Bisect the Corruption

A pipeline of n stages transforms a value; exactly one stage is broken (it flips sign). You receive the stage functions pre-implemented in your editor and must implement size_t find_bad_stage(const int *injections, size_t n) — injections holds each stage's output for the known input; find the first index where the value's sign differs from injections[0]'s sign (all stages before the bad one preserve it, all after inherit the flip).