Arbitrary-peak conjecture for rank-generating functions

Let $F_{\lambda}(q)$ be the rank-generating function for partitions contained inside a partition $\lambda$. A polynomial is unimodal if its coefficients weakly increase and then weakly decrease; a peak is a local maximum in its coefficient sequence. Arbitrary-peak conjecture. For every integer $N\ge 2$, there exists a partition $\lambda$ such that $F_{\lambda}(q)$ is nonunimodal with (exactly?) $N$ peaks. The parenthetical qualification is part of the source statement, so it is unclear whether the intended assertion is exactly $N$ peaks or merely $N$ peaks; no resolution is supplied.