Identifier
-
Mp00234:
Binary words
—valleys-to-peaks⟶
Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
St000390: Binary words ⟶ ℤ
Values
0 => 1 => 1 => 0 => 0
1 => 1 => 1 => 0 => 0
00 => 01 => 10 => 01 => 1
01 => 10 => 00 => 11 => 1
10 => 11 => 11 => 00 => 0
11 => 11 => 11 => 00 => 0
000 => 001 => 101 => 010 => 1
001 => 010 => 000 => 111 => 1
010 => 101 => 100 => 011 => 1
011 => 101 => 100 => 011 => 1
100 => 101 => 100 => 011 => 1
101 => 110 => 001 => 110 => 1
110 => 111 => 111 => 000 => 0
111 => 111 => 111 => 000 => 0
0000 => 0001 => 1011 => 0100 => 1
0001 => 0010 => 0001 => 1110 => 1
0010 => 0101 => 1000 => 0111 => 1
0011 => 0101 => 1000 => 0111 => 1
0100 => 1001 => 1010 => 0101 => 2
0101 => 1010 => 0000 => 1111 => 1
0110 => 1011 => 1100 => 0011 => 1
0111 => 1011 => 1100 => 0011 => 1
1000 => 1001 => 1010 => 0101 => 2
1001 => 1010 => 0000 => 1111 => 1
1010 => 1101 => 1001 => 0110 => 1
1011 => 1101 => 1001 => 0110 => 1
1100 => 1101 => 1001 => 0110 => 1
1101 => 1110 => 0011 => 1100 => 1
1110 => 1111 => 1111 => 0000 => 0
1111 => 1111 => 1111 => 0000 => 0
00000 => 00001 => 10111 => 01000 => 1
00001 => 00010 => 00011 => 11100 => 1
00010 => 00101 => 10001 => 01110 => 1
00011 => 00101 => 10001 => 01110 => 1
00100 => 01001 => 10100 => 01011 => 2
00101 => 01010 => 00000 => 11111 => 1
00110 => 01011 => 11000 => 00111 => 1
00111 => 01011 => 11000 => 00111 => 1
01000 => 10001 => 10110 => 01001 => 2
01001 => 10010 => 00010 => 11101 => 2
01010 => 10101 => 10000 => 01111 => 1
01011 => 10101 => 10000 => 01111 => 1
01100 => 10101 => 10000 => 01111 => 1
01101 => 10110 => 00100 => 11011 => 2
01110 => 10111 => 11100 => 00011 => 1
01111 => 10111 => 11100 => 00011 => 1
10000 => 10001 => 10110 => 01001 => 2
10001 => 10010 => 00010 => 11101 => 2
10010 => 10101 => 10000 => 01111 => 1
10011 => 10101 => 10000 => 01111 => 1
10100 => 11001 => 10101 => 01010 => 2
10101 => 11010 => 00001 => 11110 => 1
10110 => 11011 => 11001 => 00110 => 1
10111 => 11011 => 11001 => 00110 => 1
11000 => 11001 => 10101 => 01010 => 2
11001 => 11010 => 00001 => 11110 => 1
11010 => 11101 => 10011 => 01100 => 1
11011 => 11101 => 10011 => 01100 => 1
11100 => 11101 => 10011 => 01100 => 1
11101 => 11110 => 00111 => 11000 => 1
11110 => 11111 => 11111 => 00000 => 0
11111 => 11111 => 11111 => 00000 => 0
000000 => 000001 => 101111 => 010000 => 1
000001 => 000010 => 000111 => 111000 => 1
000010 => 000101 => 100011 => 011100 => 1
000011 => 000101 => 100011 => 011100 => 1
000100 => 001001 => 101001 => 010110 => 2
000101 => 001010 => 000001 => 111110 => 1
000110 => 001011 => 110001 => 001110 => 1
000111 => 001011 => 110001 => 001110 => 1
001000 => 010001 => 101100 => 010011 => 2
001001 => 010010 => 000100 => 111011 => 2
001010 => 010101 => 100000 => 011111 => 1
001011 => 010101 => 100000 => 011111 => 1
001100 => 010101 => 100000 => 011111 => 1
001101 => 010110 => 001000 => 110111 => 2
001110 => 010111 => 111000 => 000111 => 1
001111 => 010111 => 111000 => 000111 => 1
010000 => 100001 => 101110 => 010001 => 2
010001 => 100010 => 000110 => 111001 => 2
010010 => 100101 => 100010 => 011101 => 2
010011 => 100101 => 100010 => 011101 => 2
010100 => 101001 => 101000 => 010111 => 2
010101 => 101010 => 000000 => 111111 => 1
010110 => 101011 => 110000 => 001111 => 1
010111 => 101011 => 110000 => 001111 => 1
011000 => 101001 => 101000 => 010111 => 2
011001 => 101010 => 000000 => 111111 => 1
011010 => 101101 => 100100 => 011011 => 2
011011 => 101101 => 100100 => 011011 => 2
011100 => 101101 => 100100 => 011011 => 2
011101 => 101110 => 001100 => 110011 => 2
011110 => 101111 => 111100 => 000011 => 1
011111 => 101111 => 111100 => 000011 => 1
100000 => 100001 => 101110 => 010001 => 2
100001 => 100010 => 000110 => 111001 => 2
100010 => 100101 => 100010 => 011101 => 2
100011 => 100101 => 100010 => 011101 => 2
100100 => 101001 => 101000 => 010111 => 2
100101 => 101010 => 000000 => 111111 => 1
100110 => 101011 => 110000 => 001111 => 1
>>> Load all 1106 entries. <<<100111 => 101011 => 110000 => 001111 => 1
101000 => 110001 => 101101 => 010010 => 2
101001 => 110010 => 000101 => 111010 => 2
101010 => 110101 => 100001 => 011110 => 1
101011 => 110101 => 100001 => 011110 => 1
101100 => 110101 => 100001 => 011110 => 1
101101 => 110110 => 001001 => 110110 => 2
101110 => 110111 => 111001 => 000110 => 1
101111 => 110111 => 111001 => 000110 => 1
110000 => 110001 => 101101 => 010010 => 2
110001 => 110010 => 000101 => 111010 => 2
110010 => 110101 => 100001 => 011110 => 1
110011 => 110101 => 100001 => 011110 => 1
110100 => 111001 => 101011 => 010100 => 2
110101 => 111010 => 000011 => 111100 => 1
110110 => 111011 => 110011 => 001100 => 1
110111 => 111011 => 110011 => 001100 => 1
111000 => 111001 => 101011 => 010100 => 2
111001 => 111010 => 000011 => 111100 => 1
111010 => 111101 => 100111 => 011000 => 1
111011 => 111101 => 100111 => 011000 => 1
111100 => 111101 => 100111 => 011000 => 1
111101 => 111110 => 001111 => 110000 => 1
111110 => 111111 => 111111 => 000000 => 0
111111 => 111111 => 111111 => 000000 => 0
0000000 => 0000001 => 1011111 => 0100000 => 1
0000001 => 0000010 => 0001111 => 1110000 => 1
0000010 => 0000101 => 1000111 => 0111000 => 1
0000011 => 0000101 => 1000111 => 0111000 => 1
0000100 => 0001001 => 1010011 => 0101100 => 2
0000101 => 0001010 => 0000011 => 1111100 => 1
0000110 => 0001011 => 1100011 => 0011100 => 1
0000111 => 0001011 => 1100011 => 0011100 => 1
0001000 => 0010001 => 1011001 => 0100110 => 2
0001001 => 0010010 => 0001001 => 1110110 => 2
0001010 => 0010101 => 1000001 => 0111110 => 1
0001011 => 0010101 => 1000001 => 0111110 => 1
0001100 => 0010101 => 1000001 => 0111110 => 1
0001101 => 0010110 => 0010001 => 1101110 => 2
0001110 => 0010111 => 1110001 => 0001110 => 1
0001111 => 0010111 => 1110001 => 0001110 => 1
0010000 => 0100001 => 1011100 => 0100011 => 2
0010001 => 0100010 => 0001100 => 1110011 => 2
0010010 => 0100101 => 1000100 => 0111011 => 2
0010011 => 0100101 => 1000100 => 0111011 => 2
0010100 => 0101001 => 1010000 => 0101111 => 2
0010101 => 0101010 => 0000000 => 1111111 => 1
0010110 => 0101011 => 1100000 => 0011111 => 1
0010111 => 0101011 => 1100000 => 0011111 => 1
0011000 => 0101001 => 1010000 => 0101111 => 2
0011001 => 0101010 => 0000000 => 1111111 => 1
0011010 => 0101101 => 1001000 => 0110111 => 2
0011011 => 0101101 => 1001000 => 0110111 => 2
0011100 => 0101101 => 1001000 => 0110111 => 2
0011101 => 0101110 => 0011000 => 1100111 => 2
0011110 => 0101111 => 1111000 => 0000111 => 1
0011111 => 0101111 => 1111000 => 0000111 => 1
0100000 => 1000001 => 1011110 => 0100001 => 2
0100001 => 1000010 => 0001110 => 1110001 => 2
0100010 => 1000101 => 1000110 => 0111001 => 2
0100011 => 1000101 => 1000110 => 0111001 => 2
0100100 => 1001001 => 1010010 => 0101101 => 3
0100101 => 1001010 => 0000010 => 1111101 => 2
0100110 => 1001011 => 1100010 => 0011101 => 2
0100111 => 1001011 => 1100010 => 0011101 => 2
0101000 => 1010001 => 1011000 => 0100111 => 2
0101001 => 1010010 => 0001000 => 1110111 => 2
0101010 => 1010101 => 1000000 => 0111111 => 1
0101011 => 1010101 => 1000000 => 0111111 => 1
0101100 => 1010101 => 1000000 => 0111111 => 1
0101101 => 1010110 => 0010000 => 1101111 => 2
0101110 => 1010111 => 1110000 => 0001111 => 1
0101111 => 1010111 => 1110000 => 0001111 => 1
0110000 => 1010001 => 1011000 => 0100111 => 2
0110001 => 1010010 => 0001000 => 1110111 => 2
0110010 => 1010101 => 1000000 => 0111111 => 1
0110011 => 1010101 => 1000000 => 0111111 => 1
0110100 => 1011001 => 1010100 => 0101011 => 3
0110101 => 1011010 => 0000100 => 1111011 => 2
0110110 => 1011011 => 1100100 => 0011011 => 2
0110111 => 1011011 => 1100100 => 0011011 => 2
0111000 => 1011001 => 1010100 => 0101011 => 3
0111001 => 1011010 => 0000100 => 1111011 => 2
0111010 => 1011101 => 1001100 => 0110011 => 2
0111011 => 1011101 => 1001100 => 0110011 => 2
0111100 => 1011101 => 1001100 => 0110011 => 2
0111101 => 1011110 => 0011100 => 1100011 => 2
0111110 => 1011111 => 1111100 => 0000011 => 1
0111111 => 1011111 => 1111100 => 0000011 => 1
1000000 => 1000001 => 1011110 => 0100001 => 2
1000001 => 1000010 => 0001110 => 1110001 => 2
1000010 => 1000101 => 1000110 => 0111001 => 2
1000011 => 1000101 => 1000110 => 0111001 => 2
1000100 => 1001001 => 1010010 => 0101101 => 3
1000101 => 1001010 => 0000010 => 1111101 => 2
1000110 => 1001011 => 1100010 => 0011101 => 2
1000111 => 1001011 => 1100010 => 0011101 => 2
1001000 => 1010001 => 1011000 => 0100111 => 2
1001001 => 1010010 => 0001000 => 1110111 => 2
1001010 => 1010101 => 1000000 => 0111111 => 1
1001011 => 1010101 => 1000000 => 0111111 => 1
1001100 => 1010101 => 1000000 => 0111111 => 1
1001101 => 1010110 => 0010000 => 1101111 => 2
1001110 => 1010111 => 1110000 => 0001111 => 1
1001111 => 1010111 => 1110000 => 0001111 => 1
1010000 => 1100001 => 1011101 => 0100010 => 2
1010001 => 1100010 => 0001101 => 1110010 => 2
1010010 => 1100101 => 1000101 => 0111010 => 2
1010011 => 1100101 => 1000101 => 0111010 => 2
1010100 => 1101001 => 1010001 => 0101110 => 2
1010101 => 1101010 => 0000001 => 1111110 => 1
1010110 => 1101011 => 1100001 => 0011110 => 1
1010111 => 1101011 => 1100001 => 0011110 => 1
1011000 => 1101001 => 1010001 => 0101110 => 2
1011001 => 1101010 => 0000001 => 1111110 => 1
1011010 => 1101101 => 1001001 => 0110110 => 2
1011011 => 1101101 => 1001001 => 0110110 => 2
1011100 => 1101101 => 1001001 => 0110110 => 2
1011101 => 1101110 => 0011001 => 1100110 => 2
1011110 => 1101111 => 1111001 => 0000110 => 1
1011111 => 1101111 => 1111001 => 0000110 => 1
1100000 => 1100001 => 1011101 => 0100010 => 2
1100001 => 1100010 => 0001101 => 1110010 => 2
1100010 => 1100101 => 1000101 => 0111010 => 2
1100011 => 1100101 => 1000101 => 0111010 => 2
1100100 => 1101001 => 1010001 => 0101110 => 2
1100101 => 1101010 => 0000001 => 1111110 => 1
1100110 => 1101011 => 1100001 => 0011110 => 1
1100111 => 1101011 => 1100001 => 0011110 => 1
1101000 => 1110001 => 1011011 => 0100100 => 2
1101001 => 1110010 => 0001011 => 1110100 => 2
1101010 => 1110101 => 1000011 => 0111100 => 1
1101011 => 1110101 => 1000011 => 0111100 => 1
1101100 => 1110101 => 1000011 => 0111100 => 1
1101101 => 1110110 => 0010011 => 1101100 => 2
1101110 => 1110111 => 1110011 => 0001100 => 1
1101111 => 1110111 => 1110011 => 0001100 => 1
1110000 => 1110001 => 1011011 => 0100100 => 2
1110001 => 1110010 => 0001011 => 1110100 => 2
1110010 => 1110101 => 1000011 => 0111100 => 1
1110011 => 1110101 => 1000011 => 0111100 => 1
1110100 => 1111001 => 1010111 => 0101000 => 2
1110101 => 1111010 => 0000111 => 1111000 => 1
1110110 => 1111011 => 1100111 => 0011000 => 1
1110111 => 1111011 => 1100111 => 0011000 => 1
1111000 => 1111001 => 1010111 => 0101000 => 2
1111001 => 1111010 => 0000111 => 1111000 => 1
1111010 => 1111101 => 1001111 => 0110000 => 1
1111011 => 1111101 => 1001111 => 0110000 => 1
1111100 => 1111101 => 1001111 => 0110000 => 1
1111101 => 1111110 => 0011111 => 1100000 => 1
1111110 => 1111111 => 1111111 => 0000000 => 0
1111111 => 1111111 => 1111111 => 0000000 => 0
00000000 => 00000001 => 10111111 => 01000000 => 1
00000001 => 00000010 => 00011111 => 11100000 => 1
00000010 => 00000101 => 10001111 => 01110000 => 1
00000011 => 00000101 => 10001111 => 01110000 => 1
00000100 => 00001001 => 10100111 => 01011000 => 2
00000101 => 00001010 => 00000111 => 11111000 => 1
00000110 => 00001011 => 11000111 => 00111000 => 1
00000111 => 00001011 => 11000111 => 00111000 => 1
00001000 => 00010001 => 10110011 => 01001100 => 2
00001001 => 00010010 => 00010011 => 11101100 => 2
00001010 => 00010101 => 10000011 => 01111100 => 1
00001011 => 00010101 => 10000011 => 01111100 => 1
00001100 => 00010101 => 10000011 => 01111100 => 1
00001101 => 00010110 => 00100011 => 11011100 => 2
00001110 => 00010111 => 11100011 => 00011100 => 1
00001111 => 00010111 => 11100011 => 00011100 => 1
00010000 => 00100001 => 10111001 => 01000110 => 2
00010001 => 00100010 => 00011001 => 11100110 => 2
00010010 => 00100101 => 10001001 => 01110110 => 2
00010011 => 00100101 => 10001001 => 01110110 => 2
00010100 => 00101001 => 10100001 => 01011110 => 2
00010101 => 00101010 => 00000001 => 11111110 => 1
00010110 => 00101011 => 11000001 => 00111110 => 1
00010111 => 00101011 => 11000001 => 00111110 => 1
00011000 => 00101001 => 10100001 => 01011110 => 2
00011001 => 00101010 => 00000001 => 11111110 => 1
00011010 => 00101101 => 10010001 => 01101110 => 2
00011011 => 00101101 => 10010001 => 01101110 => 2
00011100 => 00101101 => 10010001 => 01101110 => 2
00011101 => 00101110 => 00110001 => 11001110 => 2
00011110 => 00101111 => 11110001 => 00001110 => 1
00011111 => 00101111 => 11110001 => 00001110 => 1
00100000 => 01000001 => 10111100 => 01000011 => 2
00100001 => 01000010 => 00011100 => 11100011 => 2
00100010 => 01000101 => 10001100 => 01110011 => 2
00100011 => 01000101 => 10001100 => 01110011 => 2
00100100 => 01001001 => 10100100 => 01011011 => 3
00100101 => 01001010 => 00000100 => 11111011 => 2
00100110 => 01001011 => 11000100 => 00111011 => 2
00100111 => 01001011 => 11000100 => 00111011 => 2
00101000 => 01010001 => 10110000 => 01001111 => 2
00101001 => 01010010 => 00010000 => 11101111 => 2
00101010 => 01010101 => 10000000 => 01111111 => 1
00101011 => 01010101 => 10000000 => 01111111 => 1
00101100 => 01010101 => 10000000 => 01111111 => 1
00101101 => 01010110 => 00100000 => 11011111 => 2
00101110 => 01010111 => 11100000 => 00011111 => 1
00101111 => 01010111 => 11100000 => 00011111 => 1
00110000 => 01010001 => 10110000 => 01001111 => 2
00110001 => 01010010 => 00010000 => 11101111 => 2
00110010 => 01010101 => 10000000 => 01111111 => 1
00110011 => 01010101 => 10000000 => 01111111 => 1
00110100 => 01011001 => 10101000 => 01010111 => 3
00110101 => 01011010 => 00001000 => 11110111 => 2
00110110 => 01011011 => 11001000 => 00110111 => 2
00110111 => 01011011 => 11001000 => 00110111 => 2
00111000 => 01011001 => 10101000 => 01010111 => 3
00111001 => 01011010 => 00001000 => 11110111 => 2
00111010 => 01011101 => 10011000 => 01100111 => 2
00111011 => 01011101 => 10011000 => 01100111 => 2
00111100 => 01011101 => 10011000 => 01100111 => 2
00111101 => 01011110 => 00111000 => 11000111 => 2
00111110 => 01011111 => 11111000 => 00000111 => 1
00111111 => 01011111 => 11111000 => 00000111 => 1
01000000 => 10000001 => 10111110 => 01000001 => 2
01000001 => 10000010 => 00011110 => 11100001 => 2
01000010 => 10000101 => 10001110 => 01110001 => 2
01000011 => 10000101 => 10001110 => 01110001 => 2
01000100 => 10001001 => 10100110 => 01011001 => 3
01000101 => 10001010 => 00000110 => 11111001 => 2
01000110 => 10001011 => 11000110 => 00111001 => 2
01000111 => 10001011 => 11000110 => 00111001 => 2
01001000 => 10010001 => 10110010 => 01001101 => 3
01001001 => 10010010 => 00010010 => 11101101 => 3
01001010 => 10010101 => 10000010 => 01111101 => 2
01001011 => 10010101 => 10000010 => 01111101 => 2
01001100 => 10010101 => 10000010 => 01111101 => 2
01001101 => 10010110 => 00100010 => 11011101 => 3
01001110 => 10010111 => 11100010 => 00011101 => 2
01001111 => 10010111 => 11100010 => 00011101 => 2
01010000 => 10100001 => 10111000 => 01000111 => 2
01010001 => 10100010 => 00011000 => 11100111 => 2
01010010 => 10100101 => 10001000 => 01110111 => 2
01010011 => 10100101 => 10001000 => 01110111 => 2
01010100 => 10101001 => 10100000 => 01011111 => 2
01010101 => 10101010 => 00000000 => 11111111 => 1
01010110 => 10101011 => 11000000 => 00111111 => 1
01010111 => 10101011 => 11000000 => 00111111 => 1
01011000 => 10101001 => 10100000 => 01011111 => 2
01011001 => 10101010 => 00000000 => 11111111 => 1
01011010 => 10101101 => 10010000 => 01101111 => 2
01011011 => 10101101 => 10010000 => 01101111 => 2
01011100 => 10101101 => 10010000 => 01101111 => 2
01011101 => 10101110 => 00110000 => 11001111 => 2
01011110 => 10101111 => 11110000 => 00001111 => 1
01011111 => 10101111 => 11110000 => 00001111 => 1
01100000 => 10100001 => 10111000 => 01000111 => 2
01100001 => 10100010 => 00011000 => 11100111 => 2
01100010 => 10100101 => 10001000 => 01110111 => 2
01100011 => 10100101 => 10001000 => 01110111 => 2
01100100 => 10101001 => 10100000 => 01011111 => 2
01100101 => 10101010 => 00000000 => 11111111 => 1
01100110 => 10101011 => 11000000 => 00111111 => 1
01100111 => 10101011 => 11000000 => 00111111 => 1
01101000 => 10110001 => 10110100 => 01001011 => 3
01101001 => 10110010 => 00010100 => 11101011 => 3
01101010 => 10110101 => 10000100 => 01111011 => 2
01101011 => 10110101 => 10000100 => 01111011 => 2
01101100 => 10110101 => 10000100 => 01111011 => 2
01101101 => 10110110 => 00100100 => 11011011 => 3
01101110 => 10110111 => 11100100 => 00011011 => 2
01101111 => 10110111 => 11100100 => 00011011 => 2
01110000 => 10110001 => 10110100 => 01001011 => 3
01110001 => 10110010 => 00010100 => 11101011 => 3
01110010 => 10110101 => 10000100 => 01111011 => 2
01110011 => 10110101 => 10000100 => 01111011 => 2
01110100 => 10111001 => 10101100 => 01010011 => 3
01110101 => 10111010 => 00001100 => 11110011 => 2
01110110 => 10111011 => 11001100 => 00110011 => 2
01110111 => 10111011 => 11001100 => 00110011 => 2
01111000 => 10111001 => 10101100 => 01010011 => 3
01111001 => 10111010 => 00001100 => 11110011 => 2
01111010 => 10111101 => 10011100 => 01100011 => 2
01111011 => 10111101 => 10011100 => 01100011 => 2
01111100 => 10111101 => 10011100 => 01100011 => 2
01111101 => 10111110 => 00111100 => 11000011 => 2
01111110 => 10111111 => 11111100 => 00000011 => 1
01111111 => 10111111 => 11111100 => 00000011 => 1
10000000 => 10000001 => 10111110 => 01000001 => 2
10000001 => 10000010 => 00011110 => 11100001 => 2
10000010 => 10000101 => 10001110 => 01110001 => 2
10000011 => 10000101 => 10001110 => 01110001 => 2
10000100 => 10001001 => 10100110 => 01011001 => 3
10000101 => 10001010 => 00000110 => 11111001 => 2
10000110 => 10001011 => 11000110 => 00111001 => 2
10000111 => 10001011 => 11000110 => 00111001 => 2
10001000 => 10010001 => 10110010 => 01001101 => 3
10001001 => 10010010 => 00010010 => 11101101 => 3
10001010 => 10010101 => 10000010 => 01111101 => 2
10001011 => 10010101 => 10000010 => 01111101 => 2
10001100 => 10010101 => 10000010 => 01111101 => 2
10001101 => 10010110 => 00100010 => 11011101 => 3
10001110 => 10010111 => 11100010 => 00011101 => 2
10001111 => 10010111 => 11100010 => 00011101 => 2
10010000 => 10100001 => 10111000 => 01000111 => 2
10010001 => 10100010 => 00011000 => 11100111 => 2
10010010 => 10100101 => 10001000 => 01110111 => 2
10010011 => 10100101 => 10001000 => 01110111 => 2
10010100 => 10101001 => 10100000 => 01011111 => 2
10010101 => 10101010 => 00000000 => 11111111 => 1
10010110 => 10101011 => 11000000 => 00111111 => 1
10010111 => 10101011 => 11000000 => 00111111 => 1
10011000 => 10101001 => 10100000 => 01011111 => 2
10011001 => 10101010 => 00000000 => 11111111 => 1
10011010 => 10101101 => 10010000 => 01101111 => 2
10011011 => 10101101 => 10010000 => 01101111 => 2
10011100 => 10101101 => 10010000 => 01101111 => 2
10011101 => 10101110 => 00110000 => 11001111 => 2
10011110 => 10101111 => 11110000 => 00001111 => 1
10011111 => 10101111 => 11110000 => 00001111 => 1
10100000 => 11000001 => 10111101 => 01000010 => 2
10100001 => 11000010 => 00011101 => 11100010 => 2
10100010 => 11000101 => 10001101 => 01110010 => 2
10100011 => 11000101 => 10001101 => 01110010 => 2
10100100 => 11001001 => 10100101 => 01011010 => 3
10100101 => 11001010 => 00000101 => 11111010 => 2
10100110 => 11001011 => 11000101 => 00111010 => 2
10100111 => 11001011 => 11000101 => 00111010 => 2
10101000 => 11010001 => 10110001 => 01001110 => 2
10101001 => 11010010 => 00010001 => 11101110 => 2
10101010 => 11010101 => 10000001 => 01111110 => 1
10101011 => 11010101 => 10000001 => 01111110 => 1
10101100 => 11010101 => 10000001 => 01111110 => 1
10101101 => 11010110 => 00100001 => 11011110 => 2
10101110 => 11010111 => 11100001 => 00011110 => 1
10101111 => 11010111 => 11100001 => 00011110 => 1
10110000 => 11010001 => 10110001 => 01001110 => 2
10110001 => 11010010 => 00010001 => 11101110 => 2
10110010 => 11010101 => 10000001 => 01111110 => 1
10110011 => 11010101 => 10000001 => 01111110 => 1
10110100 => 11011001 => 10101001 => 01010110 => 3
10110101 => 11011010 => 00001001 => 11110110 => 2
10110110 => 11011011 => 11001001 => 00110110 => 2
10110111 => 11011011 => 11001001 => 00110110 => 2
10111000 => 11011001 => 10101001 => 01010110 => 3
10111001 => 11011010 => 00001001 => 11110110 => 2
10111010 => 11011101 => 10011001 => 01100110 => 2
10111011 => 11011101 => 10011001 => 01100110 => 2
10111100 => 11011101 => 10011001 => 01100110 => 2
10111101 => 11011110 => 00111001 => 11000110 => 2
10111110 => 11011111 => 11111001 => 00000110 => 1
10111111 => 11011111 => 11111001 => 00000110 => 1
11000000 => 11000001 => 10111101 => 01000010 => 2
11000001 => 11000010 => 00011101 => 11100010 => 2
11000010 => 11000101 => 10001101 => 01110010 => 2
11000011 => 11000101 => 10001101 => 01110010 => 2
11000100 => 11001001 => 10100101 => 01011010 => 3
11000101 => 11001010 => 00000101 => 11111010 => 2
11000110 => 11001011 => 11000101 => 00111010 => 2
11000111 => 11001011 => 11000101 => 00111010 => 2
11001000 => 11010001 => 10110001 => 01001110 => 2
11001001 => 11010010 => 00010001 => 11101110 => 2
11001010 => 11010101 => 10000001 => 01111110 => 1
11001011 => 11010101 => 10000001 => 01111110 => 1
11001100 => 11010101 => 10000001 => 01111110 => 1
11001101 => 11010110 => 00100001 => 11011110 => 2
11001110 => 11010111 => 11100001 => 00011110 => 1
11001111 => 11010111 => 11100001 => 00011110 => 1
11010000 => 11100001 => 10111011 => 01000100 => 2
11010001 => 11100010 => 00011011 => 11100100 => 2
11010010 => 11100101 => 10001011 => 01110100 => 2
11010011 => 11100101 => 10001011 => 01110100 => 2
11010100 => 11101001 => 10100011 => 01011100 => 2
11010101 => 11101010 => 00000011 => 11111100 => 1
11010110 => 11101011 => 11000011 => 00111100 => 1
11010111 => 11101011 => 11000011 => 00111100 => 1
11011000 => 11101001 => 10100011 => 01011100 => 2
11011001 => 11101010 => 00000011 => 11111100 => 1
11011010 => 11101101 => 10010011 => 01101100 => 2
11011011 => 11101101 => 10010011 => 01101100 => 2
11011100 => 11101101 => 10010011 => 01101100 => 2
11011101 => 11101110 => 00110011 => 11001100 => 2
11011110 => 11101111 => 11110011 => 00001100 => 1
11011111 => 11101111 => 11110011 => 00001100 => 1
11100000 => 11100001 => 10111011 => 01000100 => 2
11100001 => 11100010 => 00011011 => 11100100 => 2
11100010 => 11100101 => 10001011 => 01110100 => 2
11100011 => 11100101 => 10001011 => 01110100 => 2
11100100 => 11101001 => 10100011 => 01011100 => 2
11100101 => 11101010 => 00000011 => 11111100 => 1
11100110 => 11101011 => 11000011 => 00111100 => 1
11100111 => 11101011 => 11000011 => 00111100 => 1
11101000 => 11110001 => 10110111 => 01001000 => 2
11101001 => 11110010 => 00010111 => 11101000 => 2
11101010 => 11110101 => 10000111 => 01111000 => 1
11101011 => 11110101 => 10000111 => 01111000 => 1
11101100 => 11110101 => 10000111 => 01111000 => 1
11101101 => 11110110 => 00100111 => 11011000 => 2
11101110 => 11110111 => 11100111 => 00011000 => 1
11101111 => 11110111 => 11100111 => 00011000 => 1
11110000 => 11110001 => 10110111 => 01001000 => 2
11110001 => 11110010 => 00010111 => 11101000 => 2
11110010 => 11110101 => 10000111 => 01111000 => 1
11110011 => 11110101 => 10000111 => 01111000 => 1
11110100 => 11111001 => 10101111 => 01010000 => 2
11110101 => 11111010 => 00001111 => 11110000 => 1
11110110 => 11111011 => 11001111 => 00110000 => 1
11110111 => 11111011 => 11001111 => 00110000 => 1
11111000 => 11111001 => 10101111 => 01010000 => 2
11111001 => 11111010 => 00001111 => 11110000 => 1
11111010 => 11111101 => 10011111 => 01100000 => 1
11111011 => 11111101 => 10011111 => 01100000 => 1
11111100 => 11111101 => 10011111 => 01100000 => 1
11111101 => 11111110 => 00111111 => 11000000 => 1
11111110 => 11111111 => 11111111 => 00000000 => 0
11111111 => 11111111 => 11111111 => 00000000 => 0
000000000 => 000000001 => 101111111 => 010000000 => 1
000000001 => 000000010 => 000111111 => 111000000 => 1
000000010 => 000000101 => 100011111 => 011100000 => 1
000000011 => 000000101 => 100011111 => 011100000 => 1
000000100 => 000001001 => 101001111 => 010110000 => 2
000000101 => 000001010 => 000001111 => 111110000 => 1
000000110 => 000001011 => 110001111 => 001110000 => 1
000000111 => 000001011 => 110001111 => 001110000 => 1
000001000 => 000010001 => 101100111 => 010011000 => 2
000001001 => 000010010 => 000100111 => 111011000 => 2
000001010 => 000010101 => 100000111 => 011111000 => 1
000001011 => 000010101 => 100000111 => 011111000 => 1
000001100 => 000010101 => 100000111 => 011111000 => 1
000001101 => 000010110 => 001000111 => 110111000 => 2
000001110 => 000010111 => 111000111 => 000111000 => 1
000001111 => 000010111 => 111000111 => 000111000 => 1
000010000 => 000100001 => 101110011 => 010001100 => 2
000010001 => 000100010 => 000110011 => 111001100 => 2
000010010 => 000100101 => 100010011 => 011101100 => 2
000010011 => 000100101 => 100010011 => 011101100 => 2
000010100 => 000101001 => 101000011 => 010111100 => 2
000010101 => 000101010 => 000000011 => 111111100 => 1
000010110 => 000101011 => 110000011 => 001111100 => 1
000010111 => 000101011 => 110000011 => 001111100 => 1
000011000 => 000101001 => 101000011 => 010111100 => 2
000011001 => 000101010 => 000000011 => 111111100 => 1
000011010 => 000101101 => 100100011 => 011011100 => 2
000011011 => 000101101 => 100100011 => 011011100 => 2
000011100 => 000101101 => 100100011 => 011011100 => 2
000011101 => 000101110 => 001100011 => 110011100 => 2
000011110 => 000101111 => 111100011 => 000011100 => 1
000011111 => 000101111 => 111100011 => 000011100 => 1
000100000 => 001000001 => 101111001 => 010000110 => 2
000100001 => 001000010 => 000111001 => 111000110 => 2
000100010 => 001000101 => 100011001 => 011100110 => 2
000100011 => 001000101 => 100011001 => 011100110 => 2
000100100 => 001001001 => 101001001 => 010110110 => 3
000100101 => 001001010 => 000001001 => 111110110 => 2
000100110 => 001001011 => 110001001 => 001110110 => 2
000100111 => 001001011 => 110001001 => 001110110 => 2
000101000 => 001010001 => 101100001 => 010011110 => 2
000101001 => 001010010 => 000100001 => 111011110 => 2
000101010 => 001010101 => 100000001 => 011111110 => 1
000101011 => 001010101 => 100000001 => 011111110 => 1
000101100 => 001010101 => 100000001 => 011111110 => 1
000101101 => 001010110 => 001000001 => 110111110 => 2
000101110 => 001010111 => 111000001 => 000111110 => 1
000101111 => 001010111 => 111000001 => 000111110 => 1
000110000 => 001010001 => 101100001 => 010011110 => 2
000110001 => 001010010 => 000100001 => 111011110 => 2
000110010 => 001010101 => 100000001 => 011111110 => 1
000110011 => 001010101 => 100000001 => 011111110 => 1
000110100 => 001011001 => 101010001 => 010101110 => 3
000110101 => 001011010 => 000010001 => 111101110 => 2
000110110 => 001011011 => 110010001 => 001101110 => 2
000110111 => 001011011 => 110010001 => 001101110 => 2
000111000 => 001011001 => 101010001 => 010101110 => 3
000111001 => 001011010 => 000010001 => 111101110 => 2
000111010 => 001011101 => 100110001 => 011001110 => 2
000111011 => 001011101 => 100110001 => 011001110 => 2
000111100 => 001011101 => 100110001 => 011001110 => 2
000111101 => 001011110 => 001110001 => 110001110 => 2
000111110 => 001011111 => 111110001 => 000001110 => 1
000111111 => 001011111 => 111110001 => 000001110 => 1
001000000 => 010000001 => 101111100 => 010000011 => 2
001000001 => 010000010 => 000111100 => 111000011 => 2
001000010 => 010000101 => 100011100 => 011100011 => 2
001000011 => 010000101 => 100011100 => 011100011 => 2
001000100 => 010001001 => 101001100 => 010110011 => 3
001000101 => 010001010 => 000001100 => 111110011 => 2
001000110 => 010001011 => 110001100 => 001110011 => 2
001000111 => 010001011 => 110001100 => 001110011 => 2
001001000 => 010010001 => 101100100 => 010011011 => 3
001001001 => 010010010 => 000100100 => 111011011 => 3
001001010 => 010010101 => 100000100 => 011111011 => 2
001001011 => 010010101 => 100000100 => 011111011 => 2
001001100 => 010010101 => 100000100 => 011111011 => 2
001001101 => 010010110 => 001000100 => 110111011 => 3
001001110 => 010010111 => 111000100 => 000111011 => 2
001001111 => 010010111 => 111000100 => 000111011 => 2
001010000 => 010100001 => 101110000 => 010001111 => 2
001010001 => 010100010 => 000110000 => 111001111 => 2
001010010 => 010100101 => 100010000 => 011101111 => 2
001010011 => 010100101 => 100010000 => 011101111 => 2
001010100 => 010101001 => 101000000 => 010111111 => 2
001010101 => 010101010 => 000000000 => 111111111 => 1
001010110 => 010101011 => 110000000 => 001111111 => 1
001010111 => 010101011 => 110000000 => 001111111 => 1
001011000 => 010101001 => 101000000 => 010111111 => 2
001011001 => 010101010 => 000000000 => 111111111 => 1
001011010 => 010101101 => 100100000 => 011011111 => 2
001011011 => 010101101 => 100100000 => 011011111 => 2
001011100 => 010101101 => 100100000 => 011011111 => 2
001011101 => 010101110 => 001100000 => 110011111 => 2
001011110 => 010101111 => 111100000 => 000011111 => 1
001011111 => 010101111 => 111100000 => 000011111 => 1
001100000 => 010100001 => 101110000 => 010001111 => 2
001100001 => 010100010 => 000110000 => 111001111 => 2
001100010 => 010100101 => 100010000 => 011101111 => 2
001100011 => 010100101 => 100010000 => 011101111 => 2
001100100 => 010101001 => 101000000 => 010111111 => 2
001100101 => 010101010 => 000000000 => 111111111 => 1
001100110 => 010101011 => 110000000 => 001111111 => 1
001100111 => 010101011 => 110000000 => 001111111 => 1
001101000 => 010110001 => 101101000 => 010010111 => 3
001101001 => 010110010 => 000101000 => 111010111 => 3
001101010 => 010110101 => 100001000 => 011110111 => 2
001101011 => 010110101 => 100001000 => 011110111 => 2
001101100 => 010110101 => 100001000 => 011110111 => 2
001101101 => 010110110 => 001001000 => 110110111 => 3
001101110 => 010110111 => 111001000 => 000110111 => 2
001101111 => 010110111 => 111001000 => 000110111 => 2
001110000 => 010110001 => 101101000 => 010010111 => 3
001110001 => 010110010 => 000101000 => 111010111 => 3
001110010 => 010110101 => 100001000 => 011110111 => 2
001110011 => 010110101 => 100001000 => 011110111 => 2
001110100 => 010111001 => 101011000 => 010100111 => 3
001110101 => 010111010 => 000011000 => 111100111 => 2
001110110 => 010111011 => 110011000 => 001100111 => 2
001110111 => 010111011 => 110011000 => 001100111 => 2
001111000 => 010111001 => 101011000 => 010100111 => 3
001111001 => 010111010 => 000011000 => 111100111 => 2
001111010 => 010111101 => 100111000 => 011000111 => 2
001111011 => 010111101 => 100111000 => 011000111 => 2
001111100 => 010111101 => 100111000 => 011000111 => 2
001111101 => 010111110 => 001111000 => 110000111 => 2
001111110 => 010111111 => 111111000 => 000000111 => 1
001111111 => 010111111 => 111111000 => 000000111 => 1
010000000 => 100000001 => 101111110 => 010000001 => 2
010000001 => 100000010 => 000111110 => 111000001 => 2
010000010 => 100000101 => 100011110 => 011100001 => 2
010000011 => 100000101 => 100011110 => 011100001 => 2
010000100 => 100001001 => 101001110 => 010110001 => 3
010000101 => 100001010 => 000001110 => 111110001 => 2
010000110 => 100001011 => 110001110 => 001110001 => 2
010000111 => 100001011 => 110001110 => 001110001 => 2
010001000 => 100010001 => 101100110 => 010011001 => 3
010001001 => 100010010 => 000100110 => 111011001 => 3
010001010 => 100010101 => 100000110 => 011111001 => 2
010001011 => 100010101 => 100000110 => 011111001 => 2
010001100 => 100010101 => 100000110 => 011111001 => 2
010001101 => 100010110 => 001000110 => 110111001 => 3
010001110 => 100010111 => 111000110 => 000111001 => 2
010001111 => 100010111 => 111000110 => 000111001 => 2
010010000 => 100100001 => 101110010 => 010001101 => 3
010010001 => 100100010 => 000110010 => 111001101 => 3
010010010 => 100100101 => 100010010 => 011101101 => 3
010010011 => 100100101 => 100010010 => 011101101 => 3
010010100 => 100101001 => 101000010 => 010111101 => 3
010010101 => 100101010 => 000000010 => 111111101 => 2
010010110 => 100101011 => 110000010 => 001111101 => 2
010010111 => 100101011 => 110000010 => 001111101 => 2
010011000 => 100101001 => 101000010 => 010111101 => 3
010011001 => 100101010 => 000000010 => 111111101 => 2
010011010 => 100101101 => 100100010 => 011011101 => 3
010011011 => 100101101 => 100100010 => 011011101 => 3
010011100 => 100101101 => 100100010 => 011011101 => 3
010011101 => 100101110 => 001100010 => 110011101 => 3
010011110 => 100101111 => 111100010 => 000011101 => 2
010011111 => 100101111 => 111100010 => 000011101 => 2
010100000 => 101000001 => 101111000 => 010000111 => 2
010100001 => 101000010 => 000111000 => 111000111 => 2
010100010 => 101000101 => 100011000 => 011100111 => 2
010100011 => 101000101 => 100011000 => 011100111 => 2
010100100 => 101001001 => 101001000 => 010110111 => 3
010100101 => 101001010 => 000001000 => 111110111 => 2
010100110 => 101001011 => 110001000 => 001110111 => 2
010100111 => 101001011 => 110001000 => 001110111 => 2
010101000 => 101010001 => 101100000 => 010011111 => 2
010101001 => 101010010 => 000100000 => 111011111 => 2
010101010 => 101010101 => 100000000 => 011111111 => 1
010101011 => 101010101 => 100000000 => 011111111 => 1
010101100 => 101010101 => 100000000 => 011111111 => 1
010101101 => 101010110 => 001000000 => 110111111 => 2
010101110 => 101010111 => 111000000 => 000111111 => 1
010101111 => 101010111 => 111000000 => 000111111 => 1
010110000 => 101010001 => 101100000 => 010011111 => 2
010110001 => 101010010 => 000100000 => 111011111 => 2
010110010 => 101010101 => 100000000 => 011111111 => 1
010110011 => 101010101 => 100000000 => 011111111 => 1
010110100 => 101011001 => 101010000 => 010101111 => 3
010110101 => 101011010 => 000010000 => 111101111 => 2
010110110 => 101011011 => 110010000 => 001101111 => 2
010110111 => 101011011 => 110010000 => 001101111 => 2
010111000 => 101011001 => 101010000 => 010101111 => 3
010111001 => 101011010 => 000010000 => 111101111 => 2
010111010 => 101011101 => 100110000 => 011001111 => 2
010111011 => 101011101 => 100110000 => 011001111 => 2
010111100 => 101011101 => 100110000 => 011001111 => 2
010111101 => 101011110 => 001110000 => 110001111 => 2
010111110 => 101011111 => 111110000 => 000001111 => 1
010111111 => 101011111 => 111110000 => 000001111 => 1
011000000 => 101000001 => 101111000 => 010000111 => 2
011000001 => 101000010 => 000111000 => 111000111 => 2
011000010 => 101000101 => 100011000 => 011100111 => 2
011000011 => 101000101 => 100011000 => 011100111 => 2
011000100 => 101001001 => 101001000 => 010110111 => 3
011000101 => 101001010 => 000001000 => 111110111 => 2
011000110 => 101001011 => 110001000 => 001110111 => 2
011000111 => 101001011 => 110001000 => 001110111 => 2
011001000 => 101010001 => 101100000 => 010011111 => 2
011001001 => 101010010 => 000100000 => 111011111 => 2
011001010 => 101010101 => 100000000 => 011111111 => 1
011001011 => 101010101 => 100000000 => 011111111 => 1
011001100 => 101010101 => 100000000 => 011111111 => 1
011001101 => 101010110 => 001000000 => 110111111 => 2
011001110 => 101010111 => 111000000 => 000111111 => 1
011001111 => 101010111 => 111000000 => 000111111 => 1
011010000 => 101100001 => 101110100 => 010001011 => 3
011010001 => 101100010 => 000110100 => 111001011 => 3
011010010 => 101100101 => 100010100 => 011101011 => 3
011010011 => 101100101 => 100010100 => 011101011 => 3
011010100 => 101101001 => 101000100 => 010111011 => 3
011010101 => 101101010 => 000000100 => 111111011 => 2
011010110 => 101101011 => 110000100 => 001111011 => 2
011010111 => 101101011 => 110000100 => 001111011 => 2
011011000 => 101101001 => 101000100 => 010111011 => 3
011011001 => 101101010 => 000000100 => 111111011 => 2
011011010 => 101101101 => 100100100 => 011011011 => 3
011011011 => 101101101 => 100100100 => 011011011 => 3
011011100 => 101101101 => 100100100 => 011011011 => 3
011011101 => 101101110 => 001100100 => 110011011 => 3
011011110 => 101101111 => 111100100 => 000011011 => 2
011011111 => 101101111 => 111100100 => 000011011 => 2
011100000 => 101100001 => 101110100 => 010001011 => 3
011100001 => 101100010 => 000110100 => 111001011 => 3
011100010 => 101100101 => 100010100 => 011101011 => 3
011100011 => 101100101 => 100010100 => 011101011 => 3
011100100 => 101101001 => 101000100 => 010111011 => 3
011100101 => 101101010 => 000000100 => 111111011 => 2
011100110 => 101101011 => 110000100 => 001111011 => 2
011100111 => 101101011 => 110000100 => 001111011 => 2
011101000 => 101110001 => 101101100 => 010010011 => 3
011101001 => 101110010 => 000101100 => 111010011 => 3
011101010 => 101110101 => 100001100 => 011110011 => 2
011101011 => 101110101 => 100001100 => 011110011 => 2
011101100 => 101110101 => 100001100 => 011110011 => 2
011101101 => 101110110 => 001001100 => 110110011 => 3
011101110 => 101110111 => 111001100 => 000110011 => 2
011101111 => 101110111 => 111001100 => 000110011 => 2
011110000 => 101110001 => 101101100 => 010010011 => 3
011110001 => 101110010 => 000101100 => 111010011 => 3
011110010 => 101110101 => 100001100 => 011110011 => 2
011110011 => 101110101 => 100001100 => 011110011 => 2
011110100 => 101111001 => 101011100 => 010100011 => 3
011110101 => 101111010 => 000011100 => 111100011 => 2
011110110 => 101111011 => 110011100 => 001100011 => 2
011110111 => 101111011 => 110011100 => 001100011 => 2
011111000 => 101111001 => 101011100 => 010100011 => 3
011111001 => 101111010 => 000011100 => 111100011 => 2
011111010 => 101111101 => 100111100 => 011000011 => 2
011111011 => 101111101 => 100111100 => 011000011 => 2
011111100 => 101111101 => 100111100 => 011000011 => 2
011111101 => 101111110 => 001111100 => 110000011 => 2
011111110 => 101111111 => 111111100 => 000000011 => 1
011111111 => 101111111 => 111111100 => 000000011 => 1
100000000 => 100000001 => 101111110 => 010000001 => 2
100000001 => 100000010 => 000111110 => 111000001 => 2
100000010 => 100000101 => 100011110 => 011100001 => 2
100000011 => 100000101 => 100011110 => 011100001 => 2
100000100 => 100001001 => 101001110 => 010110001 => 3
100000101 => 100001010 => 000001110 => 111110001 => 2
100000110 => 100001011 => 110001110 => 001110001 => 2
100000111 => 100001011 => 110001110 => 001110001 => 2
100001000 => 100010001 => 101100110 => 010011001 => 3
100001001 => 100010010 => 000100110 => 111011001 => 3
100001010 => 100010101 => 100000110 => 011111001 => 2
100001011 => 100010101 => 100000110 => 011111001 => 2
100001100 => 100010101 => 100000110 => 011111001 => 2
100001101 => 100010110 => 001000110 => 110111001 => 3
100001110 => 100010111 => 111000110 => 000111001 => 2
100001111 => 100010111 => 111000110 => 000111001 => 2
100010000 => 100100001 => 101110010 => 010001101 => 3
100010001 => 100100010 => 000110010 => 111001101 => 3
100010010 => 100100101 => 100010010 => 011101101 => 3
100010011 => 100100101 => 100010010 => 011101101 => 3
100010100 => 100101001 => 101000010 => 010111101 => 3
100010101 => 100101010 => 000000010 => 111111101 => 2
100010110 => 100101011 => 110000010 => 001111101 => 2
100010111 => 100101011 => 110000010 => 001111101 => 2
100011000 => 100101001 => 101000010 => 010111101 => 3
100011001 => 100101010 => 000000010 => 111111101 => 2
100011010 => 100101101 => 100100010 => 011011101 => 3
100011011 => 100101101 => 100100010 => 011011101 => 3
100011100 => 100101101 => 100100010 => 011011101 => 3
100011101 => 100101110 => 001100010 => 110011101 => 3
100011110 => 100101111 => 111100010 => 000011101 => 2
100011111 => 100101111 => 111100010 => 000011101 => 2
100100000 => 101000001 => 101111000 => 010000111 => 2
100100001 => 101000010 => 000111000 => 111000111 => 2
100100010 => 101000101 => 100011000 => 011100111 => 2
100100011 => 101000101 => 100011000 => 011100111 => 2
100100100 => 101001001 => 101001000 => 010110111 => 3
100100101 => 101001010 => 000001000 => 111110111 => 2
100100110 => 101001011 => 110001000 => 001110111 => 2
100100111 => 101001011 => 110001000 => 001110111 => 2
100101000 => 101010001 => 101100000 => 010011111 => 2
100101001 => 101010010 => 000100000 => 111011111 => 2
100101010 => 101010101 => 100000000 => 011111111 => 1
100101011 => 101010101 => 100000000 => 011111111 => 1
100101100 => 101010101 => 100000000 => 011111111 => 1
100101101 => 101010110 => 001000000 => 110111111 => 2
100101110 => 101010111 => 111000000 => 000111111 => 1
100101111 => 101010111 => 111000000 => 000111111 => 1
100110000 => 101010001 => 101100000 => 010011111 => 2
100110001 => 101010010 => 000100000 => 111011111 => 2
100110010 => 101010101 => 100000000 => 011111111 => 1
100110011 => 101010101 => 100000000 => 011111111 => 1
100110100 => 101011001 => 101010000 => 010101111 => 3
100110101 => 101011010 => 000010000 => 111101111 => 2
100110110 => 101011011 => 110010000 => 001101111 => 2
100110111 => 101011011 => 110010000 => 001101111 => 2
100111000 => 101011001 => 101010000 => 010101111 => 3
100111001 => 101011010 => 000010000 => 111101111 => 2
100111010 => 101011101 => 100110000 => 011001111 => 2
100111011 => 101011101 => 100110000 => 011001111 => 2
100111100 => 101011101 => 100110000 => 011001111 => 2
100111101 => 101011110 => 001110000 => 110001111 => 2
100111110 => 101011111 => 111110000 => 000001111 => 1
100111111 => 101011111 => 111110000 => 000001111 => 1
101000000 => 110000001 => 101111101 => 010000010 => 2
101000001 => 110000010 => 000111101 => 111000010 => 2
101000010 => 110000101 => 100011101 => 011100010 => 2
101000011 => 110000101 => 100011101 => 011100010 => 2
101000100 => 110001001 => 101001101 => 010110010 => 3
101000101 => 110001010 => 000001101 => 111110010 => 2
101000110 => 110001011 => 110001101 => 001110010 => 2
101000111 => 110001011 => 110001101 => 001110010 => 2
101001000 => 110010001 => 101100101 => 010011010 => 3
101001001 => 110010010 => 000100101 => 111011010 => 3
101001010 => 110010101 => 100000101 => 011111010 => 2
101001011 => 110010101 => 100000101 => 011111010 => 2
101001100 => 110010101 => 100000101 => 011111010 => 2
101001101 => 110010110 => 001000101 => 110111010 => 3
101001110 => 110010111 => 111000101 => 000111010 => 2
101001111 => 110010111 => 111000101 => 000111010 => 2
101010000 => 110100001 => 101110001 => 010001110 => 2
101010001 => 110100010 => 000110001 => 111001110 => 2
101010010 => 110100101 => 100010001 => 011101110 => 2
101010011 => 110100101 => 100010001 => 011101110 => 2
101010100 => 110101001 => 101000001 => 010111110 => 2
101010101 => 110101010 => 000000001 => 111111110 => 1
101010110 => 110101011 => 110000001 => 001111110 => 1
101010111 => 110101011 => 110000001 => 001111110 => 1
101011000 => 110101001 => 101000001 => 010111110 => 2
101011001 => 110101010 => 000000001 => 111111110 => 1
101011010 => 110101101 => 100100001 => 011011110 => 2
101011011 => 110101101 => 100100001 => 011011110 => 2
101011100 => 110101101 => 100100001 => 011011110 => 2
101011101 => 110101110 => 001100001 => 110011110 => 2
101011110 => 110101111 => 111100001 => 000011110 => 1
101011111 => 110101111 => 111100001 => 000011110 => 1
101100000 => 110100001 => 101110001 => 010001110 => 2
101100001 => 110100010 => 000110001 => 111001110 => 2
101100010 => 110100101 => 100010001 => 011101110 => 2
101100011 => 110100101 => 100010001 => 011101110 => 2
101100100 => 110101001 => 101000001 => 010111110 => 2
101100101 => 110101010 => 000000001 => 111111110 => 1
101100110 => 110101011 => 110000001 => 001111110 => 1
101100111 => 110101011 => 110000001 => 001111110 => 1
101101000 => 110110001 => 101101001 => 010010110 => 3
101101001 => 110110010 => 000101001 => 111010110 => 3
101101010 => 110110101 => 100001001 => 011110110 => 2
101101011 => 110110101 => 100001001 => 011110110 => 2
101101100 => 110110101 => 100001001 => 011110110 => 2
101101101 => 110110110 => 001001001 => 110110110 => 3
101101110 => 110110111 => 111001001 => 000110110 => 2
101101111 => 110110111 => 111001001 => 000110110 => 2
101110000 => 110110001 => 101101001 => 010010110 => 3
101110001 => 110110010 => 000101001 => 111010110 => 3
101110010 => 110110101 => 100001001 => 011110110 => 2
101110011 => 110110101 => 100001001 => 011110110 => 2
101110100 => 110111001 => 101011001 => 010100110 => 3
101110101 => 110111010 => 000011001 => 111100110 => 2
101110110 => 110111011 => 110011001 => 001100110 => 2
101110111 => 110111011 => 110011001 => 001100110 => 2
101111000 => 110111001 => 101011001 => 010100110 => 3
101111001 => 110111010 => 000011001 => 111100110 => 2
101111010 => 110111101 => 100111001 => 011000110 => 2
101111011 => 110111101 => 100111001 => 011000110 => 2
101111100 => 110111101 => 100111001 => 011000110 => 2
101111101 => 110111110 => 001111001 => 110000110 => 2
101111110 => 110111111 => 111111001 => 000000110 => 1
101111111 => 110111111 => 111111001 => 000000110 => 1
110000000 => 110000001 => 101111101 => 010000010 => 2
110000001 => 110000010 => 000111101 => 111000010 => 2
110000010 => 110000101 => 100011101 => 011100010 => 2
110000011 => 110000101 => 100011101 => 011100010 => 2
110000100 => 110001001 => 101001101 => 010110010 => 3
110000101 => 110001010 => 000001101 => 111110010 => 2
110000110 => 110001011 => 110001101 => 001110010 => 2
110000111 => 110001011 => 110001101 => 001110010 => 2
110001000 => 110010001 => 101100101 => 010011010 => 3
110001001 => 110010010 => 000100101 => 111011010 => 3
110001010 => 110010101 => 100000101 => 011111010 => 2
110001011 => 110010101 => 100000101 => 011111010 => 2
110001100 => 110010101 => 100000101 => 011111010 => 2
110001101 => 110010110 => 001000101 => 110111010 => 3
110001110 => 110010111 => 111000101 => 000111010 => 2
110001111 => 110010111 => 111000101 => 000111010 => 2
110010000 => 110100001 => 101110001 => 010001110 => 2
110010001 => 110100010 => 000110001 => 111001110 => 2
110010010 => 110100101 => 100010001 => 011101110 => 2
110010011 => 110100101 => 100010001 => 011101110 => 2
110010100 => 110101001 => 101000001 => 010111110 => 2
110010101 => 110101010 => 000000001 => 111111110 => 1
110010110 => 110101011 => 110000001 => 001111110 => 1
110010111 => 110101011 => 110000001 => 001111110 => 1
110011000 => 110101001 => 101000001 => 010111110 => 2
110011001 => 110101010 => 000000001 => 111111110 => 1
110011010 => 110101101 => 100100001 => 011011110 => 2
110011011 => 110101101 => 100100001 => 011011110 => 2
110011100 => 110101101 => 100100001 => 011011110 => 2
110011101 => 110101110 => 001100001 => 110011110 => 2
110011110 => 110101111 => 111100001 => 000011110 => 1
110011111 => 110101111 => 111100001 => 000011110 => 1
110100000 => 111000001 => 101111011 => 010000100 => 2
110100001 => 111000010 => 000111011 => 111000100 => 2
110100010 => 111000101 => 100011011 => 011100100 => 2
110100011 => 111000101 => 100011011 => 011100100 => 2
110100100 => 111001001 => 101001011 => 010110100 => 3
110100101 => 111001010 => 000001011 => 111110100 => 2
110100110 => 111001011 => 110001011 => 001110100 => 2
110100111 => 111001011 => 110001011 => 001110100 => 2
110101000 => 111010001 => 101100011 => 010011100 => 2
110101001 => 111010010 => 000100011 => 111011100 => 2
110101010 => 111010101 => 100000011 => 011111100 => 1
110101011 => 111010101 => 100000011 => 011111100 => 1
110101100 => 111010101 => 100000011 => 011111100 => 1
110101101 => 111010110 => 001000011 => 110111100 => 2
110101110 => 111010111 => 111000011 => 000111100 => 1
110101111 => 111010111 => 111000011 => 000111100 => 1
110110000 => 111010001 => 101100011 => 010011100 => 2
110110001 => 111010010 => 000100011 => 111011100 => 2
110110010 => 111010101 => 100000011 => 011111100 => 1
110110011 => 111010101 => 100000011 => 011111100 => 1
110110100 => 111011001 => 101010011 => 010101100 => 3
110110101 => 111011010 => 000010011 => 111101100 => 2
110110110 => 111011011 => 110010011 => 001101100 => 2
110110111 => 111011011 => 110010011 => 001101100 => 2
110111000 => 111011001 => 101010011 => 010101100 => 3
110111001 => 111011010 => 000010011 => 111101100 => 2
110111010 => 111011101 => 100110011 => 011001100 => 2
110111011 => 111011101 => 100110011 => 011001100 => 2
110111100 => 111011101 => 100110011 => 011001100 => 2
110111101 => 111011110 => 001110011 => 110001100 => 2
110111110 => 111011111 => 111110011 => 000001100 => 1
110111111 => 111011111 => 111110011 => 000001100 => 1
111000000 => 111000001 => 101111011 => 010000100 => 2
111000001 => 111000010 => 000111011 => 111000100 => 2
111000010 => 111000101 => 100011011 => 011100100 => 2
111000011 => 111000101 => 100011011 => 011100100 => 2
111000100 => 111001001 => 101001011 => 010110100 => 3
111000101 => 111001010 => 000001011 => 111110100 => 2
111000110 => 111001011 => 110001011 => 001110100 => 2
111000111 => 111001011 => 110001011 => 001110100 => 2
111001000 => 111010001 => 101100011 => 010011100 => 2
111001001 => 111010010 => 000100011 => 111011100 => 2
111001010 => 111010101 => 100000011 => 011111100 => 1
111001011 => 111010101 => 100000011 => 011111100 => 1
111001100 => 111010101 => 100000011 => 011111100 => 1
111001101 => 111010110 => 001000011 => 110111100 => 2
111001110 => 111010111 => 111000011 => 000111100 => 1
111001111 => 111010111 => 111000011 => 000111100 => 1
111010000 => 111100001 => 101110111 => 010001000 => 2
111010001 => 111100010 => 000110111 => 111001000 => 2
111010010 => 111100101 => 100010111 => 011101000 => 2
111010011 => 111100101 => 100010111 => 011101000 => 2
111010100 => 111101001 => 101000111 => 010111000 => 2
111010101 => 111101010 => 000000111 => 111111000 => 1
111010110 => 111101011 => 110000111 => 001111000 => 1
111010111 => 111101011 => 110000111 => 001111000 => 1
111011000 => 111101001 => 101000111 => 010111000 => 2
111011001 => 111101010 => 000000111 => 111111000 => 1
111011010 => 111101101 => 100100111 => 011011000 => 2
111011011 => 111101101 => 100100111 => 011011000 => 2
111011100 => 111101101 => 100100111 => 011011000 => 2
111011101 => 111101110 => 001100111 => 110011000 => 2
111011110 => 111101111 => 111100111 => 000011000 => 1
111011111 => 111101111 => 111100111 => 000011000 => 1
111100000 => 111100001 => 101110111 => 010001000 => 2
111100001 => 111100010 => 000110111 => 111001000 => 2
111100010 => 111100101 => 100010111 => 011101000 => 2
111100011 => 111100101 => 100010111 => 011101000 => 2
111100100 => 111101001 => 101000111 => 010111000 => 2
111100101 => 111101010 => 000000111 => 111111000 => 1
111100110 => 111101011 => 110000111 => 001111000 => 1
111100111 => 111101011 => 110000111 => 001111000 => 1
111101000 => 111110001 => 101101111 => 010010000 => 2
111101001 => 111110010 => 000101111 => 111010000 => 2
111101010 => 111110101 => 100001111 => 011110000 => 1
111101011 => 111110101 => 100001111 => 011110000 => 1
111101100 => 111110101 => 100001111 => 011110000 => 1
111101101 => 111110110 => 001001111 => 110110000 => 2
111101110 => 111110111 => 111001111 => 000110000 => 1
111101111 => 111110111 => 111001111 => 000110000 => 1
111110000 => 111110001 => 101101111 => 010010000 => 2
111110001 => 111110010 => 000101111 => 111010000 => 2
111110010 => 111110101 => 100001111 => 011110000 => 1
111110011 => 111110101 => 100001111 => 011110000 => 1
111110100 => 111111001 => 101011111 => 010100000 => 2
111110101 => 111111010 => 000011111 => 111100000 => 1
111110110 => 111111011 => 110011111 => 001100000 => 1
111110111 => 111111011 => 110011111 => 001100000 => 1
111111000 => 111111001 => 101011111 => 010100000 => 2
111111001 => 111111010 => 000011111 => 111100000 => 1
111111010 => 111111101 => 100111111 => 011000000 => 1
111111011 => 111111101 => 100111111 => 011000000 => 1
111111100 => 111111101 => 100111111 => 011000000 => 1
111111101 => 111111110 => 001111111 => 110000000 => 1
111111110 => 111111111 => 111111111 => 000000000 => 0
111111111 => 111111111 => 111111111 => 000000000 => 0
1111111111 => 1111111111 => 1111111111 => 0000000000 => 0
1111111110 => 1111111111 => 1111111111 => 0000000000 => 0
1100110001 => 1101010010 => 0001000001 => 1110111110 => 2
1100101001 => 1101010010 => 0001000001 => 1110111110 => 2
1011001001 => 1101010010 => 0001000001 => 1110111110 => 2
1010111110 => 1101011111 => 1111100001 => 0000011110 => 1
1010110001 => 1101010010 => 0001000001 => 1110111110 => 2
1010101001 => 1101010010 => 0001000001 => 1110111110 => 2
1001001110 => 1010010111 => 1110001000 => 0001110111 => 2
1000101011 => 1001010101 => 1000000010 => 0111111101 => 2
1000000000 => 1000000001 => 1011111110 => 0100000001 => 2
10010101010 => 10101010101 => 10000000000 => 01111111111 => 1
0100110011 => 1001010101 => 1000000010 => 0111111101 => 2
0100101011 => 1001010101 => 1000000010 => 0111111101 => 2
0011001011 => 0101010101 => 1000000000 => 0111111111 => 1
0010110011 => 0101010101 => 1000000000 => 0111111111 => 1
0010101011 => 0101010101 => 1000000000 => 0111111111 => 1
0010001111 => 0100010111 => 1110001100 => 0001110011 => 2
0001001111 => 0010010111 => 1110001001 => 0001110110 => 2
0000111011 => 0001011101 => 1001100011 => 0110011100 => 2
0000101111 => 0001010111 => 1110000011 => 0001111100 => 1
0000011111 => 0000101111 => 1111000111 => 0000111000 => 1
010100001111 => 101000010111 => 111000111000 => 000111000111 => 2
111011000001 => 111101000010 => 000111000111 => 111000111000 => 2
111010010001 => 111100100010 => 000110010111 => 111001101000 => 3
111010000101 => 111100001010 => 000001110111 => 111110001000 => 2
0000000000 => 0000000001 => 1011111111 => 0100000000 => 1
0000011110 => 0000101111 => 1111000111 => 0000111000 => 1
0001001110 => 0010010111 => 1110001001 => 0001110110 => 2
0110011000 => 1010101001 => 1010000000 => 0101111111 => 2
0100110010 => 1001010101 => 1000000010 => 0111111101 => 2
0101101000 => 1010110001 => 1011010000 => 0100101111 => 3
0010101010 => 0101010101 => 1000000000 => 0111111111 => 1
0010101100 => 0101010101 => 1000000000 => 0111111111 => 1
0010110100 => 0101011001 => 1010100000 => 0101011111 => 3
0101010100 => 1010101001 => 1010000000 => 0101111111 => 2
0010100000 => 0101000001 => 1011110000 => 0100001111 => 2
01010101011 => 10101010101 => 10000000000 => 01111111111 => 1
0011111110 => 0101111111 => 1111111000 => 0000000111 => 1
00000000000 => 00000000001 => 10111111111 => 01000000000 => 1
0000001010 => 0000010101 => 1000001111 => 0111110000 => 1
0000101110 => 0001010111 => 1110000011 => 0001111100 => 1
0010111110 => 0101011111 => 1111100000 => 0000011111 => 1
0010110010 => 0101010101 => 1000000000 => 0111111111 => 1
0010111000 => 0101011001 => 1010100000 => 0101011111 => 3
0011001010 => 0101010101 => 1000000000 => 0111111111 => 1
0011001100 => 0101010101 => 1000000000 => 0111111111 => 1
0011101000 => 0101110001 => 1011011000 => 0100100111 => 3
0011110000 => 0101110001 => 1011011000 => 0100100111 => 3
0100101010 => 1001010101 => 1000000010 => 0111111101 => 2
0100101100 => 1001010101 => 1000000010 => 0111111101 => 2
0101011000 => 1010101001 => 1010000000 => 0101111111 => 2
0101100100 => 1010101001 => 1010000000 => 0101111111 => 2
0101110000 => 1010110001 => 1011010000 => 0100101111 => 3
0110010100 => 1010101001 => 1010000000 => 0101111111 => 2
010011101000 => 100101110001 => 101101100010 => 010010011101 => 4
010011110000 => 100101110001 => 101101100010 => 010010011101 => 4
010111010000 => 101011100001 => 101110110000 => 010001001111 => 3
010111100000 => 101011100001 => 101110110000 => 010001001111 => 3
011011010000 => 101101100001 => 101110100100 => 010001011011 => 4
011011100000 => 101101100001 => 101110100100 => 010001011011 => 4
011101001000 => 101110010001 => 101100101100 => 010011010011 => 4
011101010000 => 101110100001 => 101110001100 => 010001110011 => 3
011101100000 => 101110100001 => 101110001100 => 010001110011 => 3
011110001000 => 101110010001 => 101100101100 => 010011010011 => 4
011110010000 => 101110100001 => 101110001100 => 010001110011 => 3
10101010101 => 11010101010 => 00000000001 => 11111111110 => 1
01001010101 => 10010101010 => 00000000010 => 11111111101 => 2
01010101010 => 10101010101 => 10000000000 => 01111111111 => 1
00101010100 => 01010101001 => 10100000000 => 01011111111 => 2
0100000000 => 1000000001 => 1011111110 => 0100000001 => 2
0110111111 => 1011011111 => 1111100100 => 0000011011 => 2
0000000101 => 0000001010 => 0000011111 => 1111100000 => 1
0000001101 => 0000010110 => 0010001111 => 1101110000 => 2
0000011101 => 0000101110 => 0011000111 => 1100111000 => 2
0000001001 => 0000010010 => 0001001111 => 1110110000 => 2
110110100001 => 111011000010 => 000111010011 => 111000101100 => 3
110111000001 => 111011000010 => 000111010011 => 111000101100 => 3
111010001001 => 111100010010 => 000100110111 => 111011001000 => 3
111010100001 => 111101000010 => 000111000111 => 111000111000 => 2
111100000101 => 111100001010 => 000001110111 => 111110001000 => 2
111100001001 => 111100010010 => 000100110111 => 111011001000 => 3
111100010001 => 111100100010 => 000110010111 => 111001101000 => 3
111100100001 => 111101000010 => 000111000111 => 111000111000 => 2
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Generating function
click to show known generating functions
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,2 2,6 2,12,2 2,22,8 2,36,26 2,56,66,4 2,82,150,22 2,118,302,90
$F_{1} = 2$
$F_{2} = 2 + 2\ q$
$F_{3} = 2 + 6\ q$
$F_{4} = 2 + 12\ q + 2\ q^{2}$
$F_{5} = 2 + 22\ q + 8\ q^{2}$
$F_{6} = 2 + 36\ q + 26\ q^{2}$
$F_{7} = 2 + 56\ q + 66\ q^{2} + 4\ q^{3}$
$F_{8} = 2 + 82\ q + 150\ q^{2} + 22\ q^{3}$
$F_{9} = 2 + 118\ q + 302\ q^{2} + 90\ q^{3}$
Description
The number of runs of ones in a binary word.
Map
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
Map
flag zeros to zeros
Description
Return a binary word of the same length, such that the number of zeros equals the number of occurrences of $10$ in the word obtained from the original word by prepending the reverse of the complement.
For example, the image of the word $w=1\dots 1$ is $1\dots 1$, because $0\dots 01\dots 1$ has no occurrences of $10$. The words $10\dots 10$ and $010\dots 10$ have image $0\dots 0$.
For example, the image of the word $w=1\dots 1$ is $1\dots 1$, because $0\dots 01\dots 1$ has no occurrences of $10$. The words $10\dots 10$ and $010\dots 10$ have image $0\dots 0$.
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