I'm working on the following problem:
HALFCYCLE (HALFC):
Input:
A directed graph $G = (V,E)$.
Output:
Whether the longest cycle in $G$ has length $ \lfloor |V|/2 \rfloor$.
Prove that if $\mathsf{PH} \ne \mathsf{coNP}$ then HALFCYCLE is not NP-complete.
I have no idea how to solve this implication.