Identifier
Identifier
Mp00096: Binary words Foata bijectionBinary words
Images
0 => 0
1 => 1
00 => 00
01 => 01
10 => 10
11 => 11
000 => 000
001 => 001
010 => 100
011 => 011
100 => 010
101 => 101
110 => 110
111 => 111
0000 => 0000
0001 => 0001
0010 => 1000
0011 => 0011
0100 => 0100
0101 => 1001
0110 => 1010
0111 => 0111
1000 => 0010
1001 => 0101
1010 => 1100
1011 => 1011
1100 => 0110
1101 => 1101
1110 => 1110
1111 => 1111
00000 => 00000
00001 => 00001
00010 => 10000
00011 => 00011
00100 => 01000
00101 => 10001
00110 => 10010
00111 => 00111
01000 => 00100
01001 => 01001
01010 => 11000
01011 => 10011
01100 => 01010
01101 => 10101
01110 => 10110
01111 => 01111
10000 => 00010
10001 => 00101
10010 => 10100
10011 => 01011
10100 => 01100
10101 => 11001
10110 => 11010
10111 => 10111
11000 => 00110
11001 => 01101
11010 => 11100
11011 => 11011
11100 => 01110
11101 => 11101
11110 => 11110
11111 => 11111
000000 => 000000
000001 => 000001
000010 => 100000
000011 => 000011
000100 => 010000
000101 => 100001
000110 => 100010
000111 => 000111
001000 => 001000
001001 => 010001
001010 => 110000
001011 => 100011
001100 => 010010
001101 => 100101
001110 => 100110
001111 => 001111
010000 => 000100
010001 => 001001
010010 => 101000
010011 => 010011
010100 => 011000
010101 => 110001
010110 => 110010
010111 => 100111
011000 => 001010
011001 => 010101
011010 => 110100
011011 => 101011
011100 => 010110
011101 => 101101
011110 => 101110
011111 => 011111
100000 => 000010
100001 => 000101
100010 => 100100
100011 => 001011
100100 => 010100
100101 => 101001
100110 => 101010
100111 => 010111
101000 => 001100
101001 => 011001
101010 => 111000
101011 => 110011
101100 => 011010
101101 => 110101
101110 => 110110
101111 => 101111
110000 => 000110
110001 => 001101
110010 => 101100
110011 => 011011
110100 => 011100
110101 => 111001
110110 => 111010
110111 => 110111
111000 => 001110
111001 => 011101
111010 => 111100
111011 => 111011
111100 => 011110
111101 => 111101
111110 => 111110
111111 => 111111
0000000 => 0000000
0000001 => 0000001
0000010 => 1000000
0000011 => 0000011
0000100 => 0100000
0000101 => 1000001
0000110 => 1000010
0000111 => 0000111
0001000 => 0010000
0001001 => 0100001
0001010 => 1100000
0001011 => 1000011
0001100 => 0100010
0001101 => 1000101
0001110 => 1000110
0001111 => 0001111
0010000 => 0001000
0010001 => 0010001
0010010 => 1010000
0010011 => 0100011
0010100 => 0110000
0010101 => 1100001
0010110 => 1100010
0010111 => 1000111
0011000 => 0010010
0011001 => 0100101
0011010 => 1100100
0011011 => 1001011
0011100 => 0100110
0011101 => 1001101
0011110 => 1001110
0011111 => 0011111
0100000 => 0000100
0100001 => 0001001
0100010 => 1001000
0100011 => 0010011
0100100 => 0101000
0100101 => 1010001
0100110 => 1010010
0100111 => 0100111
0101000 => 0011000
0101001 => 0110001
0101010 => 1110000
0101011 => 1100011
0101100 => 0110010
0101101 => 1100101
0101110 => 1100110
0101111 => 1001111
0110000 => 0001010
0110001 => 0010101
0110010 => 1010100
0110011 => 0101011
0110100 => 0110100
0110101 => 1101001
0110110 => 1101010
0110111 => 1010111
0111000 => 0010110
0111001 => 0101101
0111010 => 1101100
0111011 => 1011011
0111100 => 0101110
0111101 => 1011101
0111110 => 1011110
0111111 => 0111111
1000000 => 0000010
1000001 => 0000101
1000010 => 1000100
1000011 => 0001011
1000100 => 0100100
1000101 => 1001001
1000110 => 1001010
1000111 => 0010111
1001000 => 0010100
1001001 => 0101001
1001010 => 1101000
1001011 => 1010011
1001100 => 0101010
1001101 => 1010101
1001110 => 1010110
1001111 => 0101111
1010000 => 0001100
1010001 => 0011001
1010010 => 1011000
1010011 => 0110011
1010100 => 0111000
1010101 => 1110001
1010110 => 1110010
1010111 => 1100111
1011000 => 0011010
1011001 => 0110101
1011010 => 1110100
1011011 => 1101011
1011100 => 0110110
1011101 => 1101101
1011110 => 1101110
1011111 => 1011111
1100000 => 0000110
1100001 => 0001101
1100010 => 1001100
1100011 => 0011011
1100100 => 0101100
1100101 => 1011001
1100110 => 1011010
1100111 => 0110111
1101000 => 0011100
1101001 => 0111001
1101010 => 1111000
1101011 => 1110011
1101100 => 0111010
1101101 => 1110101
1101110 => 1110110
1101111 => 1101111
1110000 => 0001110
1110001 => 0011101
1110010 => 1011100
1110011 => 0111011
1110100 => 0111100
1110101 => 1111001
1110110 => 1111010
1110111 => 1110111
1111000 => 0011110
1111001 => 0111101
1111010 => 1111100
1111011 => 1111011
1111100 => 0111110
1111101 => 1111101
1111110 => 1111110
1111111 => 1111111
00000000 => 00000000
00000001 => 00000001
00000010 => 10000000
00000011 => 00000011
00000100 => 01000000
00000101 => 10000001
00000110 => 10000010
00000111 => 00000111
00001000 => 00100000
00001001 => 01000001
00001010 => 11000000
00001011 => 10000011
00001100 => 01000010
00001101 => 10000101
00001110 => 10000110
00001111 => 00001111
00010000 => 00010000
00010001 => 00100001
00010010 => 10100000
00010011 => 01000011
00010100 => 01100000
00010101 => 11000001
00010110 => 11000010
00010111 => 10000111
00011000 => 00100010
00011001 => 01000101
00011010 => 11000100
00011011 => 10001011
00011100 => 01000110
00011101 => 10001101
00011110 => 10001110
00011111 => 00011111
00100000 => 00001000
00100001 => 00010001
00100010 => 10010000
00100011 => 00100011
00100100 => 01010000
00100101 => 10100001
00100110 => 10100010
00100111 => 01000111
00101000 => 00110000
00101001 => 01100001
00101010 => 11100000
00101011 => 11000011
00101100 => 01100010
00101101 => 11000101
00101110 => 11000110
00101111 => 10001111
00110000 => 00010010
00110001 => 00100101
00110010 => 10100100
00110011 => 01001011
00110100 => 01100100
00110101 => 11001001
00110110 => 11001010
00110111 => 10010111
00111000 => 00100110
00111001 => 01001101
00111010 => 11001100
00111011 => 10011011
00111100 => 01001110
00111101 => 10011101
00111110 => 10011110
00111111 => 00111111
01000000 => 00000100
01000001 => 00001001
01000010 => 10001000
01000011 => 00010011
01000100 => 01001000
01000101 => 10010001
01000110 => 10010010
01000111 => 00100111
01001000 => 00101000
01001001 => 01010001
01001010 => 11010000
01001011 => 10100011
01001100 => 01010010
01001101 => 10100101
01001110 => 10100110
01001111 => 01001111
01010000 => 00011000
01010001 => 00110001
01010010 => 10110000
01010011 => 01100011
01010100 => 01110000
01010101 => 11100001
01010110 => 11100010
01010111 => 11000111
01011000 => 00110010
01011001 => 01100101
01011010 => 11100100
01011011 => 11001011
01011100 => 01100110
01011101 => 11001101
01011110 => 11001110
01011111 => 10011111
01100000 => 00001010
01100001 => 00010101
01100010 => 10010100
01100011 => 00101011
01100100 => 01010100
01100101 => 10101001
01100110 => 10101010
01100111 => 01010111
01101000 => 00110100
01101001 => 01101001
01101010 => 11101000
01101011 => 11010011
01101100 => 01101010
01101101 => 11010101
01101110 => 11010110
01101111 => 10101111
01110000 => 00010110
01110001 => 00101101
01110010 => 10101100
01110011 => 01011011
01110100 => 01101100
01110101 => 11011001
01110110 => 11011010
01110111 => 10110111
01111000 => 00101110
01111001 => 01011101
01111010 => 11011100
01111011 => 10111011
01111100 => 01011110
01111101 => 10111101
01111110 => 10111110
01111111 => 01111111
10000000 => 00000010
10000001 => 00000101
10000010 => 10000100
10000011 => 00001011
10000100 => 01000100
10000101 => 10001001
10000110 => 10001010
10000111 => 00010111
10001000 => 00100100
10001001 => 01001001
10001010 => 11001000
10001011 => 10010011
10001100 => 01001010
10001101 => 10010101
10001110 => 10010110
10001111 => 00101111
10010000 => 00010100
10010001 => 00101001
10010010 => 10101000
10010011 => 01010011
10010100 => 01101000
10010101 => 11010001
10010110 => 11010010
10010111 => 10100111
10011000 => 00101010
10011001 => 01010101
10011010 => 11010100
10011011 => 10101011
10011100 => 01010110
10011101 => 10101101
10011110 => 10101110
10011111 => 01011111
10100000 => 00001100
10100001 => 00011001
10100010 => 10011000
10100011 => 00110011
10100100 => 01011000
10100101 => 10110001
10100110 => 10110010
10100111 => 01100111
10101000 => 00111000
10101001 => 01110001
10101010 => 11110000
10101011 => 11100011
10101100 => 01110010
10101101 => 11100101
10101110 => 11100110
10101111 => 11001111
10110000 => 00011010
10110001 => 00110101
10110010 => 10110100
10110011 => 01101011
10110100 => 01110100
10110101 => 11101001
10110110 => 11101010
10110111 => 11010111
10111000 => 00110110
10111001 => 01101101
10111010 => 11101100
10111011 => 11011011
10111100 => 01101110
10111101 => 11011101
10111110 => 11011110
10111111 => 10111111
11000000 => 00000110
11000001 => 00001101
11000010 => 10001100
11000011 => 00011011
11000100 => 01001100
11000101 => 10011001
11000110 => 10011010
11000111 => 00110111
11001000 => 00101100
11001001 => 01011001
11001010 => 11011000
11001011 => 10110011
11001100 => 01011010
11001101 => 10110101
11001110 => 10110110
11001111 => 01101111
11010000 => 00011100
11010001 => 00111001
11010010 => 10111000
11010011 => 01110011
11010100 => 01111000
11010101 => 11110001
11010110 => 11110010
11010111 => 11100111
11011000 => 00111010
11011001 => 01110101
11011010 => 11110100
11011011 => 11101011
11011100 => 01110110
11011101 => 11101101
11011110 => 11101110
11011111 => 11011111
11100000 => 00001110
11100001 => 00011101
11100010 => 10011100
11100011 => 00111011
11100100 => 01011100
11100101 => 10111001
11100110 => 10111010
11100111 => 01110111
11101000 => 00111100
11101001 => 01111001
11101010 => 11111000
11101011 => 11110011
11101100 => 01111010
11101101 => 11110101
11101110 => 11110110
11101111 => 11101111
11110000 => 00011110
11110001 => 00111101
11110010 => 10111100
11110011 => 01111011
11110100 => 01111100
11110101 => 11111001
11110110 => 11111010
11110111 => 11110111
11111000 => 00111110
11111001 => 01111101
11111010 => 11111100
11111011 => 11111011
11111100 => 01111110
11111101 => 11111101
11111110 => 11111110
11111111 => 11111111
000000000 => 000000000
000000001 => 000000001
000000010 => 100000000
000000011 => 000000011
000000100 => 010000000
000000101 => 100000001
000000110 => 100000010
000000111 => 000000111
000001000 => 001000000
000001001 => 010000001
000001010 => 110000000
000001011 => 100000011
000001100 => 010000010
000001101 => 100000101
000001110 => 100000110
000001111 => 000001111
000010000 => 000100000
000010001 => 001000001
000010010 => 101000000
000010011 => 010000011
000010100 => 011000000
000010101 => 110000001
000010110 => 110000010
000010111 => 100000111
000011000 => 001000010
000011001 => 010000101
000011010 => 110000100
000011011 => 100001011
000011100 => 010000110
000011101 => 100001101
000011110 => 100001110
000011111 => 000011111
000100000 => 000010000
000100001 => 000100001
000100010 => 100100000
000100011 => 001000011
000100100 => 010100000
000100101 => 101000001
000100110 => 101000010
000100111 => 010000111
000101000 => 001100000
000101001 => 011000001
000101010 => 111000000
000101011 => 110000011
000101100 => 011000010
000101101 => 110000101
000101110 => 110000110
000101111 => 100001111
000110000 => 000100010
000110001 => 001000101
000110010 => 101000100
000110011 => 010001011
000110100 => 011000100
000110101 => 110001001
000110110 => 110001010
000110111 => 100010111
000111000 => 001000110
000111001 => 010001101
000111010 => 110001100
000111011 => 100011011
000111100 => 010001110
000111101 => 100011101
000111110 => 100011110
000111111 => 000111111
001000000 => 000001000
001000001 => 000010001
001000010 => 100010000
001000011 => 000100011
001000100 => 010010000
001000101 => 100100001
001000110 => 100100010
001000111 => 001000111
001001000 => 001010000
001001001 => 010100001
001001010 => 110100000
001001011 => 101000011
001001100 => 010100010
001001101 => 101000101
001001110 => 101000110
001001111 => 010001111
001010000 => 000110000
001010001 => 001100001
001010010 => 101100000
001010011 => 011000011
001010100 => 011100000
001010101 => 111000001
001010110 => 111000010
001010111 => 110000111
001011000 => 001100010
001011001 => 011000101
001011010 => 111000100
001011011 => 110001011
001011100 => 011000110
001011101 => 110001101
001011110 => 110001110
001011111 => 100011111
001100000 => 000010010
001100001 => 000100101
001100010 => 100100100
001100011 => 001001011
001100100 => 010100100
001100101 => 101001001
001100110 => 101001010
001100111 => 010010111
001101000 => 001100100
001101001 => 011001001
001101010 => 111001000
001101011 => 110010011
001101100 => 011001010
001101101 => 110010101
001101110 => 110010110
001101111 => 100101111
001110000 => 000100110
001110001 => 001001101
001110010 => 101001100
001110011 => 010011011
001110100 => 011001100
001110101 => 110011001
001110110 => 110011010
001110111 => 100110111
001111000 => 001001110
001111001 => 010011101
001111010 => 110011100
001111011 => 100111011
001111100 => 010011110
001111101 => 100111101
001111110 => 100111110
001111111 => 001111111
010000000 => 000000100
010000001 => 000001001
010000010 => 100001000
010000011 => 000010011
010000100 => 010001000
010000101 => 100010001
010000110 => 100010010
010000111 => 000100111
010001000 => 001001000
010001001 => 010010001
010001010 => 110010000
010001011 => 100100011
010001100 => 010010010
010001101 => 100100101
010001110 => 100100110
010001111 => 001001111
010010000 => 000101000
010010001 => 001010001
010010010 => 101010000
010010011 => 010100011
010010100 => 011010000
010010101 => 110100001
010010110 => 110100010
010010111 => 101000111
010011000 => 001010010
010011001 => 010100101
010011010 => 110100100
010011011 => 101001011
010011100 => 010100110
010011101 => 101001101
010011110 => 101001110
010011111 => 010011111
010100000 => 000011000
010100001 => 000110001
010100010 => 100110000
010100011 => 001100011
010100100 => 010110000
010100101 => 101100001
010100110 => 101100010
010100111 => 011000111
010101000 => 001110000
010101001 => 011100001
010101010 => 111100000
010101011 => 111000011
010101100 => 011100010
010101101 => 111000101
010101110 => 111000110
010101111 => 110001111
010110000 => 000110010
010110001 => 001100101
010110010 => 101100100
010110011 => 011001011
010110100 => 011100100
010110101 => 111001001
010110110 => 111001010
010110111 => 110010111
010111000 => 001100110
010111001 => 011001101
010111010 => 111001100
010111011 => 110011011
010111100 => 011001110
010111101 => 110011101
010111110 => 110011110
010111111 => 100111111
011000000 => 000001010
011000001 => 000010101
011000010 => 100010100
011000011 => 000101011
011000100 => 010010100
011000101 => 100101001
011000110 => 100101010
011000111 => 001010111
011001000 => 001010100
011001001 => 010101001
011001010 => 110101000
011001011 => 101010011
011001100 => 010101010
011001101 => 101010101
011001110 => 101010110
011001111 => 010101111
011010000 => 000110100
011010001 => 001101001
011010010 => 101101000
011010011 => 011010011
011010100 => 011101000
011010101 => 111010001
011010110 => 111010010
011010111 => 110100111
011011000 => 001101010
011011001 => 011010101
011011010 => 111010100
011011011 => 110101011
011011100 => 011010110
011011101 => 110101101
011011110 => 110101110
011011111 => 101011111
011100000 => 000010110
011100001 => 000101101
011100010 => 100101100
011100011 => 001011011
011100100 => 010101100
011100101 => 101011001
011100110 => 101011010
011100111 => 010110111
011101000 => 001101100
011101001 => 011011001
011101010 => 111011000
011101011 => 110110011
011101100 => 011011010
011101101 => 110110101
011101110 => 110110110
011101111 => 101101111
011110000 => 000101110
011110001 => 001011101
011110010 => 101011100
011110011 => 010111011
011110100 => 011011100
011110101 => 110111001
011110110 => 110111010
011110111 => 101110111
011111000 => 001011110
011111001 => 010111101
011111010 => 110111100
011111011 => 101111011
011111100 => 010111110
011111101 => 101111101
011111110 => 101111110
011111111 => 011111111
100000000 => 000000010
100000001 => 000000101
100000010 => 100000100
100000011 => 000001011
100000100 => 010000100
100000101 => 100001001
100000110 => 100001010
100000111 => 000010111
100001000 => 001000100
100001001 => 010001001
100001010 => 110001000
100001011 => 100010011
100001100 => 010001010
100001101 => 100010101
100001110 => 100010110
100001111 => 000101111
100010000 => 000100100
100010001 => 001001001
100010010 => 101001000
100010011 => 010010011
100010100 => 011001000
100010101 => 110010001
100010110 => 110010010
100010111 => 100100111
100011000 => 001001010
100011001 => 010010101
100011010 => 110010100
100011011 => 100101011
100011100 => 010010110
100011101 => 100101101
100011110 => 100101110
100011111 => 001011111
100100000 => 000010100
100100001 => 000101001
100100010 => 100101000
100100011 => 001010011
100100100 => 010101000
100100101 => 101010001
100100110 => 101010010
100100111 => 010100111
100101000 => 001101000
100101001 => 011010001
100101010 => 111010000
100101011 => 110100011
100101100 => 011010010
100101101 => 110100101
100101110 => 110100110
100101111 => 101001111
100110000 => 000101010
100110001 => 001010101
100110010 => 101010100
100110011 => 010101011
100110100 => 011010100
100110101 => 110101001
100110110 => 110101010
100110111 => 101010111
100111000 => 001010110
100111001 => 010101101
100111010 => 110101100
100111011 => 101011011
100111100 => 010101110
100111101 => 101011101
100111110 => 101011110
100111111 => 010111111
101000000 => 000001100
101000001 => 000011001
101000010 => 100011000
101000011 => 000110011
101000100 => 010011000
101000101 => 100110001
101000110 => 100110010
101000111 => 001100111
101001000 => 001011000
101001001 => 010110001
101001010 => 110110000
101001011 => 101100011
101001100 => 010110010
101001101 => 101100101
101001110 => 101100110
101001111 => 011001111
101010000 => 000111000
101010001 => 001110001
101010010 => 101110000
101010011 => 011100011
101010100 => 011110000
101010101 => 111100001
101010110 => 111100010
101010111 => 111000111
101011000 => 001110010
101011001 => 011100101
101011010 => 111100100
101011011 => 111001011
101011100 => 011100110
101011101 => 111001101
101011110 => 111001110
101011111 => 110011111
101100000 => 000011010
101100001 => 000110101
101100010 => 100110100
101100011 => 001101011
101100100 => 010110100
101100101 => 101101001
101100110 => 101101010
101100111 => 011010111
101101000 => 001110100
101101001 => 011101001
101101010 => 111101000
101101011 => 111010011
101101100 => 011101010
101101101 => 111010101
101101110 => 111010110
101101111 => 110101111
101110000 => 000110110
101110001 => 001101101
101110010 => 101101100
101110011 => 011011011
101110100 => 011101100
101110101 => 111011001
101110110 => 111011010
101110111 => 110110111
101111000 => 001101110
101111001 => 011011101
101111010 => 111011100
101111011 => 110111011
101111100 => 011011110
101111101 => 110111101
101111110 => 110111110
101111111 => 101111111
110000000 => 000000110
110000001 => 000001101
110000010 => 100001100
110000011 => 000011011
110000100 => 010001100
110000101 => 100011001
110000110 => 100011010
110000111 => 000110111
110001000 => 001001100
110001001 => 010011001
110001010 => 110011000
110001011 => 100110011
110001100 => 010011010
110001101 => 100110101
110001110 => 100110110
110001111 => 001101111
110010000 => 000101100
110010001 => 001011001
110010010 => 101011000
110010011 => 010110011
110010100 => 011011000
110010101 => 110110001
110010110 => 110110010
110010111 => 101100111
110011000 => 001011010
110011001 => 010110101
110011010 => 110110100
110011011 => 101101011
110011100 => 010110110
110011101 => 101101101
110011110 => 101101110
110011111 => 011011111
110100000 => 000011100
110100001 => 000111001
110100010 => 100111000
110100011 => 001110011
110100100 => 010111000
110100101 => 101110001
110100110 => 101110010
110100111 => 011100111
110101000 => 001111000
110101001 => 011110001
110101010 => 111110000
110101011 => 111100011
110101100 => 011110010
110101101 => 111100101
110101110 => 111100110
110101111 => 111001111
110110000 => 000111010
110110001 => 001110101
110110010 => 101110100
110110011 => 011101011
110110100 => 011110100
110110101 => 111101001
110110110 => 111101010
110110111 => 111010111
110111000 => 001110110
110111001 => 011101101
110111010 => 111101100
110111011 => 111011011
110111100 => 011101110
110111101 => 111011101
110111110 => 111011110
110111111 => 110111111
111000000 => 000001110
111000001 => 000011101
111000010 => 100011100
111000011 => 000111011
111000100 => 010011100
111000101 => 100111001
111000110 => 100111010
111000111 => 001110111
111001000 => 001011100
111001001 => 010111001
111001010 => 110111000
111001011 => 101110011
111001100 => 010111010
111001101 => 101110101
111001110 => 101110110
111001111 => 011101111
111010000 => 000111100
111010001 => 001111001
111010010 => 101111000
111010011 => 011110011
111010100 => 011111000
111010101 => 111110001
111010110 => 111110010
111010111 => 111100111
111011000 => 001111010
111011001 => 011110101
111011010 => 111110100
111011011 => 111101011
111011100 => 011110110
111011101 => 111101101
111011110 => 111101110
111011111 => 111011111
111100000 => 000011110
111100001 => 000111101
111100010 => 100111100
111100011 => 001111011
111100100 => 010111100
111100101 => 101111001
111100110 => 101111010
111100111 => 011110111
111101000 => 001111100
111101001 => 011111001
111101010 => 111111000
111101011 => 111110011
111101100 => 011111010
111101101 => 111110101
111101110 => 111110110
111101111 => 111101111
111110000 => 000111110
111110001 => 001111101
111110010 => 101111100
111110011 => 011111011
111110100 => 011111100
111110101 => 111111001
111110110 => 111111010
111110111 => 111110111
111111000 => 001111110
111111001 => 011111101
111111010 => 111111100
111111011 => 111111011
111111100 => 011111110
111111101 => 111111101
111111110 => 111111110
111111111 => 111111111
1010101010 => 1111100000
1010101100 => 0111100010
1010110010 => 1011100100
1010110100 => 0111100100
1010111000 => 0011100110
1011001010 => 1101101000
1011001100 => 0101101010
1011010010 => 1011101000
1011010100 => 0111101000
1011011000 => 0011101010
1011100010 => 1001101100
1011100100 => 0101101100
1011101000 => 0011101100
1011110000 => 0001101110
1100101010 => 1110110000
1100101100 => 0110110010
1100110010 => 1010110100
1100110100 => 0110110100
1100111000 => 0010110110
1101001010 => 1101110000
1101001100 => 0101110010
1101010010 => 1011110000
1101010100 => 0111110000
1101011000 => 0011110010
1101100010 => 1001110100
1101100100 => 0101110100
1101101000 => 0011110100
1101110000 => 0001110110
1110001010 => 1100111000
1110001100 => 0100111010
1110010010 => 1010111000
1110010100 => 0110111000
1110011000 => 0010111010
1110100010 => 1001111000
1110100100 => 0101111000
1110101000 => 0011111000
1110110000 => 0001111010
1111000010 => 1000111100
1111000100 => 0100111100
1111001000 => 0010111100
1111010000 => 0001111100
1111100000 => 0000111110
101010101010 => 111111000000
101010101100 => 011111000010
101010110010 => 101111000100
101010110100 => 011111000100
101010111000 => 001111000110
101011001010 => 110111001000
101011001100 => 010111001010
101011010010 => 101111001000
101011010100 => 011111001000
101011011000 => 001111001010
101011100010 => 100111001100
101011100100 => 010111001100
101011101000 => 001111001100
101011110000 => 000111001110
101100101010 => 111011010000
101100101100 => 011011010010
101100110010 => 101011010100
101100110100 => 011011010100
101100111000 => 001011010110
101101001010 => 110111010000
101101001100 => 010111010010
101101010010 => 101111010000
101101010100 => 011111010000
101101011000 => 001111010010
101101100010 => 100111010100
101101100100 => 010111010100
101101101000 => 001111010100
101101110000 => 000111010110
101110001010 => 110011011000
101110001100 => 010011011010
101110010010 => 101011011000
101110010100 => 011011011000
101110011000 => 001011011010
101110100010 => 100111011000
101110100100 => 010111011000
101110101000 => 001111011000
101110110000 => 000111011010
101111000010 => 100011011100
101111000100 => 010011011100
101111001000 => 001011011100
101111010000 => 000111011100
101111100000 => 000011011110
110010101010 => 111101100000
110010101100 => 011101100010
110010110010 => 101101100100
110010110100 => 011101100100
110010111000 => 001101100110
110011001010 => 110101101000
110011001100 => 010101101010
110011010010 => 101101101000
110011010100 => 011101101000
110011011000 => 001101101010
110011100010 => 100101101100
110011100100 => 010101101100
110011101000 => 001101101100
110011110000 => 000101101110
110100101010 => 111011100000
110100101100 => 011011100010
110100110010 => 101011100100
110100110100 => 011011100100
110100111000 => 001011100110
110101001010 => 110111100000
110101001100 => 010111100010
110101010010 => 101111100000
110101010100 => 011111100000
110101011000 => 001111100010
110101100010 => 100111100100
110101100100 => 010111100100
110101101000 => 001111100100
110101110000 => 000111100110
110110001010 => 110011101000
110110001100 => 010011101010
110110010010 => 101011101000
110110010100 => 011011101000
110110011000 => 001011101010
110110100010 => 100111101000
110110100100 => 010111101000
110110101000 => 001111101000
110110110000 => 000111101010
110111000010 => 100011101100
110111000100 => 010011101100
110111001000 => 001011101100
110111010000 => 000111101100
110111100000 => 000011101110
111000101010 => 111001110000
111000101100 => 011001110010
111000110010 => 101001110100
111000110100 => 011001110100
111000111000 => 001001110110
111001001010 => 110101110000
111001001100 => 010101110010
111001010010 => 101101110000
111001010100 => 011101110000
111001011000 => 001101110010
111001100010 => 100101110100
111001100100 => 010101110100
111001101000 => 001101110100
111001110000 => 000101110110
111010001010 => 110011110000
111010001100 => 010011110010
111010010010 => 101011110000
111010010100 => 011011110000
111010011000 => 001011110010
111010100010 => 100111110000
111010100100 => 010111110000
111010101000 => 001111110000
111010110000 => 000111110010
111011000010 => 100011110100
111011000100 => 010011110100
111011001000 => 001011110100
111011010000 => 000111110100
111011100000 => 000011110110
111100001010 => 110001111000
111100001100 => 010001111010
111100010010 => 101001111000
111100010100 => 011001111000
111100011000 => 001001111010
111100100010 => 100101111000
111100100100 => 010101111000
111100101000 => 001101111000
111100110000 => 000101111010
111101000010 => 100011111000
111101000100 => 010011111000
111101001000 => 001011111000
111101010000 => 000111111000
111101100000 => 000011111010
111110000010 => 100001111100
111110000100 => 010001111100
111110001000 => 001001111100
111110010000 => 000101111100
111110100000 => 000011111100
111111000000 => 000001111110
10101010101100 => 01111110000010
10101010110010 => 10111110000100
10101010110100 => 01111110000100
10101011001100 => 01011110001010
10101011010010 => 10111110001000
10101011010100 => 01111110001000
10101011011000 => 00111110001010
10101011100010 => 10011110001100
10101011100100 => 01011110001100
10101100101100 => 01101110010010
10101100110010 => 10101110010100
10101100110100 => 01101110010100
10101101001010 => 11011110010000
10101101001100 => 01011110010010
10101101010010 => 10111110010000
10101101010100 => 01111110010000
10101101011000 => 00111110010010
10101101100010 => 10011110010100
10101101100100 => 01011110010100
10101110001010 => 11001110011000
10101110001100 => 01001110011010
10101110010010 => 10101110011000
10101110100010 => 10011110011000
10101110100100 => 01011110011000
10101111000010 => 10001110011100
10101111000100 => 01001110011100
10101111001000 => 00101110011100
10101111010000 => 00011110011100
10101111100000 => 00001110011110
10110010101010 => 11110110100000
10110010101100 => 01110110100010
10110010110100 => 01110110100100
10110011001010 => 11010110101000
10110011100010 => 10010110101100
10110011110000 => 00010110101110
10110100101010 => 11101110100000
10110100101100 => 01101110100010
10110100110100 => 01101110100100
10110101001010 => 11011110100000
10110101001100 => 01011110100010
10110101010100 => 01111110100000
10110101011000 => 00111110100010
10110110001010 => 11001110101000
10110110110000 => 00011110101010
10110111000010 => 10001110101100
10110111001000 => 00101110101100
10110111010000 => 00011110101100
10110111100000 => 00001110101110
10111000101010 => 11100110110000
10111000111000 => 00100110110110
10111001001010 => 11010110110000
10111010001010 => 11001110110000
10111011010000 => 00011110110100
10111011100000 => 00001110110110
10111100001010 => 11000110111000
10111100001100 => 01000110111010
10111100010010 => 10100110111000
10111100011000 => 00100110111010
10111100100010 => 10010110111000
10111100110000 => 00010110111010
10111101000010 => 10001110111000
10111101001000 => 00101110111000
10111101010000 => 00011110111000
10111101100000 => 00001110111010
10111110000010 => 10000110111100
10111110000100 => 01000110111100
10111110001000 => 00100110111100
10111110010000 => 00010110111100
10111110100000 => 00001110111100
10111111000000 => 00000110111110
11001010101010 => 11111011000000
11001010101100 => 01111011000010
11001010110010 => 10111011000100
11001010110100 => 01111011000100
11001010111000 => 00111011000110
11001011001010 => 11011011001000
11001011001100 => 01011011001010
11001011010010 => 10111011001000
11001011010100 => 01111011001000
11001011011000 => 00111011001010
11001011100010 => 10011011001100
11001011110000 => 00011011001110
11001100101010 => 11101011010000
11001100101100 => 01101011010010
11001100110100 => 01101011010100
11001101010010 => 10111011010000
11001101010100 => 01111011010000
11001101101000 => 00111011010100
11001101110000 => 00011011010110
11001110001010 => 11001011011000
11001110011000 => 00101011011010
11001110100100 => 01011011011000
11001110101000 => 00111011011000
11001110110000 => 00011011011010
11001111000010 => 10001011011100
11001111000100 => 01001011011100
11001111001000 => 00101011011100
11001111010000 => 00011011011100
11001111100000 => 00001011011110
11010010101010 => 11110111000000
11010010101100 => 01110111000010
11010010110100 => 01110111000100
11010011100010 => 10010111001100
11010100101010 => 11101111000000
11010100101100 => 01101111000010
11010100110100 => 01101111000100
11010101001010 => 11011111000000
11010101001100 => 01011111000010
11010101010010 => 10111111000000
11010101010100 => 01111111000000
11010101011000 => 00111111000010
11010101100010 => 10011111000100
11010101100100 => 01011111000100
11010101101000 => 00111111000100
11010101110000 => 00011111000110
11010110001010 => 11001111001000
11010110010100 => 01101111001000
11010110011000 => 00101111001010
11010110100100 => 01011111001000
11010110101000 => 00111111001000
11010110110000 => 00011111001010
11010111010000 => 00011111001100
11011000101010 => 11100111010000
11011001010100 => 01110111010000
11011010001100 => 01001111010010
11011010010100 => 01101111010000
11011010101000 => 00111111010000
11011010110000 => 00011111010010
11011011000010 => 10001111010100
11011011010000 => 00011111010100
11011100001010 => 11000111011000
11011100001100 => 01000111011010
11011110000010 => 10000111011100
11011110000100 => 01000111011100
11011110010000 => 00010111011100
11011110100000 => 00001111011100
11011111000000 => 00000111011110
11100010101010 => 11110011100000
11100010101100 => 01110011100010
11100010110100 => 01110011100100
11100011100010 => 10010011101100
11100011110000 => 00010011101110
11100100101010 => 11101011100000
11100100101100 => 01101011100010
11100100110100 => 01101011100100
11100101001010 => 11011011100000
11100101010010 => 10111011100000
11100101010100 => 01111011100000
11100101100100 => 01011011100100
11100110001100 => 01001011101010
11100110010100 => 01101011101000
11100110101000 => 00111011101000
11100111000010 => 10001011101100
11101000101010 => 11100111100000
11101000101100 => 01100111100010
11101001001100 => 01010111100010
11101001010100 => 01110111100000
11101001100010 => 10010111100100
11101001100100 => 01010111100100
11101010001010 => 11001111100000
11101010001100 => 01001111100010
11101010010100 => 01101111100000
11101010011000 => 00101111100010
11101010100010 => 10011111100000
11101010100100 => 01011111100000
11101010101000 => 00111111100000
11101010110000 => 00011111100010
11101011000010 => 10001111100100
11101011001000 => 00101111100100
11101011010000 => 00011111100100
11101011100000 => 00001111100110
11101100001100 => 01000111101010
11101101000010 => 10001111101000
11101101000100 => 01001111101000
11101110000010 => 10000111101100
11101110000100 => 01000111101100
11101110010000 => 00010111101100
11101110100000 => 00001111101100
11101111000000 => 00000111101110
11110000101100 => 01100011110010
11110000110010 => 10100011110100
11110000111000 => 00100011110110
11110001001100 => 01010011110010
11110001100010 => 10010011110100
11110010001100 => 01001011110010
11110010010010 => 10101011110000
11110010100100 => 01011011110000
11110010101000 => 00111011110000
11110011000010 => 10001011110100
11110011000100 => 01001011110100
11110100001100 => 01000111110010
11110100100010 => 10010111110000
11110100100100 => 01010111110000
11110101000010 => 10001111110000
11110101000100 => 01001111110000
11110101010000 => 00011111110000
11110110000010 => 10000111110100
11110110000100 => 01000111110100
11110110001000 => 00100111110100
11110110010000 => 00010111110100
11110110100000 => 00001111110100
11110111000000 => 00000111110110
11111000001100 => 01000011111010
11111000010010 => 10100011111000
11111000010100 => 01100011111000
11111000100010 => 10010011111000
11111000100100 => 01010011111000
11111000110000 => 00010011111010
11111001000010 => 10001011111000
11111001000100 => 01001011111000
11111001001000 => 00101011111000
11111001100000 => 00001011111010
11111010000010 => 10000111111000
11111010000100 => 01000111111000
11111010001000 => 00100111111000
11111010010000 => 00010111111000
11111010100000 => 00001111111000
11111011000000 => 00000111111010
11111100000010 => 10000011111100
11111100000100 => 01000011111100
11111100001000 => 00100011111100
11111100010000 => 00010011111100
11111100100000 => 00001011111100
11111101000000 => 00000111111100
11111110000000 => 00000011111110
1010101010101100 => 0111111100000010
1010101010110100 => 0111111100000100
1010101011001100 => 0101111100001010
1010101011010100 => 0111111100001000
1010101011100100 => 0101111100001100
1010101100101100 => 0110111100010010
1010101111000100 => 0100111100011100
1010110010101100 => 0111011100100010
1010110010110100 => 0111011100100100
1010110101011000 => 0011111100100010
1010110111000010 => 1000111100101100
1010111000101010 => 1110011100110000
1010111010100010 => 1001111100110000
1010111011000010 => 1000111100110100
1010111100010010 => 1010011100111000
1010111100100010 => 1001011100111000
1010111101000010 => 1000111100111000
1010111110000010 => 1000011100111100
1010111110010000 => 0001011100111100
1010111110100000 => 0000111100111100
1010111111000000 => 0000011100111110
1011001010101100 => 0111101101000010
1011001010110100 => 0111101101000100
1011001111100000 => 0000101101011110
1011010010101100 => 0111011101000010
1011010010110100 => 0111011101000100
1011010101011000 => 0011111101000010
1011011011010000 => 0001111101010100
1011011100001010 => 1100011101011000
1011011101001000 => 0010111101011000
1011100010101010 => 1111001101100000
1011100011110000 => 0001001101101110
1011101001101000 => 0011011101100100
1011101010001010 => 1100111101100000
1011101100001010 => 1100011101101000
1011101101000100 => 0100111101101000
1011110001001010 => 1101001101110000
1011110010001010 => 1100101101110000
1011110100001010 => 1100011101110000
1011110100100100 => 0101011101110000
1011110111000000 => 0000011101110110
1011111000001010 => 1100001101111000
1011111000001100 => 0100001101111010
1011111010100000 => 0000111101111000
1011111011000000 => 0000011101111010
1011111100000010 => 1000001101111100
1011111100010000 => 0001001101111100
1011111100100000 => 0000101101111100
1011111101000000 => 0000011101111100
1011111110000000 => 0000001101111110
1100101010101010 => 1111110110000000
1100101010101100 => 0111110110000010
1100101010110010 => 1011110110000100
1100101010110100 => 0111110110000100
1100101010111000 => 0011110110000110
1100101011001010 => 1101110110001000
1100101011010100 => 0111110110001000
1100101101010100 => 0111110110010000
1100110011001100 => 0101010110101010
1100110011101000 => 0011010110101100
1100110011110000 => 0001010110101110
1100110101010100 => 0111110110100000
1100111000101010 => 1110010110110000
1100111010001100 => 0100110110110010
1100111011001000 => 0010110110110100
1100111011100000 => 0000110110110110
1100111100001100 => 0100010110111010
1100111101010000 => 0001110110111000
1100111101100000 => 0000110110111010
1100111110000010 => 1000010110111100
1100111110000100 => 0100010110111100
1100111110001000 => 0010010110111100
1100111110010000 => 0001010110111100
1100111110100000 => 0000110110111100
1100111111000000 => 0000010110111110
1101001010101100 => 0111101110000010
1101001010110100 => 0111101110000100
1101001101101000 => 0011101110010100
1101001110100100 => 0101101110011000
1101010100101010 => 1110111110000000
1101010100101100 => 0110111110000010
1101010101001010 => 1101111110000000
1101010101001100 => 0101111110000010
1101010101010010 => 1011111110000000
1101010101010100 => 0111111110000000
1101010101011000 => 0011111110000010
1101010101100100 => 0101111110000100
1101010101101000 => 0011111110000100
1101010101110000 => 0001111110000110
1101010110010100 => 0110111110001000
1101010110101000 => 0011111110001000
1101011000101010 => 1110011110010000
1101011001010100 => 0111011110010000
1101100010101010 => 1111001110100000
1101100101010100 => 0111101110100000
1101101000110100 => 0110011110100100
1101101101000010 => 1000111110101000
1101110100100010 => 1001011110110000
1101111000001100 => 0100001110111010
1101111100100000 => 0000101110111100
1101111101000000 => 0000011110111100
1101111110000000 => 0000001110111110
1110001010101010 => 1111100111000000
1110001010101100 => 0111100111000010
1110001010110100 => 0111100111000100
1110001111000010 => 1000100111011100
1110010101001010 => 1101110111000000
1110010101010010 => 1011110111000000
1110010101010100 => 0111110111000000
1110011001010100 => 0111010111010000
1110100011001100 => 0101001111001010
1110100011101000 => 0011001111001100
1110100011110000 => 0001001111001110
1110100100110100 => 0110101111000100
1110100101010100 => 0111101111000000
1110100110100010 => 1001101111001000
1110101000101010 => 1110011111000000
1110101001010100 => 0111011111000000
1110101010001010 => 1100111111000000
1110101010001100 => 0100111111000010
1110101010100010 => 1001111111000000
1110101010100100 => 0101111111000000
1110101010101000 => 0011111111000000
1110101010110000 => 0001111111000010
1110110010001100 => 0100101111010010
1110110011001000 => 0010101111010100
1110110011100000 => 0000101111010110
1110110100010010 => 1010011111010000
1110111000001100 => 0100001111011010
1110111001010000 => 0001101111011000
1110111001100000 => 0000101111011010
1110111100000010 => 1000001111011100
1110111100001000 => 0010001111011100
1110111100010000 => 0001001111011100
1110111100100000 => 0000101111011100
1110111101000000 => 0000011111011100
1110111110000000 => 0000001111011110
1111000011001100 => 0101000111101010
1111000011101000 => 0011000111101100
1111000011110000 => 0001000111101110
1111001010101000 => 0011110111100000
1111010010010010 => 1010101111100000
1111010100001100 => 0100011111100010
1111010110000010 => 1000011111100100
1111010110001000 => 0010011111100100
1111010110100000 => 0000111111100100
1111010111000000 => 0000011111100110
1111011000001100 => 0100001111101010
1111011010010000 => 0001011111101000
1111011011000000 => 0000011111101010
1111011100000010 => 1000001111101100
1111011100000100 => 0100001111101100
1111011100001000 => 0010001111101100
1111011100010000 => 0001001111101100
1111011101000000 => 0000011111101100
1111011110000000 => 0000001111101110
1111100010001100 => 0100100111110010
1111100011000010 => 1000100111110100
1111100011001000 => 0010100111110100
1111100011100000 => 0000100111110110
1111100100001100 => 0100010111110010
1111100110000010 => 1000010111110100
1111100110001000 => 0010010111110100
1111100111000000 => 0000010111110110
1111101000001100 => 0100001111110010
1111101010000010 => 1000011111110000
1111101010000100 => 0100011111110000
1111101010100000 => 0000111111110000
1111101011000000 => 0000011111110010
1111101100000010 => 1000001111110100
1111101100000100 => 0100001111110100
1111101100001000 => 0010001111110100
1111101100010000 => 0001001111110100
1111101100100000 => 0000101111110100
1111101101000000 => 0000011111110100
1111101110000000 => 0000001111110110
1111110000001100 => 0100000111111010
1111110001000010 => 1000100111111000
1111110001000100 => 0100100111111000
1111110001010000 => 0001100111111000
1111110001100000 => 0000100111111010
1111110010000010 => 1000010111111000
1111110010000100 => 0100010111111000
1111110010010000 => 0001010111111000
1111110010100000 => 0000110111111000
1111110011000000 => 0000010111111010
1111110100000010 => 1000001111111000
1111110100000100 => 0100001111111000
1111110100010000 => 0001001111111000
1111110100100000 => 0000101111111000
1111110101000000 => 0000011111111000
1111110110000000 => 0000001111111010
1111111000000010 => 1000000111111100
1111111000000100 => 0100000111111100
1111111000001000 => 0010000111111100
1111111000010000 => 0001000111111100
1111111000100000 => 0000100111111100
1111111001000000 => 0000010111111100
1111111010000000 => 0000001111111100
1111111100000000 => 0000000111111110
1111111111 => 1111111111
1111111110 => 1111111110
1111111101 => 1111111101
1111111011 => 1111111011
1111111010 => 1111111100
1111110110 => 1111111010
1111110010 => 1011111100
1111101110 => 1111110110
1111101011 => 1111110011
1111101010 => 1111111000
1111100100 => 0101111100
1111100010 => 1001111100
1111100001 => 0001111101
1111011110 => 1111101110
1111010010 => 1011111000
1111000001 => 0000111101
1110111110 => 1111011110
1110111011 => 1111011011
1110110100 => 0111110100
1110101111 => 1111001111
1110101010 => 1111110000
1110100001 => 0001111001
1110011110 => 1011101110
1110011100 => 0101110110
1110010110 => 1101110010
1110010011 => 0101110011
1110010001 => 0010111001
1110010000 => 0001011100
1110001001 => 0100111001
1110001000 => 0010011100
1110000101 => 1000111001
1110000011 => 0000111011
1110000010 => 1000011100
1110000001 => 0000011101
1101111110 => 1110111110
1101111101 => 1110111101
1101111001 => 0111011101
1101110001 => 0011101101
1101100001 => 0001110101
1101010001 => 0011110001
1101010000 => 0001111000
1101001110 => 1011100110
1101001001 => 0101110001
1101001000 => 0010111000
1101000101 => 1001110001
1101000011 => 0001110011
1101000010 => 1000111000
1101000001 => 0000111001
1100111101 => 1011011101
1100111001 => 0101101101
1100110001 => 0010110101
1100101001 => 0110110001
1100100110 => 1010110010
1100100101 => 1010110001
1100100100 => 0101011000
1100100011 => 0010110011
1100100001 => 0001011001
1100011111 => 0011011111
1100011101 => 1001101101
1100011100 => 0100110110
1100011010 => 1100110100
1100011001 => 0100110101
1100010110 => 1100110010
1100010101 => 1100110001
1100010011 => 0100110011
1100010010 => 1010011000
1100010001 => 0010011001
1100010000 => 0001001100
1100001111 => 0001101111
1100001101 => 1000110101
1100001011 => 1000110011
1100001001 => 0100011001
1100001000 => 0010001100
1100000111 => 0000110111
1100000110 => 1000011010
1100000101 => 1000011001
1100000011 => 0000011011
1100000010 => 1000001100
1100000001 => 0000001101
1100000000 => 0000000110
1011111111 => 1011111111
1011111110 => 1101111110
1011111101 => 1101111101
1011111100 => 0110111110
1011111011 => 1101111011
1011111010 => 1110111100
1011111000 => 0011011110
1011110100 => 0111011100
1011101111 => 1101101111
1011101110 => 1110110110
1011101010 => 1111011000
1011100110 => 1011011010
1011100001 => 0001101101
1011100000 => 0000110110
1011011111 => 1101011111
1011011100 => 0111010110
1011010110 => 1111010010
1011010011 => 0111010011
1011010001 => 0011101001
1011010000 => 0001110100
1011001001 => 0101101001
1011001000 => 0010110100
1011000101 => 1001101001
1011000011 => 0001101011
1011000001 => 0000110101
1011000000 => 0000011010
1010111111 => 1100111111
1010111110 => 1110011110
1010111010 => 1111001100
1010110001 => 0011100101
1010101111 => 1110001111
1010101110 => 1111000110
1010101011 => 1111000011
1010101001 => 0111100001
1010101000 => 0011110000
1010100110 => 1011100010
1010100101 => 1011100001
1010100100 => 0101110000
1010100011 => 0011100011
1010100000 => 0000111000
1010011111 => 0110011111
1010011101 => 1011001101
1010011100 => 0101100110
1010011010 => 1101100100
1010011001 => 0101100101
1010011000 => 0010110010
1010010111 => 1011000111
1010010110 => 1101100010
1010010101 => 1101100001
1010010011 => 0101100011
1010010000 => 0001011000
1010001111 => 0011001111
1010001110 => 1001100110
1010001101 => 1001100101
1010001011 => 1001100011
1010001000 => 0010011000
1010000111 => 0001100111
1010000101 => 1000110001
1010000011 => 0000110011
1010000010 => 1000011000
1010000001 => 0000011001
1010000000 => 0000001100
1001111111 => 0101111111
1001111110 => 1010111110
1001111101 => 1010111101
1001111100 => 0101011110
1001111000 => 0010101110
1001110110 => 1101011010
1001110100 => 0110101100
1001110011 => 0101011011
1001110001 => 0010101101
1001101100 => 0110101010
1001101010 => 1110101000
1001101001 => 0110101001
1001101000 => 0011010100
1001100110 => 1010101010
1001100101 => 1010101001
1001100011 => 0010101011
1001011110 => 1101001110
1001011100 => 0110100110
1001011011 => 1101001011
1001011010 => 1110100100
1001011001 => 0110100101
1001010110 => 1110100010
1001010101 => 1110100001
1001010100 => 0111010000
1001010011 => 0110100011
1001001111 => 0101001111
1001001110 => 1010100110
1001001101 => 1010100101
1001001011 => 1010100011
1001001010 => 1101010000
1001001000 => 0010101000
1001000111 => 0010100111
1001000000 => 0000010100
1000111110 => 1001011110
1000111101 => 1001011101
1000111100 => 0100101110
1000111010 => 1100101100
1000111001 => 0100101101
1000111000 => 0010010110
1000110110 => 1100101010
1000110101 => 1100101001
1000110011 => 0100101011
1000101110 => 1100100110
1000101101 => 1100100101
1000101100 => 0110010010
1000101011 => 1100100011
1000100111 => 0100100111
1000100110 => 1010010010
1000100101 => 1010010001
1000100011 => 0010010011
1000011110 => 1000101110
1000011101 => 1000101101
1000011011 => 1000101011
1000010111 => 1000100111
1000010110 => 1100010010
1000010001 => 0010001001
1000010000 => 0001000100
1000001111 => 0000101111
1000001110 => 1000010110
1000001101 => 1000010101
1000001010 => 1100001000
1000001000 => 0010000100
1000000110 => 1000001010
1000000101 => 1000001001
1000000100 => 0100000100
1000000011 => 0000001011
1000000010 => 1000000100
1000000001 => 0000000101
1000000000 => 0000000010
10000000000 => 00000000010
10000000010 => 10000000100
10000000110 => 10000001010
10000001110 => 10000010110
10000011110 => 10000101110
10000111110 => 10001011110
10001111110 => 10010111110
10011111110 => 10101111110
10111111110 => 11011111110
11111111110 => 11111111110
10000000100 => 01000000100
10000001010 => 11000001000
10000010110 => 11000010010
10000101110 => 11000100110
100000111110 => 100001011110
10001011110 => 11001001110
10010111110 => 11010011110
10101111110 => 11100111110
11011111110 => 11101111110
101111111110 => 110111111110
100001011110 => 110001001110
100101111110 => 110100111110
11101111110 => 11110111110
10000010000 => 00010000100
10000100010 => 10010001000
100010011110 => 101001001110
100001101110 => 110001010110
10101011110 => 11110001110
10111011110 => 11101101110
11110111110 => 11111011110
111011111110 => 111101111110
10000100000 => 00001000100
10001000010 => 10001001000
10000100100 => 01010001000
100001000110 => 100100010010
10001001010 => 11010010000
100100011110 => 100101001110
100010101110 => 111001000110
100001110110 => 110001011010
10101101110 => 11110010110
101010111110 => 111100011110
100111011110 => 110101101110
11100111110 => 10111011110
11011011110 => 11110101110
10111101110 => 11101110110
11111011110 => 11111101110
100000100000 => 000010000100
10001000000 => 00000100100
10001000100 => 01001001000
10000101000 => 00110001000
10010001010 => 11001010000
10001010010 => 10110010000
101000011110 => 100011001110
100100101110 => 110101000110
100011001110 => 101001010110
100010110110 => 111001001010
100001111010 => 110001011100
11010011110 => 10111001110
10110101110 => 11110100110
10101110110 => 11110011010
11101011110 => 11111001110
11011101110 => 11110110110
10111110110 => 11101111010
11111101110 => 11111110110
111110111110 => 111111011110
1000000100000 => 0000100000100
1000001000010 => 1000100001000
10010000100 => 01000101000
10001001000 => 00101001000
100010001010 => 110010010000
100001001100 => 010100010010
10010010010 => 10101010000
10001010100 => 01110010000
101000101110 => 110011000110
10010101010 => 11110100000
100101001110 => 101101000110
100100110110 => 110101001010
100011010110 => 111001010010
100010111010 => 111001001100
100001111100 => 010001011110
11001001110 => 10101100110
10101010110 => 11111000010
11010101110 => 11111000110
10110110110 => 11110101010
101101011110 => 111101001110
10101111010 => 11110011100
101011101110 => 111100110110
100111110110 => 110101111010
11110011110 => 10111101110
11101101110 => 11111010110
11011110110 => 11110111010
10111111010 => 11101111100
11111110110 => 11111111010
1000001000100 => 0100100001000
10100000000 => 00000001100
11000000010 => 10000001100
10010001000 => 00100101000
10001010000 => 00011001000
10100010010 => 10100110000
10010100010 => 10011010000
10010010100 => 01101010000
11000100110 => 10100110010
110000101110 => 110001100110
10100101010 => 11101100000
101001001110 => 101011000110
101000110110 => 110011001010
100110001110 => 100101010110
100101010110 => 111101000010
100100111010 => 110101001100
100011100110 => 101001011010
100011011010 => 111001010100
100010111100 => 011001001110
10101011010 => 11111000100
11010110110 => 11111001010
10111010110 => 11110110010
10110111010 => 11110101100
11110101110 => 11111100110
11101110110 => 11111011010
10111111100 => 01101111110
11111111010 => 11111111100
111111101110 => 111111110110
=>
0000111110 => 1000011110
0001111010 => 1100011100
0001111100 => 0100011110
0001110110 => 1100011010
0011110010 => 1010011100
0011110100 => 0110011100
0010111010 => 1110001100
0010111100 => 0110001110
0011111000 => 0010011110
0001101110 => 1100010110
0011101010 => 1110011000
0011101100 => 0110011010
0011100110 => 1010011010
0111100010 => 1001011100
0111100100 => 0101011100
0100111010 => 1101001100
0100111100 => 0101001110
0111101000 => 0011011100
0010110110 => 1110001010
0110110010 => 1011010100
0110110100 => 0111010100
0101101010 => 1111001000
0101101100 => 0111001010
0110111000 => 0011010110
0101110010 => 1011001100
0101110100 => 0111001100
0101111000 => 0011001110
0111110000 => 0001011110
0101010101 => 1111000001
0000011111 => 0000011111
0100001111 => 0001001111
0000110111 => 1000010111
0000101111 => 1000001111
0101000111 => 0011000111
0000111011 => 1000011011
0100011011 => 1001001011
0001101011 => 1100010011
0001011011 => 1100001011
0100010111 => 1001000111
0001100111 => 0100010111
0001001111 => 0100001111
0001010111 => 1100000111
0101010011 => 0111000011
0000111101 => 1000011101
0100011101 => 1001001101
0001101101 => 1100010101
0001011101 => 1100001101
0101001101 => 1011000101
0001110101 => 1100011001
0100110101 => 1101001001
0011010101 => 1110010001
0010110101 => 1110001001
0100101101 => 1101000101
0011000111 => 0010010111
0010001111 => 0010001111
0010101101 => 1110000101
0101001011 => 1011000011
0001110011 => 0100011011
0100110011 => 0101001011
0011010011 => 0110010011
0010110011 => 0110001011
0100100111 => 0101000111
0011001101 => 1010010101
0010011101 => 1010001101
0010100111 => 0110000111
0100101011 => 1101000011
0011001011 => 1010010011
0010011011 => 1010001011
0010010111 => 1010000111
0010101011 => 1110000011
0111100001 => 0001011101
0111000101 => 1001011001
0110110001 => 0011010101
0111010001 => 0011011001
0110010101 => 1101010001
0101110001 => 0011001101
0101100101 => 1011001001
0101011001 => 0111000101
0101101001 => 0111001001
0110100101 => 1011010001
0110101001 => 0111010001
0110011001 => 0101010101
0111001001 => 0101011001
0111011000 => 0011011010
0110101100 => 0111010010
0111001100 => 0101011010
0111010100 => 0111011000
0101011100 => 0111000110
0101010110 => 1111000010
0101011010 => 1111000100
0111000110 => 1001011010
0110011100 => 0101010110
0110010110 => 1101010010
0110011010 => 1101010100
0101100110 => 1011001010
0111001010 => 1101011000
0110100110 => 1011010010
0111010010 => 1011011000
0110101010 => 1111010000
00001000001 => 00001000001
000011011110 => 110000101110
010000011111 => 000010011111
000001111101 => 100000111101
111100000101 => 100001111001
011111000001 => 000010111101
010111110000 => 000110011110
0011011100 => 0110010110
0001011110 => 1100001110
0011010110 => 1110010010
0010101110 => 1110000110
0011001110 => 1010010110
0010011110 => 1010001110
0100101110 => 1101000110
0101001110 => 1011000110
0110001110 => 1001010110
0100011110 => 1001001110
0011011001 => 0110010101
0011011010 => 1110010100
0100110110 => 1101001010
0010111001 => 0110001101
0001111001 => 0100011101
0011110001 => 0010011101
0110010011 => 0101010011
0110001011 => 1001010011
0110000111 => 0001010111
0111000011 => 0001011011
0011101001 => 0110011001
0011100101 => 1010011001
0100111001 => 0101001101
0011100011 => 0010011011
0101100011 => 0011001011
0110100011 => 0011010011
10110110110110100000 => 00001111110101010100
10110110111010010000 => 00010111110101011000
10110111010011010000 => 00011011110101100100
10110111011010001000 => 00100111110101101000
10110111101001001000 => 00101011110101110000
10111010011011010000 => 00011101110110010100
10111010011101001000 => 00101101110110011000
10111011010001101000 => 00110011110110100100
10111011011010000100 => 01000111110110101000
10111011101001000100 => 01001011110110110000
10111101001001101000 => 00110101110111000100
10111101001101000100 => 01001101110111001000
10111101101000100100 => 01010011110111010000
10111110100100100100 => 01010101110111100000
11010011011011010000 => 00011110111001010100
11010011011101001000 => 00101110111001011000
11010011101001101000 => 00110110111001100100
11010011101101000100 => 01001110111001101000
11010011110100100100 => 01010110111001110000
11011010001101101000 => 00111001111010010100
11011010001110100100 => 01011001111010011000
11011011010000110100 => 01100011111010100100
11011011011010000010 => 10000111111010101000
11011011101001000010 => 10001011111010110000
11011101001000110100 => 01100101111011000100
11011101001101000010 => 10001101111011001000
11011101101000100010 => 10010011111011010000
11011110100100100010 => 10010101111011100000
11101001001101101000 => 00111010111100010100
11101001001110100100 => 01011010111100011000
11101001101000110100 => 01100110111100100100
11101001101101000010 => 10001110111100101000
11101001110100100010 => 10010110111100110000
11101101000100110100 => 01101001111101000100
11101101000110100010 => 10011001111101001000
11101101101000010010 => 10100011111101010000
11101110100100010010 => 10100101111101100000
11110100100100110100 => 01101010111110000100
11110100100110100010 => 10011010111110001000
11110100110100010010 => 10100110111110010000
11110110100010010010 => 10101001111110100000
11111010010010010010 => 10101010111111000000
10100100010000 => 00010010110000
111111110000000010 => 100000001111111100
101111111100000000 => 000000011011111110
11111111100000000010 => 10000000011111111100
111111101000000010 => 100000011111111000
101111111010000000 => 000000111011111100
10111111111000000000 => 00000000110111111110
1111111111000000000010 => 1000000000111111111100
11111111010000000010 => 10000000111111111000
111111100100000010 => 100000101111111000
111111011000000010 => 100000011111110100
101111111001000000 => 000001011011111100
101111110110000000 => 000000111011111010
10111111110100000000 => 00000001110111111100
1011111111110000000000 => 0000000001101111111110
0000000010 => 1000000000
00000000010 => 10000000000
0100000100 => 0100001000
0000000001 => 0000000001
0100000001 => 0000001001
0110000001 => 0000010101
0111000001 => 0000101101
0111110001 => 0010111101
0111111001 => 0101111101
0111111101 => 1011111101
0111111111 => 0111111111
00000000001 => 00000000001
01000000001 => 00000001001
0010000001 => 0000010001
01100000001 => 00000010101
0101000001 => 0000110001
01110000001 => 00000101101
0110100001 => 0001101001
01111000001 => 00001011101
01111100001 => 00010111101
0111101001 => 0110111001
01111110001 => 00101111101
0111110101 => 1101111001
01111111001 => 01011111101
0111111011 => 1011111011
01111111101 => 10111111101
01111111111 => 01111111111
0000000101 => 1000000001
0000001101 => 1000000101
0000011101 => 1000001101
0001111101 => 1000111101
0011111101 => 1001111101
00000000101 => 10000000001
0000001001 => 0100000001
00000001101 => 10000000101
0000010101 => 1100000001
00000011101 => 10000001101
0000101101 => 1100000101
00000111101 => 10000011101
00001111101 => 10000111101
0010111101 => 1100011101
00011111101 => 10001111101
0101111101 => 1100111101
00111111101 => 10011111101
11111111101 => 11111111101
0100000000 => 0000000100
0100000011 => 0000010011
0100000111 => 0000100111
0100011111 => 0010011111
0100111111 => 0100111111
0101111111 => 1001111111
01000000000 => 00000000100
0100000010 => 1000001000
01000000011 => 00000010011
0100000101 => 1000010001
01000000111 => 00000100111
0100001011 => 1000100011
01000001111 => 00001001111
01000011111 => 00010011111
0100101111 => 1010001111
01000111111 => 00100111111
0101011111 => 1100011111
01001111111 => 01001111111
0110111111 => 1010111111
01011111111 => 10011111111
0000000000 => 0000000000
101010101010101100 => 011111111000000010
101010101010110100 => 011111111000000100
10101010101010101100 => 01111111110000000010
110010101010101100 => 011111101100000010
110010101010110100 => 011111101100000100
10101010101010110100 => 01111111110000000100
1010101010101010101100 => 0111111111100000000010
11001010101010101100 => 01111111011000000010
101100101010101100 => 011111011010000010
110100101010101100 => 011111011100000010
101100101010110100 => 011111011010000100
110100101010110100 => 011111011100000100
11001010101010110100 => 01111111011000000100
1010101010101010110100 => 0111111111100000000100
110101010101010100 => 011111111100000000
111000101010101010 => 111111001110000000
111001010101010100 => 011111101110000000
11010101010101010100 => 01111111111000000000
11100010101010101010 => 11111110011100000000
101110001010101010 => 111110011011000000
110110001010101010 => 111110011101000000
110110010101010100 => 011111011101000000
111010010101010100 => 011111011110000000
11100101010101010100 => 01111111011100000000
1101010101010101010100 => 0111111111110000000000
101011111110000000 => 000000111001111110
101111111000000010 => 100000011011111100
10101111111100000000 => 00000001110011111110
101100111111000000 => 000001011010111110
110011111100000010 => 100000101101111100
10111111110000000010 => 10000000110111111100
110010101010101010 => 111111101100000000
110101010101011000 => 001111111100000010
11001010101010101010 => 11111111011000000000
11010101010101011000 => 00111111111000000010
110101010101101000 => 001111111100000100
110101010101100100 => 010111111100000100
110010101010110010 => 101111101100000100
1100101010101010101010 => 1111111110110000000000
101011111100000010 => 100000111001111100
101111110000001010 => 110000011011111000
10101111111000000010 => 10000001110011111100
101011111010000010 => 100001111001111000
101111101000001010 => 110000111011110000
10111111100000001010 => 11000000110111111000
1010111111110000000010 => 1000000011100111111100
10101111110100000010 => 10000011110011111000
101011110110000010 => 100001111001110100
101011111001000010 => 100010111001111000
101111011000001010 => 110000111011101000
101111100100001010 => 110001011011110000
10111111010000001010 => 11000001110111110000
1011111111000000001010 => 1100000001101111111000
111111110000000100 => 010000001111111100
111111101000000100 => 010000011111111000
11111111100000000100 => 01000000011111111100
101010101011001100 => 010111111000001010
101010101011100100 => 010111111000001100
111111011000000100 => 010000011111110100
111111100100000100 => 010000101111111000
11111111010000000100 => 01000000111111111000
1111111111000000000100 => 0100000000111111111100
111001010101010010 => 101111101110000000
110011010101010100 => 011111101101000000
110101010101001100 => 010111111100000010
101101010101011000 => 001111111010000010
111111110100000000 => 000000011111111100
111111110010000000 => 000000101111111100
11111111101000000000 => 00000000111111111100
11111111100100000000 => 00000001011111111100
1111111111010000000000 => 0000000001111111111100
110111111010000000 => 000000111101111100
110111111001000000 => 000001011101111100
10111111110010000000 => 00000010110111111100
1111111111001000000000 => 0000000010111111111100
111010101010101000 => 001111111110000000
110101010101010010 => 101111111100000000
111010101010100010 => 100111111110000000
11101010101010101000 => 00111111111100000000
11010101010101010010 => 10111111111000000000
110101010101001010 => 110111111100000000
111010101010001010 => 110011111110000000
111010101010100100 => 010111111110000000
11101010101010100010 => 10011111111100000000
1110101010101010101000 => 0011111111111000000000
110111111100000000 => 000000011101111110
101111110000001100 => 010000011011111010
111111110000001000 => 001000001111111100
111011111100000000 => 000000011110111110
11011111111000000000 => 00000000111011111110
111111011010000000 => 000000111111110100
11111110110100000000 => 00000001111111110100
111110111010000000 => 000000111111101100
111111011001000000 => 000001011111110100
111110111000000010 => 100000011111101100
111111001100000010 => 100000101111110100
11111110110000000010 => 10000000111111110100
110011111110000000 => 000000101101111110
111111111000000000 => 000000001111111110
11001111111100000000 => 00000001011011111110
110011111101000000 => 000001101101111100
11111111110000000000 => 00000000011111111110
1100111111111000000000 => 0000000010110111111110
11001111111010000000 => 00000011011011111100
110011111011000000 => 000001101101111010
110011111100100000 => 000010101101111100
111111101100000000 => 000000011111111010
1111111111100000000000 => 0000000000111111111110
111111100000001100 => 010000001111111010
111111010000001100 => 010000011111110010
11111111000000001100 => 01000000011111111010
111110110000001100 => 010000011111101010
111111001000001100 => 010000101111110010
11111110100000001100 => 01000000111111110010
1111111110000000001100 => 0100000000111111111010
11000000000 => 00000000110
10000000001 => 00000000101
00010100001 => 00011000001
0000010000001 => 0000010000001
100000001000000 => 000001000000100
1000001010000 => 0001100001000
00100100001 => 00010100001
00010010001 => 00101000001
0000101000001 => 0000110000001
000000100000001 => 000000100000001
10000000010000000 => 00000010000000100
100000010100000 => 000011000001000
1000010010000 => 0001010001000
1000001001000 => 0010100001000
01000001000 => 00100001000
01000100001 => 00010010001
00101010001 => 00111000001
0001001000001 => 0000101000001
00010000010 => 10000100000
00010001001 => 01001000001
0000100100001 => 0001010000001
000001010000001 => 000001100000001
00000001000000001 => 00000001000000001
1000000000100000000 => 0000000100000000100
10000000101000000 => 00000110000001000
100000100100000 => 000010100001000
100000010010000 => 000101000001000
1000100010000 => 0001001001000
1000010101000 => 0011100010000
10100001000 => 00100011000
10000100001 => 00010001001
01000010100 => 01100010000
01001010001 => 00110100001
0010001000001 => 0000100100001
00100000100 => 01000010000
00100010001 => 00100100001
00101000010 => 10001100000
00101001001 => 01011000001
0001010100001 => 0001110000001
000010010000001 => 000001010000001
00010000101 => 10001000001
0000100010001 => 0010010000001
000001001000001 => 000010100000001
00000010100000001 => 00000011000000001
0000000010000000001 => 0000000010000000001
100000000001000000000 => 000000001000000000100
1000000001010000000 => 0000001100000001000
10000001001000000 => 00000101000001000
10000000100100000 => 00001010000001000
100001000100000 => 000010010001000
100000101010000 => 000111000010000
100000010001000 => 001001000001000
1001000010000 => 0001000101000
1000100101000 => 0011010010000
1000010001000 => 0010010001000
1000010100100 => 0101100010000
0100000010000 => 0001000001000
10100010100 => 01100110000
10010100100 => 01011010000
10001010001 => 00110010001
0100001000001 => 0000100010001
01000100100 => 01010010000
01000010010 => 10100010000
01010000100 => 01000110000
01010010001 => 00101100001
01001000010 => 10001010000
01001001001 => 01010100001
0010010100001 => 0001101000001
000100010000001 => 000001001000001
00100001010 => 11000100000
00100100010 => 10010100000
00100101001 => 01101000001
0001000100001 => 0001001000001
00101000101 => 10011000001
0001010010001 => 0010110000001
000010101000001 => 000011100000001
00000100100000001 => 00000010100000001
0000100000010 => 1000001000000
0000100001001 => 0100010000001
000001000100001 => 000100100000001
00000010010000001 => 00000101000000001
0000000101000000001 => 0000000110000000001
000000000100000000001 => 000000000100000000001
00000110111110 => 11000001011110
000111011100 => 011000110110
100011111000 => 001001011110
10000011111100 => 01000010111110
0000001101111110 => 1100000010111110
00001110111100 => 01100001101110
000111011010 => 111000110100
001011011100 => 011100010110
100011110100 => 011001011100
100101111000 => 001101001110
10000111111000 => 00100010111110
1000000111111100 => 0100000101111110
000000011011111110 => 110000000101111110
0000011101111100 => 0110000011011110
00001110111010 => 11100001101100
00010110111100 => 01110000101110
000111010110 => 111000110010
001111011000 => 001100111010
010011011100 => 011010010110
000101101110 => 111000010110
100011101100 => 011001011010
100111110000 => 000101011110
10000111110100 => 01100010111100
010001111010 => 110010011100
101001111000 => 001011001110
10001011111000 => 00110010011110
1000001111111000 => 0010000101111110
100000001111111100 => 010000001011111110
00000000110111111110 => 11000000001011111110
000000111011111100 => 011000000110111110
0000011101111010 => 1110000011011100
0000101101111100 => 0111000001011110
00001110110110 => 11100001101010
00011110111000 => 00110001110110
00100110111100 => 01101000101110
000111001110 => 101000110110
001111010100 => 011100111000
001011011010 => 111100010100
010111011000 => 001110011010
100011011100 => 011001010110
001101101100 => 011100101010
100111101000 => 001101011100
10000111101100 => 01100010111010
001001110110 => 110100011010
100101110100 => 011101001100
010011110010 => 101010011100
10001111110000 => 00010010111110
1000001111110100 => 0110000101111100
110001111000 => 001001101110
10010011111000 => 00101010011110
1000010111111000 => 0011000100111110
100000011111111000 => 001000001011111110
10000000011111111100 => 01000000010111111110
0000000001101111111110 => 1100000000010111111110
00000001110111111100 => 01100000001101111110
000000111011111010 => 111000000110111100
000001011011111100 => 011100000010111110
0000011101110110 => 1110000011011010
0000111101111000 => 0011000011101110
0001001101111100 => 0110100001011110
00001110101110 => 11100001100110
00011110110100 => 01110001110100
00010110111010 => 11110000101100
00101110111000 => 00111000110110
01000110111100 => 01100100101110
00001011011110 => 11100000101110
001111001100 => 010100111010
001111010010 => 101100111000
010111010100 => 011110011000
011011011000 => 001110101010
100111011000 => 001101011010
10000111011100 => 01100010110110
001101101010 => 111100101000
010101101100 => 011110001010
001011100110 => 101100011010
100111100100 => 010101011100
010011101010 => 111010011000
10001111101000 => 00110010111100
1000001111101100 => 0110000101111010
011001110100 => 011010101100
010101110010 => 101110001100
10001011110100 => 01110010011100
10010111110000 => 00011010011110
1000011111110000 => 0001000101111110
100000011111110100 => 011000001011111100
01000011111010 => 11000100111100
10100011111000 => 00100110011110
1000100111111000 => 0010100100111110
100000101111111000 => 001100001001111110
10000000111111111000 => 00100000010111111110
1000000000111111111100 => 0100000000101111111110
00000011111101 => 10000001111101
000010111101 => 110000011101
010000101111 => 100010001111
01000000111111 => 00000100111111
0000000111111101 => 1000000011111101
00000101111101 => 11000000111101
000011011101 => 110000101101
000100111101 => 101000011101
010000110111 => 100010010111
010001001111 => 010010001111
01000001011111 => 10000100011111
0100000001111111 => 0000001001111111
000000001111111101 => 100000000111111101
0000001011111101 => 1100000001111101
00000110111101 => 11000001011101
00001001111101 => 10100000111101
000011101101 => 110000110101
000101011101 => 111000001101
001000111101 => 100100011101
000011110011 => 010000111011
010000111011 => 100010011011
010001010111 => 110010000111
01000001101111 => 10000100101111
001100001111 => 000100101111
010010001111 => 001010001111
01000010011111 => 01000100011111
0100000010111111 => 1000001000111111
010000000011111111 => 000000010011111111
00000000011111111101 => 10000000001111111101
000000010111111101 => 110000000011111101
0000001101111101 => 1100000010111101
0000010011111101 => 1010000001111101
00000111011101 => 11000001101101
00001010111101 => 11100000011101
00010001111101 => 10010000111101
000011110101 => 110000111001
000101101101 => 111000010101
000110011101 => 101000101101
001001011101 => 110100001101
010000111101 => 100010011101
000101110011 => 011000011011
010001011011 => 110010001011
01000001110111 => 10000100110111
000111000111 => 001000110111
010001100111 => 010010010111
001100010111 => 100100100111
010010010111 => 101010000111
01000010101111 => 11000100001111
0100000011011111 => 1000001001011111
010100001111 => 000110001111
01000100011111 => 00100100011111
0100000100111111 => 0100001000111111
010000000101111111 => 100000010001111111
01000000000111111111 => 00000000100111111111
0000000000111111111101 => 1000000000011111111101
00000000101111111101 => 11000000000111111101
000000011011111101 => 110000000101111101
000000100111111101 => 101000000011111101
0000001110111101 => 1100000011011101
0000010101111101 => 1110000000111101
0000100011111101 => 1001000001111101
00000111101101 => 11000001110101
00001011011101 => 11100000101101
00001100111101 => 10100001011101
00010010111101 => 11010000011101
00100001111101 => 10001000111101
00000111110011 => 01000001111011
000101110101 => 111000011001
000110101101 => 111000100101
001001101101 => 110100010101
001010011101 => 101100001101
010001011101 => 110010001101
01000001111011 => 10000100111011
000110110011 => 011000101011
001001110011 => 010100011011
000111001011 => 101000110011
010001101011 => 110010010011
001100011011 => 100100101011
010010011011 => 101010001011
01000010110111 => 11000100010111
0100000011101111 => 1000001001101111
001011000111 => 001100010111
001100100111 => 010100100111
010010100111 => 011010000111
01000011001111 => 01000100101111
010100010111 => 100110000111
01000100101111 => 10100100001111
0100000101011111 => 1100001000011111
010000000110111111 => 100000010010111111
00110000011111 => 00001001011111
01001000011111 => 00010100011111
0100001000111111 => 0010001000111111
010000001001111111 => 010000010001111111
01000000001011111111 => 10000000100011111111
0100000000001111111111 => 0000000001001111111111
01111110000001 => 00000101111101
011110100001 => 000110111001
111010000101 => 100011110001
11111000000101 => 10000011111001
0111111100000001 => 0000001011111101
01111101000001 => 00001101111001
011101100001 => 000110110101
011110010001 => 001010111001
110110000101 => 100011101001
111001000101 => 100101110001
11110100000101 => 10000111110001
1111110000000101 => 1000000111111001
011111111000000001 => 000000010111111101
0111111010000001 => 0000011011111001
01111011000001 => 00001101110101
01111100100001 => 00010101111001
011011100001 => 000110101101
011101010001 => 001110110001
011110001001 => 010010111001
100111100001 => 000101011101
101110000101 => 100011011001
110101000101 => 100111100001
11101100000101 => 10000111101001
111000011001 => 010001110101
111000100101 => 101001110001
11110010000101 => 10001011110001
1111101000000101 => 1000001111110001
111111100000000101 => 100000001111111001
01111111110000000001 => 00000000101111111101
011111110100000001 => 000000110111111001
0111110110000001 => 0000011011110101
0111111001000001 => 0000101011111001
01110111000001 => 00001101101101
01111010100001 => 00011101110001
01111100010001 => 00100101111001
010111100001 => 000110011101
011011010001 => 001110101001
011100110001 => 001010110101
011101001001 => 010110110001
011110000101 => 100010111001
100111010001 => 001101011001
101101000101 => 100111010001
11011100000101 => 10000111011001
110001110001 => 001001101101
110011000101 => 100101101001
110100011001 => 010011100101
110100100101 => 101011100001
11101010000101 => 10001111100001
1111011000000101 => 1000001111101001
111000010101 => 110001110001
11110001000101 => 10010011110001
1111100100000101 => 1000010111110001
111111010000000101 => 100000011111110001
11111111000000000101 => 10000000011111111001
0111111111100000000001 => 0000000001011111111101
01111111101000000001 => 00000001101111111001
011111101100000001 => 000000110111110101
011111110010000001 => 000001010111111001
0111101110000001 => 0000011011101101
0111110101000001 => 0000111011110001
0111111000100001 => 0001001011111001
01101111000001 => 00001101011101
01110110100001 => 00011101101001
01111001100001 => 00010101110101
01111010010001 => 00101101110001
01111100001001 => 01000101111001
10011111000001 => 00001010111101
010111010001 => 001110011001
011010110001 => 001110100101
011011001001 => 010110101001
011100101001 => 011010110001
011101000101 => 100110110001
10111100000101 => 10000110111001
100110110001 => 001101010101
100111001001 => 010101011001
101001110001 => 001011001101
101011000101 => 100111001001
101100011001 => 010011010101
101100100101 => 101011010001
11011010000101 => 10001111010001
1110111000000101 => 1000001111011001
110001101001 => 011001101001
110010011001 => 010101100101
110010100101 => 101101100001
11100110000101 => 10001011101001
110100010101 => 110011100001
11101001000101 => 10010111100001
1111010100000101 => 1000011111100001
111110110000000101 => 100000011111101001
11110000011001 => 01000011110101
11110000100101 => 10100011110001
1111100010000101 => 1000100111110001
111111001000000101 => 100000101111110001
11111110100000000101 => 10000000111111110001
1111111110000000000101 => 1000000000111111111001
01011111100000 => 00001100111110
010111101000 => 001110011100
0101111111000000 => 0000011001111110
01011111010000 => 00011100111100
010111100100 => 010110011100
010111111110000000 => 000000110011111110
0101111110100000 => 0000111001111100
01011110110000 => 00011100111010
01011111001000 => 00101100111100
010110111000 => 001110010110
010111100010 => 100110011100
011001111000 => 001010101110
011110000110 => 100010111010
01011111111100000000 => 00000001100111111110
010111111101000000 => 000001110011111100
0101111101100000 => 0000111001111010
0101111110010000 => 0001011001111100
01011101110000 => 00011100110110
01011110101000 => 00111100111000
01011111000100 => 01001100111100
010101111000 => 001110001110
010110110100 => 011110010100
010111001100 => 010110011010
010111010010 => 101110011000
011100011100 => 010010110110
011101000110 => 100110110010
0101111111111000000000 => 0000000011001111111110
01011111111010000000 => 00000011100111111100
010111111011000000 => 000001110011111010
010111111100100000 => 000010110011111100
0101111011100000 => 0000111001110110
0101111101010000 => 0001111001111000
0101111110001000 => 0010011001111100
01011011110000 => 00011100101110
01011101101000 => 00111100110100
01011110011000 => 00101100111010
01011110100100 => 01011100111000
01011111000010 => 10001100111100
01100111110000 => 00010101011110
010101110100 => 011110001100
010110101100 => 011110010010
010110110010 => 101110010100
010111001010 => 110110011000
011001101100 => 011010101010
011001110010 => 101010101100
011010011100 => 010110100110
011011000110 => 100110101010
011100011010 => 110010110100
011100100110 => 101010110010
01111100000110 => 10000101111010
11100000001 => 00000011101
11010000001 => 00000111001
11001000001 => 00001011001
11000100001 => 00010011001
11000010001 => 00100011001
11000001001 => 01000011001
11000000101 => 10000011001
11000000011 => 00000011011
11000010010 => 10100011000
0010001100 => 0100100010
11000001000 => 00100001100
0100001000 => 0010001000
01000000100 => 01000001000
01111111011 => 10111111011
0111110111 => 1011110111
01111110101 => 11011111001
0111100111 => 0101110111
01111101001 => 01101111001
0111001011 => 1010110011
01111010001 => 00110111001
01110100001 => 00011011001
0100100011 => 0010100011
01101000001 => 00001101001
0001000011 => 0001000011
01010000001 => 00000110001
0010000010 => 1000010000
00100000001 => 00000010001
0001000001 => 0000100001
0001100001 => 0001000101
0010110001 => 0011000101
0011101101 => 1100110101
0011110111 => 1001110111
0000000100 => 0100000000
10111111101 => 11011111101
01011111101 => 11001111101
00101111101 => 11000111101
00010111101 => 11000011101
00001011101 => 11000001101
00000101101 => 11000000101
00000010101 => 11000000001
00000001001 => 01000000001
00000000100 => 01000000000
01101111111 => 10101111111
0111011111 => 1011011111
01010111111 => 11000111111
0111001111 => 0101101111
01001011111 => 10100011111
0110100111 => 0110100111
01000101111 => 10010001111
01000010111 => 10001000111
0110001001 => 0100101001
01000001011 => 10000100011
0110000100 => 0100010100
01000000101 => 10000010001
01000000010 => 10000001000
0110111001 => 0110101101
0001101001 => 0110001001
0000110001 => 0010000101
0000010001 => 0010000001
11111110010 => 10111111100
11111100010 => 10011111100
11111000010 => 10001111100
11110000010 => 10000111100
11100000010 => 10000011100
10111111111 => 10111111111
10111111000 => 00110111110
10111110000 => 00011011110
10111100000 => 00001101110
10111000000 => 00000110110
10110000000 => 00000011010
10011111101 => 10101111101
10001111101 => 10010111101
10000111101 => 10001011101
10000011101 => 10000101101
10000001101 => 10000010101
10000000101 => 10000001001
0111111010 => 1101111100
0011111010 => 1100111100
0000111010 => 1100001100
0000011010 => 1100000100
0000001010 => 1100000000
11111111011 => 11111111011
01111111010 => 11011111100
00111111010 => 11001111100
0101111010 => 1110011100
00011111010 => 11000111100
00001111010 => 11000011100
0001011010 => 1110000100
00000111010 => 11000001100
0000101010 => 1110000000
00000011010 => 11000000100
0000010010 => 1010000000
00000001010 => 11000000000
0010011111 => 0100011111
0000100111 => 0100000111
0000010011 => 0100000011
10011111111 => 01011111111
00100111111 => 01000111111
00010011111 => 01000011111
00001001111 => 01000001111
00000100111 => 01000000111
00000010011 => 01000000011
0010000000 => 0000001000
10101111111 => 11001111111
10100111111 => 01100111111
10100011111 => 00110011111
10100001111 => 00011001111
10100000111 => 00001100111
10100000011 => 00000110011
10100000001 => 00000011001
00100000000 => 00000001000
0001010101 => 1110000001
10110101010 => 11111010000
11010101010 => 11111100000
10101101010 => 11111001000
10101010100 => 01111100000
101010001110 => 100111000110
10101010010 => 10111100000
101010100110 => 101111000010
101000111010 => 110011001100
10101001010 => 11011100000
101010011010 => 110111000100
100011101010 => 111001011000
100110101010 => 111101010000
101001101010 => 111011001000
101001010110 => 111011000010
100101011010 => 111101000100
101010010110 => 110111000010
101001100110 => 101011001010
101001011010 => 111011000100
100110011010 => 110101010100
100101101010 => 111101001000
11111111100 => 01111111110
01001001010 => 11010100000
01001010010 => 10110100000
01010001010 => 11001100000
01010010010 => 10101100000
00100010010 => 10100100000
10100100010 => 10010110000
10100100100 => 01010110000
00100101010 => 11101000000
01010101010 => 11111000000
01010100010 => 10011100000
01000101010 => 11100100000
01000100010 => 10010010000
10101000100 => 01001110000
00101010010 => 10111000000
00101001010 => 11011000000
01001000100 => 01001010000
00100010101 => 11001000001
01001000101 => 10010100001
10001000101 => 10010010001
01000010001 => 00100010001
10100010001 => 00100110001
00101010100 => 01111000000
00101000100 => 01001100000
00100100100 => 01010100000
01010100100 => 01011100000
10010010001 => 00101010001
00010010100 => 01101000000
00100010100 => 01100100000
00010010010 => 10101000000
00010001010 => 11001000000
00100001001 => 01000100001
10010001001 => 01001010001
01001010101 => 11101000001
01010010100 => 01101100000
01000100101 => 10100100001
01010010101 => 11011000001
01010001000 => 00100110000
01010101001 => 01111000001
01001010100 => 01110100000
01000101001 => 01100100001
01010100101 => 10111000001
01001001000 => 00101010000
01010001001 => 01001100001
01000101000 => 00110010000
00101001000 => 00101100000
10010100101 => 10110100001
10100101001 => 01101100001
10010010101 => 11010100001
10100100101 => 10101100001
10101001001 => 01011100001
10101010101 => 11111000001
00001000010 => 10001000000
00010100010 => 10011000000
0000100010010 => 1010010000000
00010000100 => 01000100000
00001000100 => 01001000000
00010100100 => 01011000000
00100100101 => 10101000001
10001001001 => 01010010001
00001001000 => 00101000000
00001010000 => 00011000000
00010001000 => 00100100000
00100101000 => 00110100000
00010101000 => 00111000000
00100010000 => 00010010000
00000100000 => 00001000000
00010010000 => 00010100000
01000010000 => 00010001000
00100001000 => 00100010000
011111000100 => 010010111100
011111000010 => 100010111100
011101100100 => 010110110100
011101100010 => 100110110100
011011100100 => 010110101100
011011010100 => 011110101000
011011100010 => 100110101100
011011010010 => 101110101000
011111010000 => 000110111100
011111001000 => 001010111100
001111001010 => 110100111000
011101110000 => 000110110110
011111100000 => 000010111110
011101101000 => 001110110100
010101101010 => 111110001000
001111000110 => 100100111010
010011110100 => 011010011100
010011101100 => 011010011010
011011110000 => 000110101110
011011101000 => 001110101100
010011011010 => 111010010100
001101100110 => 101100101010
001011010101 => 111100010001
001101010101 => 111100100001
001011010011 => 011100010011
001101010011 => 011100100011
001011001011 => 101100010011
001011001101 => 101100010101
001101001011 => 101100100011
001101001101 => 101100100101
001001110101 => 110100011001
001010101101 => 111100000101
001100101101 => 110100100101
001101000111 => 001100100111
001010110101 => 111100001001
001100110101 => 110100101001
001001100111 => 010100010111
001001101011 => 110100010011
000110110101 => 111000101001
001010100111 => 011100000111
001010101011 => 111100000011
001100101011 => 110100100011
001010110011 => 011100001011
001100110011 => 010100101011
000111010101 => 111000110001
001000110111 => 100100010111
001000111011 => 100100011011
001001010111 => 110100000111
001001011011 => 110100001011
001010010111 => 101100000111
001010011011 => 101100001011
001100011101 => 100100101101
000111010011 => 011000110011
010101001011 => 101110000011
010101010011 => 011110000011
010011001011 => 101010010011
010011010011 => 011010010011
010100011011 => 100110001011
010010101011 => 111010000011
010010110011 => 011010001011
010100101011 => 110110000011
010100110011 => 010110001011
000110011011 => 101000101011
010100100111 => 010110000111
000110101011 => 111000100011
010101000111 => 001110000111
000100111011 => 101000011011
000101011011 => 111000001011
000101101011 => 111000010011
010001110011 => 010010011011
010101101001 => 011110001001
010101011001 => 011110000101
100101101001 => 011101001001
100101011001 => 011101000101
101001101001 => 011011001001
011001101001 => 011010101001
101001011001 => 011011000101
011001011001 => 011010100101
010111001001 => 010110011001
011010101001 => 011110100001
011010011001 => 010110100101
110001011001 => 011001100101
010110101001 => 011110010001
010110011001 => 010110010101
110011001001 => 010101101001
101011001001 => 010111001001
010110110001 => 001110010101
110010101001 => 011101100001
101010101001 => 011111000001
101010011001 => 010111000101
100110101001 => 011101010001
100110011001 => 010101010101
010101110001 => 001110001101
110110001001 => 010011101001
101110001001 => 010011011001
110101001001 => 010111100001
101101001001 => 010111010001
110100101001 => 011011100001
101100101001 => 011011010001
011100011001 => 010010110101
100101110001 => 001101001101
010101011010 => 111110000100
010101010110 => 111110000010
011001011010 => 111010100100
011001010110 => 111010100010
011010011010 => 110110100100
010110011010 => 110110010100
011010010110 => 110110100010
010110010110 => 110110010010
010110101010 => 111110010000
010110100110 => 101110010010
011100010110 => 110010110010
010101100110 => 101110001010
011100110010 => 101010110100
011010110010 => 101110100100
011100101010 => 111010110000
011010101010 => 111110100000
011010100110 => 101110100010
011001101010 => 111010101000
011001100110 => 101010101010
010101011100 => 011110000110
011101010010 => 101110110000
011101001010 => 110110110000
011011001010 => 110110101000
010111000110 => 100110011010
011001011100 => 011010100110
100101101100 => 011101001010
100111001100 => 010101011010
001111110000 => 000100111110
001011110010 => 101100011100
001101110010 => 101100101100
001111100010 => 100100111100
100111010100 => 011101011000
001101111000 => 001100101110
001101110100 => 011100101100
001011101010 => 111100011000
001011010110 => 111100010010
010100011101 => 100110001101
010001110101 => 110010011001
000101010111 => 111000000111
000110010111 => 101000100111
000110100111 => 011000100111
010001101101 => 110010010101
000101001111 => 011000001111
000101100111 => 011000010111
001001001111 => 010100001111
001010001111 => 001100001111
000111001101 => 101000110101
010010011101 => 101010001101
000011010111 => 110000100111
000011011011 => 110000101011
000011101011 => 110000110011
010011000111 => 001010010111
110001010101 => 111001100001
101100010101 => 110011010001
011100010101 => 110010110001
100111000101 => 100101011001
010111000101 => 100110011001
110101010001 => 001111100001
110100110001 => 001011100101
110010110001 => 001101100101
101010110001 => 001111000101
011011000101 => 100110101001
111001010001 => 001101110001
110011010001 => 001101101001
111001001001 => 010101110001
101100110001 => 001011010101
111000101001 => 011001110001
011001110001 => 001010101101
011101010100 => 011110110000
011101001100 => 010110110010
011100101100 => 011010110010
011010101100 => 011110100010
011110010100 => 011010111000
011100110100 => 011010110100
011110010010 => 101010111000
011011001100 => 010110101010
011110001010 => 110010111000
010110011100 => 010110010110
101001110100 => 011011001100
010011001101 => 101010010101
110001100101 => 101001101001
011001100101 => 101010101001
001111100100 => 010100111100
000111100110 => 101000111010
001111101000 => 001100111100
000111101010 => 111000111000
001011101100 => 011100011010
000111101100 => 011000111010
000111110010 => 101000111100
000010111011 => 110000011011
001000101111 => 100100001111
100101010101 => 111101000001
100101100101 => 101101001001
101011010001 => 001111001001
100110010101 => 110101010001
101001010101 => 111011000001
101011100001 => 000111001101
101010100101 => 101111000001
101101010001 => 001111010001
100110100101 => 101101010001
101010010101 => 110111000001
101101100001 => 000111010101
101001100101 => 101011001001
101110010001 => 001011011001
101110100001 => 000111011001
110101100001 => 000111100101
011001010101 => 111010100001
011010110100 => 011110100100
011010010101 => 110110100001
011010111000 => 001110100110
011010100101 => 101110100001
011101011000 => 001110110010
010100101101 => 110110000101
010010110101 => 111010001001
010101001101 => 101110000101
010100110101 => 110110001001
010011010101 => 111010010001
010101010101 => 111110000001
010110100101 => 101110010001
010110010101 => 110110010001
010101100101 => 101110001001
010001111100 => 010010011110
010011111000 => 001010011110
001001111010 => 110100011100
001001111100 => 010100011110
001011111000 => 001100011110
001000011111 => 000100011111
000110001111 => 001000101111
000100011111 => 001000011111
000100101111 => 101000001111
000001111011 => 100000111011
000011100111 => 010000110111
000001110111 => 100000110111
000010110111 => 110000010111
111100001001 => 010001111001
111010001001 => 010011110001
111000110001 => 001001110101
111100010001 => 001001111001
111010010001 => 001011110001
011110100010 => 100110111000
011110001100 => 010010111010
011110100100 => 010110111000
110010010101 => 110101100001
011100100101 => 101010110001
000101111100 => 011000011110
000011111100 => 010000111110
001011110100 => 011100011100
000101111010 => 111000011100
000111110100 => 011000111100
000111111000 => 001000111110
000010011111 => 010000011111
000001011111 => 100000011111
000100110111 => 101000010111
000011001111 => 010000101111
000010101111 => 110000001111
000001101111 => 100000101111
111100100001 => 000101111001
111101000001 => 000011111001
110110010001 => 001011101001
111001100001 => 000101110101
110110100001 => 000111101001
111010100001 => 000111110001
011110011000 => 001010111010
011110101000 => 001110111000
000011110110 => 110000111010
000001111110 => 100000111110
000011111010 => 110000111100
000000111111 => 000000111111
110111000001 => 000011101101
111110000001 => 000001111101
111011000001 => 000011110101
011110110000 => 000110111010
000011101110 => 110000110110
000101110110 => 111000011010
101111000001 => 000011011101
110011100001 => 000101101101
011100111000 => 001010110110
00111111111 => 00111111111
00000000000 => 00000000000
01111101111 => 10111101111
01111010111 => 11011100111
01111011011 => 11011101011
01110110111 => 11011010111
11101111101 => 11110111101
01111011101 => 11011101101
01110101011 => 11101100011
10111110111 => 11011110111
01101110111 => 11010110111
11101111010 => 11111011100
01111011110 => 11011101110
11010111101 => 11110011101
01110101101 => 11101100101
11011111011 => 11101111011
01110111011 => 11011011011
10111101011 => 11101110011
01101101011 => 11101010011
01011110111 => 11001110111
11010111010 => 11111001100
11011010110 => 11111010010
01110101110 => 11101100110
11011011101 => 11110101101
10110111101 => 11101011101
11011110101 => 11110111001
01110110101 => 11101101001
10111101101 => 11101110101
01101101101 => 11101010101
10101111011 => 11100111011
10111011011 => 11101101011
01101011011 => 11101001011
01011101011 => 11100110011
00000100010 => 10010000000
01000100000 => 00001001000
00000010010 => 10100000000
00100000010 => 10000010000
00000001000 => 00100000000
00010000000 => 00000010000
01001000000 => 00000101000
01010000000 => 00000011000
00001010010 => 10110000000
00000100100 => 01010000000
00100100000 => 00001010000
01001010000 => 00011010000
00011000001 => 00001000101
00110001000 => 00100100100
00101000001 => 00001100001
01001000001 => 00001010001
00111000001 => 00001001101
01110010000 => 00010101100
10001000001 => 00001001001
01011000001 => 00001100101
00110100001 => 00011001001
10001100000 => 00001001010
10110010000 => 00010110100
01100010000 => 00010010100
01101010000 => 00011101000
00100011000 => 00100100010
10011000001 => 00001010101
01010100001 => 00011100001
00101100001 => 00011000101
00110010001 => 00101001001
10010100000 => 00001101000
11000100000 => 00001001100
11010010000 => 00010111000
10100010000 => 00010011000
10101010000 => 00011110000
01000110000 => 00010010010
01010010000 => 00010110000
01011010000 => 00011100100
01100110000 => 00010101010
00000100001 => 00010000001
00001010001 => 00110000001
00001001001 => 01010000001
00001000101 => 10010000001
00010101001 => 01110000001
00001000011 => 00010000011
00010100101 => 10110000001
00010100011 => 00110000011
00010010101 => 11010000001
10010010000 => 00010101000
10010101000 => 00111010000
10100101000 => 00110110000
11000010000 => 00010001100
10101001000 => 00101110000
11000101000 => 00110011000
11110111101 => 11111011101
10111101111 => 11011101111
11111011101 => 11111101101
10111011111 => 11011011111
11111101101 => 11111110101
11101011101 => 11111001101
11011111101 => 11101111101
11111110111 => 11111110111
10111111011 => 11011111011
10111010111 => 11101100111
11101111111 => 11101111111
10110111111 => 11010111111
11111110101 => 11111111001
11101101101 => 11111010101
11101110111 => 11110110111
11111011111 => 11111011111
10110110111 => 11101010111
11101110101 => 11111011001
11110101101 => 11111100101
11011101101 => 11110110101
10111011101 => 11101101101
11110110111 => 11111010111
11011110111 => 11101110111
11111011011 => 11111101011
11101111011 => 11110111011
10110111011 => 11101011011
11011011111 => 11101011111
11101101111 => 11110101111
10110101111 => 11101001111
10101110111 => 11100110111
10101111101 => 11100111101
10101011111 => 11100011111
01101111101 => 11010111101
10001111111 => 00101111111
11101011111 => 11110011111
10011011111 => 10101011111
10111110101 => 11101111001
01110111101 => 11011011101
01111110111 => 10111110111
11111001111 => 01111101111
10011101111 => 10101101111
11100111111 => 01110111111
10010111111 => 10100111111
01111011111 => 10111011111
11111111001 => 01111111101
11111010101 => 11111110001
11111011001 => 01111110101
11111110001 => 00111111101
11111010111 => 11111100111
11111101001 => 01111111001
11110111001 => 01111101101
11111100111 => 01111110111
11110011111 => 01111011111
100001000011 => 000100010011
111000010000 => 000100011100
100011100011 => 001001011011
100010110011 => 011001001011
100110100011 => 001101010011
100010011011 => 101001001011
100111110011 => 010101111011
101100100011 => 001011010011
111000100110 => 101001110010
111001111100 => 010111011110
101010001000 => 001001110000
100010001111 => 001001001111
100111011011 => 110101101011
100101010011 => 011101000011
101101110011 => 011101011011
111000100011 => 001001110011
100111001010 => 110101011000
111001110110 => 110111011010
100100100100 => 010101010000
101010011100 => 010111000110
111011011100 => 011111010110
100111001111 => 010101101111
100101111011 => 110100111011
101101011011 => 111101001011
101111010011 => 011101110011
111001110011 => 010111011011
111001011110 => 110111001110
111011010110 => 111111010010
111011110100 => 011111011100
111110011100 => 010111110110
010001011110 => 110010001110
001001011110 => 110100001110
011000110110 => 110010101010
001101001110 => 101100100110
001011001110 => 101100010110
000101011110 => 111000001110
110010011100 => 010101100110
001100111010 => 110100101100
111000010110 => 110001110010
001001101110 => 110100010110
001101011100 => 011100100110
001110011010 => 110100110100
110100011010 => 110011100100
001101011010 => 111100100100
001110101010 => 111100110000
101100011010 => 110011010100
010100111010 => 110110001100
001111100001 => 000100111101
000111110001 => 001000111101
001110111000 => 001100110110
000111101001 => 011000111001
001011110001 => 001100011101
001110110100 => 011100110100
000111100101 => 101000111001
000011111001 => 010000111101
001101110001 => 001100101101
001110110010 => 101100110100
000110111100 => 011000101110
000111100011 => 001000111011
001011101001 => 011100011001
000101111001 => 011000011101
001110110001 => 001100110101
000110111010 => 111000101100
001010111100 => 011100001110
001001111001 => 010100011101
000110111001 => 011000101101
000110110110 => 111000101010
001010111010 => 111100001100
010010111100 => 011010001110
001100111100 => 010100101110
011110000011 => 000010111011
011100000111 => 000010110111
011010000111 => 000110100111
011100001011 => 100010110011
110100100011 => 001011100011
010110000111 => 000110010111
011000001111 => 000010101111
011100010011 => 010010110011
110000100111 => 010001100111
001110000111 => 000100110111
011010001011 => 100110100011
011000010111 => 100010100111
011100100011 => 001010110011
101100001101 => 100011010101
101000100111 => 010011000111
110010010011 => 010101100011
110000101011 => 110001100011
011000011011 => 100010101011
011000100111 => 010010100111
101010001101 => 100111000101
100110001011 => 100101010011
100100100111 => 010101000111
101010010011 => 010111000011
101000101011 => 110011000011
110000101101 => 110001100101
110000110011 => 010001101011
010011110001 => 001010011101
000111011001 => 011000110101
100110111000 => 001101010110
001110101100 => 011100110010
100011110001 => 001001011101
001111010001 => 001100111001
001110011100 => 010100110110
001111001001 => 010100111001
010000111110 => 100010011110
010100111100 => 010110001110
010001110110 => 110010011010
011000111100 => 010010101110
010010111010 => 111010001100
010001101110 => 110010010110
001010111001 => 011100001101
001010110110 => 111100001010
100000111101 => 100001011101
110000011101 => 100001101101
100010010111 => 101001000111
101000011101 => 100011001101
110010000111 => 000101100111
100100011101 => 100101001101
111000001101 => 100001110101
110000110101 => 110001101001
101010000111 => 000111000111
110010001011 => 100101100011
100010011101 => 101001001101
110100001101 => 100011100101
101000101101 => 110011000101
110000111001 => 010001101101
100110000111 => 000101010111
101010001011 => 100111000011
110010001101 => 100101100101
100100101011 => 110101000011
101000110011 => 010011001011
011000101011 => 110010100011
011000011110 => 100010101110
011000101110 => 110010100110
001110001110 => 100100110110
011001001110 => 101010100110
010110001110 => 100110010110
010011100110 => 101010011010
001110010110 => 110100110010
101000001111 => 000011001111
101000010111 => 100011000111
101000011011 => 100011001011
101001000111 => 001011000111
100001111001 => 010001011101
101001001011 => 101011000011
100010111001 => 011001001101
101001010011 => 011011000011
101001001101 => 101011000101
101000110101 => 110011001001
100110010011 => 010101010011
100110001101 => 100101010101
100101100011 => 001101001011
100100111001 => 010101001101
100011100101 => 101001011001
100011011001 => 011001010101
100011101001 => 011001011001
010010111001 => 011010001101
010011100101 => 101010011001
001101011001 => 011100100101
001110101001 => 011100110001
001110100101 => 101100110001
001110011001 => 010100110101
111000001011 => 100001110011
110100001011 => 100011100011
101100001011 => 100011010011
110001001011 => 101001100011
001111000011 => 000100111011
001110100011 => 001100110011
100101001011 => 101101000011
011001001011 => 101010100011
010110001011 => 100110010011
100100110011 => 010101001011
011000110011 => 010010101011
100011010011 => 011001010011
001110010011 => 010100110011
010011100011 => 001010011011
001101100011 => 001100101011
000110011110 => 101000101110
100110011100 => 010101010110
001010101110 => 111100000110
100110110010 => 101101010100
010010110110 => 111010001010
001110001101 => 100100110101
001011100101 => 101100011001
001100111001 => 010100101101
001011011001 => 011100010101
001100110110 => 110100101010
11100010000 => 00010011100
11100100000 => 00001011100
11101000000 => 00000111100
11111000001 => 00001111101
0010001000 => 0010010000
10100111101 => 10110011101
01110111111 => 10110111111
11111101010 => 11111111000
10101000000 => 00000111000
10110100000 => 00001110100
0001000101 => 1001000001
00000101010 => 11100000000
0000100011 => 0010000011
0001001011 => 1010000011
10100101111 => 10110001111
0000100010 => 1001000000
11111100101 => 10111111001
01011000000 => 00000110010
0101010000 => 0001110000
01011100000 => 00001100110
11011111111 => 11011111111
10010111101 => 11010011101
10111000001 => 00001101101
10111111001 => 01101111101
00000010100 => 01100000000
0000100100 => 0101000000
11111110100 => 01111111100
0010010011 => 0101000011
11001000000 => 00000101100
11101100000 => 00001111010
11011000000 => 00000111010
0001000111 => 0010000111
11010111111 => 11100111111
10010101001 => 01110100001
010010101101 => 111010000101
00001000100101 => 10100100000001
0000100010011 => 0100100000011
000010001001 => 010010000001
0000100010101 => 1100100000001
000010001010 => 110010000000
000010001011 => 100100000011
00001000111 => 00100000111
0000100100101 => 1010100000001
000010010010 => 101010000000
000010010011 => 010100000011
000010010101 => 110100000001
00001001010 => 11010000000
00001001011 => 10100000011
0000100101 => 1010000001
00001010101 => 11100000001
0000101011 => 1100000011
0001000100101 => 1010010000001
000100010010 => 101001000000
000100010011 => 010010000011
0001000100 => 0100100000
000100010101 => 110010000001
00010001011 => 10010000011
000100100101 => 101010000001
00010010011 => 01010000011
0001001001 => 0101000001
0001001010 => 1101000000
0010010010 => 1010100000
0010010101 => 1101000001
0100100010000 => 0001001010000
1100100010000 => 0001001011000
100100010000 => 000100101000
1010100010000 => 0001001110000
010100010000 => 000100110000
110100010000 => 000100111000
0100010000 => 0001001000
1010010010000 => 0001010110000
010010010000 => 000101010000
110010010000 => 000101011000
0010010000 => 0001010000
101010010000 => 000101110000
1010010001000 => 0010010110000
010010001000 => 001001010000
110010001000 => 001001011000
11010001000 => 00100111000
101001001000 => 001010110000
11001001000 => 00101011000
0101001000 => 0010110000
0100100100 => 0101010000
11010100000 => 00001111000
10100100000 => 00001011000
11011011010 => 11111010100
111011101010 => 111111011000
11110101010 => 11111110000
11110110101 => 11111101001
11110111010 => 11111101100
11110111011 => 11111011011
01011011011 => 11100101011
01010101111 => 11100001111
10101101111 => 11100101111
01011101111 => 11001101111
11011101111 => 11101101111
01100100000 => 00001010100
00010100000 => 00001100000
10101000001 => 00001110001
00010101010 => 11110000000
01010110000 => 00011100010
00101010000 => 00011100000
00100110000 => 00010100010
10100100001 => 00010110001
01010101000 => 00111100000
01101101010 => 11110101000
11011101010 => 11111011000
01011011010 => 11110010100
10111011010 => 11110110100
01101011010 => 11110100100
01110111010 => 11101101100
01010110110 => 11110001010
01101110110 => 11101011010
01011010110 => 11110010010
01101010110 => 11110100010
01110110110 => 11101101010
01011101110 => 11100110110
01101101110 => 11101010110
01010101101 => 11110000101
10110101101 => 11110100101
10101101101 => 11110010101
01011011101 => 11100101101
01101011101 => 11101001101
10101011101 => 11110001101
01010110101 => 11110001001
10110110101 => 11110101001
01101110101 => 11101011001
10101110101 => 11110011001
01011010101 => 11110010001
10111010101 => 11110110001
01101010101 => 11110100001
11011010101 => 11111010001
11010110101 => 11111001001
01011101101 => 11100110101
11010101101 => 11111000101
01010111011 => 11100011011
01101111011 => 11010111011
10101011011 => 11110001011
11011011011 => 11110101011
11010111011 => 11110011011
10101101011 => 11110010011
11011101011 => 11110110011
10110101011 => 11110100011
11010101011 => 11111000011
11101101011 => 11111010011
11101011011 => 11111001011
11010110111 => 11110010111
11011010111 => 11110100111
11101010111 => 11111000111
11110101111 => 11111001111
01000001010 => 11000010000
01010000010 => 10000110000
00000101000 => 00110000000
00001010100 => 01110000000
01010100000 => 00001110000
00000010000 => 00010000000
00101000000 => 00000110000
00001000000 => 00000100000
11101000001 => 00001111001
11010100001 => 00011110001
11011000001 => 00001110101
10101100001 => 00011100101
10110100001 => 00011101001
10010100001 => 00011010001
01011100001 => 00011001101
01001100001 => 00010100101
01101100001 => 00011010101
01100100001 => 00010101001
00100110001 => 00101000101
10101100000 => 00001110010
10010110000 => 00011010010
10011010000 => 00011010100
10011100000 => 00001010110
11011100000 => 00001110110
11001010000 => 00011011000
11001100000 => 00001011010
11110100000 => 00001111100
11111000000 => 00000111110
10100110000 => 00010110010
10011000000 => 00000101010
01001110000 => 00010100110
01001100000 => 00001010010
01101100000 => 00001101010
01110100000 => 00001101100
01111000000 => 00000101110
01101000000 => 00000110100
00101100000 => 00001100010
00110010000 => 00010100100
00110100000 => 00001100100
00111000000 => 00000100110
00011000000 => 00000100010
01010101011 => 11110000011
00100101011 => 11010000011
01001001011 => 10101000011
00101001011 => 10110000011
01010010011 => 01011000011
00100010011 => 01001000011
01001010011 => 01101000011
00101010011 => 01110000011
01000100011 => 00100100011
00100100011 => 00101000011
00101010101 => 11110000001
11001001010 => 11010110000
11010010010 => 10101110000
11001010010 => 10110110000
11000100010 => 10010011000
11010100100 => 01011110000
11001000100 => 01001011000
11010010100 => 01101110000
11001010100 => 01110110000
11000100100 => 01010011000
11101010101 => 11111100001
10101010111 => 11110000111
11110101011 => 11111100011
11111101011 => 11111110011
11010101111 => 11110001111
11111101111 => 11111101111
11110111111 => 11110111111
11111111111 => 11111111111
01111010101 => 11101110001
10011110101 => 11010111001
01011110101 => 11100111001
11100111101 => 10111011101
01010111101 => 11100011101
10011110111 => 10101110111
10101001111 => 01110001111
11101001111 => 01111001111
10111001111 => 01101101111
01111001111 => 01011101111
11100101111 => 10111001111
10010101111 => 11010001111
01110101111 => 11011001111
00111101111 => 10011101111
00101111111 => 10001111111
01011011111 => 11001011111
01101011111 => 11010011111
11110010101 => 11011110001
10111100101 => 10110111001
11110100101 => 10111110001
11110011101 => 10111101101
10101111001 => 01110011101
11101111001 => 01111011101
10111101001 => 01110111001
11110101001 => 01111110001
11110010111 => 10111100111
10111100111 => 01101110111
11110100111 => 01111100111
10111101010 => 11110111000
11111011010 => 11111110100
11111010110 => 11111110010
11110111100 => 01111101110
111111111111 => 111111111111
101011111111 => 110011111111
111010111111 => 111100111111
101110111111 => 110110111111
100100111111 => 010100111111
111110101111 => 111111001111
101010101111 => 111100001111
111011101111 => 111101101111
101111101111 => 110111101111
100101101111 => 110100101111
111001001111 => 010111001111
101101001111 => 011101001111
111111101011 => 111111110011
101011101011 => 111100110011
111010101011 => 111111000011
101110101011 => 111101100011
111110111011 => 111111011011
101010111011 => 111100011011
111011111011 => 111101111011
101111111011 => 110111111011
111001011011 => 110111001011
111110010011 => 010111110011
111011010011 => 011111010011
111111111010 => 111111111100
101011111010 => 111100111100
111010111010 => 111111001100
101110111010 => 111101101100
111110101010 => 111111110000
101111101010 => 111101111000
111010101110 => 111111000110
101110101110 => 111101100110
111110010110 => 110111110010
101111010110 => 111101110010
101101110110 => 111101011010
101100100110 => 101011010010
100110100110 => 101101010010
111111100100 => 010111111100
111110110100 => 011111110100
101111110100 => 011101111100
100010010100 => 011010010000
101111011100 => 011101110110
100101011100 => 011101000110
101101111100 => 011101011110
100111111100 => 010101111110
100110101100 => 011101010010
100101001000 => 001011010000
100010101000 => 001110010000
100001011000 => 001100010010
101100010000 => 000100110100
100110010000 => 000101010100
100011010000 => 000110010100
100001110000 => 000100010110
100110110100 => 011101010100
000010111110 => 110000011110
000110101110 => 111000100110
001010011110 => 101100001110
010010011110 => 101010001110
100100111100 => 010101001110
101100011100 => 010011010110
110100011100 => 010011100110
000100111110 => 101000011110
001100101110 => 110100100110
001100011110 => 100100101110
010100011110 => 100110001110
111000011010 => 110001110100
101000111100 => 010011001110
111000011100 => 010001110110
011000111010 => 110010101100
001000111110 => 100100011110
110000110110 => 110001101010
110000111010 => 110001101100
110000111100 => 010001101110
001101101001 => 011100101001
011010010011 => 010110100011
100100101101 => 110101000101
100000111011 => 100001011011
100100011011 => 100101001011
100000110111 => 100001010111
100000101111 => 100001001111
100000011111 => 000001011111
100100010111 => 100101000111
100100001111 => 000101001111
101100010011 => 010011010011
101100000111 => 000011010111
101110000011 => 000011011011
110000011011 => 100001101011
110000010111 => 100001100111
110000001111 => 000001101111
110100010011 => 010011100011
110100000111 => 000011100111
110110000011 => 000011101011
111000010011 => 010001110011
111000000111 => 000001110111
111010000011 => 000011110011
111100000011 => 000001111011
010011101001 => 011010011001
100110010110 => 110101010010
100101100110 => 101101001010
011010001110 => 100110100110
010101001110 => 101110000110
010100110110 => 110110001010
010100101110 => 110110000110
010011010110 => 111010010010
010011001110 => 101010010110
010010101110 => 111010000110
001110100110 => 101100110010
001101010110 => 111100100010
101010100011 => 001111000011
101001100011 => 001011001011
101000111001 => 010011001101
100101001101 => 101101000101
100101000111 => 001101000111
100100110101 => 110101001001
100011010101 => 111001010001
100011001101 => 101001010101
100011001011 => 101001010011
100011000111 => 001001010111
100010110101 => 111001001001
100010101101 => 111001000101
100010101011 => 111001000011
100010100111 => 011001000111
100001110101 => 110001011001
100001110011 => 010001011011
100001101101 => 110001010101
100001101011 => 110001010011
100001100111 => 010001010111
100001011101 => 110001001101
100001011011 => 110001001011
100001010111 => 110001000111
100001001111 => 010001001111
010011011001 => 011010010101
010001111001 => 010010011101
001110010101 => 110100110001
001111000101 => 100100111001
001101100101 => 101100101001
001110001011 => 100100110011
011001010011 => 011010100011
110001010011 => 011001100011
010110010011 => 010110010011
001011100011 => 001100011011
010101100011 => 001110001011
011001100011 => 001010101011
110001100011 => 001001101011
010110100011 => 001110010011
011010100011 => 001110100011
110010100011 => 001101100011
010111000011 => 000110011011
100111000011 => 000101011011
011011000011 => 000110101011
101011000011 => 000111001011
110011000011 => 000101101011
011101000011 => 000110110011
101101000011 => 000111010011
110101000011 => 000111100011
111001000011 => 000101110011
111111010010010010010010 => 101010101011111110000000
111110100100100100110100 => 011010101011111100000100
111110100100100110100010 => 100110101011111100001000
111101001001001110100100 => 010110101011111000011000
111101001001001101101000 => 001110101011111000010100
111110100100110100010010 => 101001101011111100010000
111101001001101000110100 => 011001101011111000100100
111101001001110100100010 => 100101101011111000110000
111010010011110100100100 => 010101101011110001110000
111010010011101001101000 => 001101101011110001100100
111101001001101101000010 => 100011101011111000101000
111010010011101101000100 => 010011101011110001101000
111010010011011101001000 => 001011101011110001011000
111010010011011011010000 => 000111101011110001010100
111110100110100010010010 => 101010011011111100100000
111101001101000100110100 => 011010011011111001000100
111101001101000110100010 => 100110011011111001001000
111010011010001110100100 => 010110011011110010011000
111010011010001101101000 => 001110011011110010010100
111101001110100100010010 => 101001011011111001100000
111010011101001000110100 => 011001011011110011000100
111010011110100100100010 => 100101011011110011100000
110100111110100100100100 => 010101011011100111100000
110100111101001001101000 => 001101011011100111000100
111010011101001101000010 => 100011011011110011001000
110100111101001101000100 => 010011011011100111001000
110100111010011101001000 => 001011011011100110011000
110100111010011011010000 => 000111011011100110010100
111101001101101000010010 => 101000111011111001010000
111010011011010000110100 => 011000111011110010100100
111010011101101000100010 => 100100111011110011010000
110100111101101000100100 => 010100111011100111010000
110100111011010001101000 => 001100111011100110100100
111010011011101001000010 => 100010111011110010110000
110100111011101001000100 => 010010111011100110110000
110100110111101001001000 => 001010111011100101110000
110100110111010011010000 => 000110111011100101100100
111010011011011010000010 => 100001111011110010101000
110100111011011010000100 => 010001111011100110101000
110100110111011010001000 => 001001111011100101101000
110100110110111010010000 => 000101111011100101011000
110100110110110110100000 => 000011111011100101010100
111110110100010010010010 => 101010100111111101000000
111101101000100100110100 => 011010100111111010000100
111101101000100110100010 => 100110100111111010001000
111011010001001110100100 => 010110100111110100011000
111011010001001101101000 => 001110100111110100010100
111101101000110100010010 => 101001100111111010010000
111011010001101000110100 => 011001100111110100100100
111011010001110100100010 => 100101100111110100110000
110110100011110100100100 => 010101100111101001110000
110110100011101001101000 => 001101100111101001100100
111011010001101101000010 => 100011100111110100101000
110110100011101101000100 => 010011100111101001101000
110110100011011101001000 => 001011100111101001011000
110110100011011011010000 => 000111100111101001010100
111101110100100010010010 => 101010010111111011000000
111011101001000100110100 => 011010010111110110000100
111011101001000110100010 => 100110010111110110001000
110111010010001110100100 => 010110010111101100011000
110111010010001101101000 => 001110010111101100010100
111011110100100100010010 => 101001010111110111000000
110111101001001000110100 => 011001010111101110000100
110111110100100100100010 => 100101010111101111000000
101111110100100100100100 => 010101010111011111000000
101111101001001001101000 => 001101010111011110000100
110111101001001101000010 => 100011010111101110001000
101111101001001101000100 => 010011010111011110001000
101111010010011101001000 => 001011010111011100011000
101111010010011011010000 => 000111010111011100010100
111011101001101000010010 => 101000110111110110010000
110111010011010000110100 => 011000110111101100100100
110111101001101000100010 => 100100110111101110010000
101111101001101000100100 => 010100110111011110010000
101111010011010001101000 => 001100110111011100100100
110111010011101001000010 => 100010110111101100110000
101111010011101001000100 => 010010110111011100110000
101110100111101001001000 => 001010110111011001110000
101110100111010011010000 => 000110110111011001100100
110111010011011010000010 => 100001110111101100101000
101111010011011010000100 => 010001110111011100101000
101110100111011010001000 => 001001110111011001101000
101110100110111010010000 => 000101110111011001011000
101110100110110110100000 => 000011110111011001010100
111101101101000010010010 => 101010001111111010100000
111011011010000100110100 => 011010001111110101000100
111011011010000110100010 => 100110001111110101001000
110110110100001110100100 => 010110001111101010011000
110110110100001101101000 => 001110001111101010010100
111011101101000100010010 => 101001001111110110100000
110111011010001000110100 => 011001001111101101000100
110111101101000100100010 => 100101001111101110100000
101111101101000100100100 => 010101001111011110100000
101111011010001001101000 => 001101001111011101000100
110111011010001101000010 => 100011001111101101001000
101111011010001101000100 => 010011001111011101001000
101110110100011101001000 => 001011001111011010011000
101110110100011011010000 => 000111001111011010010100
111011011101001000010010 => 101000101111110101100000
110110111010010000110100 => 011000101111101011000100
110111011101001000100010 => 100100101111101101100000
101111011101001000100100 => 010100101111011101100000
101110111010010001101000 => 001100101111011011000100
110110111101001001000010 => 100010101111101011100000
101110111101001001000100 => 010010101111011011100000
101101111101001001001000 => 001010101111010111100000
101101111010010011010000 => 000110101111010111000100
110110111010011010000010 => 100001101111101011001000
101110111010011010000100 => 010001101111011011001000
101101111010011010001000 => 001001101111010111001000
101101110100111010010000 => 000101101111010110011000
101101110100110110100000 => 000011101111010110010100
111011011011010000010010 => 101000011111110101010000
110110110110100000110100 => 011000011111101010100100
110111011011010000100010 => 100100011111101101010000
101111011011010000100100 => 010100011111011101010000
101110110110100001101000 => 001100011111011010100100
110110111011010001000010 => 100010011111101011010000
101110111011010001000100 => 010010011111011011010000
101101111011010001001000 => 001010011111010111010000
101101110110100011010000 => 000110011111010110100100
110110110111010010000010 => 100001011111101010110000
101110110111010010000100 => 010001011111011010110000
101101110111010010001000 => 001001011111010110110000
101101101111010010010000 => 000101011111010101110000
101101101110100110100000 => 000011011111010101100100
110110110110110100000010 => 100000111111101010101000
101110110110110100000100 => 010000111111011010101000
101101110110110100001000 => 001000111111010110101000
101101101110110100010000 => 000100111111010101101000
101101101101110100100000 => 000010111111010101011000
101101101101101101000000 => 000001111111010101010100
Download as text // json // pdf //
Description
The Foata bijection $\phi$ is a bijection on the set of words of given content (by a slight generalization of Section 2 in [1]).
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$. At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
For instance, to compute $\phi(4154223)$, the sequence of words is
  • 4,
  • |4|1 -- > 41,
  • |4|1|5 -- > 415,
  • |415|4 -- > 5414,
  • |5|4|14|2 -- > 54412,
  • |5441|2|2 -- > 154422,
  • |1|5442|2|3 -- > 1254423.
So $\phi(4154223) = 1254423$.
References
[1] Foata, D., Sch├╝tzenberger, M.-P. Major index and inversion number of permutations MathSciNet:0506852
[2] Foata bijection Mp00067
Properties
bijective, graded
Sage code
def mapping(w):
    return w.foata_bijection()

Created
Jan 29, 2020 at 13:26 by FindStatCrew
Updated
Jan 29, 2020 at 13:26 by Martin Rubey