// numbers 0, 7, 2*7, 3*7, ..., 257*7 in binary
0000000000000000
0000000000000111
0000000000001110
0000000000010101
0000000000011100
0000000000100011
0000000000101010
0000000000110001
0000000000111000
0000000000111111
0000000001000110
0000000001001101
0000000001010100
0000000001011011
0000000001100010
0000000001101001
0000000001110000
0000000001110111
0000000001111110
0000000010000101
0000000010001100
0000000010010011
0000000010011010
0000000010100001
0000000010101000
0000000010101111
0000000010110110
0000000010111101
0000000011000100
0000000011001011
0000000011010010
0000000011011001
0000000011100000
0000000011100111
0000000011101110
0000000011110101
0000000011111100
0000000100000011
0000000100001010
0000000100010001
0000000100011000
0000000100011111
0000000100100110
0000000100101101
0000000100110100
0000000100111011
0000000101000010
0000000101001001
0000000101010000
0000000101010111
0000000101011110
0000000101100101
0000000101101100
0000000101110011
0000000101111010
0000000110000001
0000000110001000
0000000110001111
0000000110010110
0000000110011101
0000000110100100
0000000110101011
0000000110110010
0000000110111001
0000000111000000
0000000111000111
0000000111001110
0000000111010101
0000000111011100
0000000111100011
0000000111101010
0000000111110001
0000000111111000
0000000111111111
0000001000000110
0000001000001101
0000001000010100
0000001000011011
0000001000100010
0000001000101001
0000001000110000
0000001000110111
0000001000111110
0000001001000101
0000001001001100
0000001001010011
0000001001011010
0000001001100001
0000001001101000
0000001001101111
0000001001110110
0000001001111101
0000001010000100
0000001010001011
0000001010010010
0000001010011001
0000001010100000
0000001010100111
0000001010101110
0000001010110101
0000001010111100
0000001011000011
0000001011001010
0000001011010001
0000001011011000
0000001011011111
0000001011100110
0000001011101101
0000001011110100
0000001011111011
0000001100000010
0000001100001001
0000001100010000
0000001100010111
0000001100011110
0000001100100101
0000001100101100
0000001100110011
0000001100111010
0000001101000001
0000001101001000
0000001101001111
0000001101010110
0000001101011101
0000001101100100
0000001101101011
0000001101110010
0000001101111001
0000001110000000
0000001110000111
0000001110001110
0000001110010101
0000001110011100
0000001110100011
0000001110101010
0000001110110001
0000001110111000
0000001110111111
0000001111000110
0000001111001101
0000001111010100
0000001111011011
0000001111100010
0000001111101001
0000001111110000
0000001111110111
0000001111111110
0000010000000101
0000010000001100
0000010000010011
0000010000011010
0000010000100001
0000010000101000
0000010000101111
0000010000110110
0000010000111101
0000010001000100
0000010001001011
0000010001010010
0000010001011001
0000010001100000
0000010001100111
0000010001101110
0000010001110101
0000010001111100
0000010010000011
0000010010001010
0000010010010001
0000010010011000
0000010010011111
0000010010100110
0000010010101101
0000010010110100
0000010010111011
0000010011000010
0000010011001001
0000010011010000
0000010011010111
0000010011011110
0000010011100101
0000010011101100
0000010011110011
0000010011111010
0000010100000001
0000010100001000
0000010100001111
0000010100010110
0000010100011101
0000010100100100
0000010100101011
0000010100110010
0000010100111001
0000010101000000
0000010101000111
0000010101001110
0000010101010101
0000010101011100
0000010101100011
0000010101101010
0000010101110001
0000010101111000
0000010101111111
0000010110000110
0000010110001101
0000010110010100
0000010110011011
0000010110100010
0000010110101001
0000010110110000
0000010110110111
0000010110111110
0000010111000101
0000010111001100
0000010111010011
0000010111011010
0000010111100001
0000010111101000
0000010111101111
0000010111110110
0000010111111101
0000011000000100
0000011000001011
0000011000010010
0000011000011001
0000011000100000
0000011000100111
0000011000101110
0000011000110101
0000011000111100
0000011001000011
0000011001001010
0000011001010001
0000011001011000
0000011001011111
0000011001100110
0000011001101101
0000011001110100
0000011001111011
0000011010000010
0000011010001001
0000011010010000
0000011010010111
0000011010011110
0000011010100101
0000011010101100
0000011010110011
0000011010111010
0000011011000001
0000011011001000
0000011011001111
0000011011010110
0000011011011101
0000011011100100
0000011011101011
0000011011110010
0000011011111001
0000011100000000
0000011100000111