An integral over $SU(N)$.

Question

A physics textbook I am reading uses the following inequality: $$ \int_{SU(N)} d \gamma \overline{\chi_r(\gamma)} \left( \chi_f(\gamma) \right)^m \left( \overline{\chi_f(\gamma)} \right)^n \geq 0$$ where $\chi_r$ is the character for some irreducible representation, $\chi_f$ is the character of the $N$ dimensional/fundamental representation of $SU(N)$, and $m$ and $n$ are non-negative integers, and $d \gamma$ is the Haar-measure. How can I establish this inequality?