Identifier
Mp00105:
Binary words
—complement⟶
Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Images
=>
0=>1=>1=>1
1=>0=>0=>0
00=>11=>11=>11
01=>10=>10=>01
10=>01=>01=>10
11=>00=>00=>00
000=>111=>111=>111
001=>110=>110=>011
010=>101=>101=>110
011=>100=>010=>001
100=>011=>011=>101
101=>010=>100=>010
110=>001=>001=>100
111=>000=>000=>000
0000=>1111=>1111=>1111
0001=>1110=>1110=>0111
0010=>1101=>1101=>1110
0011=>1100=>0110=>0011
0100=>1011=>1011=>1101
0101=>1010=>1100=>0110
0110=>1001=>0101=>1010
0111=>1000=>0010=>0001
1000=>0111=>0111=>1011
1001=>0110=>1010=>0101
1010=>0101=>1001=>1100
1011=>0100=>0100=>0010
1100=>0011=>0011=>1001
1101=>0010=>1000=>0100
1110=>0001=>0001=>1000
1111=>0000=>0000=>0000
00000=>11111=>11111=>11111
00001=>11110=>11110=>01111
00010=>11101=>11101=>11110
00011=>11100=>01110=>00111
00100=>11011=>11011=>11101
00101=>11010=>11100=>01110
00110=>11001=>01101=>10110
00111=>11000=>00110=>00011
01000=>10111=>10111=>11011
01001=>10110=>11010=>01101
01010=>10101=>11001=>11100
01011=>10100=>01100=>00110
01100=>10011=>01011=>10101
01101=>10010=>10100=>01010
01110=>10001=>00101=>10010
01111=>10000=>00010=>00001
10000=>01111=>01111=>10111
10001=>01110=>10110=>01011
10010=>01101=>10101=>11010
10011=>01100=>01010=>00101
10100=>01011=>10011=>11001
10101=>01010=>11000=>01100
10110=>01001=>01001=>10100
10111=>01000=>00100=>00010
11000=>00111=>00111=>10011
11001=>00110=>10010=>01001
11010=>00101=>10001=>11000
11011=>00100=>01000=>00100
11100=>00011=>00011=>10001
11101=>00010=>10000=>01000
11110=>00001=>00001=>10000
11111=>00000=>00000=>00000
000000=>111111=>111111=>111111
000001=>111110=>111110=>011111
000010=>111101=>111101=>111110
000011=>111100=>011110=>001111
000100=>111011=>111011=>111101
000101=>111010=>111100=>011110
000110=>111001=>011101=>101110
000111=>111000=>001110=>000111
001000=>110111=>110111=>111011
001001=>110110=>111010=>011101
001010=>110101=>111001=>111100
001011=>110100=>011100=>001110
001100=>110011=>011011=>101101
001101=>110010=>101100=>010110
001110=>110001=>001101=>100110
001111=>110000=>000110=>000011
010000=>101111=>101111=>110111
010001=>101110=>110110=>011011
010010=>101101=>110101=>111010
010011=>101100=>011010=>001101
010100=>101011=>110011=>111001
010101=>101010=>111000=>011100
010110=>101001=>011001=>101100
010111=>101000=>001100=>000110
011000=>100111=>010111=>101011
011001=>100110=>101010=>010101
011010=>100101=>101001=>110100
011011=>100100=>010100=>001010
011100=>100011=>001011=>100101
011101=>100010=>100100=>010010
011110=>100001=>000101=>100010
011111=>100000=>000010=>000001
100000=>011111=>011111=>101111
100001=>011110=>101110=>010111
100010=>011101=>101101=>110110
100011=>011100=>010110=>001011
100100=>011011=>101011=>110101
100101=>011010=>110100=>011010
100110=>011001=>010101=>101010
100111=>011000=>001010=>000101
101000=>010111=>100111=>110011
101001=>010110=>110010=>011001
101010=>010101=>110001=>111000
101011=>010100=>011000=>001100
101100=>010011=>010011=>101001
101101=>010010=>101000=>010100
101110=>010001=>001001=>100100
101111=>010000=>000100=>000010
110000=>001111=>001111=>100111
110001=>001110=>100110=>010011
110010=>001101=>100101=>110010
110011=>001100=>010010=>001001
110100=>001011=>100011=>110001
110101=>001010=>110000=>011000
110110=>001001=>010001=>101000
110111=>001000=>001000=>000100
111000=>000111=>000111=>100011
111001=>000110=>100010=>010001
111010=>000101=>100001=>110000
111011=>000100=>010000=>001000
111100=>000011=>000011=>100001
111101=>000010=>100000=>010000
111110=>000001=>000001=>100000
111111=>000000=>000000=>000000
0000000=>1111111=>1111111=>1111111
0000001=>1111110=>1111110=>0111111
0000010=>1111101=>1111101=>1111110
0000011=>1111100=>0111110=>0011111
0000100=>1111011=>1111011=>1111101
0000101=>1111010=>1111100=>0111110
0000110=>1111001=>0111101=>1011110
0000111=>1111000=>0011110=>0001111
0001000=>1110111=>1110111=>1111011
0001001=>1110110=>1111010=>0111101
0001010=>1110101=>1111001=>1111100
0001011=>1110100=>0111100=>0011110
0001100=>1110011=>0111011=>1011101
0001101=>1110010=>1011100=>0101110
0001110=>1110001=>0011101=>1001110
0001111=>1110000=>0001110=>0000111
0010000=>1101111=>1101111=>1110111
0010001=>1101110=>1110110=>0111011
0010010=>1101101=>1110101=>1111010
0010011=>1101100=>0111010=>0011101
0010100=>1101011=>1110011=>1111001
0010101=>1101010=>1111000=>0111100
0010110=>1101001=>0111001=>1011100
0010111=>1101000=>0011100=>0001110
0011000=>1100111=>0110111=>1011011
0011001=>1100110=>1011010=>0101101
0011010=>1100101=>1011001=>1101100
0011011=>1100100=>0101100=>0010110
0011100=>1100011=>0011011=>1001101
0011101=>1100010=>1001100=>0100110
0011110=>1100001=>0001101=>1000110
0011111=>1100000=>0000110=>0000011
0100000=>1011111=>1011111=>1101111
0100001=>1011110=>1101110=>0110111
0100010=>1011101=>1101101=>1110110
0100011=>1011100=>0110110=>0011011
0100100=>1011011=>1101011=>1110101
0100101=>1011010=>1110100=>0111010
0100110=>1011001=>0110101=>1011010
0100111=>1011000=>0011010=>0001101
0101000=>1010111=>1100111=>1110011
0101001=>1010110=>1110010=>0111001
0101010=>1010101=>1110001=>1111000
0101011=>1010100=>0111000=>0011100
0101100=>1010011=>0110011=>1011001
0101101=>1010010=>1011000=>0101100
0101110=>1010001=>0011001=>1001100
0101111=>1010000=>0001100=>0000110
0110000=>1001111=>0101111=>1010111
0110001=>1001110=>1010110=>0101011
0110010=>1001101=>1010101=>1101010
0110011=>1001100=>0101010=>0010101
0110100=>1001011=>1010011=>1101001
0110101=>1001010=>1101000=>0110100
0110110=>1001001=>0101001=>1010100
0110111=>1001000=>0010100=>0001010
0111000=>1000111=>0010111=>1001011
0111001=>1000110=>1001010=>0100101
0111010=>1000101=>1001001=>1100100
0111011=>1000100=>0100100=>0010010
0111100=>1000011=>0001011=>1000101
0111101=>1000010=>1000100=>0100010
0111110=>1000001=>0000101=>1000010
0111111=>1000000=>0000010=>0000001
1000000=>0111111=>0111111=>1011111
1000001=>0111110=>1011110=>0101111
1000010=>0111101=>1011101=>1101110
1000011=>0111100=>0101110=>0010111
1000100=>0111011=>1011011=>1101101
1000101=>0111010=>1101100=>0110110
1000110=>0111001=>0101101=>1010110
1000111=>0111000=>0010110=>0001011
1001000=>0110111=>1010111=>1101011
1001001=>0110110=>1101010=>0110101
1001010=>0110101=>1101001=>1110100
1001011=>0110100=>0110100=>0011010
1001100=>0110011=>0101011=>1010101
1001101=>0110010=>1010100=>0101010
1001110=>0110001=>0010101=>1001010
1001111=>0110000=>0001010=>0000101
1010000=>0101111=>1001111=>1100111
1010001=>0101110=>1100110=>0110011
1010010=>0101101=>1100101=>1110010
1010011=>0101100=>0110010=>0011001
1010100=>0101011=>1100011=>1110001
1010101=>0101010=>1110000=>0111000
1010110=>0101001=>0110001=>1011000
1010111=>0101000=>0011000=>0001100
1011000=>0100111=>0100111=>1010011
1011001=>0100110=>1010010=>0101001
1011010=>0100101=>1010001=>1101000
1011011=>0100100=>0101000=>0010100
1011100=>0100011=>0010011=>1001001
1011101=>0100010=>1001000=>0100100
1011110=>0100001=>0001001=>1000100
1011111=>0100000=>0000100=>0000010
1100000=>0011111=>0011111=>1001111
1100001=>0011110=>1001110=>0100111
1100010=>0011101=>1001101=>1100110
1100011=>0011100=>0100110=>0010011
1100100=>0011011=>1001011=>1100101
1100101=>0011010=>1100100=>0110010
1100110=>0011001=>0100101=>1010010
1100111=>0011000=>0010010=>0001001
1101000=>0010111=>1000111=>1100011
1101001=>0010110=>1100010=>0110001
1101010=>0010101=>1100001=>1110000
1101011=>0010100=>0110000=>0011000
1101100=>0010011=>0100011=>1010001
1101101=>0010010=>1010000=>0101000
1101110=>0010001=>0010001=>1001000
1101111=>0010000=>0001000=>0000100
1110000=>0001111=>0001111=>1000111
1110001=>0001110=>1000110=>0100011
1110010=>0001101=>1000101=>1100010
1110011=>0001100=>0100010=>0010001
1110100=>0001011=>1000011=>1100001
1110101=>0001010=>1100000=>0110000
1110110=>0001001=>0100001=>1010000
1110111=>0001000=>0010000=>0001000
1111000=>0000111=>0000111=>1000011
1111001=>0000110=>1000010=>0100001
1111010=>0000101=>1000001=>1100000
1111011=>0000100=>0100000=>0010000
1111100=>0000011=>0000011=>1000001
1111101=>0000010=>1000000=>0100000
1111110=>0000001=>0000001=>1000000
1111111=>0000000=>0000000=>0000000
00000000=>11111111=>11111111=>11111111
00000001=>11111110=>11111110=>01111111
00000010=>11111101=>11111101=>11111110
00000011=>11111100=>01111110=>00111111
00000100=>11111011=>11111011=>11111101
00000101=>11111010=>11111100=>01111110
00000110=>11111001=>01111101=>10111110
00000111=>11111000=>00111110=>00011111
00001000=>11110111=>11110111=>11111011
00001001=>11110110=>11111010=>01111101
00001010=>11110101=>11111001=>11111100
00001011=>11110100=>01111100=>00111110
00001100=>11110011=>01111011=>10111101
00001101=>11110010=>10111100=>01011110
00001110=>11110001=>00111101=>10011110
00001111=>11110000=>00011110=>00001111
00010000=>11101111=>11101111=>11110111
00010001=>11101110=>11110110=>01111011
00010010=>11101101=>11110101=>11111010
00010011=>11101100=>01111010=>00111101
00010100=>11101011=>11110011=>11111001
00010101=>11101010=>11111000=>01111100
00010110=>11101001=>01111001=>10111100
00010111=>11101000=>00111100=>00011110
00011000=>11100111=>01110111=>10111011
00011001=>11100110=>10111010=>01011101
00011010=>11100101=>10111001=>11011100
00011011=>11100100=>01011100=>00101110
00011100=>11100011=>00111011=>10011101
00011101=>11100010=>10011100=>01001110
00011110=>11100001=>00011101=>10001110
00011111=>11100000=>00001110=>00000111
00100000=>11011111=>11011111=>11101111
00100001=>11011110=>11101110=>01110111
00100010=>11011101=>11101101=>11110110
00100011=>11011100=>01110110=>00111011
00100100=>11011011=>11101011=>11110101
00100101=>11011010=>11110100=>01111010
00100110=>11011001=>01110101=>10111010
00100111=>11011000=>00111010=>00011101
00101000=>11010111=>11100111=>11110011
00101001=>11010110=>11110010=>01111001
00101010=>11010101=>11110001=>11111000
00101011=>11010100=>01111000=>00111100
00101100=>11010011=>01110011=>10111001
00101101=>11010010=>10111000=>01011100
00101110=>11010001=>00111001=>10011100
00101111=>11010000=>00011100=>00001110
00110000=>11001111=>01101111=>10110111
00110001=>11001110=>10110110=>01011011
00110010=>11001101=>10110101=>11011010
00110011=>11001100=>01011010=>00101101
00110100=>11001011=>10110011=>11011001
00110101=>11001010=>11011000=>01101100
00110110=>11001001=>01011001=>10101100
00110111=>11001000=>00101100=>00010110
00111000=>11000111=>00110111=>10011011
00111001=>11000110=>10011010=>01001101
00111010=>11000101=>10011001=>11001100
00111011=>11000100=>01001100=>00100110
00111100=>11000011=>00011011=>10001101
00111101=>11000010=>10001100=>01000110
00111110=>11000001=>00001101=>10000110
00111111=>11000000=>00000110=>00000011
01000000=>10111111=>10111111=>11011111
01000001=>10111110=>11011110=>01101111
01000010=>10111101=>11011101=>11101110
01000011=>10111100=>01101110=>00110111
01000100=>10111011=>11011011=>11101101
01000101=>10111010=>11101100=>01110110
01000110=>10111001=>01101101=>10110110
01000111=>10111000=>00110110=>00011011
01001000=>10110111=>11010111=>11101011
01001001=>10110110=>11101010=>01110101
01001010=>10110101=>11101001=>11110100
01001011=>10110100=>01110100=>00111010
01001100=>10110011=>01101011=>10110101
01001101=>10110010=>10110100=>01011010
01001110=>10110001=>00110101=>10011010
01001111=>10110000=>00011010=>00001101
01010000=>10101111=>11001111=>11100111
01010001=>10101110=>11100110=>01110011
01010010=>10101101=>11100101=>11110010
01010011=>10101100=>01110010=>00111001
01010100=>10101011=>11100011=>11110001
01010101=>10101010=>11110000=>01111000
01010110=>10101001=>01110001=>10111000
01010111=>10101000=>00111000=>00011100
01011000=>10100111=>01100111=>10110011
01011001=>10100110=>10110010=>01011001
01011010=>10100101=>10110001=>11011000
01011011=>10100100=>01011000=>00101100
01011100=>10100011=>00110011=>10011001
01011101=>10100010=>10011000=>01001100
01011110=>10100001=>00011001=>10001100
01011111=>10100000=>00001100=>00000110
01100000=>10011111=>01011111=>10101111
01100001=>10011110=>10101110=>01010111
01100010=>10011101=>10101101=>11010110
01100011=>10011100=>01010110=>00101011
01100100=>10011011=>10101011=>11010101
01100101=>10011010=>11010100=>01101010
01100110=>10011001=>01010101=>10101010
01100111=>10011000=>00101010=>00010101
01101000=>10010111=>10100111=>11010011
01101001=>10010110=>11010010=>01101001
01101010=>10010101=>11010001=>11101000
01101011=>10010100=>01101000=>00110100
01101100=>10010011=>01010011=>10101001
01101101=>10010010=>10101000=>01010100
01101110=>10010001=>00101001=>10010100
01101111=>10010000=>00010100=>00001010
01110000=>10001111=>00101111=>10010111
01110001=>10001110=>10010110=>01001011
01110010=>10001101=>10010101=>11001010
01110011=>10001100=>01001010=>00100101
01110100=>10001011=>10010011=>11001001
01110101=>10001010=>11001000=>01100100
01110110=>10001001=>01001001=>10100100
01110111=>10001000=>00100100=>00010010
01111000=>10000111=>00010111=>10001011
01111001=>10000110=>10001010=>01000101
01111010=>10000101=>10001001=>11000100
01111011=>10000100=>01000100=>00100010
01111100=>10000011=>00001011=>10000101
01111101=>10000010=>10000100=>01000010
01111110=>10000001=>00000101=>10000010
01111111=>10000000=>00000010=>00000001
10000000=>01111111=>01111111=>10111111
10000001=>01111110=>10111110=>01011111
10000010=>01111101=>10111101=>11011110
10000011=>01111100=>01011110=>00101111
10000100=>01111011=>10111011=>11011101
10000101=>01111010=>11011100=>01101110
10000110=>01111001=>01011101=>10101110
10000111=>01111000=>00101110=>00010111
10001000=>01110111=>10110111=>11011011
10001001=>01110110=>11011010=>01101101
10001010=>01110101=>11011001=>11101100
10001011=>01110100=>01101100=>00110110
10001100=>01110011=>01011011=>10101101
10001101=>01110010=>10101100=>01010110
10001110=>01110001=>00101101=>10010110
10001111=>01110000=>00010110=>00001011
10010000=>01101111=>10101111=>11010111
10010001=>01101110=>11010110=>01101011
10010010=>01101101=>11010101=>11101010
10010011=>01101100=>01101010=>00110101
10010100=>01101011=>11010011=>11101001
10010101=>01101010=>11101000=>01110100
10010110=>01101001=>01101001=>10110100
10010111=>01101000=>00110100=>00011010
10011000=>01100111=>01010111=>10101011
10011001=>01100110=>10101010=>01010101
10011010=>01100101=>10101001=>11010100
10011011=>01100100=>01010100=>00101010
10011100=>01100011=>00101011=>10010101
10011101=>01100010=>10010100=>01001010
10011110=>01100001=>00010101=>10001010
10011111=>01100000=>00001010=>00000101
10100000=>01011111=>10011111=>11001111
10100001=>01011110=>11001110=>01100111
10100010=>01011101=>11001101=>11100110
10100011=>01011100=>01100110=>00110011
10100100=>01011011=>11001011=>11100101
10100101=>01011010=>11100100=>01110010
10100110=>01011001=>01100101=>10110010
10100111=>01011000=>00110010=>00011001
10101000=>01010111=>11000111=>11100011
10101001=>01010110=>11100010=>01110001
10101010=>01010101=>11100001=>11110000
10101011=>01010100=>01110000=>00111000
10101100=>01010011=>01100011=>10110001
10101101=>01010010=>10110000=>01011000
10101110=>01010001=>00110001=>10011000
10101111=>01010000=>00011000=>00001100
10110000=>01001111=>01001111=>10100111
10110001=>01001110=>10100110=>01010011
10110010=>01001101=>10100101=>11010010
10110011=>01001100=>01010010=>00101001
10110100=>01001011=>10100011=>11010001
10110101=>01001010=>11010000=>01101000
10110110=>01001001=>01010001=>10101000
10110111=>01001000=>00101000=>00010100
10111000=>01000111=>00100111=>10010011
10111001=>01000110=>10010010=>01001001
10111010=>01000101=>10010001=>11001000
10111011=>01000100=>01001000=>00100100
10111100=>01000011=>00010011=>10001001
10111101=>01000010=>10001000=>01000100
10111110=>01000001=>00001001=>10000100
10111111=>01000000=>00000100=>00000010
11000000=>00111111=>00111111=>10011111
11000001=>00111110=>10011110=>01001111
11000010=>00111101=>10011101=>11001110
11000011=>00111100=>01001110=>00100111
11000100=>00111011=>10011011=>11001101
11000101=>00111010=>11001100=>01100110
11000110=>00111001=>01001101=>10100110
11000111=>00111000=>00100110=>00010011
11001000=>00110111=>10010111=>11001011
11001001=>00110110=>11001010=>01100101
11001010=>00110101=>11001001=>11100100
11001011=>00110100=>01100100=>00110010
11001100=>00110011=>01001011=>10100101
11001101=>00110010=>10100100=>01010010
11001110=>00110001=>00100101=>10010010
11001111=>00110000=>00010010=>00001001
11010000=>00101111=>10001111=>11000111
11010001=>00101110=>11000110=>01100011
11010010=>00101101=>11000101=>11100010
11010011=>00101100=>01100010=>00110001
11010100=>00101011=>11000011=>11100001
11010101=>00101010=>11100000=>01110000
11010110=>00101001=>01100001=>10110000
11010111=>00101000=>00110000=>00011000
11011000=>00100111=>01000111=>10100011
11011001=>00100110=>10100010=>01010001
11011010=>00100101=>10100001=>11010000
11011011=>00100100=>01010000=>00101000
11011100=>00100011=>00100011=>10010001
11011101=>00100010=>10010000=>01001000
11011110=>00100001=>00010001=>10001000
11011111=>00100000=>00001000=>00000100
11100000=>00011111=>00011111=>10001111
11100001=>00011110=>10001110=>01000111
11100010=>00011101=>10001101=>11000110
11100011=>00011100=>01000110=>00100011
11100100=>00011011=>10001011=>11000101
11100101=>00011010=>11000100=>01100010
11100110=>00011001=>01000101=>10100010
11100111=>00011000=>00100010=>00010001
11101000=>00010111=>10000111=>11000011
11101001=>00010110=>11000010=>01100001
11101010=>00010101=>11000001=>11100000
11101011=>00010100=>01100000=>00110000
11101100=>00010011=>01000011=>10100001
11101101=>00010010=>10100000=>01010000
11101110=>00010001=>00100001=>10010000
11101111=>00010000=>00010000=>00001000
11110000=>00001111=>00001111=>10000111
11110001=>00001110=>10000110=>01000011
11110010=>00001101=>10000101=>11000010
11110011=>00001100=>01000010=>00100001
11110100=>00001011=>10000011=>11000001
11110101=>00001010=>11000000=>01100000
11110110=>00001001=>01000001=>10100000
11110111=>00001000=>00100000=>00010000
11111000=>00000111=>00000111=>10000011
11111001=>00000110=>10000010=>01000001
11111010=>00000101=>10000001=>11000000
11111011=>00000100=>01000000=>00100000
11111100=>00000011=>00000011=>10000001
11111101=>00000010=>10000000=>01000000
11111110=>00000001=>00000001=>10000000
11111111=>00000000=>00000000=>00000000
000000000=>111111111=>111111111=>111111111
000000001=>111111110=>111111110=>011111111
000000010=>111111101=>111111101=>111111110
000000011=>111111100=>011111110=>001111111
000000100=>111111011=>111111011=>111111101
000000101=>111111010=>111111100=>011111110
000000110=>111111001=>011111101=>101111110
000000111=>111111000=>001111110=>000111111
000001000=>111110111=>111110111=>111111011
000001001=>111110110=>111111010=>011111101
000001010=>111110101=>111111001=>111111100
000001011=>111110100=>011111100=>001111110
000001100=>111110011=>011111011=>101111101
000001101=>111110010=>101111100=>010111110
000001110=>111110001=>001111101=>100111110
000001111=>111110000=>000111110=>000011111
000010000=>111101111=>111101111=>111110111
000010001=>111101110=>111110110=>011111011
000010010=>111101101=>111110101=>111111010
000010011=>111101100=>011111010=>001111101
000010100=>111101011=>111110011=>111111001
000010101=>111101010=>111111000=>011111100
000010110=>111101001=>011111001=>101111100
000010111=>111101000=>001111100=>000111110
000011000=>111100111=>011110111=>101111011
000011001=>111100110=>101111010=>010111101
000011010=>111100101=>101111001=>110111100
000011011=>111100100=>010111100=>001011110
000011100=>111100011=>001111011=>100111101
000011101=>111100010=>100111100=>010011110
000011110=>111100001=>000111101=>100011110
000011111=>111100000=>000011110=>000001111
000100000=>111011111=>111011111=>111101111
000100001=>111011110=>111101110=>011110111
000100010=>111011101=>111101101=>111110110
000100011=>111011100=>011110110=>001111011
000100100=>111011011=>111101011=>111110101
000100101=>111011010=>111110100=>011111010
000100110=>111011001=>011110101=>101111010
000100111=>111011000=>001111010=>000111101
000101000=>111010111=>111100111=>111110011
000101001=>111010110=>111110010=>011111001
000101010=>111010101=>111110001=>111111000
000101011=>111010100=>011111000=>001111100
000101100=>111010011=>011110011=>101111001
000101101=>111010010=>101111000=>010111100
000101110=>111010001=>001111001=>100111100
000101111=>111010000=>000111100=>000011110
000110000=>111001111=>011101111=>101110111
000110001=>111001110=>101110110=>010111011
000110010=>111001101=>101110101=>110111010
000110011=>111001100=>010111010=>001011101
000110100=>111001011=>101110011=>110111001
000110101=>111001010=>110111000=>011011100
000110110=>111001001=>010111001=>101011100
000110111=>111001000=>001011100=>000101110
000111000=>111000111=>001110111=>100111011
000111001=>111000110=>100111010=>010011101
000111010=>111000101=>100111001=>110011100
000111011=>111000100=>010011100=>001001110
000111100=>111000011=>000111011=>100011101
000111101=>111000010=>100011100=>010001110
000111110=>111000001=>000011101=>100001110
000111111=>111000000=>000001110=>000000111
001000000=>110111111=>110111111=>111011111
001000001=>110111110=>111011110=>011101111
001000010=>110111101=>111011101=>111101110
001000011=>110111100=>011101110=>001110111
001000100=>110111011=>111011011=>111101101
001000101=>110111010=>111101100=>011110110
001000110=>110111001=>011101101=>101110110
001000111=>110111000=>001110110=>000111011
001001000=>110110111=>111010111=>111101011
001001001=>110110110=>111101010=>011110101
001001010=>110110101=>111101001=>111110100
001001011=>110110100=>011110100=>001111010
001001100=>110110011=>011101011=>101110101
001001101=>110110010=>101110100=>010111010
001001110=>110110001=>001110101=>100111010
001001111=>110110000=>000111010=>000011101
001010000=>110101111=>111001111=>111100111
001010001=>110101110=>111100110=>011110011
001010010=>110101101=>111100101=>111110010
001010011=>110101100=>011110010=>001111001
001010100=>110101011=>111100011=>111110001
001010101=>110101010=>111110000=>011111000
001010110=>110101001=>011110001=>101111000
001010111=>110101000=>001111000=>000111100
001011000=>110100111=>011100111=>101110011
001011001=>110100110=>101110010=>010111001
001011010=>110100101=>101110001=>110111000
001011011=>110100100=>010111000=>001011100
001011100=>110100011=>001110011=>100111001
001011101=>110100010=>100111000=>010011100
001011110=>110100001=>000111001=>100011100
001011111=>110100000=>000011100=>000001110
001100000=>110011111=>011011111=>101101111
001100001=>110011110=>101101110=>010110111
001100010=>110011101=>101101101=>110110110
001100011=>110011100=>010110110=>001011011
001100100=>110011011=>101101011=>110110101
001100101=>110011010=>110110100=>011011010
001100110=>110011001=>010110101=>101011010
001100111=>110011000=>001011010=>000101101
001101000=>110010111=>101100111=>110110011
001101001=>110010110=>110110010=>011011001
001101010=>110010101=>110110001=>111011000
001101011=>110010100=>011011000=>001101100
001101100=>110010011=>010110011=>101011001
001101101=>110010010=>101011000=>010101100
001101110=>110010001=>001011001=>100101100
001101111=>110010000=>000101100=>000010110
001110000=>110001111=>001101111=>100110111
001110001=>110001110=>100110110=>010011011
001110010=>110001101=>100110101=>110011010
001110011=>110001100=>010011010=>001001101
001110100=>110001011=>100110011=>110011001
001110101=>110001010=>110011000=>011001100
001110110=>110001001=>010011001=>101001100
001110111=>110001000=>001001100=>000100110
001111000=>110000111=>000110111=>100011011
001111001=>110000110=>100011010=>010001101
001111010=>110000101=>100011001=>110001100
001111011=>110000100=>010001100=>001000110
001111100=>110000011=>000011011=>100001101
001111101=>110000010=>100001100=>010000110
001111110=>110000001=>000001101=>100000110
001111111=>110000000=>000000110=>000000011
010000000=>101111111=>101111111=>110111111
010000001=>101111110=>110111110=>011011111
010000010=>101111101=>110111101=>111011110
010000011=>101111100=>011011110=>001101111
010000100=>101111011=>110111011=>111011101
010000101=>101111010=>111011100=>011101110
010000110=>101111001=>011011101=>101101110
010000111=>101111000=>001101110=>000110111
010001000=>101110111=>110110111=>111011011
010001001=>101110110=>111011010=>011101101
010001010=>101110101=>111011001=>111101100
010001011=>101110100=>011101100=>001110110
010001100=>101110011=>011011011=>101101101
010001101=>101110010=>101101100=>010110110
010001110=>101110001=>001101101=>100110110
010001111=>101110000=>000110110=>000011011
010010000=>101101111=>110101111=>111010111
010010001=>101101110=>111010110=>011101011
010010010=>101101101=>111010101=>111101010
010010011=>101101100=>011101010=>001110101
010010100=>101101011=>111010011=>111101001
010010101=>101101010=>111101000=>011110100
010010110=>101101001=>011101001=>101110100
010010111=>101101000=>001110100=>000111010
010011000=>101100111=>011010111=>101101011
010011001=>101100110=>101101010=>010110101
010011010=>101100101=>101101001=>110110100
010011011=>101100100=>010110100=>001011010
010011100=>101100011=>001101011=>100110101
010011101=>101100010=>100110100=>010011010
010011110=>101100001=>000110101=>100011010
010011111=>101100000=>000011010=>000001101
010100000=>101011111=>110011111=>111001111
010100001=>101011110=>111001110=>011100111
010100010=>101011101=>111001101=>111100110
010100011=>101011100=>011100110=>001110011
010100100=>101011011=>111001011=>111100101
010100101=>101011010=>111100100=>011110010
010100110=>101011001=>011100101=>101110010
010100111=>101011000=>001110010=>000111001
010101000=>101010111=>111000111=>111100011
010101001=>101010110=>111100010=>011110001
010101010=>101010101=>111100001=>111110000
010101011=>101010100=>011110000=>001111000
010101100=>101010011=>011100011=>101110001
010101101=>101010010=>101110000=>010111000
010101110=>101010001=>001110001=>100111000
010101111=>101010000=>000111000=>000011100
010110000=>101001111=>011001111=>101100111
010110001=>101001110=>101100110=>010110011
010110010=>101001101=>101100101=>110110010
010110011=>101001100=>010110010=>001011001
010110100=>101001011=>101100011=>110110001
010110101=>101001010=>110110000=>011011000
010110110=>101001001=>010110001=>101011000
010110111=>101001000=>001011000=>000101100
010111000=>101000111=>001100111=>100110011
010111001=>101000110=>100110010=>010011001
010111010=>101000101=>100110001=>110011000
010111011=>101000100=>010011000=>001001100
010111100=>101000011=>000110011=>100011001
010111101=>101000010=>100011000=>010001100
010111110=>101000001=>000011001=>100001100
010111111=>101000000=>000001100=>000000110
011000000=>100111111=>010111111=>101011111
011000001=>100111110=>101011110=>010101111
011000010=>100111101=>101011101=>110101110
011000011=>100111100=>010101110=>001010111
011000100=>100111011=>101011011=>110101101
011000101=>100111010=>110101100=>011010110
011000110=>100111001=>010101101=>101010110
011000111=>100111000=>001010110=>000101011
011001000=>100110111=>101010111=>110101011
011001001=>100110110=>110101010=>011010101
011001010=>100110101=>110101001=>111010100
011001011=>100110100=>011010100=>001101010
011001100=>100110011=>010101011=>101010101
011001101=>100110010=>101010100=>010101010
011001110=>100110001=>001010101=>100101010
011001111=>100110000=>000101010=>000010101
011010000=>100101111=>101001111=>110100111
011010001=>100101110=>110100110=>011010011
011010010=>100101101=>110100101=>111010010
011010011=>100101100=>011010010=>001101001
011010100=>100101011=>110100011=>111010001
011010101=>100101010=>111010000=>011101000
011010110=>100101001=>011010001=>101101000
011010111=>100101000=>001101000=>000110100
011011000=>100100111=>010100111=>101010011
011011001=>100100110=>101010010=>010101001
011011010=>100100101=>101010001=>110101000
011011011=>100100100=>010101000=>001010100
011011100=>100100011=>001010011=>100101001
011011101=>100100010=>100101000=>010010100
011011110=>100100001=>000101001=>100010100
011011111=>100100000=>000010100=>000001010
011100000=>100011111=>001011111=>100101111
011100001=>100011110=>100101110=>010010111
011100010=>100011101=>100101101=>110010110
011100011=>100011100=>010010110=>001001011
011100100=>100011011=>100101011=>110010101
011100101=>100011010=>110010100=>011001010
011100110=>100011001=>010010101=>101001010
011100111=>100011000=>001001010=>000100101
011101000=>100010111=>100100111=>110010011
011101001=>100010110=>110010010=>011001001
011101010=>100010101=>110010001=>111001000
011101011=>100010100=>011001000=>001100100
011101100=>100010011=>010010011=>101001001
011101101=>100010010=>101001000=>010100100
011101110=>100010001=>001001001=>100100100
011101111=>100010000=>000100100=>000010010
011110000=>100001111=>000101111=>100010111
011110001=>100001110=>100010110=>010001011
011110010=>100001101=>100010101=>110001010
011110011=>100001100=>010001010=>001000101
011110100=>100001011=>100010011=>110001001
011110101=>100001010=>110001000=>011000100
011110110=>100001001=>010001001=>101000100
011110111=>100001000=>001000100=>000100010
011111000=>100000111=>000010111=>100001011
011111001=>100000110=>100001010=>010000101
011111010=>100000101=>100001001=>110000100
011111011=>100000100=>010000100=>001000010
011111100=>100000011=>000001011=>100000101
011111101=>100000010=>100000100=>010000010
011111110=>100000001=>000000101=>100000010
011111111=>100000000=>000000010=>000000001
100000000=>011111111=>011111111=>101111111
100000001=>011111110=>101111110=>010111111
100000010=>011111101=>101111101=>110111110
100000011=>011111100=>010111110=>001011111
100000100=>011111011=>101111011=>110111101
100000101=>011111010=>110111100=>011011110
100000110=>011111001=>010111101=>101011110
100000111=>011111000=>001011110=>000101111
100001000=>011110111=>101110111=>110111011
100001001=>011110110=>110111010=>011011101
100001010=>011110101=>110111001=>111011100
100001011=>011110100=>011011100=>001101110
100001100=>011110011=>010111011=>101011101
100001101=>011110010=>101011100=>010101110
100001110=>011110001=>001011101=>100101110
100001111=>011110000=>000101110=>000010111
100010000=>011101111=>101101111=>110110111
100010001=>011101110=>110110110=>011011011
100010010=>011101101=>110110101=>111011010
100010011=>011101100=>011011010=>001101101
100010100=>011101011=>110110011=>111011001
100010101=>011101010=>111011000=>011101100
100010110=>011101001=>011011001=>101101100
100010111=>011101000=>001101100=>000110110
100011000=>011100111=>010110111=>101011011
100011001=>011100110=>101011010=>010101101
100011010=>011100101=>101011001=>110101100
100011011=>011100100=>010101100=>001010110
100011100=>011100011=>001011011=>100101101
100011101=>011100010=>100101100=>010010110
100011110=>011100001=>000101101=>100010110
100011111=>011100000=>000010110=>000001011
100100000=>011011111=>101011111=>110101111
100100001=>011011110=>110101110=>011010111
100100010=>011011101=>110101101=>111010110
100100011=>011011100=>011010110=>001101011
100100100=>011011011=>110101011=>111010101
100100101=>011011010=>111010100=>011101010
100100110=>011011001=>011010101=>101101010
100100111=>011011000=>001101010=>000110101
100101000=>011010111=>110100111=>111010011
100101001=>011010110=>111010010=>011101001
100101010=>011010101=>111010001=>111101000
100101011=>011010100=>011101000=>001110100
100101100=>011010011=>011010011=>101101001
100101101=>011010010=>101101000=>010110100
100101110=>011010001=>001101001=>100110100
100101111=>011010000=>000110100=>000011010
100110000=>011001111=>010101111=>101010111
100110001=>011001110=>101010110=>010101011
100110010=>011001101=>101010101=>110101010
100110011=>011001100=>010101010=>001010101
100110100=>011001011=>101010011=>110101001
100110101=>011001010=>110101000=>011010100
100110110=>011001001=>010101001=>101010100
100110111=>011001000=>001010100=>000101010
100111000=>011000111=>001010111=>100101011
100111001=>011000110=>100101010=>010010101
100111010=>011000101=>100101001=>110010100
100111011=>011000100=>010010100=>001001010
100111100=>011000011=>000101011=>100010101
100111101=>011000010=>100010100=>010001010
100111110=>011000001=>000010101=>100001010
100111111=>011000000=>000001010=>000000101
101000000=>010111111=>100111111=>110011111
101000001=>010111110=>110011110=>011001111
101000010=>010111101=>110011101=>111001110
101000011=>010111100=>011001110=>001100111
101000100=>010111011=>110011011=>111001101
101000101=>010111010=>111001100=>011100110
101000110=>010111001=>011001101=>101100110
101000111=>010111000=>001100110=>000110011
101001000=>010110111=>110010111=>111001011
101001001=>010110110=>111001010=>011100101
101001010=>010110101=>111001001=>111100100
101001011=>010110100=>011100100=>001110010
101001100=>010110011=>011001011=>101100101
101001101=>010110010=>101100100=>010110010
101001110=>010110001=>001100101=>100110010
101001111=>010110000=>000110010=>000011001
101010000=>010101111=>110001111=>111000111
101010001=>010101110=>111000110=>011100011
101010010=>010101101=>111000101=>111100010
101010011=>010101100=>011100010=>001110001
101010100=>010101011=>111000011=>111100001
101010101=>010101010=>111100000=>011110000
101010110=>010101001=>011100001=>101110000
101010111=>010101000=>001110000=>000111000
101011000=>010100111=>011000111=>101100011
101011001=>010100110=>101100010=>010110001
101011010=>010100101=>101100001=>110110000
101011011=>010100100=>010110000=>001011000
101011100=>010100011=>001100011=>100110001
101011101=>010100010=>100110000=>010011000
101011110=>010100001=>000110001=>100011000
101011111=>010100000=>000011000=>000001100
101100000=>010011111=>010011111=>101001111
101100001=>010011110=>101001110=>010100111
101100010=>010011101=>101001101=>110100110
101100011=>010011100=>010100110=>001010011
101100100=>010011011=>101001011=>110100101
101100101=>010011010=>110100100=>011010010
101100110=>010011001=>010100101=>101010010
101100111=>010011000=>001010010=>000101001
101101000=>010010111=>101000111=>110100011
101101001=>010010110=>110100010=>011010001
101101010=>010010101=>110100001=>111010000
101101011=>010010100=>011010000=>001101000
101101100=>010010011=>010100011=>101010001
101101101=>010010010=>101010000=>010101000
101101110=>010010001=>001010001=>100101000
101101111=>010010000=>000101000=>000010100
101110000=>010001111=>001001111=>100100111
101110001=>010001110=>100100110=>010010011
101110010=>010001101=>100100101=>110010010
101110011=>010001100=>010010010=>001001001
101110100=>010001011=>100100011=>110010001
101110101=>010001010=>110010000=>011001000
101110110=>010001001=>010010001=>101001000
101110111=>010001000=>001001000=>000100100
101111000=>010000111=>000100111=>100010011
101111001=>010000110=>100010010=>010001001
101111010=>010000101=>100010001=>110001000
101111011=>010000100=>010001000=>001000100
101111100=>010000011=>000010011=>100001001
101111101=>010000010=>100001000=>010000100
101111110=>010000001=>000001001=>100000100
101111111=>010000000=>000000100=>000000010
110000000=>001111111=>001111111=>100111111
110000001=>001111110=>100111110=>010011111
110000010=>001111101=>100111101=>110011110
110000011=>001111100=>010011110=>001001111
110000100=>001111011=>100111011=>110011101
110000101=>001111010=>110011100=>011001110
110000110=>001111001=>010011101=>101001110
110000111=>001111000=>001001110=>000100111
110001000=>001110111=>100110111=>110011011
110001001=>001110110=>110011010=>011001101
110001010=>001110101=>110011001=>111001100
110001011=>001110100=>011001100=>001100110
110001100=>001110011=>010011011=>101001101
110001101=>001110010=>101001100=>010100110
110001110=>001110001=>001001101=>100100110
110001111=>001110000=>000100110=>000010011
110010000=>001101111=>100101111=>110010111
110010001=>001101110=>110010110=>011001011
110010010=>001101101=>110010101=>111001010
110010011=>001101100=>011001010=>001100101
110010100=>001101011=>110010011=>111001001
110010101=>001101010=>111001000=>011100100
110010110=>001101001=>011001001=>101100100
110010111=>001101000=>001100100=>000110010
110011000=>001100111=>010010111=>101001011
110011001=>001100110=>101001010=>010100101
110011010=>001100101=>101001001=>110100100
110011011=>001100100=>010100100=>001010010
110011100=>001100011=>001001011=>100100101
110011101=>001100010=>100100100=>010010010
110011110=>001100001=>000100101=>100010010
110011111=>001100000=>000010010=>000001001
110100000=>001011111=>100011111=>110001111
110100001=>001011110=>110001110=>011000111
110100010=>001011101=>110001101=>111000110
110100011=>001011100=>011000110=>001100011
110100100=>001011011=>110001011=>111000101
110100101=>001011010=>111000100=>011100010
110100110=>001011001=>011000101=>101100010
110100111=>001011000=>001100010=>000110001
110101000=>001010111=>110000111=>111000011
110101001=>001010110=>111000010=>011100001
110101010=>001010101=>111000001=>111100000
110101011=>001010100=>011100000=>001110000
110101100=>001010011=>011000011=>101100001
110101101=>001010010=>101100000=>010110000
110101110=>001010001=>001100001=>100110000
110101111=>001010000=>000110000=>000011000
110110000=>001001111=>010001111=>101000111
110110001=>001001110=>101000110=>010100011
110110010=>001001101=>101000101=>110100010
110110011=>001001100=>010100010=>001010001
110110100=>001001011=>101000011=>110100001
110110101=>001001010=>110100000=>011010000
110110110=>001001001=>010100001=>101010000
110110111=>001001000=>001010000=>000101000
110111000=>001000111=>001000111=>100100011
110111001=>001000110=>100100010=>010010001
110111010=>001000101=>100100001=>110010000
110111011=>001000100=>010010000=>001001000
110111100=>001000011=>000100011=>100010001
110111101=>001000010=>100010000=>010001000
110111110=>001000001=>000010001=>100001000
110111111=>001000000=>000001000=>000000100
111000000=>000111111=>000111111=>100011111
111000001=>000111110=>100011110=>010001111
111000010=>000111101=>100011101=>110001110
111000011=>000111100=>010001110=>001000111
111000100=>000111011=>100011011=>110001101
111000101=>000111010=>110001100=>011000110
111000110=>000111001=>010001101=>101000110
111000111=>000111000=>001000110=>000100011
111001000=>000110111=>100010111=>110001011
111001001=>000110110=>110001010=>011000101
111001010=>000110101=>110001001=>111000100
111001011=>000110100=>011000100=>001100010
111001100=>000110011=>010001011=>101000101
111001101=>000110010=>101000100=>010100010
111001110=>000110001=>001000101=>100100010
111001111=>000110000=>000100010=>000010001
111010000=>000101111=>100001111=>110000111
111010001=>000101110=>110000110=>011000011
111010010=>000101101=>110000101=>111000010
111010011=>000101100=>011000010=>001100001
111010100=>000101011=>110000011=>111000001
111010101=>000101010=>111000000=>011100000
111010110=>000101001=>011000001=>101100000
111010111=>000101000=>001100000=>000110000
111011000=>000100111=>010000111=>101000011
111011001=>000100110=>101000010=>010100001
111011010=>000100101=>101000001=>110100000
111011011=>000100100=>010100000=>001010000
111011100=>000100011=>001000011=>100100001
111011101=>000100010=>100100000=>010010000
111011110=>000100001=>000100001=>100010000
111011111=>000100000=>000010000=>000001000
111100000=>000011111=>000011111=>100001111
111100001=>000011110=>100001110=>010000111
111100010=>000011101=>100001101=>110000110
111100011=>000011100=>010000110=>001000011
111100100=>000011011=>100001011=>110000101
111100101=>000011010=>110000100=>011000010
111100110=>000011001=>010000101=>101000010
111100111=>000011000=>001000010=>000100001
111101000=>000010111=>100000111=>110000011
111101001=>000010110=>110000010=>011000001
111101010=>000010101=>110000001=>111000000
111101011=>000010100=>011000000=>001100000
111101100=>000010011=>010000011=>101000001
111101101=>000010010=>101000000=>010100000
111101110=>000010001=>001000001=>100100000
111101111=>000010000=>000100000=>000010000
111110000=>000001111=>000001111=>100000111
111110001=>000001110=>100000110=>010000011
111110010=>000001101=>100000101=>110000010
111110011=>000001100=>010000010=>001000001
111110100=>000001011=>100000011=>110000001
111110101=>000001010=>110000000=>011000000
111110110=>000001001=>010000001=>101000000
111110111=>000001000=>001000000=>000100000
111111000=>000000111=>000000111=>100000011
111111001=>000000110=>100000010=>010000001
111111010=>000000101=>100000001=>110000000
111111011=>000000100=>010000000=>001000000
111111100=>000000011=>000000011=>100000001
111111101=>000000010=>100000000=>010000000
111111110=>000000001=>000000001=>100000000
111111111=>000000000=>000000000=>000000000
1010101010=>0101010101=>1111000001=>1111100000
1010101100=>0101010011=>0111000011=>1011100001
1010111000=>0101000111=>0011000111=>1001100011
1011001100=>0100110011=>0101001011=>1010100101
1011010100=>0100101011=>1101000011=>1110100001
1011011000=>0100100111=>0101000111=>1010100011
1011110000=>0100001111=>0001001111=>1000100111
1100101010=>0011010101=>1110010001=>1111001000
1100101100=>0011010011=>0110010011=>1011001001
1100111000=>0011000111=>0010010111=>1001001011
1101010100=>0010101011=>1110000011=>1111000001
1101110000=>0010001111=>0010001111=>1001000111
1110001100=>0001110011=>0100011011=>1010001101
1110011000=>0001100111=>0100010111=>1010001011
1110101000=>0001010111=>1100000111=>1110000011
1110110000=>0001001111=>0100001111=>1010000111
1111100000=>0000011111=>0000011111=>1000001111
101010101010=>010101010101=>111110000001=>111111000000
101010101100=>010101010011=>011110000011=>101111000001
101010110010=>010101001101=>101110000101=>110111000010
101011010100=>010100101011=>110110000011=>111011000001
101011100010=>010100011101=>100110001101=>110011000110
101011101000=>010100010111=>100110000111=>110011000011
101011110000=>010100001111=>000110001111=>100011000111
101100101010=>010011010101=>111010010001=>111101001000
101100110010=>010011001101=>101010010101=>110101001010
101100111000=>010011000111=>001010010111=>100101001011
101101001100=>010010110011=>011010001011=>101101000101
101101010010=>010010101101=>111010000101=>111101000010
101101010100=>010010101011=>111010000011=>111101000001
101101101000=>010010010111=>101010000111=>110101000011
101101110000=>010010001111=>001010001111=>100101000111
101110001100=>010001110011=>010010011011=>101001001101
101110011000=>010001100111=>010010010111=>101001001011
101110110000=>010001001111=>010010001111=>101001000111
101111000010=>010000111101=>100010011101=>110001001110
101111001000=>010000110111=>100010010111=>110001001011
101111100000=>010000011111=>000010011111=>100001001111
110010101010=>001101010101=>111100100001=>111110010000
110010110010=>001101001101=>101100100101=>110110010010
110010110100=>001101001011=>101100100011=>110110010001
110010111000=>001101000111=>001100100111=>100110010011
110011001100=>001100110011=>010100101011=>101010010101
110011011000=>001100100111=>010100100111=>101010010011
110011101000=>001100010111=>100100100111=>110010010011
110011110000=>001100001111=>000100101111=>100010010111
110100101010=>001011010101=>111100010001=>111110001000
110100101100=>001011010011=>011100010011=>101110001001
110100110100=>001011001011=>101100010011=>110110001001
110100111000=>001011000111=>001100010111=>100110001011
110101010100=>001010101011=>111100000011=>111110000001
110101011000=>001010100111=>011100000111=>101110000011
110101100010=>001010011101=>101100001101=>110110000110
110101101000=>001010010111=>101100000111=>110110000011
110101110000=>001010001111=>001100001111=>100110000111
110110001100=>001001110011=>010100011011=>101010001101
110110011000=>001001100111=>010100010111=>101010001011
110110101000=>001001010111=>110100000111=>111010000011
110110110000=>001001001111=>010100001111=>101010000111
110111000100=>001000111011=>100100011011=>110010001101
110111001000=>001000110111=>100100010111=>110010001011
110111100000=>001000011111=>000100011111=>100010001111
111000101010=>000111010101=>111000110001=>111100011000
111000110010=>000111001101=>101000110101=>110100011010
111000110100=>000111001011=>101000110011=>110100011001
111000111000=>000111000111=>001000110111=>100100011011
111001001100=>000110110011=>011000101011=>101100010101
111001010010=>000110101101=>111000100101=>111100010010
111001101000=>000110010111=>101000100111=>110100010011
111001110000=>000110001111=>001000101111=>100100010111
111010001010=>000101110101=>111000011001=>111100001100
111010011000=>000101100111=>011000010111=>101100001011
111010100010=>000101011101=>111000001101=>111100000110
111010101000=>000101010111=>111000000111=>111100000011
111011000010=>000100111101=>101000011101=>110100001110
111011000100=>000100111011=>101000011011=>110100001101
111011001000=>000100110111=>101000010111=>110100001011
111011100000=>000100011111=>001000011111=>100100001111
111100001100=>000011110011=>010000111011=>101000011101
111100011000=>000011100111=>010000110111=>101000011011
111100110000=>000011001111=>010000101111=>101000010111
111101010000=>000010101111=>110000001111=>111000000111
111101100000=>000010011111=>010000011111=>101000001111
111110000010=>000001111101=>100000111101=>110000011110
111110001000=>000001110111=>100000110111=>110000011011
111110100000=>000001011111=>100000011111=>110000001111
111111000000=>000000111111=>000000111111=>100000011111
1111111111=>0000000000=>0000000000=>0000000000
1111111110=>0000000001=>0000000001=>1000000000
1111111101=>0000000010=>1000000000=>0100000000
1111111100=>0000000011=>0000000011=>1000000001
1111111010=>0000000101=>1000000001=>1100000000
1111110001=>0000001110=>1000000110=>0100000011
1111101110=>0000010001=>0010000001=>1001000000
1111100001=>0000011110=>1000001110=>0100000111
1111000001=>0000111110=>1000011110=>0100001111
1110101010=>0001010101=>1110000001=>1111000000
1110010110=>0001101001=>0110001001=>1011000100
1110001000=>0001110111=>1000110111=>1100011011
1110000001=>0001111110=>1000111110=>0100011111
1101111110=>0010000001=>0000010001=>1000001000
1101000001=>0010111110=>1100011110=>0110001111
1100111001=>0011000110=>1001001010=>0100100101
1100100001=>0011011110=>1100101110=>0110010111
1100011101=>0011100010=>1001001100=>0100100110
1100001010=>0011110101=>1100111001=>1110011100
1100000011=>0011111100=>0100111110=>0010011111
1100000001=>0011111110=>1001111110=>0100111111
1100000000=>0011111111=>0011111111=>1001111111
1011101100=>0100010011=>0100100011=>1010010001
1011010110=>0100101001=>0110100001=>1011010000
1011001000=>0100110111=>1010010111=>1101001011
1011000110=>0100111001=>0101001101=>1010100110
1010111100=>0101000011=>0001100011=>1000110001
1010111010=>0101000101=>1001100001=>1100110000
1010011100=>0101100011=>0011001011=>1001100101
1010011000=>0101100111=>0110010111=>1011001011
1010001110=>0101110001=>0011001101=>1001100110
1010001100=>0101110011=>0110011011=>1011001101
1001110110=>0110001001=>0100101001=>1010010100
1001101100=>0110010011=>0101010011=>1010101001
1001101010=>0110010101=>1101010001=>1110101000
1001100110=>0110011001=>0101010101=>1010101010
1001011110=>0110100001=>0001101001=>1000110100
1001011000=>0110100111=>0110100111=>1011010011
1001010100=>0110101011=>1110100011=>1111010001
1001010000=>0110101111=>1101001111=>1110100111
1001001110=>0110110001=>0011010101=>1001101010
1001001100=>0110110011=>0110101011=>1011010101
1001001010=>0110110101=>1110101001=>1111010100
1000110010=>0111001101=>1010110101=>1101011010
1000101100=>0111010011=>0110110011=>1011011001
1000101010=>0111010101=>1110110001=>1111011000
1000100110=>0111011001=>0110110101=>1011011010
1000011110=>0111100001=>0001011101=>1000101110
1000010110=>0111101001=>0110111001=>1011011100
1000000010=>0111111101=>1011111101=>1101111110
1000000001=>0111111110=>1011111110=>0101111111
1000000000=>0111111111=>0111111111=>1011111111
10000000000=>01111111111=>01111111111=>10111111111
11111111110=>00000000001=>00000000001=>10000000000
100010011110=>011101100001=>000110110101=>100011011010
100111011110=>011000100001=>000100101001=>100010010100
100000100000=>011111011111=>101111011111=>110111101111
100010001010=>011101110101=>111011011001=>111101101100
100010101010=>011101010101=>111101100001=>111110110000
100101010110=>011010101001=>011110100001=>101111010000
100011100110=>011100011001=>010010110101=>101001011010
100010111100=>011101000011=>000110110011=>100011011001
0111111111=>1000000000=>0000000010=>0000000001
0111111101=>1000000010=>1000000100=>0100000010
0111111001=>1000000110=>1000001010=>0100000101
0111110001=>1000001110=>1000010110=>0100001011
0111100001=>1000011110=>1000101110=>0100010111
0111000001=>1000111110=>1001011110=>0100101111
0110000001=>1001111110=>1010111110=>0101011111
0100000001=>1011111110=>1101111110=>0110111111
0000000001=>1111111110=>1111111110=>0111111111
01111111111=>10000000000=>00000000010=>00000000001
0111111011=>1000000100=>0100000100=>0010000010
0010000001=>1101111110=>1110111110=>0111011111
00000000001=>11111111110=>11111111110=>01111111111
0101010101=>1010101010=>1111100000=>0111110000
0101001101=>1010110010=>1011100100=>0101110010
0101001011=>1010110100=>0111100100=>0011110010
0100110101=>1011001010=>1101101000=>0110110100
0100101101=>1011010010=>1011101000=>0101110100
0100101011=>1011010100=>0111101000=>0011110100
0011010101=>1100101010=>1110110000=>0111011000
0011001101=>1100110010=>1010110100=>0101011010
0010110101=>1101001010=>1101110000=>0110111000
0010101101=>1101010010=>1011110000=>0101111000
0010101011=>1101010100=>0111110000=>0011111000
0010010111=>1101101000=>0011110100=>0001111010
0001110101=>1110001010=>1100111000=>0110011100
0001101101=>1110010010=>1010111000=>0101011100
0001010111=>1110101000=>0011111000=>0001111100
0000101111=>1111010000=>0001111100=>0000111110
0000011111=>1111100000=>0000111110=>0000011111
010101010101=>101010101010=>111111000000=>011111100000
010101001101=>101010110010=>101111000100=>010111100010
010101001011=>101010110100=>011111000100=>001111100010
010100110101=>101011001010=>110111001000=>011011100100
010100101101=>101011010010=>101111001000=>010111100100
010100101011=>101011010100=>011111001000=>001111100100
010100010111=>101011101000=>001111001100=>000111100110
010011010101=>101100101010=>111011010000=>011101101000
010011001101=>101100110010=>101011010100=>010101101010
010011001011=>101100110100=>011011010100=>001101101010
010010110101=>101101001010=>110111010000=>011011101000
010010101101=>101101010010=>101111010000=>010111101000
010010101011=>101101010100=>011111010000=>001111101000
010010010111=>101101101000=>001111010100=>000111101010
010001110101=>101110001010=>110011011000=>011001101100
010001101101=>101110010010=>101011011000=>010101101100
010001010111=>101110101000=>001111011000=>000111101100
010000111011=>101111000100=>010011011100=>001001101110
010000101111=>101111010000=>000111011100=>000011101110
001101010101=>110010101010=>111101100000=>011110110000
001101001101=>110010110010=>101101100100=>010110110010
001101001011=>110010110100=>011101100100=>001110110010
001100110101=>110011001010=>110101101000=>011010110100
001100101101=>110011010010=>101101101000=>010110110100
001100101011=>110011010100=>011101101000=>001110110100
001100011011=>110011100100=>010101101100=>001010110110
001011010101=>110100101010=>111011100000=>011101110000
001011001101=>110100110010=>101011100100=>010101110010
001010110101=>110101001010=>110111100000=>011011110000
001010101101=>110101010010=>101111100000=>010111110000
001010101011=>110101010100=>011111100000=>001111110000
001010010111=>110101101000=>001111100100=>000111110010
001001110101=>110110001010=>110011101000=>011001110100
001001101101=>110110010010=>101011101000=>010101110100
001001010111=>110110101000=>001111101000=>000111110100
000111010101=>111000101010=>111001110000=>011100111000
000110110101=>111001001010=>110101110000=>011010111000
000110101101=>111001010010=>101101110000=>010110111000
000110101011=>111001010100=>011101110000=>001110111000
000101110101=>111010001010=>110011110000=>011001111000
000101101101=>111010010010=>101011110000=>010101111000
000101010111=>111010101000=>001111110000=>000111111000
000100101111=>111011010000=>000111110100=>000011111010
000011110101=>111100001010=>110001111000=>011000111100
000010101111=>111101010000=>000111111000=>000011111100
000001011111=>111110100000=>000011111100=>000001111110
111111111111=>000000000000=>000000000000=>000000000000
0000000000=>1111111111=>1111111111=>1111111111
0000000110=>1111111001=>0111111101=>1011111110
0000011110=>1111100001=>0001111101=>1000111110
0001111000=>1110000111=>0001110111=>1000111011
0001001110=>1110110001=>0011110101=>1001111010
0001011010=>1110100101=>1011110001=>1101111000
0110011110=>1001100001=>0001010101=>1000101010
0110010010=>1001101101=>1101010101=>1110101010
0111100110=>1000011001=>0100010101=>1010001010
0111111110=>1000000001=>0000000101=>1000000010
0111110010=>1000001101=>1000010101=>1100001010
0100100000=>1011011111=>1101011111=>1110101111
0100100110=>1011011001=>0111010101=>1011101010
0100111000=>1011000111=>0011010111=>1001101011
0100111110=>1011000001=>0000110101=>1000011010
0100110010=>1011001101=>1011010101=>1101101010
0100011010=>1011100101=>1011011001=>1101101100
0101101000=>1010010111=>1011000111=>1101100011
0101100010=>1010011101=>1011001101=>1101100110
0101001010=>1010110101=>1111001001=>1111100100
000000000000=>111111111111=>111111111111=>111111111111
000001100000=>111110011111=>011111011111=>101111101111
000001111110=>111110000001=>000001111101=>100000111110
000110011110=>111001100001=>000101110101=>100010111010
000111100110=>111000011001=>010001110101=>101000111010
000111111000=>111000000111=>000001110111=>100000111011
000111001110=>111000110001=>001001110101=>100100111010
000111011010=>111000100101=>101001110001=>110100111000
000100111110=>111011000001=>000011110101=>100001111010
000100011010=>111011100101=>101111011001=>110111101100
000101101000=>111010010111=>101111000111=>110111100011
000101100010=>111010011101=>101111001101=>110111100110
000101111010=>111010000101=>100011110001=>110001111000
011000011000=>100111100111=>010101110111=>101010111011
011000011110=>100111100001=>000101011101=>100010101110
011001100110=>100110011001=>010101010101=>101010101010
011001111000=>100110000111=>000101010111=>100010101011
011001111110=>100110000001=>000001010101=>100000101010
011110000110=>100001111001=>010001011101=>101000101110
011110011000=>100001100111=>010001010111=>101000101011
011110011110=>100001100001=>000100010101=>100010001010
011111100000=>100000011111=>000001011111=>100000101111
011111100110=>100000011001=>010000010101=>101000001010
011111111110=>100000000001=>000000000101=>100000000010
011100111000=>100011000111=>001001010111=>100100101011
011101101000=>100010010111=>101001000111=>110100100011
011101100010=>100010011101=>101001001101=>110100100110
010010011000=>101101100111=>011101010111=>101110101011
010011100110=>101100011001=>010011010101=>101001101010
010011111000=>101100000111=>000011010111=>100001101011
010011011010=>101100100101=>101011010001=>110101101000
010000111110=>101111000001=>000011011101=>100001101110
010001101000=>101110010111=>101101100111=>110110110011
010001111010=>101110000101=>100011011001=>110001101100
010110111000=>101001000111=>001011000111=>100101100011
010110110010=>101001001101=>101011000101=>110101100010
010110001000=>101001110111=>101100110111=>110110011011
010111101000=>101000010111=>100011000111=>110001100011
010111100010=>101000011101=>100011001101=>110001100110
010101101010=>101010010101=>110111000001=>111011100000
0010101010=>1101010101=>1111100001=>1111110000
0010101100=>1101010011=>0111100011=>1011110001
0010100000=>1101011111=>1110011111=>1111001111
00000000000=>11111111111=>11111111111=>11111111111
0000101110=>1111010001=>0011111001=>1001111100
0010110010=>1101001101=>1011100101=>1101110010
0011001010=>1100110101=>1101101001=>1110110100
0011100010=>1100011101=>1001101101=>1100110110
0011110000=>1100001111=>0001101111=>1000110111
0100101010=>1011010101=>1111010001=>1111101000
001010101010=>110101010101=>111111000001=>111111100000
001010101100=>110101010011=>011111000011=>101111100001
001010111000=>110101000111=>001111000111=>100111100011
001011001010=>110100110101=>110111001001=>111011100100
001100101010=>110011010101=>111011010001=>111101101000
001110001010=>110001110101=>110011011001=>111001101100
010011101000=>101100010111=>100110100111=>110011010011
010111000100=>101000111011=>100110011011=>110011001101
010111001000=>101000110111=>100110010111=>110011001011
011011010000=>100100101111=>101010001111=>110101000111
0110101010=>1001010101=>1110100001=>1111010000
010101111000=>101010000111=>000111000111=>100011100011
010111001100=>101000110011=>010011001011=>101001100101
010111011000=>101000100111=>010011000111=>101001100011
011001011100=>100110100011=>001101010011=>100110101001
011001101100=>100110010011=>010101010011=>101010101001
011010111000=>100101000111=>001101000111=>100110100011
011011000110=>100100111001=>010101001101=>101010100110
011011011000=>100100100111=>010101000111=>101010100011
011011101000=>100100010111=>100101000111=>110010100011
010011011100=>101100100011=>001011010011=>100101101001
100011101100=>011100010011=>010010110011=>101001011001
010011101100=>101100010011=>010011010011=>101001101001
100101110100=>011010001011=>100110100011=>110011010001
100011111000=>011100000111=>000010110111=>100001011011
11111111101=>00000000010=>10000000000=>01000000000
0001101100=>1110010011=>0101110011=>1010111001
0001011100=>1110100011=>0011110011=>1001111001
0001101010=>1110010101=>1101110001=>1110111000
0000111010=>1111000101=>1001111001=>1100111100
0010100110=>1101011001=>0111100101=>1011110010
0010010110=>1101101001=>0111101001=>1011110100
0001010110=>1110101001=>0111110001=>1011111000
0000110110=>1111001001=>0101111001=>1010111100
001001011100=>110110100011=>001111010011=>100111101001
000101011100=>111010100011=>001111100011=>100111110001
000010111100=>111101000011=>000111110011=>100011111001
000111001010=>111000110101=>110011101001=>111001110100
000110101010=>111001010101=>111011100001=>111101110000
001001101010=>110110010101=>110111010001=>111011101000
000101101010=>111010010101=>110111100001=>111011110000
000011101010=>111100010101=>110011110001=>111001111000
000011011010=>111100100101=>101011110001=>110101111000
001010100110=>110101011001=>011111000101=>101111100010
001010010110=>110101101001=>011111001001=>101111100100
001001010110=>110110101001=>011111010001=>101111101000
000101010110=>111010101001=>011111100001=>101111110000
001010001110=>110101110001=>001111001101=>100111100110
001001001110=>110110110001=>001111010101=>100111101010
000101001110=>111010110001=>001111100101=>100111110010
001000101110=>110111010001=>001111011001=>100111101100
000100101110=>111011010001=>001111101001=>100111110100
000010101110=>111101010001=>001111110001=>100111111000
000010011110=>111101100001=>000111110101=>100011111010
000001011110=>111110100001=>000111111001=>100011111100
000000111110=>111111000001=>000011111101=>100001111110
10000000001=>01111111110=>10111111110=>01011111111
11100000001=>00011111110=>10001111110=>01000111111
11111000001=>00000111110=>10000011110=>01000001111
11111110001=>00000001110=>10000000110=>01000000011
100101101010=>011010010101=>110110100001=>111011010000
100100101011=>011011010100=>011110101000=>001111010100
010001011110=>101110100001=>000111011001=>100011101100
0010000000=>1101111111=>1101111111=>1110111111
110101010011=>001010101100=>011110000010=>001111000001
101101010011=>010010101100=>011101000010=>001110100001
110011010011=>001100101100=>011010010010=>001101001001
101011010011=>010100101100=>011011000010=>001101100001
100111010011=>011000101100=>011001010010=>001100101001
110100110011=>001011001100=>010110001010=>001011000101
101100110011=>010011001100=>010101001010=>001010100101
110010110011=>001101001100=>010110010010=>001011001001
101010110011=>010101001100=>010111000010=>001011100001
100110110011=>011001001100=>010101010010=>001010101001
101001110011=>010110001100=>010011001010=>001001100101
100101110011=>011010001100=>010011010010=>001001101001
110101001011=>001010110100=>011110000100=>001111000010
101101001011=>010010110100=>011101000100=>001110100010
110011001011=>001100110100=>011010010100=>001101001010
101011001011=>010100110100=>011011000100=>001101100010
100111001011=>011000110100=>011001010100=>001100101010
110100101011=>001011010100=>011110001000=>001111000100
101100101011=>010011010100=>011101001000=>001110100100
110010101011=>001101010100=>011110010000=>001111001000
101010101011=>010101010100=>011111000000=>001111100000
100110101011=>011001010100=>011101010000=>001110101000
110001101011=>001110010100=>011010011000=>001101001100
101001101011=>010110010100=>011011001000=>001101100100
100101101011=>011010010100=>011011010000=>001101101000
100011101011=>011100010100=>011001011000=>001100101100
110100011011=>001011100100=>010110001100=>001011000110
101100011011=>010011100100=>010101001100=>001010100110
110010011011=>001101100100=>010110010100=>001011001010
101010011011=>010101100100=>010111000100=>001011100010
100110011011=>011001100100=>010101010100=>001010101010
110001011011=>001110100100=>010110011000=>001011001100
101001011011=>010110100100=>010111001000=>001011100100
100101011011=>011010100100=>010111010000=>001011101000
100011011011=>011100100100=>010101011000=>001010101100
101000111011=>010111000100=>010011001100=>001001100110
100100111011=>011011000100=>010011010100=>001001101010
100010111011=>011101000100=>010011011000=>001001101100
110100100111=>001011011000=>001110001010=>000111000101
101100100111=>010011011000=>001101001010=>000110100101
110010100111=>001101011000=>001110010010=>000111001001
101010100111=>010101011000=>001111000010=>000111100001
100110100111=>011001011000=>001101010010=>000110101001
101001100111=>010110011000=>001011001010=>000101100101
100101100111=>011010011000=>001011010010=>000101101001
110100010111=>001011101000=>001110001100=>000111000110
101100010111=>010011101000=>001101001100=>000110100110
110010010111=>001101101000=>001110010100=>000111001010
101010010111=>010101101000=>001111000100=>000111100010
100110010111=>011001101000=>001101010100=>000110101010
110001010111=>001110101000=>001110011000=>000111001100
101001010111=>010110101000=>001111001000=>000111100100
100101010111=>011010101000=>001111010000=>000111101000
100011010111=>011100101000=>001101011000=>000110101100
101000110111=>010111001000=>001011001100=>000101100110
100100110111=>011011001000=>001011010100=>000101101010
100010110111=>011101001000=>001011011000=>000101101100
0000010111=>1111101000=>0011111100=>0001111110
010100111100=>101011000011=>000111001011=>100011100101
010010111100=>101101000011=>000111010011=>100011101001
0000100111=>1111011000=>0011111010=>0001111101
0110101101=>1001010010=>1011010000=>0101101000
0101010111=>1010101000=>0011110000=>0001111000
0001010101=>1110101010=>1111110000=>0111111000
0110011011=>1001100100=>0101010100=>0010101010
100110111000=>011001000111=>001010100111=>100101010011
101100100110=>010011011001=>011010010101=>101101001010
111000100110=>000111011001=>011000110101=>101100011010
101010001000=>010101110111=>111000110111=>111100011011
100010101000=>011101010111=>111011000111=>111101100011
100101001000=>011010110111=>111010010111=>111101001011
111011010110=>000100101001=>011010000001=>101101000000
111001011110=>000110100001=>000110001001=>100011000100
011011011110=>100100100001=>000101010001=>100010101000
111110010110=>000001101001=>011000001001=>101100000100
111001110110=>000110001001=>010010001001=>101001000100
110000011010=>001111100101=>101001111001=>110100111100
111000001010=>000111110101=>110001111001=>111000111100
00100000000=>11011111111=>11011111111=>11101111111
11000000000=>00111111111=>00111111111=>10011111111
11111111100=>00000000011=>00000000011=>10000000001
0001000111=>1110111000=>0011110110=>0001111011
0110011101=>1001100010=>1001010100=>0100101010
0111001101=>1000110010=>1010010100=>0101001010
0100111101=>1011000010=>1000110100=>0100011010
100010101100=>011101010011=>011101100011=>101110110001
100011001010=>011100110101=>110101101001=>111010110100
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
Map
Foata bijection
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.
For instance, to compute $\phi(4154223)$, the sequence of words is
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 $w_{i+1} < v_k$.
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.
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.
This is the word obtained by moving the last letter to the beginnig.
searching the database
Sorry, this map was not found in the database.