Identifier
-
Mp00234:
Binary words
—valleys-to-peaks⟶
Binary words
Mp00224: Binary words —runsort⟶ Binary words
St000347: Binary words ⟶ ℤ
Values
0 => 1 => 1 => 0
1 => 1 => 1 => 0
00 => 01 => 01 => 0
01 => 10 => 01 => 0
10 => 11 => 11 => 0
11 => 11 => 11 => 0
000 => 001 => 001 => 0
001 => 010 => 001 => 0
010 => 101 => 011 => 0
011 => 101 => 011 => 0
100 => 101 => 011 => 0
101 => 110 => 011 => 0
110 => 111 => 111 => 0
111 => 111 => 111 => 0
0000 => 0001 => 0001 => 0
0001 => 0010 => 0001 => 0
0010 => 0101 => 0101 => 1
0011 => 0101 => 0101 => 1
0100 => 1001 => 0011 => 0
0101 => 1010 => 0011 => 0
0110 => 1011 => 0111 => 0
0111 => 1011 => 0111 => 0
1000 => 1001 => 0011 => 0
1001 => 1010 => 0011 => 0
1010 => 1101 => 0111 => 0
1011 => 1101 => 0111 => 0
1100 => 1101 => 0111 => 0
1101 => 1110 => 0111 => 0
1110 => 1111 => 1111 => 0
1111 => 1111 => 1111 => 0
00000 => 00001 => 00001 => 0
00001 => 00010 => 00001 => 0
00010 => 00101 => 00101 => 1
00011 => 00101 => 00101 => 1
00100 => 01001 => 00101 => 1
00101 => 01010 => 00101 => 1
00110 => 01011 => 01011 => 1
00111 => 01011 => 01011 => 1
01000 => 10001 => 00011 => 0
01001 => 10010 => 00011 => 0
01010 => 10101 => 01011 => 1
01011 => 10101 => 01011 => 1
01100 => 10101 => 01011 => 1
01101 => 10110 => 00111 => 0
01110 => 10111 => 01111 => 0
01111 => 10111 => 01111 => 0
10000 => 10001 => 00011 => 0
10001 => 10010 => 00011 => 0
10010 => 10101 => 01011 => 1
10011 => 10101 => 01011 => 1
10100 => 11001 => 00111 => 0
10101 => 11010 => 00111 => 0
10110 => 11011 => 01111 => 0
10111 => 11011 => 01111 => 0
11000 => 11001 => 00111 => 0
11001 => 11010 => 00111 => 0
11010 => 11101 => 01111 => 0
11011 => 11101 => 01111 => 0
11100 => 11101 => 01111 => 0
11101 => 11110 => 01111 => 0
11110 => 11111 => 11111 => 0
11111 => 11111 => 11111 => 0
000000 => 000001 => 000001 => 0
000001 => 000010 => 000001 => 0
000010 => 000101 => 000101 => 1
000011 => 000101 => 000101 => 1
000100 => 001001 => 001001 => 3
000101 => 001010 => 000101 => 1
000110 => 001011 => 001011 => 1
000111 => 001011 => 001011 => 1
001000 => 010001 => 000101 => 1
001001 => 010010 => 000101 => 1
001010 => 010101 => 010101 => 5
001011 => 010101 => 010101 => 5
001100 => 010101 => 010101 => 5
001101 => 010110 => 001011 => 1
001110 => 010111 => 010111 => 1
001111 => 010111 => 010111 => 1
010000 => 100001 => 000011 => 0
010001 => 100010 => 000011 => 0
010010 => 100101 => 001011 => 1
010011 => 100101 => 001011 => 1
010100 => 101001 => 001011 => 1
010101 => 101010 => 001011 => 1
010110 => 101011 => 010111 => 1
010111 => 101011 => 010111 => 1
011000 => 101001 => 001011 => 1
011001 => 101010 => 001011 => 1
011010 => 101101 => 010111 => 1
011011 => 101101 => 010111 => 1
011100 => 101101 => 010111 => 1
011101 => 101110 => 001111 => 0
011110 => 101111 => 011111 => 0
011111 => 101111 => 011111 => 0
100000 => 100001 => 000011 => 0
100001 => 100010 => 000011 => 0
100010 => 100101 => 001011 => 1
100011 => 100101 => 001011 => 1
100100 => 101001 => 001011 => 1
100101 => 101010 => 001011 => 1
100110 => 101011 => 010111 => 1
>>> Load all 1184 entries. <<<100111 => 101011 => 010111 => 1
101000 => 110001 => 000111 => 0
101001 => 110010 => 000111 => 0
101010 => 110101 => 010111 => 1
101011 => 110101 => 010111 => 1
101100 => 110101 => 010111 => 1
101101 => 110110 => 001111 => 0
101110 => 110111 => 011111 => 0
101111 => 110111 => 011111 => 0
110000 => 110001 => 000111 => 0
110001 => 110010 => 000111 => 0
110010 => 110101 => 010111 => 1
110011 => 110101 => 010111 => 1
110100 => 111001 => 001111 => 0
110101 => 111010 => 001111 => 0
110110 => 111011 => 011111 => 0
110111 => 111011 => 011111 => 0
111000 => 111001 => 001111 => 0
111001 => 111010 => 001111 => 0
111010 => 111101 => 011111 => 0
111011 => 111101 => 011111 => 0
111100 => 111101 => 011111 => 0
111101 => 111110 => 011111 => 0
111110 => 111111 => 111111 => 0
111111 => 111111 => 111111 => 0
0000000 => 0000001 => 0000001 => 0
0000001 => 0000010 => 0000001 => 0
0000010 => 0000101 => 0000101 => 1
0000011 => 0000101 => 0000101 => 1
0000100 => 0001001 => 0001001 => 3
0000101 => 0001010 => 0000101 => 1
0000110 => 0001011 => 0001011 => 1
0000111 => 0001011 => 0001011 => 1
0001000 => 0010001 => 0001001 => 3
0001001 => 0010010 => 0001001 => 3
0001010 => 0010101 => 0010101 => 5
0001011 => 0010101 => 0010101 => 5
0001100 => 0010101 => 0010101 => 5
0001101 => 0010110 => 0001011 => 1
0001110 => 0010111 => 0010111 => 1
0001111 => 0010111 => 0010111 => 1
0010000 => 0100001 => 0000101 => 1
0010001 => 0100010 => 0000101 => 1
0010010 => 0100101 => 0010101 => 5
0010011 => 0100101 => 0010101 => 5
0010100 => 0101001 => 0010101 => 5
0010101 => 0101010 => 0010101 => 5
0010110 => 0101011 => 0101011 => 5
0010111 => 0101011 => 0101011 => 5
0011000 => 0101001 => 0010101 => 5
0011001 => 0101010 => 0010101 => 5
0011010 => 0101101 => 0101011 => 5
0011011 => 0101101 => 0101011 => 5
0011100 => 0101101 => 0101011 => 5
0011101 => 0101110 => 0010111 => 1
0011110 => 0101111 => 0101111 => 1
0011111 => 0101111 => 0101111 => 1
0100000 => 1000001 => 0000011 => 0
0100001 => 1000010 => 0000011 => 0
0100010 => 1000101 => 0001011 => 1
0100011 => 1000101 => 0001011 => 1
0100100 => 1001001 => 0010011 => 3
0100101 => 1001010 => 0001011 => 1
0100110 => 1001011 => 0010111 => 1
0100111 => 1001011 => 0010111 => 1
0101000 => 1010001 => 0001011 => 1
0101001 => 1010010 => 0001011 => 1
0101010 => 1010101 => 0101011 => 5
0101011 => 1010101 => 0101011 => 5
0101100 => 1010101 => 0101011 => 5
0101101 => 1010110 => 0010111 => 1
0101110 => 1010111 => 0101111 => 1
0101111 => 1010111 => 0101111 => 1
0110000 => 1010001 => 0001011 => 1
0110001 => 1010010 => 0001011 => 1
0110010 => 1010101 => 0101011 => 5
0110011 => 1010101 => 0101011 => 5
0110100 => 1011001 => 0010111 => 1
0110101 => 1011010 => 0010111 => 1
0110110 => 1011011 => 0110111 => 3
0110111 => 1011011 => 0110111 => 3
0111000 => 1011001 => 0010111 => 1
0111001 => 1011010 => 0010111 => 1
0111010 => 1011101 => 0101111 => 1
0111011 => 1011101 => 0101111 => 1
0111100 => 1011101 => 0101111 => 1
0111101 => 1011110 => 0011111 => 0
0111110 => 1011111 => 0111111 => 0
0111111 => 1011111 => 0111111 => 0
1000000 => 1000001 => 0000011 => 0
1000001 => 1000010 => 0000011 => 0
1000010 => 1000101 => 0001011 => 1
1000011 => 1000101 => 0001011 => 1
1000100 => 1001001 => 0010011 => 3
1000101 => 1001010 => 0001011 => 1
1000110 => 1001011 => 0010111 => 1
1000111 => 1001011 => 0010111 => 1
1001000 => 1010001 => 0001011 => 1
1001001 => 1010010 => 0001011 => 1
1001010 => 1010101 => 0101011 => 5
1001011 => 1010101 => 0101011 => 5
1001100 => 1010101 => 0101011 => 5
1001101 => 1010110 => 0010111 => 1
1001110 => 1010111 => 0101111 => 1
1001111 => 1010111 => 0101111 => 1
1010000 => 1100001 => 0000111 => 0
1010001 => 1100010 => 0000111 => 0
1010010 => 1100101 => 0010111 => 1
1010011 => 1100101 => 0010111 => 1
1010100 => 1101001 => 0010111 => 1
1010101 => 1101010 => 0010111 => 1
1010110 => 1101011 => 0101111 => 1
1010111 => 1101011 => 0101111 => 1
1011000 => 1101001 => 0010111 => 1
1011001 => 1101010 => 0010111 => 1
1011010 => 1101101 => 0101111 => 1
1011011 => 1101101 => 0101111 => 1
1011100 => 1101101 => 0101111 => 1
1011101 => 1101110 => 0011111 => 0
1011110 => 1101111 => 0111111 => 0
1011111 => 1101111 => 0111111 => 0
1100000 => 1100001 => 0000111 => 0
1100001 => 1100010 => 0000111 => 0
1100010 => 1100101 => 0010111 => 1
1100011 => 1100101 => 0010111 => 1
1100100 => 1101001 => 0010111 => 1
1100101 => 1101010 => 0010111 => 1
1100110 => 1101011 => 0101111 => 1
1100111 => 1101011 => 0101111 => 1
1101000 => 1110001 => 0001111 => 0
1101001 => 1110010 => 0001111 => 0
1101010 => 1110101 => 0101111 => 1
1101011 => 1110101 => 0101111 => 1
1101100 => 1110101 => 0101111 => 1
1101101 => 1110110 => 0011111 => 0
1101110 => 1110111 => 0111111 => 0
1101111 => 1110111 => 0111111 => 0
1110000 => 1110001 => 0001111 => 0
1110001 => 1110010 => 0001111 => 0
1110010 => 1110101 => 0101111 => 1
1110011 => 1110101 => 0101111 => 1
1110100 => 1111001 => 0011111 => 0
1110101 => 1111010 => 0011111 => 0
1110110 => 1111011 => 0111111 => 0
1110111 => 1111011 => 0111111 => 0
1111000 => 1111001 => 0011111 => 0
1111001 => 1111010 => 0011111 => 0
1111010 => 1111101 => 0111111 => 0
1111011 => 1111101 => 0111111 => 0
1111100 => 1111101 => 0111111 => 0
1111101 => 1111110 => 0111111 => 0
1111110 => 1111111 => 1111111 => 0
1111111 => 1111111 => 1111111 => 0
00000000 => 00000001 => 00000001 => 0
00000001 => 00000010 => 00000001 => 0
00000010 => 00000101 => 00000101 => 1
00000011 => 00000101 => 00000101 => 1
00000100 => 00001001 => 00001001 => 3
00000101 => 00001010 => 00000101 => 1
00000110 => 00001011 => 00001011 => 1
00000111 => 00001011 => 00001011 => 1
00001000 => 00010001 => 00010001 => 6
00001001 => 00010010 => 00001001 => 3
00001010 => 00010101 => 00010101 => 5
00001011 => 00010101 => 00010101 => 5
00001100 => 00010101 => 00010101 => 5
00001101 => 00010110 => 00001011 => 1
00001110 => 00010111 => 00010111 => 1
00001111 => 00010111 => 00010111 => 1
00010000 => 00100001 => 00001001 => 3
00010001 => 00100010 => 00001001 => 3
00010010 => 00100101 => 00100101 => 8
00010011 => 00100101 => 00100101 => 8
00010100 => 00101001 => 00100101 => 8
00010101 => 00101010 => 00010101 => 5
00010110 => 00101011 => 00101011 => 5
00010111 => 00101011 => 00101011 => 5
00011000 => 00101001 => 00100101 => 8
00011001 => 00101010 => 00010101 => 5
00011010 => 00101101 => 00101011 => 5
00011011 => 00101101 => 00101011 => 5
00011100 => 00101101 => 00101011 => 5
00011101 => 00101110 => 00010111 => 1
00011110 => 00101111 => 00101111 => 1
00011111 => 00101111 => 00101111 => 1
00100000 => 01000001 => 00000101 => 1
00100001 => 01000010 => 00000101 => 1
00100010 => 01000101 => 00010101 => 5
00100011 => 01000101 => 00010101 => 5
00100100 => 01001001 => 00100101 => 8
00100101 => 01001010 => 00010101 => 5
00100110 => 01001011 => 00101011 => 5
00100111 => 01001011 => 00101011 => 5
00101000 => 01010001 => 00010101 => 5
00101001 => 01010010 => 00010101 => 5
00101010 => 01010101 => 01010101 => 14
00101011 => 01010101 => 01010101 => 14
00101100 => 01010101 => 01010101 => 14
00101101 => 01010110 => 00101011 => 5
00101110 => 01010111 => 01010111 => 5
00101111 => 01010111 => 01010111 => 5
00110000 => 01010001 => 00010101 => 5
00110001 => 01010010 => 00010101 => 5
00110010 => 01010101 => 01010101 => 14
00110011 => 01010101 => 01010101 => 14
00110100 => 01011001 => 00101011 => 5
00110101 => 01011010 => 00101011 => 5
00110110 => 01011011 => 01011011 => 8
00110111 => 01011011 => 01011011 => 8
00111000 => 01011001 => 00101011 => 5
00111001 => 01011010 => 00101011 => 5
00111010 => 01011101 => 01010111 => 5
00111011 => 01011101 => 01010111 => 5
00111100 => 01011101 => 01010111 => 5
00111101 => 01011110 => 00101111 => 1
00111110 => 01011111 => 01011111 => 1
00111111 => 01011111 => 01011111 => 1
01000000 => 10000001 => 00000011 => 0
01000001 => 10000010 => 00000011 => 0
01000010 => 10000101 => 00001011 => 1
01000011 => 10000101 => 00001011 => 1
01000100 => 10001001 => 00010011 => 3
01000101 => 10001010 => 00001011 => 1
01000110 => 10001011 => 00010111 => 1
01000111 => 10001011 => 00010111 => 1
01001000 => 10010001 => 00010011 => 3
01001001 => 10010010 => 00010011 => 3
01001010 => 10010101 => 00101011 => 5
01001011 => 10010101 => 00101011 => 5
01001100 => 10010101 => 00101011 => 5
01001101 => 10010110 => 00010111 => 1
01001110 => 10010111 => 00101111 => 1
01001111 => 10010111 => 00101111 => 1
01010000 => 10100001 => 00001011 => 1
01010001 => 10100010 => 00001011 => 1
01010010 => 10100101 => 00101011 => 5
01010011 => 10100101 => 00101011 => 5
01010100 => 10101001 => 00101011 => 5
01010101 => 10101010 => 00101011 => 5
01010110 => 10101011 => 01010111 => 5
01010111 => 10101011 => 01010111 => 5
01011000 => 10101001 => 00101011 => 5
01011001 => 10101010 => 00101011 => 5
01011010 => 10101101 => 01010111 => 5
01011011 => 10101101 => 01010111 => 5
01011100 => 10101101 => 01010111 => 5
01011101 => 10101110 => 00101111 => 1
01011110 => 10101111 => 01011111 => 1
01011111 => 10101111 => 01011111 => 1
01100000 => 10100001 => 00001011 => 1
01100001 => 10100010 => 00001011 => 1
01100010 => 10100101 => 00101011 => 5
01100011 => 10100101 => 00101011 => 5
01100100 => 10101001 => 00101011 => 5
01100101 => 10101010 => 00101011 => 5
01100110 => 10101011 => 01010111 => 5
01100111 => 10101011 => 01010111 => 5
01101000 => 10110001 => 00010111 => 1
01101001 => 10110010 => 00010111 => 1
01101010 => 10110101 => 01010111 => 5
01101011 => 10110101 => 01010111 => 5
01101100 => 10110101 => 01010111 => 5
01101101 => 10110110 => 00110111 => 3
01101110 => 10110111 => 01101111 => 3
01101111 => 10110111 => 01101111 => 3
01110000 => 10110001 => 00010111 => 1
01110001 => 10110010 => 00010111 => 1
01110010 => 10110101 => 01010111 => 5
01110011 => 10110101 => 01010111 => 5
01110100 => 10111001 => 00101111 => 1
01110101 => 10111010 => 00101111 => 1
01110110 => 10111011 => 01101111 => 3
01110111 => 10111011 => 01101111 => 3
01111000 => 10111001 => 00101111 => 1
01111001 => 10111010 => 00101111 => 1
01111010 => 10111101 => 01011111 => 1
01111011 => 10111101 => 01011111 => 1
01111100 => 10111101 => 01011111 => 1
01111101 => 10111110 => 00111111 => 0
01111110 => 10111111 => 01111111 => 0
01111111 => 10111111 => 01111111 => 0
10000000 => 10000001 => 00000011 => 0
10000001 => 10000010 => 00000011 => 0
10000010 => 10000101 => 00001011 => 1
10000011 => 10000101 => 00001011 => 1
10000100 => 10001001 => 00010011 => 3
10000101 => 10001010 => 00001011 => 1
10000110 => 10001011 => 00010111 => 1
10000111 => 10001011 => 00010111 => 1
10001000 => 10010001 => 00010011 => 3
10001001 => 10010010 => 00010011 => 3
10001010 => 10010101 => 00101011 => 5
10001011 => 10010101 => 00101011 => 5
10001100 => 10010101 => 00101011 => 5
10001101 => 10010110 => 00010111 => 1
10001110 => 10010111 => 00101111 => 1
10001111 => 10010111 => 00101111 => 1
10010000 => 10100001 => 00001011 => 1
10010001 => 10100010 => 00001011 => 1
10010010 => 10100101 => 00101011 => 5
10010011 => 10100101 => 00101011 => 5
10010100 => 10101001 => 00101011 => 5
10010101 => 10101010 => 00101011 => 5
10010110 => 10101011 => 01010111 => 5
10010111 => 10101011 => 01010111 => 5
10011000 => 10101001 => 00101011 => 5
10011001 => 10101010 => 00101011 => 5
10011010 => 10101101 => 01010111 => 5
10011011 => 10101101 => 01010111 => 5
10011100 => 10101101 => 01010111 => 5
10011101 => 10101110 => 00101111 => 1
10011110 => 10101111 => 01011111 => 1
10011111 => 10101111 => 01011111 => 1
10100000 => 11000001 => 00000111 => 0
10100001 => 11000010 => 00000111 => 0
10100010 => 11000101 => 00010111 => 1
10100011 => 11000101 => 00010111 => 1
10100100 => 11001001 => 00100111 => 3
10100101 => 11001010 => 00010111 => 1
10100110 => 11001011 => 00101111 => 1
10100111 => 11001011 => 00101111 => 1
10101000 => 11010001 => 00010111 => 1
10101001 => 11010010 => 00010111 => 1
10101010 => 11010101 => 01010111 => 5
10101011 => 11010101 => 01010111 => 5
10101100 => 11010101 => 01010111 => 5
10101101 => 11010110 => 00101111 => 1
10101110 => 11010111 => 01011111 => 1
10101111 => 11010111 => 01011111 => 1
10110000 => 11010001 => 00010111 => 1
10110001 => 11010010 => 00010111 => 1
10110010 => 11010101 => 01010111 => 5
10110011 => 11010101 => 01010111 => 5
10110100 => 11011001 => 00101111 => 1
10110101 => 11011010 => 00101111 => 1
10110110 => 11011011 => 01101111 => 3
10110111 => 11011011 => 01101111 => 3
10111000 => 11011001 => 00101111 => 1
10111001 => 11011010 => 00101111 => 1
10111010 => 11011101 => 01011111 => 1
10111011 => 11011101 => 01011111 => 1
10111100 => 11011101 => 01011111 => 1
10111101 => 11011110 => 00111111 => 0
10111110 => 11011111 => 01111111 => 0
10111111 => 11011111 => 01111111 => 0
11000000 => 11000001 => 00000111 => 0
11000001 => 11000010 => 00000111 => 0
11000010 => 11000101 => 00010111 => 1
11000011 => 11000101 => 00010111 => 1
11000100 => 11001001 => 00100111 => 3
11000101 => 11001010 => 00010111 => 1
11000110 => 11001011 => 00101111 => 1
11000111 => 11001011 => 00101111 => 1
11001000 => 11010001 => 00010111 => 1
11001001 => 11010010 => 00010111 => 1
11001010 => 11010101 => 01010111 => 5
11001011 => 11010101 => 01010111 => 5
11001100 => 11010101 => 01010111 => 5
11001101 => 11010110 => 00101111 => 1
11001110 => 11010111 => 01011111 => 1
11001111 => 11010111 => 01011111 => 1
11010000 => 11100001 => 00001111 => 0
11010001 => 11100010 => 00001111 => 0
11010010 => 11100101 => 00101111 => 1
11010011 => 11100101 => 00101111 => 1
11010100 => 11101001 => 00101111 => 1
11010101 => 11101010 => 00101111 => 1
11010110 => 11101011 => 01011111 => 1
11010111 => 11101011 => 01011111 => 1
11011000 => 11101001 => 00101111 => 1
11011001 => 11101010 => 00101111 => 1
11011010 => 11101101 => 01011111 => 1
11011011 => 11101101 => 01011111 => 1
11011100 => 11101101 => 01011111 => 1
11011101 => 11101110 => 00111111 => 0
11011110 => 11101111 => 01111111 => 0
11011111 => 11101111 => 01111111 => 0
11100000 => 11100001 => 00001111 => 0
11100001 => 11100010 => 00001111 => 0
11100010 => 11100101 => 00101111 => 1
11100011 => 11100101 => 00101111 => 1
11100100 => 11101001 => 00101111 => 1
11100101 => 11101010 => 00101111 => 1
11100110 => 11101011 => 01011111 => 1
11100111 => 11101011 => 01011111 => 1
11101000 => 11110001 => 00011111 => 0
11101001 => 11110010 => 00011111 => 0
11101010 => 11110101 => 01011111 => 1
11101011 => 11110101 => 01011111 => 1
11101100 => 11110101 => 01011111 => 1
11101101 => 11110110 => 00111111 => 0
11101110 => 11110111 => 01111111 => 0
11101111 => 11110111 => 01111111 => 0
11110000 => 11110001 => 00011111 => 0
11110001 => 11110010 => 00011111 => 0
11110010 => 11110101 => 01011111 => 1
11110011 => 11110101 => 01011111 => 1
11110100 => 11111001 => 00111111 => 0
11110101 => 11111010 => 00111111 => 0
11110110 => 11111011 => 01111111 => 0
11110111 => 11111011 => 01111111 => 0
11111000 => 11111001 => 00111111 => 0
11111001 => 11111010 => 00111111 => 0
11111010 => 11111101 => 01111111 => 0
11111011 => 11111101 => 01111111 => 0
11111100 => 11111101 => 01111111 => 0
11111101 => 11111110 => 01111111 => 0
11111110 => 11111111 => 11111111 => 0
11111111 => 11111111 => 11111111 => 0
000000000 => 000000001 => 000000001 => 0
000000001 => 000000010 => 000000001 => 0
000000010 => 000000101 => 000000101 => 1
000000011 => 000000101 => 000000101 => 1
000000100 => 000001001 => 000001001 => 3
000000101 => 000001010 => 000000101 => 1
000000110 => 000001011 => 000001011 => 1
000000111 => 000001011 => 000001011 => 1
000001000 => 000010001 => 000010001 => 6
000001001 => 000010010 => 000001001 => 3
000001010 => 000010101 => 000010101 => 5
000001011 => 000010101 => 000010101 => 5
000001100 => 000010101 => 000010101 => 5
000001101 => 000010110 => 000001011 => 1
000001110 => 000010111 => 000010111 => 1
000001111 => 000010111 => 000010111 => 1
000010000 => 000100001 => 000010001 => 6
000010001 => 000100010 => 000010001 => 6
000010010 => 000100101 => 000100101 => 8
000010011 => 000100101 => 000100101 => 8
000010100 => 000101001 => 000100101 => 8
000010101 => 000101010 => 000010101 => 5
000010110 => 000101011 => 000101011 => 5
000010111 => 000101011 => 000101011 => 5
000011000 => 000101001 => 000100101 => 8
000011001 => 000101010 => 000010101 => 5
000011010 => 000101101 => 000101011 => 5
000011011 => 000101101 => 000101011 => 5
000011100 => 000101101 => 000101011 => 5
000011101 => 000101110 => 000010111 => 1
000011110 => 000101111 => 000101111 => 1
000011111 => 000101111 => 000101111 => 1
000100000 => 001000001 => 000001001 => 3
000100001 => 001000010 => 000001001 => 3
000100010 => 001000101 => 000100101 => 8
000100011 => 001000101 => 000100101 => 8
000100100 => 001001001 => 001001001 => 15
000100101 => 001001010 => 000100101 => 8
000100110 => 001001011 => 001001011 => 8
000100111 => 001001011 => 001001011 => 8
000101000 => 001010001 => 000100101 => 8
000101001 => 001010010 => 000100101 => 8
000101010 => 001010101 => 001010101 => 14
000101011 => 001010101 => 001010101 => 14
000101100 => 001010101 => 001010101 => 14
000101101 => 001010110 => 000101011 => 5
000101110 => 001010111 => 001010111 => 5
000101111 => 001010111 => 001010111 => 5
000110000 => 001010001 => 000100101 => 8
000110001 => 001010010 => 000100101 => 8
000110010 => 001010101 => 001010101 => 14
000110011 => 001010101 => 001010101 => 14
000110100 => 001011001 => 001001011 => 8
000110101 => 001011010 => 000101011 => 5
000110110 => 001011011 => 001011011 => 8
000110111 => 001011011 => 001011011 => 8
000111000 => 001011001 => 001001011 => 8
000111001 => 001011010 => 000101011 => 5
000111010 => 001011101 => 001010111 => 5
000111011 => 001011101 => 001010111 => 5
000111100 => 001011101 => 001010111 => 5
000111101 => 001011110 => 000101111 => 1
000111110 => 001011111 => 001011111 => 1
000111111 => 001011111 => 001011111 => 1
001000000 => 010000001 => 000000101 => 1
001000001 => 010000010 => 000000101 => 1
001000010 => 010000101 => 000010101 => 5
001000011 => 010000101 => 000010101 => 5
001000100 => 010001001 => 000100101 => 8
001000101 => 010001010 => 000010101 => 5
001000110 => 010001011 => 000101011 => 5
001000111 => 010001011 => 000101011 => 5
001001000 => 010010001 => 000100101 => 8
001001001 => 010010010 => 000100101 => 8
001001010 => 010010101 => 001010101 => 14
001001011 => 010010101 => 001010101 => 14
001001100 => 010010101 => 001010101 => 14
001001101 => 010010110 => 000101011 => 5
001001110 => 010010111 => 001010111 => 5
001001111 => 010010111 => 001010111 => 5
001010000 => 010100001 => 000010101 => 5
001010001 => 010100010 => 000010101 => 5
001010010 => 010100101 => 001010101 => 14
001010011 => 010100101 => 001010101 => 14
001010100 => 010101001 => 001010101 => 14
001010101 => 010101010 => 001010101 => 14
001010110 => 010101011 => 010101011 => 14
001010111 => 010101011 => 010101011 => 14
001011000 => 010101001 => 001010101 => 14
001011001 => 010101010 => 001010101 => 14
001011010 => 010101101 => 010101011 => 14
001011011 => 010101101 => 010101011 => 14
001011100 => 010101101 => 010101011 => 14
001011101 => 010101110 => 001010111 => 5
001011110 => 010101111 => 010101111 => 5
001011111 => 010101111 => 010101111 => 5
001100000 => 010100001 => 000010101 => 5
001100001 => 010100010 => 000010101 => 5
001100010 => 010100101 => 001010101 => 14
001100011 => 010100101 => 001010101 => 14
001100100 => 010101001 => 001010101 => 14
001100101 => 010101010 => 001010101 => 14
001100110 => 010101011 => 010101011 => 14
001100111 => 010101011 => 010101011 => 14
001101000 => 010110001 => 000101011 => 5
001101001 => 010110010 => 000101011 => 5
001101010 => 010110101 => 010101011 => 14
001101011 => 010110101 => 010101011 => 14
001101100 => 010110101 => 010101011 => 14
001101101 => 010110110 => 001011011 => 8
001101110 => 010110111 => 010110111 => 8
001101111 => 010110111 => 010110111 => 8
001110000 => 010110001 => 000101011 => 5
001110001 => 010110010 => 000101011 => 5
001110010 => 010110101 => 010101011 => 14
001110011 => 010110101 => 010101011 => 14
001110100 => 010111001 => 001010111 => 5
001110101 => 010111010 => 001010111 => 5
001110110 => 010111011 => 010110111 => 8
001110111 => 010111011 => 010110111 => 8
001111000 => 010111001 => 001010111 => 5
001111001 => 010111010 => 001010111 => 5
001111010 => 010111101 => 010101111 => 5
001111011 => 010111101 => 010101111 => 5
001111100 => 010111101 => 010101111 => 5
001111101 => 010111110 => 001011111 => 1
001111110 => 010111111 => 010111111 => 1
001111111 => 010111111 => 010111111 => 1
010000000 => 100000001 => 000000011 => 0
010000001 => 100000010 => 000000011 => 0
010000010 => 100000101 => 000001011 => 1
010000011 => 100000101 => 000001011 => 1
010000100 => 100001001 => 000010011 => 3
010000101 => 100001010 => 000001011 => 1
010000110 => 100001011 => 000010111 => 1
010000111 => 100001011 => 000010111 => 1
010001000 => 100010001 => 000100011 => 6
010001001 => 100010010 => 000010011 => 3
010001010 => 100010101 => 000101011 => 5
010001011 => 100010101 => 000101011 => 5
010001100 => 100010101 => 000101011 => 5
010001101 => 100010110 => 000010111 => 1
010001110 => 100010111 => 000101111 => 1
010001111 => 100010111 => 000101111 => 1
010010000 => 100100001 => 000010011 => 3
010010001 => 100100010 => 000010011 => 3
010010010 => 100100101 => 001001011 => 8
010010011 => 100100101 => 001001011 => 8
010010100 => 100101001 => 001001011 => 8
010010101 => 100101010 => 000101011 => 5
010010110 => 100101011 => 001010111 => 5
010010111 => 100101011 => 001010111 => 5
010011000 => 100101001 => 001001011 => 8
010011001 => 100101010 => 000101011 => 5
010011010 => 100101101 => 001010111 => 5
010011011 => 100101101 => 001010111 => 5
010011100 => 100101101 => 001010111 => 5
010011101 => 100101110 => 000101111 => 1
010011110 => 100101111 => 001011111 => 1
010011111 => 100101111 => 001011111 => 1
010100000 => 101000001 => 000001011 => 1
010100001 => 101000010 => 000001011 => 1
010100010 => 101000101 => 000101011 => 5
010100011 => 101000101 => 000101011 => 5
010100100 => 101001001 => 001001011 => 8
010100101 => 101001010 => 000101011 => 5
010100110 => 101001011 => 001010111 => 5
010100111 => 101001011 => 001010111 => 5
010101000 => 101010001 => 000101011 => 5
010101001 => 101010010 => 000101011 => 5
010101010 => 101010101 => 010101011 => 14
010101011 => 101010101 => 010101011 => 14
010101100 => 101010101 => 010101011 => 14
010101101 => 101010110 => 001010111 => 5
010101110 => 101010111 => 010101111 => 5
010101111 => 101010111 => 010101111 => 5
010110000 => 101010001 => 000101011 => 5
010110001 => 101010010 => 000101011 => 5
010110010 => 101010101 => 010101011 => 14
010110011 => 101010101 => 010101011 => 14
010110100 => 101011001 => 001010111 => 5
010110101 => 101011010 => 001010111 => 5
010110110 => 101011011 => 010110111 => 8
010110111 => 101011011 => 010110111 => 8
010111000 => 101011001 => 001010111 => 5
010111001 => 101011010 => 001010111 => 5
010111010 => 101011101 => 010101111 => 5
010111011 => 101011101 => 010101111 => 5
010111100 => 101011101 => 010101111 => 5
010111101 => 101011110 => 001011111 => 1
010111110 => 101011111 => 010111111 => 1
010111111 => 101011111 => 010111111 => 1
011000000 => 101000001 => 000001011 => 1
011000001 => 101000010 => 000001011 => 1
011000010 => 101000101 => 000101011 => 5
011000011 => 101000101 => 000101011 => 5
011000100 => 101001001 => 001001011 => 8
011000101 => 101001010 => 000101011 => 5
011000110 => 101001011 => 001010111 => 5
011000111 => 101001011 => 001010111 => 5
011001000 => 101010001 => 000101011 => 5
011001001 => 101010010 => 000101011 => 5
011001010 => 101010101 => 010101011 => 14
011001011 => 101010101 => 010101011 => 14
011001100 => 101010101 => 010101011 => 14
011001101 => 101010110 => 001010111 => 5
011001110 => 101010111 => 010101111 => 5
011001111 => 101010111 => 010101111 => 5
011010000 => 101100001 => 000010111 => 1
011010001 => 101100010 => 000010111 => 1
011010010 => 101100101 => 001010111 => 5
011010011 => 101100101 => 001010111 => 5
011010100 => 101101001 => 001010111 => 5
011010101 => 101101010 => 001010111 => 5
011010110 => 101101011 => 010110111 => 8
011010111 => 101101011 => 010110111 => 8
011011000 => 101101001 => 001010111 => 5
011011001 => 101101010 => 001010111 => 5
011011010 => 101101101 => 010110111 => 8
011011011 => 101101101 => 010110111 => 8
011011100 => 101101101 => 010110111 => 8
011011101 => 101101110 => 001101111 => 3
011011110 => 101101111 => 011011111 => 3
011011111 => 101101111 => 011011111 => 3
011100000 => 101100001 => 000010111 => 1
011100001 => 101100010 => 000010111 => 1
011100010 => 101100101 => 001010111 => 5
011100011 => 101100101 => 001010111 => 5
011100100 => 101101001 => 001010111 => 5
011100101 => 101101010 => 001010111 => 5
011100110 => 101101011 => 010110111 => 8
011100111 => 101101011 => 010110111 => 8
011101000 => 101110001 => 000101111 => 1
011101001 => 101110010 => 000101111 => 1
011101010 => 101110101 => 010101111 => 5
011101011 => 101110101 => 010101111 => 5
011101100 => 101110101 => 010101111 => 5
011101101 => 101110110 => 001101111 => 3
011101110 => 101110111 => 011101111 => 6
011101111 => 101110111 => 011101111 => 6
011110000 => 101110001 => 000101111 => 1
011110001 => 101110010 => 000101111 => 1
011110010 => 101110101 => 010101111 => 5
011110011 => 101110101 => 010101111 => 5
011110100 => 101111001 => 001011111 => 1
011110101 => 101111010 => 001011111 => 1
011110110 => 101111011 => 011011111 => 3
011110111 => 101111011 => 011011111 => 3
011111000 => 101111001 => 001011111 => 1
011111001 => 101111010 => 001011111 => 1
011111010 => 101111101 => 010111111 => 1
011111011 => 101111101 => 010111111 => 1
011111100 => 101111101 => 010111111 => 1
011111101 => 101111110 => 001111111 => 0
011111110 => 101111111 => 011111111 => 0
011111111 => 101111111 => 011111111 => 0
100000000 => 100000001 => 000000011 => 0
100000001 => 100000010 => 000000011 => 0
100000010 => 100000101 => 000001011 => 1
100000011 => 100000101 => 000001011 => 1
100000100 => 100001001 => 000010011 => 3
100000101 => 100001010 => 000001011 => 1
100000110 => 100001011 => 000010111 => 1
100000111 => 100001011 => 000010111 => 1
100001000 => 100010001 => 000100011 => 6
100001001 => 100010010 => 000010011 => 3
100001010 => 100010101 => 000101011 => 5
100001011 => 100010101 => 000101011 => 5
100001100 => 100010101 => 000101011 => 5
100001101 => 100010110 => 000010111 => 1
100001110 => 100010111 => 000101111 => 1
100001111 => 100010111 => 000101111 => 1
100010000 => 100100001 => 000010011 => 3
100010001 => 100100010 => 000010011 => 3
100010010 => 100100101 => 001001011 => 8
100010011 => 100100101 => 001001011 => 8
100010100 => 100101001 => 001001011 => 8
100010101 => 100101010 => 000101011 => 5
100010110 => 100101011 => 001010111 => 5
100010111 => 100101011 => 001010111 => 5
100011000 => 100101001 => 001001011 => 8
100011001 => 100101010 => 000101011 => 5
100011010 => 100101101 => 001010111 => 5
100011011 => 100101101 => 001010111 => 5
100011100 => 100101101 => 001010111 => 5
100011101 => 100101110 => 000101111 => 1
100011110 => 100101111 => 001011111 => 1
100011111 => 100101111 => 001011111 => 1
100100000 => 101000001 => 000001011 => 1
100100001 => 101000010 => 000001011 => 1
100100010 => 101000101 => 000101011 => 5
100100011 => 101000101 => 000101011 => 5
100100100 => 101001001 => 001001011 => 8
100100101 => 101001010 => 000101011 => 5
100100110 => 101001011 => 001010111 => 5
100100111 => 101001011 => 001010111 => 5
100101000 => 101010001 => 000101011 => 5
100101001 => 101010010 => 000101011 => 5
100101010 => 101010101 => 010101011 => 14
100101011 => 101010101 => 010101011 => 14
100101100 => 101010101 => 010101011 => 14
100101101 => 101010110 => 001010111 => 5
100101110 => 101010111 => 010101111 => 5
100101111 => 101010111 => 010101111 => 5
100110000 => 101010001 => 000101011 => 5
100110001 => 101010010 => 000101011 => 5
100110010 => 101010101 => 010101011 => 14
100110011 => 101010101 => 010101011 => 14
100110100 => 101011001 => 001010111 => 5
100110101 => 101011010 => 001010111 => 5
100110110 => 101011011 => 010110111 => 8
100110111 => 101011011 => 010110111 => 8
100111000 => 101011001 => 001010111 => 5
100111001 => 101011010 => 001010111 => 5
100111010 => 101011101 => 010101111 => 5
100111011 => 101011101 => 010101111 => 5
100111100 => 101011101 => 010101111 => 5
100111101 => 101011110 => 001011111 => 1
100111110 => 101011111 => 010111111 => 1
100111111 => 101011111 => 010111111 => 1
101000000 => 110000001 => 000000111 => 0
101000001 => 110000010 => 000000111 => 0
101000010 => 110000101 => 000010111 => 1
101000011 => 110000101 => 000010111 => 1
101000100 => 110001001 => 000100111 => 3
101000101 => 110001010 => 000010111 => 1
101000110 => 110001011 => 000101111 => 1
101000111 => 110001011 => 000101111 => 1
101001000 => 110010001 => 000100111 => 3
101001001 => 110010010 => 000100111 => 3
101001010 => 110010101 => 001010111 => 5
101001011 => 110010101 => 001010111 => 5
101001100 => 110010101 => 001010111 => 5
101001101 => 110010110 => 000101111 => 1
101001110 => 110010111 => 001011111 => 1
101001111 => 110010111 => 001011111 => 1
101010000 => 110100001 => 000010111 => 1
101010001 => 110100010 => 000010111 => 1
101010010 => 110100101 => 001010111 => 5
101010011 => 110100101 => 001010111 => 5
101010100 => 110101001 => 001010111 => 5
101010101 => 110101010 => 001010111 => 5
101010110 => 110101011 => 010101111 => 5
101010111 => 110101011 => 010101111 => 5
101011000 => 110101001 => 001010111 => 5
101011001 => 110101010 => 001010111 => 5
101011010 => 110101101 => 010101111 => 5
101011011 => 110101101 => 010101111 => 5
101011100 => 110101101 => 010101111 => 5
101011101 => 110101110 => 001011111 => 1
101011110 => 110101111 => 010111111 => 1
101011111 => 110101111 => 010111111 => 1
101100000 => 110100001 => 000010111 => 1
101100001 => 110100010 => 000010111 => 1
101100010 => 110100101 => 001010111 => 5
101100011 => 110100101 => 001010111 => 5
101100100 => 110101001 => 001010111 => 5
101100101 => 110101010 => 001010111 => 5
101100110 => 110101011 => 010101111 => 5
101100111 => 110101011 => 010101111 => 5
101101000 => 110110001 => 000101111 => 1
101101001 => 110110010 => 000101111 => 1
101101010 => 110110101 => 010101111 => 5
101101011 => 110110101 => 010101111 => 5
101101100 => 110110101 => 010101111 => 5
101101101 => 110110110 => 001101111 => 3
101101110 => 110110111 => 011011111 => 3
101101111 => 110110111 => 011011111 => 3
101110000 => 110110001 => 000101111 => 1
101110001 => 110110010 => 000101111 => 1
101110010 => 110110101 => 010101111 => 5
101110011 => 110110101 => 010101111 => 5
101110100 => 110111001 => 001011111 => 1
101110101 => 110111010 => 001011111 => 1
101110110 => 110111011 => 011011111 => 3
101110111 => 110111011 => 011011111 => 3
101111000 => 110111001 => 001011111 => 1
101111001 => 110111010 => 001011111 => 1
101111010 => 110111101 => 010111111 => 1
101111011 => 110111101 => 010111111 => 1
101111100 => 110111101 => 010111111 => 1
101111101 => 110111110 => 001111111 => 0
101111110 => 110111111 => 011111111 => 0
101111111 => 110111111 => 011111111 => 0
110000000 => 110000001 => 000000111 => 0
110000001 => 110000010 => 000000111 => 0
110000010 => 110000101 => 000010111 => 1
110000011 => 110000101 => 000010111 => 1
110000100 => 110001001 => 000100111 => 3
110000101 => 110001010 => 000010111 => 1
110000110 => 110001011 => 000101111 => 1
110000111 => 110001011 => 000101111 => 1
110001000 => 110010001 => 000100111 => 3
110001001 => 110010010 => 000100111 => 3
110001010 => 110010101 => 001010111 => 5
110001011 => 110010101 => 001010111 => 5
110001100 => 110010101 => 001010111 => 5
110001101 => 110010110 => 000101111 => 1
110001110 => 110010111 => 001011111 => 1
110001111 => 110010111 => 001011111 => 1
110010000 => 110100001 => 000010111 => 1
110010001 => 110100010 => 000010111 => 1
110010010 => 110100101 => 001010111 => 5
110010011 => 110100101 => 001010111 => 5
110010100 => 110101001 => 001010111 => 5
110010101 => 110101010 => 001010111 => 5
110010110 => 110101011 => 010101111 => 5
110010111 => 110101011 => 010101111 => 5
110011000 => 110101001 => 001010111 => 5
110011001 => 110101010 => 001010111 => 5
110011010 => 110101101 => 010101111 => 5
110011011 => 110101101 => 010101111 => 5
110011100 => 110101101 => 010101111 => 5
110011101 => 110101110 => 001011111 => 1
110011110 => 110101111 => 010111111 => 1
110011111 => 110101111 => 010111111 => 1
110100000 => 111000001 => 000001111 => 0
110100001 => 111000010 => 000001111 => 0
110100010 => 111000101 => 000101111 => 1
110100011 => 111000101 => 000101111 => 1
110100100 => 111001001 => 001001111 => 3
110100101 => 111001010 => 000101111 => 1
110100110 => 111001011 => 001011111 => 1
110100111 => 111001011 => 001011111 => 1
110101000 => 111010001 => 000101111 => 1
110101001 => 111010010 => 000101111 => 1
110101010 => 111010101 => 010101111 => 5
110101011 => 111010101 => 010101111 => 5
110101100 => 111010101 => 010101111 => 5
110101101 => 111010110 => 001011111 => 1
110101110 => 111010111 => 010111111 => 1
110101111 => 111010111 => 010111111 => 1
110110000 => 111010001 => 000101111 => 1
110110001 => 111010010 => 000101111 => 1
110110010 => 111010101 => 010101111 => 5
110110011 => 111010101 => 010101111 => 5
110110100 => 111011001 => 001011111 => 1
110110101 => 111011010 => 001011111 => 1
110110110 => 111011011 => 011011111 => 3
110110111 => 111011011 => 011011111 => 3
110111000 => 111011001 => 001011111 => 1
110111001 => 111011010 => 001011111 => 1
110111010 => 111011101 => 010111111 => 1
110111011 => 111011101 => 010111111 => 1
110111100 => 111011101 => 010111111 => 1
110111101 => 111011110 => 001111111 => 0
110111110 => 111011111 => 011111111 => 0
110111111 => 111011111 => 011111111 => 0
111000000 => 111000001 => 000001111 => 0
111000001 => 111000010 => 000001111 => 0
111000010 => 111000101 => 000101111 => 1
111000011 => 111000101 => 000101111 => 1
111000100 => 111001001 => 001001111 => 3
111000101 => 111001010 => 000101111 => 1
111000110 => 111001011 => 001011111 => 1
111000111 => 111001011 => 001011111 => 1
111001000 => 111010001 => 000101111 => 1
111001001 => 111010010 => 000101111 => 1
111001010 => 111010101 => 010101111 => 5
111001011 => 111010101 => 010101111 => 5
111001100 => 111010101 => 010101111 => 5
111001101 => 111010110 => 001011111 => 1
111001110 => 111010111 => 010111111 => 1
111001111 => 111010111 => 010111111 => 1
111010000 => 111100001 => 000011111 => 0
111010001 => 111100010 => 000011111 => 0
111010010 => 111100101 => 001011111 => 1
111010011 => 111100101 => 001011111 => 1
111010100 => 111101001 => 001011111 => 1
111010101 => 111101010 => 001011111 => 1
111010110 => 111101011 => 010111111 => 1
111010111 => 111101011 => 010111111 => 1
111011000 => 111101001 => 001011111 => 1
111011001 => 111101010 => 001011111 => 1
111011010 => 111101101 => 010111111 => 1
111011011 => 111101101 => 010111111 => 1
111011100 => 111101101 => 010111111 => 1
111011101 => 111101110 => 001111111 => 0
111011110 => 111101111 => 011111111 => 0
111011111 => 111101111 => 011111111 => 0
111100000 => 111100001 => 000011111 => 0
111100001 => 111100010 => 000011111 => 0
111100010 => 111100101 => 001011111 => 1
111100011 => 111100101 => 001011111 => 1
111100100 => 111101001 => 001011111 => 1
111100101 => 111101010 => 001011111 => 1
111100110 => 111101011 => 010111111 => 1
111100111 => 111101011 => 010111111 => 1
111101000 => 111110001 => 000111111 => 0
111101001 => 111110010 => 000111111 => 0
111101010 => 111110101 => 010111111 => 1
111101011 => 111110101 => 010111111 => 1
111101100 => 111110101 => 010111111 => 1
111101101 => 111110110 => 001111111 => 0
111101110 => 111110111 => 011111111 => 0
111101111 => 111110111 => 011111111 => 0
111110000 => 111110001 => 000111111 => 0
111110001 => 111110010 => 000111111 => 0
111110010 => 111110101 => 010111111 => 1
111110011 => 111110101 => 010111111 => 1
111110100 => 111111001 => 001111111 => 0
111110101 => 111111010 => 001111111 => 0
111110110 => 111111011 => 011111111 => 0
111110111 => 111111011 => 011111111 => 0
111111000 => 111111001 => 001111111 => 0
111111001 => 111111010 => 001111111 => 0
111111010 => 111111101 => 011111111 => 0
111111011 => 111111101 => 011111111 => 0
111111100 => 111111101 => 011111111 => 0
111111101 => 111111110 => 011111111 => 0
111111110 => 111111111 => 111111111 => 0
111111111 => 111111111 => 111111111 => 0
1101010010 => 1110100101 => 0010101111 => 5
1101100010 => 1110100101 => 0010101111 => 5
1101101000 => 1110110001 => 0001011111 => 1
1101110000 => 1110110001 => 0001011111 => 1
1110010010 => 1110100101 => 0010101111 => 5
1111010000 => 1111100001 => 0000111111 => 0
1111100000 => 1111100001 => 0000111111 => 0
1111000001 => 1111000010 => 0000011111 => 0
1110100001 => 1111000010 => 0000011111 => 0
1110010001 => 1110100010 => 0000101111 => 1
1110001001 => 1110010010 => 0001001111 => 3
1110000101 => 1110001010 => 0000101111 => 1
1101100001 => 1110100010 => 0000101111 => 1
1101010011 => 1110100101 => 0010101111 => 5
1101010001 => 1110100010 => 0000101111 => 1
1101001001 => 1110010010 => 0001001111 => 3
1101000101 => 1110001010 => 0000101111 => 1
1101000011 => 1110000101 => 0000101111 => 1
1100110001 => 1101010010 => 0001010111 => 5
1100101001 => 1101010010 => 0001010111 => 5
1100100110 => 1101001011 => 0010101111 => 5
1100100101 => 1101001010 => 0001010111 => 5
1100011001 => 1100101010 => 0001010111 => 5
1100010101 => 1100101010 => 0001010111 => 5
1100010010 => 1100100101 => 0010010111 => 8
1100001011 => 1100010101 => 0001010111 => 5
1011100001 => 1101100010 => 0000101111 => 1
1011010001 => 1101100010 => 0000101111 => 1
1011001001 => 1101010010 => 0001010111 => 5
1011000111 => 1101001011 => 0010101111 => 5
1011000101 => 1101001010 => 0001010111 => 5
1010110001 => 1101010010 => 0001010111 => 5
1010101001 => 1101010010 => 0001010111 => 5
1010100110 => 1101001011 => 0010101111 => 5
1010100101 => 1101001010 => 0001010111 => 5
1010011001 => 1100101010 => 0001010111 => 5
1010010111 => 1100101011 => 0010101111 => 5
1010010110 => 1100101011 => 0010101111 => 5
1010010101 => 1100101010 => 0001010111 => 5
1001110001 => 1010110010 => 0001010111 => 5
1001101001 => 1010110010 => 0001010111 => 5
1001100101 => 1010101010 => 0010101011 => 14
1001011001 => 1010101010 => 0010101011 => 14
1001010101 => 1010101010 => 0010101011 => 14
1001001110 => 1010010111 => 0010101111 => 5
1000111101 => 1001011110 => 0001011111 => 1
1000101011 => 1001010101 => 0010101011 => 14
1000010110 => 1000101011 => 0001010111 => 5
1000001101 => 1000010110 => 0000010111 => 1
1000000001 => 1000000010 => 0000000011 => 0
1000000000 => 1000000001 => 0000000011 => 0
0111100001 => 1011100010 => 0000101111 => 1
0100000001 => 1000000010 => 0000000011 => 0
0000000001 => 0000000010 => 0000000001 => 0
0111010001 => 1011100010 => 0000101111 => 1
0010000001 => 0100000010 => 0000000101 => 1
0101010101 => 1010101010 => 0010101011 => 14
0101010011 => 1010100101 => 0010101011 => 14
0101001101 => 1010010110 => 0001010111 => 5
0101001011 => 1010010101 => 0010101011 => 14
0100110101 => 1001011010 => 0001010111 => 5
0100110011 => 1001010101 => 0010101011 => 14
0100101101 => 1001010110 => 0001010111 => 5
0100101011 => 1001010101 => 0010101011 => 14
0100011101 => 1000101110 => 0000101111 => 1
0100010111 => 1000101011 => 0001010111 => 5
0011010101 => 0101101010 => 0010101011 => 14
0011010011 => 0101100101 => 0010101011 => 14
0011001101 => 0101010110 => 0010101011 => 14
0011000111 => 0101001011 => 0010101011 => 14
0010110101 => 0101011010 => 0010101011 => 14
0010101101 => 0101010110 => 0010101011 => 14
0010100111 => 0101001011 => 0010101011 => 14
0010011011 => 0100101101 => 0010101011 => 14
0010010111 => 0100101011 => 0010101011 => 14
0010001111 => 0100010111 => 0001010111 => 5
0001110101 => 0010111010 => 0001010111 => 5
0001110011 => 0010110101 => 0010101011 => 14
0001101101 => 0010110110 => 0001011011 => 8
0001101011 => 0010110101 => 0010101011 => 14
0001100111 => 0010101011 => 0010101011 => 14
0001011101 => 0010101110 => 0001010111 => 5
0001011011 => 0010101101 => 0010101011 => 14
0001010111 => 0010101011 => 0010101011 => 14
0001001111 => 0010010111 => 0010010111 => 8
0000111101 => 0001011110 => 0000101111 => 1
0000111011 => 0001011101 => 0001010111 => 5
0000110111 => 0001011011 => 0001011011 => 8
0000101111 => 0001010111 => 0001010111 => 5
0000011111 => 0000101111 => 0000101111 => 1
0000000000 => 0000000001 => 0000000001 => 0
0000011110 => 0000101111 => 0000101111 => 1
0001100110 => 0010101011 => 0010101011 => 14
0001110010 => 0010110101 => 0010101011 => 14
0001001110 => 0010010111 => 0010010111 => 8
0001011010 => 0010101101 => 0010101011 => 14
0110011000 => 1010101001 => 0010101011 => 14
0110010010 => 1010100101 => 0010101011 => 14
0111100000 => 1011100001 => 0000101111 => 1
0111001000 => 1011010001 => 0001010111 => 5
0111000010 => 1011000101 => 0001010111 => 5
0100111000 => 1001011001 => 0010010111 => 8
0100110010 => 1001010101 => 0010101011 => 14
0101101000 => 1010110001 => 0001010111 => 5
0101100010 => 1010100101 => 0010101011 => 14
0101001010 => 1010010101 => 0010101011 => 14
0010110100 => 0101011001 => 0010101011 => 14
0011010100 => 0101101001 => 0010101011 => 14
0101010100 => 1010101001 => 0010101011 => 14
0010100000 => 0101000001 => 0000010101 => 5
0000000010 => 0000000101 => 0000000101 => 1
0000000100 => 0000001001 => 0000001001 => 3
0000001010 => 0000010101 => 0000010101 => 5
0000101110 => 0001010111 => 0001010111 => 5
0010111000 => 0101011001 => 0010101011 => 14
0011010010 => 0101100101 => 0010101011 => 14
0011011000 => 0101101001 => 0010101011 => 14
0011100010 => 0101100101 => 0010101011 => 14
0011100100 => 0101101001 => 0010101011 => 14
0011101000 => 0101110001 => 0001010111 => 5
0011110000 => 0101110001 => 0001010111 => 5
0100101010 => 1001010101 => 0010101011 => 14
0100101100 => 1001010101 => 0010101011 => 14
0100110100 => 1001011001 => 0010010111 => 8
0101001100 => 1010010101 => 0010101011 => 14
0101010010 => 1010100101 => 0010101011 => 14
0101011000 => 1010101001 => 0010101011 => 14
0101100100 => 1010101001 => 0010101011 => 14
0101110000 => 1010110001 => 0001010111 => 5
0110001010 => 1010010101 => 0010101011 => 14
0110001100 => 1010010101 => 0010101011 => 14
0110010100 => 1010101001 => 0010101011 => 14
0110100010 => 1011000101 => 0001010111 => 5
0110100100 => 1011001001 => 0010010111 => 8
0110101000 => 1011010001 => 0001010111 => 5
0110110000 => 1011010001 => 0001010111 => 5
0111000100 => 1011001001 => 0010010111 => 8
0111010000 => 1011100001 => 0000101111 => 1
0100000000 => 1000000001 => 0000000011 => 0
0100000101 => 1000001010 => 0000001011 => 1
0101011001 => 1010101010 => 0010101011 => 14
0101100101 => 1010101010 => 0010101011 => 14
0101101001 => 1010110010 => 0001010111 => 5
0101110001 => 1010110010 => 0001010111 => 5
0110010101 => 1010101010 => 0010101011 => 14
0110011001 => 1010101010 => 0010101011 => 14
0110100101 => 1011001010 => 0001010111 => 5
0110101001 => 1011010010 => 0001010111 => 5
0110110001 => 1011010010 => 0001010111 => 5
0111000101 => 1011001010 => 0001010111 => 5
0111001001 => 1011010010 => 0001010111 => 5
0111010010 => 1011100101 => 0010101111 => 5
0111100010 => 1011100101 => 0010101111 => 5
0111101000 => 1011110001 => 0001011111 => 1
0111110000 => 1011110001 => 0001011111 => 1
0001111010 => 0010111101 => 0010101111 => 5
0001111100 => 0010111101 => 0010101111 => 5
0000000101 => 0000001010 => 0000000101 => 1
0000001101 => 0000010110 => 0000001011 => 1
0000011101 => 0000101110 => 0000010111 => 1
0001111101 => 0010111110 => 0001011111 => 1
0000001001 => 0000010010 => 0000001001 => 3
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
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
14,2 21,11 28,32,0,1,0,3 35,64,0,7,0,22 42,106,0,19,0,76,1,0,7,0,0,0,0,0,5 49,158,0,33,0,174,7,0,47,0,0,0,0,0,43,1
$F_{1} = 2$
$F_{2} = 4$
$F_{3} = 8$
$F_{4} = 14 + 2\ q$
$F_{5} = 21 + 11\ q$
$F_{6} = 28 + 32\ q + q^{3} + 3\ q^{5}$
$F_{7} = 35 + 64\ q + 7\ q^{3} + 22\ q^{5}$
$F_{8} = 42 + 106\ q + 19\ q^{3} + 76\ q^{5} + q^{6} + 7\ q^{8} + 5\ q^{14}$
$F_{9} = 49 + 158\ q + 33\ q^{3} + 174\ q^{5} + 7\ q^{6} + 47\ q^{8} + 43\ q^{14} + q^{15}$
Description
The inversion sum of a binary word.
A pair $a < b$ is an inversion of a binary word $w = w_1 \cdots w_n$ if $w_a = 1 > 0 = w_b$. The inversion sum is given by $\sum(b-a)$ over all inversions of $\pi$.
A pair $a < b$ is an inversion of a binary word $w = w_1 \cdots w_n$ if $w_a = 1 > 0 = w_b$. The inversion sum is given by $\sum(b-a)$ over all inversions of $\pi$.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.
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.
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!