The following 7-strings resulted from transmitting codewords of the binary [7, 4]-Hamming code across a noisy channel: 1000000, 0101011, 1001111, 1100100, 1101010, 1100110, 0011111, 0111000, 1110110, and 1010100. Use the labeled Fano plane below to decode each string, expressing your work in accordance with the following paradigm: string -> subset of {1, 2, . . . , 7} -> adjusted subset -> desired codeword.