What is the residue modulo 13 of the sum of the modulo 13 inverses of the first 12 positive integers? Express your answer as an integer from 0 to 12, inclusive.

Modulo 13 inverses of the first 12 positive integers are: 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12 =78 - Their total sum. 78 mod 13 =0 - Remainder.