(15,14),(16,19),(16,20),(17,13),(17,21),(18,7),(18,14),(19,15),(19,18),(20,12),(20,18),(21,8),(21,15)],22) => 1
1110100 => ([(0,4),(0,5),(1,13),(2,3),(2,20),(3,7),(4,1),(4,19),(4,21),(5,2),(5,19),(5,21),(7,9),(8,11),(9,12),(10,8),(11,6),(12,6),(13,10),(14,10),(14,17),(15,16),(15,17),(16,9),(16,18),(17,8),(17,18),(18,11),(18,12),(19,14),(19,15),(20,7),(20,16),(21,13),(21,14),(21,15),(21,20)],22) => 1
1110101 => ([(0,3),(0,4),(1,2),(1,17),(2,6),(3,16),(3,19),(4,1),(4,16),(4,19),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,9),(12,14),(13,8),(13,15),(14,7),(14,15),(15,10),(15,11),(16,12),(16,18),(17,6),(17,13),(18,9),(18,13),(18,14),(19,12),(19,17),(19,18)],20) => 1
1110110 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20) => 1
1110111 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,6),(2,7),(3,16),(3,17),(4,1),(4,16),(4,17),(6,9),(7,8),(8,10),(9,11),(10,5),(11,5),(12,14),(12,15),(13,10),(13,11),(14,8),(14,13),(15,9),(15,13),(16,12),(16,18),(17,12),(17,19),(18,7),(18,14),(19,6),(19,15)],20) => 1
1111000 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20) => 1
1111001 => ([(0,5),(0,6),(1,3),(1,15),(2,14),(3,2),(3,20),(4,8),(4,16),(5,1),(5,13),(5,19),(6,4),(6,13),(6,19),(8,9),(9,10),(10,11),(11,7),(12,7),(13,8),(14,12),(15,18),(15,20),(16,9),(16,18),(17,11),(17,12),(18,10),(18,17),(19,15),(19,16),(20,14),(20,17)],21) => 1
1111010 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20) => 1
1111011 => ([(0,4),(0,5),(1,2),(1,17),(2,7),(3,1),(3,8),(3,16),(4,18),(4,19),(5,3),(5,18),(5,19),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,10),(13,14),(14,11),(14,12),(15,9),(15,13),(16,13),(16,17),(17,7),(17,14),(18,15),(18,16),(19,8),(19,15)],20) => 1
1111100 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18) => 1
1111101 => ([(0,5),(0,6),(1,4),(1,14),(2,13),(3,2),(3,16),(4,3),(4,17),(5,12),(5,15),(6,1),(6,12),(6,15),(8,11),(9,10),(10,8),(11,7),(12,9),(13,7),(14,10),(14,17),(15,9),(15,14),(16,11),(16,13),(17,8),(17,16)],18) => 1
1111110 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14) => 1
1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
00000001 => ([(0,2),(0,8),(1,10),(2,9),(3,5),(3,11),(4,3),(4,13),(5,7),(5,12),(6,4),(6,15),(7,1),(7,14),(8,6),(8,9),(9,15),(11,12),(12,14),(13,11),(14,10),(15,13)],16) => 1
00000011 => ([(0,7),(0,8),(1,11),(2,4),(2,16),(3,15),(4,5),(4,18),(5,6),(5,20),(6,3),(6,19),(7,2),(7,17),(8,1),(8,17),(10,12),(11,10),(12,13),(13,14),(14,9),(15,9),(16,10),(16,18),(17,11),(17,16),(18,12),(18,20),(19,14),(19,15),(20,13),(20,19)],21) => 1
00001001 => ([(0,4),(0,5),(1,2),(1,21),(2,7),(3,1),(3,17),(3,24),(4,22),(4,23),(5,3),(5,22),(5,23),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,11),(14,19),(15,12),(15,13),(16,14),(16,18),(17,8),(17,14),(18,19),(18,20),(19,9),(19,15),(20,10),(20,15),(21,7),(21,20),(22,16),(22,17),(23,16),(23,24),(24,8),(24,18),(24,21)],25) => 1
00001111 => ([(0,7),(0,8),(1,6),(1,19),(2,5),(2,18),(3,14),(4,15),(5,3),(5,23),(6,4),(6,24),(7,2),(7,20),(8,1),(8,20),(10,12),(11,13),(12,9),(13,9),(14,10),(15,11),(16,21),(16,22),(17,12),(17,13),(18,16),(18,23),(19,16),(19,24),(20,18),(20,19),(21,10),(21,17),(22,11),(22,17),(23,14),(23,21),(24,15),(24,22)],25) => 1
00010001 => ([(0,3),(0,4),(1,2),(1,22),(1,23),(2,20),(2,21),(3,17),(3,18),(4,1),(4,17),(4,18),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,16),(12,19),(13,8),(13,15),(14,9),(14,15),(15,10),(15,11),(16,13),(16,14),(17,12),(17,22),(18,12),(18,23),(19,7),(19,14),(20,6),(20,13),(21,6),(21,7),(22,16),(22,20),(23,19),(23,21)],24) => 1
00010111 => ([(0,5),(0,6),(1,4),(1,26),(2,3),(2,25),(3,8),(4,9),(5,2),(5,24),(5,27),(6,1),(6,24),(6,27),(8,12),(9,13),(10,14),(11,15),(12,10),(13,11),(14,7),(15,7),(16,22),(16,23),(17,14),(17,15),(18,12),(18,22),(19,13),(19,23),(20,16),(20,18),(21,16),(21,19),(22,10),(22,17),(23,11),(23,17),(24,20),(24,21),(25,8),(25,18),(26,9),(26,19),(27,20),(27,21),(27,25),(27,26)],28) => 1
00011011 => ([(0,4),(0,5),(1,14),(2,1),(2,18),(3,19),(3,25),(4,2),(4,24),(4,26),(5,3),(5,24),(5,26),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,11),(15,22),(16,12),(16,13),(17,8),(17,15),(18,14),(18,21),(19,15),(19,20),(20,22),(20,23),(21,7),(21,23),(22,9),(22,16),(23,10),(23,16),(24,17),(24,19),(25,8),(25,20),(25,21),(26,17),(26,18),(26,25)],27) => 1
00011101 => ([(0,5),(0,6),(1,2),(1,24),(2,8),(3,4),(3,25),(3,26),(4,20),(4,23),(5,1),(5,21),(5,27),(6,3),(6,21),(6,27),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,10),(17,19),(18,11),(18,19),(19,15),(19,16),(20,17),(20,18),(21,9),(21,26),(22,14),(22,18),(23,13),(23,17),(24,8),(24,22),(25,20),(25,22),(26,12),(26,23),(27,9),(27,24),(27,25)],28) => 1
00100001 => ([(0,4),(0,5),(1,3),(1,18),(1,22),(2,14),(2,24),(3,2),(3,13),(3,23),(4,19),(4,20),(5,1),(5,19),(5,20),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,14),(14,7),(15,9),(15,17),(16,11),(16,12),(17,10),(17,16),(18,15),(18,23),(19,21),(19,22),(20,18),(20,21),(21,8),(21,15),(22,8),(22,13),(23,17),(23,24),(24,7),(24,16)],25) => 1
00100111 => ([(0,4),(0,5),(1,14),(2,1),(2,18),(3,19),(3,25),(4,2),(4,24),(4,26),(5,3),(5,24),(5,26),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,11),(15,22),(16,12),(16,13),(17,8),(17,15),(18,14),(18,21),(19,15),(19,20),(20,22),(20,23),(21,7),(21,23),(22,9),(22,16),(23,10),(23,16),(24,17),(24,19),(25,8),(25,20),(25,21),(26,17),(26,18),(26,25)],27) => 1
00101001 => ([(0,2),(0,3),(1,17),(1,18),(2,22),(2,23),(3,1),(3,22),(3,23),(5,10),(6,9),(7,11),(8,12),(9,8),(10,7),(11,4),(12,4),(13,11),(13,12),(14,10),(14,20),(15,20),(15,21),(16,9),(16,21),(17,5),(17,14),(18,5),(18,6),(19,15),(19,16),(20,7),(20,13),(21,8),(21,13),(22,17),(22,19),(22,24),(23,18),(23,19),(23,24),(24,6),(24,14),(24,15),(24,16)],25) => 1
00101011 => ([(0,3),(0,4),(1,15),(2,14),(3,2),(3,20),(3,24),(4,1),(4,20),(4,24),(6,10),(7,11),(8,6),(9,7),(10,12),(11,13),(12,5),(13,5),(14,8),(15,9),(16,17),(16,18),(17,10),(17,19),(18,11),(18,19),(19,12),(19,13),(20,21),(20,22),(21,8),(21,16),(21,23),(22,9),(22,16),(22,23),(23,6),(23,7),(23,17),(23,18),(24,14),(24,15),(24,21),(24,22)],25) => 1
00101101 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,7),(11,6),(12,5),(13,5),(14,10),(15,10),(15,18),(16,11),(16,23),(17,19),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27) => 1
00110001 => ([(0,4),(0,5),(1,23),(1,25),(2,3),(2,24),(2,26),(3,8),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,10),(12,9),(13,6),(14,6),(15,13),(15,14),(16,12),(16,21),(17,21),(17,22),(18,11),(18,22),(19,23),(19,24),(20,25),(20,26),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,17),(24,18),(25,7),(25,16),(26,7),(26,8)],27) => 1
00110011 => ([(0,3),(0,4),(1,22),(1,24),(2,21),(2,23),(3,2),(3,16),(3,17),(4,1),(4,16),(4,17),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,8),(12,14),(13,9),(13,14),(14,10),(14,11),(15,12),(15,13),(16,21),(16,22),(17,23),(17,24),(18,6),(18,12),(19,7),(19,13),(20,6),(20,7),(21,15),(21,18),(22,15),(22,19),(23,18),(23,20),(24,19),(24,20)],25) => 1
00110101 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,6),(11,7),(12,5),(13,5),(14,10),(15,11),(15,18),(16,19),(16,23),(17,10),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27) => 1
00111001 => ([(0,4),(0,5),(1,24),(1,26),(2,3),(2,23),(2,25),(3,17),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,13),(15,14),(16,12),(16,22),(17,21),(17,22),(18,11),(18,21),(19,25),(19,26),(20,23),(20,24),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,7),(24,16),(25,8),(25,18),(26,7),(26,8)],27) => 1
00111111 => ([(0,7),(0,8),(1,11),(2,4),(2,16),(3,15),(4,5),(4,18),(5,6),(5,20),(6,3),(6,19),(7,2),(7,17),(8,1),(8,17),(10,12),(11,10),(12,13),(13,14),(14,9),(15,9),(16,10),(16,18),(17,11),(17,16),(18,12),(18,20),(19,14),(19,15),(20,13),(20,19)],21) => 1
01000001 => ([(0,5),(0,6),(1,4),(1,11),(1,20),(2,16),(2,22),(3,2),(3,17),(3,23),(4,3),(4,15),(4,21),(5,18),(5,19),(6,1),(6,18),(6,19),(8,9),(9,13),(10,8),(11,15),(12,10),(13,7),(14,7),(15,17),(16,14),(17,16),(18,11),(18,12),(19,12),(19,20),(20,10),(20,21),(21,8),(21,23),(22,13),(22,14),(23,9),(23,22)],24) => 1
01000101 => ([(0,3),(0,4),(1,2),(1,21),(1,22),(2,16),(2,17),(3,23),(3,24),(4,1),(4,23),(4,24),(6,10),(7,9),(8,6),(9,11),(10,12),(11,13),(12,14),(13,5),(14,5),(15,10),(15,19),(16,18),(16,19),(17,9),(17,18),(18,11),(18,20),(19,12),(19,20),(20,13),(20,14),(21,7),(21,17),(22,15),(22,16),(23,8),(23,22),(23,25),(24,8),(24,21),(24,25),(25,6),(25,7),(25,15)],26) => 1
01000111 => ([(0,5),(0,6),(1,2),(1,24),(2,8),(3,4),(3,25),(3,26),(4,20),(4,23),(5,1),(5,21),(5,27),(6,3),(6,21),(6,27),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,10),(17,19),(18,11),(18,19),(19,15),(19,16),(20,17),(20,18),(21,9),(21,26),(22,14),(22,18),(23,13),(23,17),(24,8),(24,22),(25,20),(25,22),(26,12),(26,23),(27,9),(27,24),(27,25)],28) => 1
01001001 => ([(0,2),(0,3),(1,14),(1,15),(2,19),(2,20),(3,1),(3,19),(3,20),(5,7),(6,8),(7,4),(8,4),(9,16),(9,18),(10,17),(10,18),(11,16),(11,17),(12,7),(12,8),(13,9),(13,11),(14,9),(14,10),(15,10),(15,11),(16,5),(16,12),(17,6),(17,12),(18,5),(18,6),(19,13),(19,14),(20,13),(20,15)],21) => 1
01001011 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,7),(11,6),(12,5),(13,5),(14,10),(15,10),(15,18),(16,11),(16,23),(17,19),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27) => 1
01001101 => ([(0,3),(0,4),(1,23),(1,25),(2,22),(2,24),(3,2),(3,26),(3,27),(4,1),(4,26),(4,27),(6,10),(7,11),(8,6),(9,7),(10,12),(11,13),(12,14),(13,15),(14,5),(15,5),(16,19),(16,20),(17,10),(17,19),(18,11),(18,20),(19,12),(19,21),(20,13),(20,21),(21,14),(21,15),(22,6),(22,17),(23,7),(23,18),(24,16),(24,17),(25,16),(25,18),(26,8),(26,9),(26,24),(26,25),(27,8),(27,9),(27,22),(27,23)],28) => 1
01010001 => ([(0,3),(0,4),(1,2),(1,14),(1,22),(2,6),(2,15),(3,23),(3,24),(4,1),(4,23),(4,24),(6,8),(7,9),(8,10),(9,13),(10,12),(11,7),(12,5),(13,5),(14,6),(15,8),(15,19),(16,19),(16,20),(17,11),(17,18),(18,7),(18,20),(19,10),(19,21),(20,9),(20,21),(21,12),(21,13),(22,15),(22,16),(23,17),(23,22),(23,25),(24,14),(24,17),(24,25),(25,11),(25,16),(25,18)],26) => 1
01010011 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,6),(11,7),(12,5),(13,5),(14,10),(15,11),(15,18),(16,19),(16,23),(17,10),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27) => 1
01010101 => ([(0,1),(0,2),(1,14),(1,15),(2,14),(2,15),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,12),(8,13),(9,12),(9,13),(10,6),(10,7),(11,6),(11,7),(12,4),(12,5),(13,4),(13,5),(14,10),(14,11),(15,10),(15,11)],16) => 1
01011001 => ([(0,3),(0,4),(1,23),(1,25),(2,15),(2,24),(3,1),(3,26),(3,27),(4,2),(4,26),(4,27),(6,10),(7,8),(8,9),(9,11),(10,12),(11,14),(12,13),(13,5),(14,5),(15,6),(16,20),(16,21),(17,10),(17,20),(18,8),(18,19),(19,9),(19,21),(20,12),(20,22),(21,11),(21,22),(22,13),(22,14),(23,16),(23,19),(24,6),(24,17),(25,16),(25,17),(26,7),(26,18),(26,24),(26,25),(27,7),(27,15),(27,18),(27,23)],28) => 1
01011101 => ([(0,3),(0,4),(1,2),(1,21),(1,22),(2,16),(2,17),(3,23),(3,24),(4,1),(4,23),(4,24),(6,10),(7,9),(8,6),(9,11),(10,12),(11,13),(12,14),(13,5),(14,5),(15,10),(15,19),(16,18),(16,19),(17,9),(17,18),(18,11),(18,20),(19,12),(19,20),(20,13),(20,14),(21,7),(21,17),(22,15),(22,16),(23,8),(23,22),(23,25),(24,8),(24,21),(24,25),(25,6),(25,7),(25,15)],26) => 1
01100001 => ([(0,5),(0,6),(1,4),(1,16),(1,26),(2,17),(2,25),(3,10),(3,22),(4,3),(4,8),(4,18),(5,1),(5,20),(5,21),(6,2),(6,20),(6,21),(8,10),(9,11),(10,13),(11,12),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,22),(18,23),(19,11),(19,23),(20,25),(20,26),(21,16),(21,17),(22,13),(22,24),(23,12),(23,24),(24,14),(24,15),(25,9),(25,19),(26,18),(26,19)],27) => 1
01100011 => ([(0,4),(0,5),(1,24),(1,26),(2,3),(2,23),(2,25),(3,17),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,13),(15,14),(16,12),(16,22),(17,21),(17,22),(18,11),(18,21),(19,25),(19,26),(20,23),(20,24),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,7),(24,16),(25,8),(25,18),(26,7),(26,8)],27) => 1
01100101 => ([(0,3),(0,4),(1,23),(1,25),(2,15),(2,24),(3,1),(3,26),(3,27),(4,2),(4,26),(4,27),(6,10),(7,8),(8,9),(9,11),(10,12),(11,14),(12,13),(13,5),(14,5),(15,6),(16,20),(16,21),(17,10),(17,20),(18,8),(18,19),(19,9),(19,21),(20,12),(20,22),(21,11),(21,22),(22,13),(22,14),(23,16),(23,19),(24,6),(24,17),(25,16),(25,17),(26,7),(26,18),(26,24),(26,25),(27,7),(27,15),(27,18),(27,23)],28) => 1
01101001 => ([(0,3),(0,4),(1,15),(1,25),(2,14),(2,24),(3,2),(3,26),(3,27),(4,1),(4,26),(4,27),(6,8),(7,9),(8,10),(9,11),(10,12),(11,13),(12,5),(13,5),(14,6),(15,7),(16,18),(16,23),(17,19),(17,23),(18,8),(18,21),(19,9),(19,22),(20,12),(20,13),(21,10),(21,20),(22,11),(22,20),(23,21),(23,22),(24,6),(24,18),(25,7),(25,19),(26,16),(26,17),(26,24),(26,25),(27,14),(27,15),(27,16),(27,17)],28) => 1
01101011 => ([(0,2),(0,3),(1,17),(1,18),(2,22),(2,23),(3,1),(3,22),(3,23),(5,10),(6,9),(7,11),(8,12),(9,8),(10,7),(11,4),(12,4),(13,11),(13,12),(14,10),(14,20),(15,20),(15,21),(16,9),(16,21),(17,5),(17,14),(18,5),(18,6),(19,15),(19,16),(20,7),(20,13),(21,8),(21,13),(22,17),(22,19),(22,24),(23,18),(23,19),(23,24),(24,6),(24,14),(24,15),(24,16)],25) => 1
01101101 => ([(0,2),(0,3),(1,14),(1,15),(2,19),(2,20),(3,1),(3,19),(3,20),(5,7),(6,8),(7,4),(8,4),(9,16),(9,18),(10,17),(10,18),(11,16),(11,17),(12,7),(12,8),(13,9),(13,11),(14,9),(14,10),(15,10),(15,11),(16,5),(16,12),(17,6),(17,12),(18,5),(18,6),(19,13),(19,14),(20,13),(20,15)],21) => 1
01101111 => ([(0,4),(0,5),(1,2),(1,21),(2,7),(3,1),(3,17),(3,24),(4,22),(4,23),(5,3),(5,22),(5,23),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,11),(14,19),(15,12),(15,13),(16,14),(16,18),(17,8),(17,14),(18,19),(18,20),(19,9),(19,15),(20,10),(20,15),(21,7),(21,20),(22,16),(22,17),(23,16),(23,24),(24,8),(24,18),(24,21)],25) => 1
01110001 => ([(0,5),(0,6),(1,4),(1,17),(1,27),(2,3),(2,16),(2,26),(3,8),(3,19),(4,9),(4,20),(5,2),(5,21),(5,22),(6,1),(6,21),(6,22),(8,10),(9,11),(10,12),(11,13),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,23),(18,24),(19,10),(19,23),(20,11),(20,24),(21,26),(21,27),(22,16),(22,17),(23,12),(23,25),(24,13),(24,25),(25,14),(25,15),(26,18),(26,19),(27,18),(27,20)],28) => 1
01110011 => ([(0,4),(0,5),(1,23),(1,25),(2,3),(2,24),(2,26),(3,8),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,10),(12,9),(13,6),(14,6),(15,13),(15,14),(16,12),(16,21),(17,21),(17,22),(18,11),(18,22),(19,23),(19,24),(20,25),(20,26),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,17),(24,18),(25,7),(25,16),(26,7),(26,8)],27) => 1
01110101 => ([(0,3),(0,4),(1,2),(1,14),(1,22),(2,6),(2,15),(3,23),(3,24),(4,1),(4,23),(4,24),(6,8),(7,9),(8,10),(9,13),(10,12),(11,7),(12,5),(13,5),(14,6),(15,8),(15,19),(16,19),(16,20),(17,11),(17,18),(18,7),(18,20),(19,10),(19,21),(20,9),(20,21),(21,12),(21,13),(22,15),(22,16),(23,17),(23,22),(23,25),(24,14),(24,17),(24,25),(25,11),(25,16),(25,18)],26) => 1
01110111 => ([(0,3),(0,4),(1,2),(1,22),(1,23),(2,20),(2,21),(3,17),(3,18),(4,1),(4,17),(4,18),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,16),(12,19),(13,8),(13,15),(14,9),(14,15),(15,10),(15,11),(16,13),(16,14),(17,12),(17,22),(18,12),(18,23),(19,7),(19,14),(20,6),(20,13),(21,6),(21,7),(22,16),(22,20),(23,19),(23,21)],24) => 1
01111001 => ([(0,5),(0,6),(1,4),(1,16),(1,26),(2,17),(2,25),(3,10),(3,22),(4,3),(4,8),(4,18),(5,1),(5,20),(5,21),(6,2),(6,20),(6,21),(8,10),(9,11),(10,13),(11,12),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,22),(18,23),(19,11),(19,23),(20,25),(20,26),(21,16),(21,17),(22,13),(22,24),(23,12),(23,24),(24,14),(24,15),(25,9),(25,19),(26,18),(26,19)],27) => 1
01111011 => ([(0,4),(0,5),(1,3),(1,18),(1,22),(2,14),(2,24),(3,2),(3,13),(3,23),(4,19),(4,20),(5,1),(5,19),(5,20),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,14),(14,7),(15,9),(15,17),(16,11),(16,12),(17,10),(17,16),(18,15),(18,23),(19,21),(19,22),(20,18),(20,21),(21,8),(21,15),(22,8),(22,13),(23,17),(23,24),(24,7),(24,16)],25) => 1
01111101 => ([(0,5),(0,6),(1,4),(1,11),(1,20),(2,16),(2,22),(3,2),(3,17),(3,23),(4,3),(4,15),(4,21),(5,18),(5,19),(6,1),(6,18),(6,19),(8,9),(9,13),(10,8),(11,15),(12,10),(13,7),(14,7),(15,17),(16,14),(17,16),(18,11),(18,12),(19,12),(19,20),(20,10),(20,21),(21,8),(21,23),(22,13),(22,14),(23,9),(23,22)],24) => 1
01111111 => ([(0,2),(0,8),(1,10),(2,9),(3,5),(3,11),(4,3),(4,13),(5,7),(5,12),(6,4),(6,15),(7,1),(7,14),(8,6),(8,9),(9,15),(11,12),(12,14),(13,11),(14,10),(15,13)],16) => 1
10000000 => ([(0,2),(0,8),(1,10),(2,9),(3,5),(3,11),(4,3),(4,13),(5,7),(5,12),(6,4),(6,15),(7,1),(7,14),(8,6),(8,9),(9,15),(11,12),(12,14),(13,11),(14,10),(15,13)],16) => 1
10000010 => ([(0,5),(0,6),(1,4),(1,11),(1,20),(2,16),(2,22),(3,2),(3,17),(3,23),(4,3),(4,15),(4,21),(5,18),(5,19),(6,1),(6,18),(6,19),(8,9),(9,13),(10,8),(11,15),(12,10),(13,7),(14,7),(15,17),(16,14),(17,16),(18,11),(18,12),(19,12),(19,20),(20,10),(20,21),(21,8),(21,23),(22,13),(22,14),(23,9),(23,22)],24) => 1
10000100 => ([(0,4),(0,5),(1,3),(1,18),(1,22),(2,14),(2,24),(3,2),(3,13),(3,23),(4,19),(4,20),(5,1),(5,19),(5,20),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,14),(14,7),(15,9),(15,17),(16,11),(16,12),(17,10),(17,16),(18,15),(18,23),(19,21),(19,22),(20,18),(20,21),(21,8),(21,15),(22,8),(22,13),(23,17),(23,24),(24,7),(24,16)],25) => 1
10000110 => ([(0,5),(0,6),(1,4),(1,16),(1,26),(2,17),(2,25),(3,10),(3,22),(4,3),(4,8),(4,18),(5,1),(5,20),(5,21),(6,2),(6,20),(6,21),(8,10),(9,11),(10,13),(11,12),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,22),(18,23),(19,11),(19,23),(20,25),(20,26),(21,16),(21,17),(22,13),(22,24),(23,12),(23,24),(24,14),(24,15),(25,9),(25,19),(26,18),(26,19)],27) => 1
10001000 => ([(0,3),(0,4),(1,2),(1,22),(1,23),(2,20),(2,21),(3,17),(3,18),(4,1),(4,17),(4,18),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,16),(12,19),(13,8),(13,15),(14,9),(14,15),(15,10),(15,11),(16,13),(16,14),(17,12),(17,22),(18,12),(18,23),(19,7),(19,14),(20,6),(20,13),(21,6),(21,7),(22,16),(22,20),(23,19),(23,21)],24) => 1
10001010 => ([(0,3),(0,4),(1,2),(1,14),(1,22),(2,6),(2,15),(3,23),(3,24),(4,1),(4,23),(4,24),(6,8),(7,9),(8,10),(9,13),(10,12),(11,7),(12,5),(13,5),(14,6),(15,8),(15,19),(16,19),(16,20),(17,11),(17,18),(18,7),(18,20),(19,10),(19,21),(20,9),(20,21),(21,12),(21,13),(22,15),(22,16),(23,17),(23,22),(23,25),(24,14),(24,17),(24,25),(25,11),(25,16),(25,18)],26) => 1
10001100 => ([(0,4),(0,5),(1,23),(1,25),(2,3),(2,24),(2,26),(3,8),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,10),(12,9),(13,6),(14,6),(15,13),(15,14),(16,12),(16,21),(17,21),(17,22),(18,11),(18,22),(19,23),(19,24),(20,25),(20,26),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,17),(24,18),(25,7),(25,16),(26,7),(26,8)],27) => 1
10001110 => ([(0,5),(0,6),(1,4),(1,17),(1,27),(2,3),(2,16),(2,26),(3,8),(3,19),(4,9),(4,20),(5,2),(5,21),(5,22),(6,1),(6,21),(6,22),(8,10),(9,11),(10,12),(11,13),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,23),(18,24),(19,10),(19,23),(20,11),(20,24),(21,26),(21,27),(22,16),(22,17),(23,12),(23,25),(24,13),(24,25),(25,14),(25,15),(26,18),(26,19),(27,18),(27,20)],28) => 1
10010000 => ([(0,4),(0,5),(1,2),(1,21),(2,7),(3,1),(3,17),(3,24),(4,22),(4,23),(5,3),(5,22),(5,23),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,11),(14,19),(15,12),(15,13),(16,14),(16,18),(17,8),(17,14),(18,19),(18,20),(19,9),(19,15),(20,10),(20,15),(21,7),(21,20),(22,16),(22,17),(23,16),(23,24),(24,8),(24,18),(24,21)],25) => 1
10010010 => ([(0,2),(0,3),(1,14),(1,15),(2,19),(2,20),(3,1),(3,19),(3,20),(5,7),(6,8),(7,4),(8,4),(9,16),(9,18),(10,17),(10,18),(11,16),(11,17),(12,7),(12,8),(13,9),(13,11),(14,9),(14,10),(15,10),(15,11),(16,5),(16,12),(17,6),(17,12),(18,5),(18,6),(19,13),(19,14),(20,13),(20,15)],21) => 1
10010100 => ([(0,2),(0,3),(1,17),(1,18),(2,22),(2,23),(3,1),(3,22),(3,23),(5,10),(6,9),(7,11),(8,12),(9,8),(10,7),(11,4),(12,4),(13,11),(13,12),(14,10),(14,20),(15,20),(15,21),(16,9),(16,21),(17,5),(17,14),(18,5),(18,6),(19,15),(19,16),(20,7),(20,13),(21,8),(21,13),(22,17),(22,19),(22,24),(23,18),(23,19),(23,24),(24,6),(24,14),(24,15),(24,16)],25) => 1
10010110 => ([(0,3),(0,4),(1,15),(1,25),(2,14),(2,24),(3,2),(3,26),(3,27),(4,1),(4,26),(4,27),(6,8),(7,9),(8,10),(9,11),(10,12),(11,13),(12,5),(13,5),(14,6),(15,7),(16,18),(16,23),(17,19),(17,23),(18,8),(18,21),(19,9),(19,22),(20,12),(20,13),(21,10),(21,20),(22,11),(22,20),(23,21),(23,22),(24,6),(24,18),(25,7),(25,19),(26,16),(26,17),(26,24),(26,25),(27,14),(27,15),(27,16),(27,17)],28) => 1
10011010 => ([(0,3),(0,4),(1,23),(1,25),(2,15),(2,24),(3,1),(3,26),(3,27),(4,2),(4,26),(4,27),(6,10),(7,8),(8,9),(9,11),(10,12),(11,14),(12,13),(13,5),(14,5),(15,6),(16,20),(16,21),(17,10),(17,20),(18,8),(18,19),(19,9),(19,21),(20,12),(20,22),(21,11),(21,22),(22,13),(22,14),(23,16),(23,19),(24,6),(24,17),(25,16),(25,17),(26,7),(26,18),(26,24),(26,25),(27,7),(27,15),(27,18),(27,23)],28) => 1
10011100 => ([(0,4),(0,5),(1,24),(1,26),(2,3),(2,23),(2,25),(3,17),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,13),(15,14),(16,12),(16,22),(17,21),(17,22),(18,11),(18,21),(19,25),(19,26),(20,23),(20,24),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,7),(24,16),(25,8),(25,18),(26,7),(26,8)],27) => 1
10011110 => ([(0,5),(0,6),(1,4),(1,16),(1,26),(2,17),(2,25),(3,10),(3,22),(4,3),(4,8),(4,18),(5,1),(5,20),(5,21),(6,2),(6,20),(6,21),(8,10),(9,11),(10,13),(11,12),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,22),(18,23),(19,11),(19,23),(20,25),(20,26),(21,16),(21,17),(22,13),(22,24),(23,12),(23,24),(24,14),(24,15),(25,9),(25,19),(26,18),(26,19)],27) => 1
10100010 => ([(0,3),(0,4),(1,2),(1,21),(1,22),(2,16),(2,17),(3,23),(3,24),(4,1),(4,23),(4,24),(6,10),(7,9),(8,6),(9,11),(10,12),(11,13),(12,14),(13,5),(14,5),(15,10),(15,19),(16,18),(16,19),(17,9),(17,18),(18,11),(18,20),(19,12),(19,20),(20,13),(20,14),(21,7),(21,17),(22,15),(22,16),(23,8),(23,22),(23,25),(24,8),(24,21),(24,25),(25,6),(25,7),(25,15)],26) => 1
10100110 => ([(0,3),(0,4),(1,23),(1,25),(2,15),(2,24),(3,1),(3,26),(3,27),(4,2),(4,26),(4,27),(6,10),(7,8),(8,9),(9,11),(10,12),(11,14),(12,13),(13,5),(14,5),(15,6),(16,20),(16,21),(17,10),(17,20),(18,8),(18,19),(19,9),(19,21),(20,12),(20,22),(21,11),(21,22),(22,13),(22,14),(23,16),(23,19),(24,6),(24,17),(25,16),(25,17),(26,7),(26,18),(26,24),(26,25),(27,7),(27,15),(27,18),(27,23)],28) => 1
10101010 => ([(0,1),(0,2),(1,14),(1,15),(2,14),(2,15),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,12),(8,13),(9,12),(9,13),(10,6),(10,7),(11,6),(11,7),(12,4),(12,5),(13,4),(13,5),(14,10),(14,11),(15,10),(15,11)],16) => 1
10101100 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,6),(11,7),(12,5),(13,5),(14,10),(15,11),(15,18),(16,19),(16,23),(17,10),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27) => 1
10101110 => ([(0,3),(0,4),(1,2),(1,14),(1,22),(2,6),(2,15),(3,23),(3,24),(4,1),(4,23),(4,24),(6,8),(7,9),(8,10),(9,13),(10,12),(11,7),(12,5),(13,5),(14,6),(15,8),(15,19),(16,19),(16,20),(17,11),(17,18),(18,7),(18,20),(19,10),(19,21),(20,9),(20,21),(21,12),(21,13),(22,15),(22,16),(23,17),(23,22),(23,25),(24,14),(24,17),(24,25),(25,11),(25,16),(25,18)],26) => 1
10110010 => ([(0,3),(0,4),(1,23),(1,25),(2,22),(2,24),(3,2),(3,26),(3,27),(4,1),(4,26),(4,27),(6,10),(7,11),(8,6),(9,7),(10,12),(11,13),(12,14),(13,15),(14,5),(15,5),(16,19),(16,20),(17,10),(17,19),(18,11),(18,20),(19,12),(19,21),(20,13),(20,21),(21,14),(21,15),(22,6),(22,17),(23,7),(23,18),(24,16),(24,17),(25,16),(25,18),(26,8),(26,9),(26,24),(26,25),(27,8),(27,9),(27,22),(27,23)],28) => 1
10110100 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,7),(11,6),(12,5),(13,5),(14,10),(15,10),(15,18),(16,11),(16,23),(17,19),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27) => 1
10110110 => ([(0,2),(0,3),(1,14),(1,15),(2,19),(2,20),(3,1),(3,19),(3,20),(5,7),(6,8),(7,4),(8,4),(9,16),(9,18),(10,17),(10,18),(11,16),(11,17),(12,7),(12,8),(13,9),(13,11),(14,9),(14,10),(15,10),(15,11),(16,5),(16,12),(17,6),(17,12),(18,5),(18,6),(19,13),(19,14),(20,13),(20,15)],21) => 1
10111000 => ([(0,5),(0,6),(1,2),(1,24),(2,8),(3,4),(3,25),(3,26),(4,20),(4,23),(5,1),(5,21),(5,27),(6,3),(6,21),(6,27),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,10),(17,19),(18,11),(18,19),(19,15),(19,16),(20,17),(20,18),(21,9),(21,26),(22,14),(22,18),(23,13),(23,17),(24,8),(24,22),(25,20),(25,22),(26,12),(26,23),(27,9),(27,24),(27,25)],28) => 1
10111010 => ([(0,3),(0,4),(1,2),(1,21),(1,22),(2,16),(2,17),(3,23),(3,24),(4,1),(4,23),(4,24),(6,10),(7,9),(8,6),(9,11),(10,12),(11,13),(12,14),(13,5),(14,5),(15,10),(15,19),(16,18),(16,19),(17,9),(17,18),(18,11),(18,20),(19,12),(19,20),(20,13),(20,14),(21,7),(21,17),(22,15),(22,16),(23,8),(23,22),(23,25),(24,8),(24,21),(24,25),(25,6),(25,7),(25,15)],26) => 1
10111110 => ([(0,5),(0,6),(1,4),(1,11),(1,20),(2,16),(2,22),(3,2),(3,17),(3,23),(4,3),(4,15),(4,21),(5,18),(5,19),(6,1),(6,18),(6,19),(8,9),(9,13),(10,8),(11,15),(12,10),(13,7),(14,7),(15,17),(16,14),(17,16),(18,11),(18,12),(19,12),(19,20),(20,10),(20,21),(21,8),(21,23),(22,13),(22,14),(23,9),(23,22)],24) => 1
11000000 => ([(0,7),(0,8),(1,11),(2,4),(2,16),(3,15),(4,5),(4,18),(5,6),(5,20),(6,3),(6,19),(7,2),(7,17),(8,1),(8,17),(10,12),(11,10),(12,13),(13,14),(14,9),(15,9),(16,10),(16,18),(17,11),(17,16),(18,12),(18,20),(19,14),(19,15),(20,13),(20,19)],21) => 1
11000110 => ([(0,4),(0,5),(1,24),(1,26),(2,3),(2,23),(2,25),(3,17),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,13),(15,14),(16,12),(16,22),(17,21),(17,22),(18,11),(18,21),(19,25),(19,26),(20,23),(20,24),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,7),(24,16),(25,8),(25,18),(26,7),(26,8)],27) => 1
11001010 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,6),(11,7),(12,5),(13,5),(14,10),(15,11),(15,18),(16,19),(16,23),(17,10),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27) => 1
11001100 => ([(0,3),(0,4),(1,22),(1,24),(2,21),(2,23),(3,2),(3,16),(3,17),(4,1),(4,16),(4,17),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,8),(12,14),(13,9),(13,14),(14,10),(14,11),(15,12),(15,13),(16,21),(16,22),(17,23),(17,24),(18,6),(18,12),(19,7),(19,13),(20,6),(20,7),(21,15),(21,18),(22,15),(22,19),(23,18),(23,20),(24,19),(24,20)],25) => 1
11001110 => ([(0,4),(0,5),(1,23),(1,25),(2,3),(2,24),(2,26),(3,8),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,10),(12,9),(13,6),(14,6),(15,13),(15,14),(16,12),(16,21),(17,21),(17,22),(18,11),(18,22),(19,23),(19,24),(20,25),(20,26),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,17),(24,18),(25,7),(25,16),(26,7),(26,8)],27) => 1
11010010 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,7),(11,6),(12,5),(13,5),(14,10),(15,10),(15,18),(16,11),(16,23),(17,19),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27) => 1
11010100 => ([(0,3),(0,4),(1,15),(2,14),(3,2),(3,20),(3,24),(4,1),(4,20),(4,24),(6,10),(7,11),(8,6),(9,7),(10,12),(11,13),(12,5),(13,5),(14,8),(15,9),(16,17),(16,18),(17,10),(17,19),(18,11),(18,19),(19,12),(19,13),(20,21),(20,22),(21,8),(21,16),(21,23),(22,9),(22,16),(22,23),(23,6),(23,7),(23,17),(23,18),(24,14),(24,15),(24,21),(24,22)],25) => 1
11010110 => ([(0,2),(0,3),(1,17),(1,18),(2,22),(2,23),(3,1),(3,22),(3,23),(5,10),(6,9),(7,11),(8,12),(9,8),(10,7),(11,4),(12,4),(13,11),(13,12),(14,10),(14,20),(15,20),(15,21),(16,9),(16,21),(17,5),(17,14),(18,5),(18,6),(19,15),(19,16),(20,7),(20,13),(21,8),(21,13),(22,17),(22,19),(22,24),(23,18),(23,19),(23,24),(24,6),(24,14),(24,15),(24,16)],25) => 1
11011000 => ([(0,4),(0,5),(1,14),(2,1),(2,18),(3,19),(3,25),(4,2),(4,24),(4,26),(5,3),(5,24),(5,26),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,11),(15,22),(16,12),(16,13),(17,8),(17,15),(18,14),(18,21),(19,15),(19,20),(20,22),(20,23),(21,7),(21,23),(22,9),(22,16),(23,10),(23,16),(24,17),(24,19),(25,8),(25,20),(25,21),(26,17),(26,18),(26,25)],27) => 1
11011110 => ([(0,4),(0,5),(1,3),(1,18),(1,22),(2,14),(2,24),(3,2),(3,13),(3,23),(4,19),(4,20),(5,1),(5,19),(5,20),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,14),(14,7),(15,9),(15,17),(16,11),(16,12),(17,10),(17,16),(18,15),(18,23),(19,21),(19,22),(20,18),(20,21),(21,8),(21,15),(22,8),(22,13),(23,17),(23,24),(24,7),(24,16)],25) => 1
11100010 => ([(0,5),(0,6),(1,2),(1,24),(2,8),(3,4),(3,25),(3,26),(4,20),(4,23),(5,1),(5,21),(5,27),(6,3),(6,21),(6,27),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,10),(17,19),(18,11),(18,19),(19,15),(19,16),(20,17),(20,18),(21,9),(21,26),(22,14),(22,18),(23,13),(23,17),(24,8),(24,22),(25,20),(25,22),(26,12),(26,23),(27,9),(27,24),(27,25)],28) => 1
11100100 => ([(0,4),(0,5),(1,14),(2,1),(2,18),(3,19),(3,25),(4,2),(4,24),(4,26),(5,3),(5,24),(5,26),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,11),(15,22),(16,12),(16,13),(17,8),(17,15),(18,14),(18,21),(19,15),(19,20),(20,22),(20,23),(21,7),(21,23),(22,9),(22,16),(23,10),(23,16),(24,17),(24,19),(25,8),(25,20),(25,21),(26,17),(26,18),(26,25)],27) => 1
11101000 => ([(0,5),(0,6),(1,4),(1,26),(2,3),(2,25),(3,8),(4,9),(5,2),(5,24),(5,27),(6,1),(6,24),(6,27),(8,12),(9,13),(10,14),(11,15),(12,10),(13,11),(14,7),(15,7),(16,22),(16,23),(17,14),(17,15),(18,12),(18,22),(19,13),(19,23),(20,16),(20,18),(21,16),(21,19),(22,10),(22,17),(23,11),(23,17),(24,20),(24,21),(25,8),(25,18),(26,9),(26,19),(27,20),(27,21),(27,25),(27,26)],28) => 1
11101110 => ([(0,3),(0,4),(1,2),(1,22),(1,23),(2,20),(2,21),(3,17),(3,18),(4,1),(4,17),(4,18),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,16),(12,19),(13,8),(13,15),(14,9),(14,15),(15,10),(15,11),(16,13),(16,14),(17,12),(17,22),(18,12),(18,23),(19,7),(19,14),(20,6),(20,13),(21,6),(21,7),(22,16),(22,20),(23,19),(23,21)],24) => 1
11110000 => ([(0,7),(0,8),(1,6),(1,19),(2,5),(2,18),(3,14),(4,15),(5,3),(5,23),(6,4),(6,24),(7,2),(7,20),(8,1),(8,20),(10,12),(11,13),(12,9),(13,9),(14,10),(15,11),(16,21),(16,22),(17,12),(17,13),(18,16),(18,23),(19,16),(19,24),(20,18),(20,19),(21,10),(21,17),(22,11),(22,17),(23,14),(23,21),(24,15),(24,22)],25) => 1
11110110 => ([(0,4),(0,5),(1,2),(1,21),(2,7),(3,1),(3,17),(3,24),(4,22),(4,23),(5,3),(5,22),(5,23),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,11),(14,19),(15,12),(15,13),(16,14),(16,18),(17,8),(17,14),(18,19),(18,20),(19,9),(19,15),(20,10),(20,15),(21,7),(21,20),(22,16),(22,17),(23,16),(23,24),(24,8),(24,18),(24,21)],25) => 1
11111100 => ([(0,7),(0,8),(1,11),(2,4),(2,16),(3,15),(4,5),(4,18),(5,6),(5,20),(6,3),(6,19),(7,2),(7,17),(8,1),(8,17),(10,12),(11,10),(12,13),(13,14),(14,9),(15,9),(16,10),(16,18),(17,11),(17,16),(18,12),(18,20),(19,14),(19,15),(20,13),(20,19)],21) => 1
11111110 => ([(0,2),(0,8),(1,10),(2,9),(3,5),(3,11),(4,3),(4,13),(5,7),(5,12),(6,4),(6,15),(7,1),(7,14),(8,6),(8,9),(9,15),(11,12),(12,14),(13,11),(14,10),(15,13)],16) => 1
11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
000000001 => ([(0,2),(0,9),(1,11),(2,10),(3,4),(3,13),(4,6),(4,12),(5,3),(5,15),(6,8),(6,14),(7,5),(7,17),(8,1),(8,16),(9,7),(9,10),(10,17),(12,14),(13,12),(14,16),(15,13),(16,11),(17,15)],18) => 1
000100001 => ([(0,4),(0,5),(1,3),(1,21),(1,22),(2,14),(2,28),(3,2),(3,27),(3,29),(4,23),(4,24),(5,1),(5,23),(5,24),(7,11),(8,9),(9,12),(10,13),(11,10),(12,6),(13,6),(14,8),(15,17),(15,20),(16,15),(16,18),(17,11),(17,25),(18,7),(18,17),(19,12),(19,13),(20,25),(20,26),(21,18),(21,29),(22,15),(22,27),(23,16),(23,22),(24,16),(24,21),(25,10),(25,19),(26,9),(26,19),(27,20),(27,28),(28,8),(28,26),(29,7),(29,14)],30) => 1
001000001 => ([(0,5),(0,6),(1,4),(1,21),(1,22),(2,16),(2,28),(3,2),(3,17),(3,29),(4,3),(4,15),(4,27),(5,23),(5,24),(6,1),(6,23),(6,24),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,17),(16,8),(17,16),(18,9),(18,25),(19,10),(19,20),(20,13),(20,14),(21,25),(21,27),(22,9),(22,15),(23,18),(23,22),(24,18),(24,21),(25,12),(25,26),(26,11),(26,19),(27,26),(27,29),(28,8),(28,20),(29,19),(29,28)],30) => 1
001100001 => ([(0,5),(0,6),(1,29),(1,31),(2,3),(2,30),(2,32),(3,4),(3,9),(3,23),(4,14),(4,27),(5,1),(5,24),(5,25),(6,2),(6,24),(6,25),(8,15),(9,14),(10,16),(11,17),(12,10),(13,11),(14,12),(15,13),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,26),(23,18),(23,27),(24,29),(24,30),(25,31),(25,32),(26,13),(26,20),(27,12),(27,19),(28,15),(28,26),(29,22),(29,28),(30,22),(30,23),(31,8),(31,28),(32,8),(32,9)],33) => 1
010000001 => ([(0,6),(0,7),(1,3),(1,11),(1,21),(2,18),(2,25),(3,4),(3,17),(3,24),(4,5),(4,20),(4,27),(5,2),(5,19),(5,26),(6,22),(6,23),(7,1),(7,22),(7,23),(9,12),(10,9),(11,17),(12,13),(13,14),(14,15),(15,8),(16,8),(17,20),(18,16),(19,18),(20,19),(21,9),(21,24),(22,10),(22,11),(23,10),(23,21),(24,12),(24,27),(25,15),(25,16),(26,14),(26,25),(27,13),(27,26)],28) => 1
010010001 => ([(0,3),(0,4),(1,2),(1,28),(1,29),(2,7),(2,26),(3,20),(3,21),(4,1),(4,20),(4,21),(6,12),(7,10),(8,13),(9,14),(10,11),(11,8),(12,9),(13,5),(14,5),(15,8),(15,17),(16,9),(16,17),(17,13),(17,14),(18,22),(18,27),(19,15),(19,16),(20,18),(20,28),(21,18),(21,29),(22,19),(22,24),(23,6),(23,24),(24,12),(24,16),(25,11),(25,15),(26,10),(26,25),(27,6),(27,19),(27,25),(28,7),(28,22),(28,23),(29,23),(29,26),(29,27)],30) => 1
010100001 => ([(0,4),(0,5),(1,3),(1,8),(1,18),(2,17),(2,28),(3,2),(3,16),(3,27),(4,29),(4,30),(5,1),(5,29),(5,30),(7,13),(8,16),(9,11),(10,9),(11,12),(12,15),(13,14),(14,6),(15,6),(16,17),(17,7),(18,22),(18,27),(19,10),(19,21),(20,13),(20,26),(21,9),(21,24),(22,23),(22,24),(23,20),(23,25),(24,11),(24,25),(25,12),(25,26),(26,14),(26,15),(27,23),(27,28),(28,7),(28,20),(29,8),(29,19),(29,31),(30,18),(30,19),(30,31),(31,10),(31,21),(31,22)],32) => 1
010110001 => ([(0,4),(0,5),(1,30),(1,31),(2,3),(2,18),(2,32),(3,7),(3,28),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,12),(9,16),(10,17),(11,13),(12,11),(13,10),(14,9),(15,14),(16,6),(17,6),(18,7),(19,20),(19,21),(20,10),(20,22),(21,9),(21,22),(22,16),(22,17),(23,19),(23,25),(24,19),(24,26),(25,13),(25,20),(26,14),(26,21),(27,11),(27,25),(28,15),(28,26),(29,12),(29,27),(30,23),(30,24),(31,23),(31,27),(32,24),(32,28),(33,8),(33,29),(33,30),(33,32),(34,8),(34,18),(34,29),(34,31)],35) => 1
011000001 => ([(0,6),(0,7),(1,15),(1,25),(2,4),(2,14),(2,24),(3,19),(3,30),(4,5),(4,18),(4,31),(5,3),(5,20),(5,29),(6,2),(6,21),(6,22),(7,1),(7,21),(7,22),(9,17),(10,12),(11,13),(12,11),(13,16),(14,18),(15,10),(16,8),(17,8),(18,20),(19,9),(20,19),(21,14),(21,15),(22,24),(22,25),(23,16),(23,17),(24,28),(24,31),(25,10),(25,28),(26,11),(26,27),(27,13),(27,23),(28,12),(28,26),(29,27),(29,30),(30,9),(30,23),(31,26),(31,29)],32) => 1
011001001 => ([(0,3),(0,4),(1,27),(1,31),(2,15),(2,26),(3,1),(3,29),(3,30),(4,2),(4,29),(4,30),(6,12),(7,11),(8,13),(9,14),(10,8),(11,9),(12,10),(13,5),(14,5),(15,6),(16,21),(16,23),(17,8),(17,19),(18,9),(18,19),(19,13),(19,14),(20,7),(20,23),(21,17),(21,18),(22,16),(22,20),(23,11),(23,18),(24,12),(24,25),(25,10),(25,17),(26,6),(26,24),(27,16),(27,28),(28,7),(28,21),(28,25),(29,22),(29,26),(29,31),(30,15),(30,22),(30,27),(31,20),(31,24),(31,28)],32) => 1
011010001 => ([(0,4),(0,5),(1,18),(1,32),(2,3),(2,17),(2,31),(3,8),(3,30),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,8),(18,7),(19,21),(19,22),(20,19),(20,27),(21,10),(21,23),(22,9),(22,23),(23,15),(23,16),(24,19),(24,28),(25,20),(25,29),(26,20),(26,24),(27,13),(27,21),(28,12),(28,22),(29,14),(29,27),(30,11),(30,28),(31,24),(31,30),(32,7),(32,29),(33,25),(33,26),(33,31),(33,32),(34,17),(34,18),(34,25),(34,26)],35) => 1
011011001 => ([(0,3),(0,4),(1,27),(1,31),(2,15),(2,26),(3,1),(3,29),(3,30),(4,2),(4,29),(4,30),(6,12),(7,11),(8,13),(9,14),(10,8),(11,9),(12,10),(13,5),(14,5),(15,6),(16,21),(16,23),(17,8),(17,19),(18,9),(18,19),(19,13),(19,14),(20,7),(20,23),(21,17),(21,18),(22,16),(22,20),(23,11),(23,18),(24,12),(24,25),(25,10),(25,17),(26,6),(26,24),(27,16),(27,28),(28,7),(28,21),(28,25),(29,22),(29,26),(29,31),(30,15),(30,22),(30,27),(31,20),(31,24),(31,28)],32) => 1
011100001 => ([(0,6),(0,7),(1,4),(1,11),(1,28),(2,5),(2,12),(2,27),(3,18),(3,33),(4,20),(4,32),(5,3),(5,19),(5,31),(6,1),(6,29),(6,30),(7,2),(7,29),(7,30),(9,13),(10,14),(11,20),(12,19),(13,15),(14,16),(15,17),(16,8),(17,8),(18,10),(19,18),(20,9),(21,22),(21,25),(22,23),(22,26),(23,15),(23,24),(24,16),(24,17),(25,13),(25,23),(26,14),(26,24),(27,21),(27,31),(28,21),(28,32),(29,27),(29,28),(30,11),(30,12),(31,22),(31,33),(32,9),(32,25),(33,10),(33,26)],34) => 1
011100101 => ([(0,4),(0,5),(1,30),(1,31),(2,3),(2,18),(2,32),(3,7),(3,28),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,12),(9,16),(10,17),(11,13),(12,11),(13,10),(14,9),(15,14),(16,6),(17,6),(18,7),(19,20),(19,21),(20,10),(20,22),(21,9),(21,22),(22,16),(22,17),(23,19),(23,25),(24,19),(24,26),(25,13),(25,20),(26,14),(26,21),(27,11),(27,25),(28,15),(28,26),(29,12),(29,27),(30,23),(30,24),(31,23),(31,27),(32,24),(32,28),(33,8),(33,29),(33,30),(33,32),(34,8),(34,18),(34,29),(34,31)],35) => 1
011101001 => ([(0,4),(0,5),(1,18),(1,32),(2,3),(2,17),(2,31),(3,8),(3,30),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,8),(18,7),(19,21),(19,22),(20,19),(20,27),(21,10),(21,23),(22,9),(22,23),(23,15),(23,16),(24,19),(24,28),(25,20),(25,29),(26,20),(26,24),(27,13),(27,21),(28,12),(28,22),(29,14),(29,27),(30,11),(30,28),(31,24),(31,30),(32,7),(32,29),(33,25),(33,26),(33,31),(33,32),(34,17),(34,18),(34,25),(34,26)],35) => 1
011101101 => ([(0,3),(0,4),(1,2),(1,28),(1,29),(2,7),(2,26),(3,20),(3,21),(4,1),(4,20),(4,21),(6,12),(7,10),(8,13),(9,14),(10,11),(11,8),(12,9),(13,5),(14,5),(15,8),(15,17),(16,9),(16,17),(17,13),(17,14),(18,22),(18,27),(19,15),(19,16),(20,18),(20,28),(21,18),(21,29),(22,19),(22,24),(23,6),(23,24),(24,12),(24,16),(25,11),(25,15),(26,10),(26,25),(27,6),(27,19),(27,25),(28,7),(28,22),(28,23),(29,23),(29,26),(29,27)],30) => 1
011110001 => ([(0,6),(0,7),(1,4),(1,11),(1,28),(2,5),(2,12),(2,27),(3,18),(3,33),(4,20),(4,32),(5,3),(5,19),(5,31),(6,1),(6,29),(6,30),(7,2),(7,29),(7,30),(9,13),(10,14),(11,20),(12,19),(13,15),(14,16),(15,17),(16,8),(17,8),(18,10),(19,18),(20,9),(21,22),(21,25),(22,23),(22,26),(23,15),(23,24),(24,16),(24,17),(25,13),(25,23),(26,14),(26,24),(27,21),(27,31),(28,21),(28,32),(29,27),(29,28),(30,11),(30,12),(31,22),(31,33),(32,9),(32,25),(33,10),(33,26)],34) => 1
011110011 => ([(0,5),(0,6),(1,29),(1,31),(2,3),(2,30),(2,32),(3,4),(3,9),(3,23),(4,14),(4,27),(5,1),(5,24),(5,25),(6,2),(6,24),(6,25),(8,15),(9,14),(10,16),(11,17),(12,10),(13,11),(14,12),(15,13),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,26),(23,18),(23,27),(24,29),(24,30),(25,31),(25,32),(26,13),(26,20),(27,12),(27,19),(28,15),(28,26),(29,22),(29,28),(30,22),(30,23),(31,8),(31,28),(32,8),(32,9)],33) => 1
011110101 => ([(0,4),(0,5),(1,3),(1,8),(1,18),(2,17),(2,28),(3,2),(3,16),(3,27),(4,29),(4,30),(5,1),(5,29),(5,30),(7,13),(8,16),(9,11),(10,9),(11,12),(12,15),(13,14),(14,6),(15,6),(16,17),(17,7),(18,22),(18,27),(19,10),(19,21),(20,13),(20,26),(21,9),(21,24),(22,23),(22,24),(23,20),(23,25),(24,11),(24,25),(25,12),(25,26),(26,14),(26,15),(27,23),(27,28),(28,7),(28,20),(29,8),(29,19),(29,31),(30,18),(30,19),(30,31),(31,10),(31,21),(31,22)],32) => 1
011110111 => ([(0,4),(0,5),(1,3),(1,21),(1,22),(2,14),(2,28),(3,2),(3,27),(3,29),(4,23),(4,24),(5,1),(5,23),(5,24),(7,11),(8,9),(9,12),(10,13),(11,10),(12,6),(13,6),(14,8),(15,17),(15,20),(16,15),(16,18),(17,11),(17,25),(18,7),(18,17),(19,12),(19,13),(20,25),(20,26),(21,18),(21,29),(22,15),(22,27),(23,16),(23,22),(24,16),(24,21),(25,10),(25,19),(26,9),(26,19),(27,20),(27,28),(28,8),(28,26),(29,7),(29,14)],30) => 1
011111001 => ([(0,6),(0,7),(1,15),(1,25),(2,4),(2,14),(2,24),(3,19),(3,30),(4,5),(4,18),(4,31),(5,3),(5,20),(5,29),(6,2),(6,21),(6,22),(7,1),(7,21),(7,22),(9,17),(10,12),(11,13),(12,11),(13,16),(14,18),(15,10),(16,8),(17,8),(18,20),(19,9),(20,19),(21,14),(21,15),(22,24),(22,25),(23,16),(23,17),(24,28),(24,31),(25,10),(25,28),(26,11),(26,27),(27,13),(27,23),(28,12),(28,26),(29,27),(29,30),(30,9),(30,23),(31,26),(31,29)],32) => 1
011111011 => ([(0,5),(0,6),(1,4),(1,21),(1,22),(2,16),(2,28),(3,2),(3,17),(3,29),(4,3),(4,15),(4,27),(5,23),(5,24),(6,1),(6,23),(6,24),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,17),(16,8),(17,16),(18,9),(18,25),(19,10),(19,20),(20,13),(20,14),(21,25),(21,27),(22,9),(22,15),(23,18),(23,22),(24,18),(24,21),(25,12),(25,26),(26,11),(26,19),(27,26),(27,29),(28,8),(28,20),(29,19),(29,28)],30) => 1
011111101 => ([(0,6),(0,7),(1,3),(1,11),(1,21),(2,18),(2,25),(3,4),(3,17),(3,24),(4,5),(4,20),(4,27),(5,2),(5,19),(5,26),(6,22),(6,23),(7,1),(7,22),(7,23),(9,12),(10,9),(11,17),(12,13),(13,14),(14,15),(15,8),(16,8),(17,20),(18,16),(19,18),(20,19),(21,9),(21,24),(22,10),(22,11),(23,10),(23,21),(24,12),(24,27),(25,15),(25,16),(26,14),(26,25),(27,13),(27,26)],28) => 1
011111111 => ([(0,2),(0,9),(1,11),(2,10),(3,4),(3,13),(4,6),(4,12),(5,3),(5,15),(6,8),(6,14),(7,5),(7,17),(8,1),(8,16),(9,7),(9,10),(10,17),(12,14),(13,12),(14,16),(15,13),(16,11),(17,15)],18) => 1
100000000 => ([(0,2),(0,9),(1,11),(2,10),(3,4),(3,13),(4,6),(4,12),(5,3),(5,15),(6,8),(6,14),(7,5),(7,17),(8,1),(8,16),(9,7),(9,10),(10,17),(12,14),(13,12),(14,16),(15,13),(16,11),(17,15)],18) => 1
100000010 => ([(0,6),(0,7),(1,3),(1,11),(1,21),(2,18),(2,25),(3,4),(3,17),(3,24),(4,5),(4,20),(4,27),(5,2),(5,19),(5,26),(6,22),(6,23),(7,1),(7,22),(7,23),(9,12),(10,9),(11,17),(12,13),(13,14),(14,15),(15,8),(16,8),(17,20),(18,16),(19,18),(20,19),(21,9),(21,24),(22,10),(22,11),(23,10),(23,21),(24,12),(24,27),(25,15),(25,16),(26,14),(26,25),(27,13),(27,26)],28) => 1
100000100 => ([(0,5),(0,6),(1,4),(1,21),(1,22),(2,16),(2,28),(3,2),(3,17),(3,29),(4,3),(4,15),(4,27),(5,23),(5,24),(6,1),(6,23),(6,24),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,17),(16,8),(17,16),(18,9),(18,25),(19,10),(19,20),(20,13),(20,14),(21,25),(21,27),(22,9),(22,15),(23,18),(23,22),(24,18),(24,21),(25,12),(25,26),(26,11),(26,19),(27,26),(27,29),(28,8),(28,20),(29,19),(29,28)],30) => 1
100000110 => ([(0,6),(0,7),(1,15),(1,25),(2,4),(2,14),(2,24),(3,19),(3,30),(4,5),(4,18),(4,31),(5,3),(5,20),(5,29),(6,2),(6,21),(6,22),(7,1),(7,21),(7,22),(9,17),(10,12),(11,13),(12,11),(13,16),(14,18),(15,10),(16,8),(17,8),(18,20),(19,9),(20,19),(21,14),(21,15),(22,24),(22,25),(23,16),(23,17),(24,28),(24,31),(25,10),(25,28),(26,11),(26,27),(27,13),(27,23),(28,12),(28,26),(29,27),(29,30),(30,9),(30,23),(31,26),(31,29)],32) => 1
100001000 => ([(0,4),(0,5),(1,3),(1,21),(1,22),(2,14),(2,28),(3,2),(3,27),(3,29),(4,23),(4,24),(5,1),(5,23),(5,24),(7,11),(8,9),(9,12),(10,13),(11,10),(12,6),(13,6),(14,8),(15,17),(15,20),(16,15),(16,18),(17,11),(17,25),(18,7),(18,17),(19,12),(19,13),(20,25),(20,26),(21,18),(21,29),(22,15),(22,27),(23,16),(23,22),(24,16),(24,21),(25,10),(25,19),(26,9),(26,19),(27,20),(27,28),(28,8),(28,26),(29,7),(29,14)],30) => 1
100001010 => ([(0,4),(0,5),(1,3),(1,8),(1,18),(2,17),(2,28),(3,2),(3,16),(3,27),(4,29),(4,30),(5,1),(5,29),(5,30),(7,13),(8,16),(9,11),(10,9),(11,12),(12,15),(13,14),(14,6),(15,6),(16,17),(17,7),(18,22),(18,27),(19,10),(19,21),(20,13),(20,26),(21,9),(21,24),(22,23),(22,24),(23,20),(23,25),(24,11),(24,25),(25,12),(25,26),(26,14),(26,15),(27,23),(27,28),(28,7),(28,20),(29,8),(29,19),(29,31),(30,18),(30,19),(30,31),(31,10),(31,21),(31,22)],32) => 1
100001100 => ([(0,5),(0,6),(1,29),(1,31),(2,3),(2,30),(2,32),(3,4),(3,9),(3,23),(4,14),(4,27),(5,1),(5,24),(5,25),(6,2),(6,24),(6,25),(8,15),(9,14),(10,16),(11,17),(12,10),(13,11),(14,12),(15,13),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,26),(23,18),(23,27),(24,29),(24,30),(25,31),(25,32),(26,13),(26,20),(27,12),(27,19),(28,15),(28,26),(29,22),(29,28),(30,22),(30,23),(31,8),(31,28),(32,8),(32,9)],33) => 1
100001110 => ([(0,6),(0,7),(1,4),(1,11),(1,28),(2,5),(2,12),(2,27),(3,18),(3,33),(4,20),(4,32),(5,3),(5,19),(5,31),(6,1),(6,29),(6,30),(7,2),(7,29),(7,30),(9,13),(10,14),(11,20),(12,19),(13,15),(14,16),(15,17),(16,8),(17,8),(18,10),(19,18),(20,9),(21,22),(21,25),(22,23),(22,26),(23,15),(23,24),(24,16),(24,17),(25,13),(25,23),(26,14),(26,24),(27,21),(27,31),(28,21),(28,32),(29,27),(29,28),(30,11),(30,12),(31,22),(31,33),(32,9),(32,25),(33,10),(33,26)],34) => 1
100010010 => ([(0,3),(0,4),(1,2),(1,28),(1,29),(2,7),(2,26),(3,20),(3,21),(4,1),(4,20),(4,21),(6,12),(7,10),(8,13),(9,14),(10,11),(11,8),(12,9),(13,5),(14,5),(15,8),(15,17),(16,9),(16,17),(17,13),(17,14),(18,22),(18,27),(19,15),(19,16),(20,18),(20,28),(21,18),(21,29),(22,19),(22,24),(23,6),(23,24),(24,12),(24,16),(25,11),(25,15),(26,10),(26,25),(27,6),(27,19),(27,25),(28,7),(28,22),(28,23),(29,23),(29,26),(29,27)],30) => 1
100010110 => ([(0,4),(0,5),(1,18),(1,32),(2,3),(2,17),(2,31),(3,8),(3,30),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,8),(18,7),(19,21),(19,22),(20,19),(20,27),(21,10),(21,23),(22,9),(22,23),(23,15),(23,16),(24,19),(24,28),(25,20),(25,29),(26,20),(26,24),(27,13),(27,21),(28,12),(28,22),(29,14),(29,27),(30,11),(30,28),(31,24),(31,30),(32,7),(32,29),(33,25),(33,26),(33,31),(33,32),(34,17),(34,18),(34,25),(34,26)],35) => 1
100011010 => ([(0,4),(0,5),(1,30),(1,31),(2,3),(2,18),(2,32),(3,7),(3,28),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,12),(9,16),(10,17),(11,13),(12,11),(13,10),(14,9),(15,14),(16,6),(17,6),(18,7),(19,20),(19,21),(20,10),(20,22),(21,9),(21,22),(22,16),(22,17),(23,19),(23,25),(24,19),(24,26),(25,13),(25,20),(26,14),(26,21),(27,11),(27,25),(28,15),(28,26),(29,12),(29,27),(30,23),(30,24),(31,23),(31,27),(32,24),(32,28),(33,8),(33,29),(33,30),(33,32),(34,8),(34,18),(34,29),(34,31)],35) => 1
100011110 => ([(0,6),(0,7),(1,4),(1,11),(1,28),(2,5),(2,12),(2,27),(3,18),(3,33),(4,20),(4,32),(5,3),(5,19),(5,31),(6,1),(6,29),(6,30),(7,2),(7,29),(7,30),(9,13),(10,14),(11,20),(12,19),(13,15),(14,16),(15,17),(16,8),(17,8),(18,10),(19,18),(20,9),(21,22),(21,25),(22,23),(22,26),(23,15),(23,24),(24,16),(24,17),(25,13),(25,23),(26,14),(26,24),(27,21),(27,31),(28,21),(28,32),(29,27),(29,28),(30,11),(30,12),(31,22),(31,33),(32,9),(32,25),(33,10),(33,26)],34) => 1
100100110 => ([(0,3),(0,4),(1,27),(1,31),(2,15),(2,26),(3,1),(3,29),(3,30),(4,2),(4,29),(4,30),(6,12),(7,11),(8,13),(9,14),(10,8),(11,9),(12,10),(13,5),(14,5),(15,6),(16,21),(16,23),(17,8),(17,19),(18,9),(18,19),(19,13),(19,14),(20,7),(20,23),(21,17),(21,18),(22,16),(22,20),(23,11),(23,18),(24,12),(24,25),(25,10),(25,17),(26,6),(26,24),(27,16),(27,28),(28,7),(28,21),(28,25),(29,22),(29,26),(29,31),(30,15),(30,22),(30,27),(31,20),(31,24),(31,28)],32) => 1
100101110 => ([(0,4),(0,5),(1,18),(1,32),(2,3),(2,17),(2,31),(3,8),(3,30),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,8),(18,7),(19,21),(19,22),(20,19),(20,27),(21,10),(21,23),(22,9),(22,23),(23,15),(23,16),(24,19),(24,28),(25,20),(25,29),(26,20),(26,24),(27,13),(27,21),(28,12),(28,22),(29,14),(29,27),(30,11),(30,28),(31,24),(31,30),(32,7),(32,29),(33,25),(33,26),(33,31),(33,32),(34,17),(34,18),(34,25),(34,26)],35) => 1
100110110 => ([(0,3),(0,4),(1,27),(1,31),(2,15),(2,26),(3,1),(3,29),(3,30),(4,2),(4,29),(4,30),(6,12),(7,11),(8,13),(9,14),(10,8),(11,9),(12,10),(13,5),(14,5),(15,6),(16,21),(16,23),(17,8),(17,19),(18,9),(18,19),(19,13),(19,14),(20,7),(20,23),(21,17),(21,18),(22,16),(22,20),(23,11),(23,18),(24,12),(24,25),(25,10),(25,17),(26,6),(26,24),(27,16),(27,28),(28,7),(28,21),(28,25),(29,22),(29,26),(29,31),(30,15),(30,22),(30,27),(31,20),(31,24),(31,28)],32) => 1
100111110 => ([(0,6),(0,7),(1,15),(1,25),(2,4),(2,14),(2,24),(3,19),(3,30),(4,5),(4,18),(4,31),(5,3),(5,20),(5,29),(6,2),(6,21),(6,22),(7,1),(7,21),(7,22),(9,17),(10,12),(11,13),(12,11),(13,16),(14,18),(15,10),(16,8),(17,8),(18,20),(19,9),(20,19),(21,14),(21,15),(22,24),(22,25),(23,16),(23,17),(24,28),(24,31),(25,10),(25,28),(26,11),(26,27),(27,13),(27,23),(28,12),(28,26),(29,27),(29,30),(30,9),(30,23),(31,26),(31,29)],32) => 1
101001110 => ([(0,4),(0,5),(1,30),(1,31),(2,3),(2,18),(2,32),(3,7),(3,28),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,12),(9,16),(10,17),(11,13),(12,11),(13,10),(14,9),(15,14),(16,6),(17,6),(18,7),(19,20),(19,21),(20,10),(20,22),(21,9),(21,22),(22,16),(22,17),(23,19),(23,25),(24,19),(24,26),(25,13),(25,20),(26,14),(26,21),(27,11),(27,25),(28,15),(28,26),(29,12),(29,27),(30,23),(30,24),(31,23),(31,27),(32,24),(32,28),(33,8),(33,29),(33,30),(33,32),(34,8),(34,18),(34,29),(34,31)],35) => 1
101011110 => ([(0,4),(0,5),(1,3),(1,8),(1,18),(2,17),(2,28),(3,2),(3,16),(3,27),(4,29),(4,30),(5,1),(5,29),(5,30),(7,13),(8,16),(9,11),(10,9),(11,12),(12,15),(13,14),(14,6),(15,6),(16,17),(17,7),(18,22),(18,27),(19,10),(19,21),(20,13),(20,26),(21,9),(21,24),(22,23),(22,24),(23,20),(23,25),(24,11),(24,25),(25,12),(25,26),(26,14),(26,15),(27,23),(27,28),(28,7),(28,20),(29,8),(29,19),(29,31),(30,18),(30,19),(30,31),(31,10),(31,21),(31,22)],32) => 1
101101110 => ([(0,3),(0,4),(1,2),(1,28),(1,29),(2,7),(2,26),(3,20),(3,21),(4,1),(4,20),(4,21),(6,12),(7,10),(8,13),(9,14),(10,11),(11,8),(12,9),(13,5),(14,5),(15,8),(15,17),(16,9),(16,17),(17,13),(17,14),(18,22),(18,27),(19,15),(19,16),(20,18),(20,28),(21,18),(21,29),(22,19),(22,24),(23,6),(23,24),(24,12),(24,16),(25,11),(25,15),(26,10),(26,25),(27,6),(27,19),(27,25),(28,7),(28,22),(28,23),(29,23),(29,26),(29,27)],30) => 1
101111110 => ([(0,6),(0,7),(1,3),(1,11),(1,21),(2,18),(2,25),(3,4),(3,17),(3,24),(4,5),(4,20),(4,27),(5,2),(5,19),(5,26),(6,22),(6,23),(7,1),(7,22),(7,23),(9,12),(10,9),(11,17),(12,13),(13,14),(14,15),(15,8),(16,8),(17,20),(18,16),(19,18),(20,19),(21,9),(21,24),(22,10),(22,11),(23,10),(23,21),(24,12),(24,27),(25,15),(25,16),(26,14),(26,25),(27,13),(27,26)],28) => 1
110011110 => ([(0,5),(0,6),(1,29),(1,31),(2,3),(2,30),(2,32),(3,4),(3,9),(3,23),(4,14),(4,27),(5,1),(5,24),(5,25),(6,2),(6,24),(6,25),(8,15),(9,14),(10,16),(11,17),(12,10),(13,11),(14,12),(15,13),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,26),(23,18),(23,27),(24,29),(24,30),(25,31),(25,32),(26,13),(26,20),(27,12),(27,19),(28,15),(28,26),(29,22),(29,28),(30,22),(30,23),(31,8),(31,28),(32,8),(32,9)],33) => 1
110111110 => ([(0,5),(0,6),(1,4),(1,21),(1,22),(2,16),(2,28),(3,2),(3,17),(3,29),(4,3),(4,15),(4,27),(5,23),(5,24),(6,1),(6,23),(6,24),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,17),(16,8),(17,16),(18,9),(18,25),(19,10),(19,20),(20,13),(20,14),(21,25),(21,27),(22,9),(22,15),(23,18),(23,22),(24,18),(24,21),(25,12),(25,26),(26,11),(26,19),(27,26),(27,29),(28,8),(28,20),(29,19),(29,28)],30) => 1
111011110 => ([(0,4),(0,5),(1,3),(1,21),(1,22),(2,14),(2,28),(3,2),(3,27),(3,29),(4,23),(4,24),(5,1),(5,23),(5,24),(7,11),(8,9),(9,12),(10,13),(11,10),(12,6),(13,6),(14,8),(15,17),(15,20),(16,15),(16,18),(17,11),(17,25),(18,7),(18,17),(19,12),(19,13),(20,25),(20,26),(21,18),(21,29),(22,15),(22,27),(23,16),(23,22),(24,16),(24,21),(25,10),(25,19),(26,9),(26,19),(27,20),(27,28),(28,8),(28,26),(29,7),(29,14)],30) => 1
111111110 => ([(0,2),(0,9),(1,11),(2,10),(3,4),(3,13),(4,6),(4,12),(5,3),(5,15),(6,8),(6,14),(7,5),(7,17),(8,1),(8,16),(9,7),(9,10),(10,17),(12,14),(13,12),(14,16),(15,13),(16,11),(17,15)],18) => 1
111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
1010101010 => ([(0,1),(0,2),(1,18),(1,19),(2,18),(2,19),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,12),(8,13),(9,12),(9,13),(10,6),(10,7),(11,6),(11,7),(12,16),(12,17),(13,16),(13,17),(14,10),(14,11),(15,10),(15,11),(16,4),(16,5),(17,4),(17,5),(18,14),(18,15),(19,14),(19,15)],20) => 1
1101010100 => ([(0,3),(0,4),(1,19),(2,18),(3,2),(3,25),(3,32),(4,1),(4,25),(4,32),(6,8),(7,9),(8,10),(9,11),(10,14),(11,15),(12,6),(13,7),(14,16),(15,17),(16,5),(17,5),(18,12),(19,13),(20,22),(20,23),(21,28),(21,29),(22,14),(22,24),(23,15),(23,24),(24,16),(24,17),(25,26),(25,27),(26,12),(26,21),(26,31),(27,13),(27,21),(27,31),(28,8),(28,20),(28,30),(29,9),(29,20),(29,30),(30,10),(30,11),(30,22),(30,23),(31,6),(31,7),(31,28),(31,29),(32,18),(32,19),(32,26),(32,27)],33) => 1
1111100000 => ([(0,9),(0,10),(1,8),(1,28),(2,7),(2,27),(3,18),(4,19),(5,3),(5,34),(6,4),(6,35),(7,5),(7,32),(8,6),(8,33),(9,2),(9,29),(10,1),(10,29),(12,14),(13,15),(14,16),(15,17),(16,11),(17,11),(18,12),(19,13),(20,22),(20,23),(21,25),(21,26),(22,14),(22,24),(23,15),(23,24),(24,16),(24,17),(25,20),(25,30),(26,20),(26,31),(27,21),(27,32),(28,21),(28,33),(29,27),(29,28),(30,12),(30,22),(31,13),(31,23),(32,25),(32,34),(33,26),(33,35),(34,18),(34,30),(35,19),(35,31)],36) => 1
101010101010 => ([(0,1),(0,2),(1,22),(1,23),(2,22),(2,23),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,12),(8,13),(9,12),(9,13),(10,6),(10,7),(11,6),(11,7),(12,16),(12,17),(13,16),(13,17),(14,10),(14,11),(15,10),(15,11),(16,20),(16,21),(17,20),(17,21),(18,14),(18,15),(19,14),(19,15),(20,4),(20,5),(21,4),(21,5),(22,18),(22,19),(23,18),(23,19)],24) => 1
1111111111 => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11) => 1
1111111110 => ([(0,2),(0,10),(1,12),(2,11),(3,5),(3,13),(4,3),(4,15),(5,7),(5,14),(6,4),(6,17),(7,9),(7,16),(8,6),(8,19),(9,1),(9,18),(10,8),(10,11),(11,19),(13,14),(14,16),(15,13),(16,18),(17,15),(18,12),(19,17)],20) => 1
1101111110 => ([(0,6),(0,7),(1,5),(1,24),(1,25),(2,18),(2,32),(3,4),(3,20),(3,34),(4,2),(4,19),(4,33),(5,3),(5,17),(5,31),(6,26),(6,27),(7,1),(7,26),(7,27),(9,15),(10,14),(11,16),(12,13),(13,11),(14,12),(15,8),(16,8),(17,20),(18,9),(19,18),(20,19),(21,10),(21,28),(22,11),(22,23),(23,15),(23,16),(24,28),(24,31),(25,10),(25,17),(26,21),(26,25),(27,21),(27,24),(28,14),(28,29),(29,12),(29,30),(30,13),(30,22),(31,29),(31,34),(32,9),(32,23),(33,22),(33,32),(34,30),(34,33)],35) => 1
1011111110 => ([(0,7),(0,8),(1,3),(1,12),(1,24),(2,20),(2,28),(3,5),(3,19),(3,27),(4,6),(4,21),(4,29),(5,4),(5,23),(5,31),(6,2),(6,22),(6,30),(7,25),(7,26),(8,1),(8,25),(8,26),(10,15),(11,10),(12,19),(13,14),(14,16),(15,13),(16,17),(17,9),(18,9),(19,23),(20,18),(21,22),(22,20),(23,21),(24,10),(24,27),(25,11),(25,12),(26,11),(26,24),(27,15),(27,31),(28,17),(28,18),(29,14),(29,30),(30,16),(30,28),(31,13),(31,29)],32) => 1
1001111110 => ([(0,7),(0,8),(1,17),(1,28),(2,4),(2,16),(2,27),(3,21),(3,35),(4,6),(4,20),(4,36),(5,3),(5,22),(5,34),(6,5),(6,23),(6,33),(7,2),(7,24),(7,25),(8,1),(8,24),(8,25),(10,19),(11,13),(12,14),(13,15),(14,11),(15,18),(16,20),(17,12),(18,9),(19,9),(20,23),(21,10),(22,21),(23,22),(24,16),(24,17),(25,27),(25,28),(26,18),(26,19),(27,32),(27,36),(28,12),(28,32),(29,11),(29,30),(30,13),(30,31),(31,15),(31,26),(32,14),(32,29),(33,30),(33,34),(34,31),(34,35),(35,10),(35,26),(36,29),(36,33)],37) => 1
1000000110 => ([(0,7),(0,8),(1,17),(1,28),(2,4),(2,16),(2,27),(3,21),(3,35),(4,6),(4,20),(4,36),(5,3),(5,22),(5,34),(6,5),(6,23),(6,33),(7,2),(7,24),(7,25),(8,1),(8,24),(8,25),(10,19),(11,13),(12,14),(13,15),(14,11),(15,18),(16,20),(17,12),(18,9),(19,9),(20,23),(21,10),(22,21),(23,22),(24,16),(24,17),(25,27),(25,28),(26,18),(26,19),(27,32),(27,36),(28,12),(28,32),(29,11),(29,30),(30,13),(30,31),(31,15),(31,26),(32,14),(32,29),(33,30),(33,34),(34,31),(34,35),(35,10),(35,26),(36,29),(36,33)],37) => 1
1000000100 => ([(0,6),(0,7),(1,5),(1,24),(1,25),(2,18),(2,32),(3,4),(3,20),(3,34),(4,2),(4,19),(4,33),(5,3),(5,17),(5,31),(6,26),(6,27),(7,1),(7,26),(7,27),(9,15),(10,14),(11,16),(12,13),(13,11),(14,12),(15,8),(16,8),(17,20),(18,9),(19,18),(20,19),(21,10),(21,28),(22,11),(22,23),(23,15),(23,16),(24,28),(24,31),(25,10),(25,17),(26,21),(26,25),(27,21),(27,24),(28,14),(28,29),(29,12),(29,30),(30,13),(30,22),(31,29),(31,34),(32,9),(32,23),(33,22),(33,32),(34,30),(34,33)],35) => 1
1000000010 => ([(0,7),(0,8),(1,3),(1,12),(1,24),(2,20),(2,28),(3,5),(3,19),(3,27),(4,6),(4,21),(4,29),(5,4),(5,23),(5,31),(6,2),(6,22),(6,30),(7,25),(7,26),(8,1),(8,25),(8,26),(10,15),(11,10),(12,19),(13,14),(14,16),(15,13),(16,17),(17,9),(18,9),(19,23),(20,18),(21,22),(22,20),(23,21),(24,10),(24,27),(25,11),(25,12),(26,11),(26,24),(27,15),(27,31),(28,17),(28,18),(29,14),(29,30),(30,16),(30,28),(31,13),(31,29)],32) => 1
1000000000 => ([(0,2),(0,10),(1,12),(2,11),(3,5),(3,13),(4,3),(4,15),(5,7),(5,14),(6,4),(6,17),(7,9),(7,16),(8,6),(8,19),(9,1),(9,18),(10,8),(10,11),(11,19),(13,14),(14,16),(15,13),(16,18),(17,15),(18,12),(19,17)],20) => 1
10000000000 => ([(0,2),(0,11),(1,13),(2,12),(3,4),(3,15),(4,6),(4,14),(5,3),(5,17),(6,8),(6,16),(7,5),(7,19),(8,10),(8,18),(9,7),(9,21),(10,1),(10,20),(11,9),(11,12),(12,21),(14,16),(15,14),(16,18),(17,15),(18,20),(19,17),(20,13),(21,19)],22) => 1
10000000010 => ([(0,8),(0,9),(1,3),(1,13),(1,27),(2,22),(2,31),(3,6),(3,21),(3,30),(4,5),(4,24),(4,33),(5,7),(5,23),(5,32),(6,4),(6,26),(6,35),(7,2),(7,25),(7,34),(8,28),(8,29),(9,1),(9,28),(9,29),(11,17),(12,11),(13,21),(14,16),(15,14),(16,18),(17,15),(18,19),(19,10),(20,10),(21,26),(22,20),(23,25),(24,23),(25,22),(26,24),(27,11),(27,30),(28,12),(28,13),(29,12),(29,27),(30,17),(30,35),(31,19),(31,20),(32,16),(32,34),(33,14),(33,32),(34,18),(34,31),(35,15),(35,33)],36) => 1
10111111110 => ([(0,8),(0,9),(1,3),(1,13),(1,27),(2,22),(2,31),(3,6),(3,21),(3,30),(4,5),(4,24),(4,33),(5,7),(5,23),(5,32),(6,4),(6,26),(6,35),(7,2),(7,25),(7,34),(8,28),(8,29),(9,1),(9,28),(9,29),(11,17),(12,11),(13,21),(14,16),(15,14),(16,18),(17,15),(18,19),(19,10),(20,10),(21,26),(22,20),(23,25),(24,23),(25,22),(26,24),(27,11),(27,30),(28,12),(28,13),(29,12),(29,27),(30,17),(30,35),(31,19),(31,20),(32,16),(32,34),(33,14),(33,32),(34,18),(34,31),(35,15),(35,33)],36) => 1
11111111110 => ([(0,2),(0,11),(1,13),(2,12),(3,4),(3,15),(4,6),(4,14),(5,3),(5,17),(6,8),(6,16),(7,5),(7,19),(8,10),(8,18),(9,7),(9,21),(10,1),(10,20),(11,9),(11,12),(12,21),(14,16),(15,14),(16,18),(17,15),(18,20),(19,17),(20,13),(21,19)],22) => 1
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
$F_{1} = 2\ q$
$F_{2} = 4\ q$
$F_{3} = 8\ q$
$F_{4} = 16\ q$
$F_{5} = 32\ q$
$F_{6} = 64\ q$
$F_{7} = 128\ q$
Description
The number of maximal elements of a poset.
Map
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!