Correlated Bernoulli III

Suppose $X \sim \text{Bernoulli}(p)$ and $Y \sim \text{Bernoulli}(q)$, where $p + q \leq 1$ and $q \leq p$. Report the sum of all values $q$ such that $\corr{X}{Y} = -1$ is possible when $p = 1/3$. If no such values of $q$ exist, report $0$.