Singular values of product of matrices with permutation matrix

Question

Let $A, B \in \mathbb{R}^{n \times n}$ and let $P \in \mathcal{P}_n$ where $\mathcal{P}_n$ is the set of all permutation matrices of size $n \times n$. Let us define $C = AB$ and $D = APB$.

What can be said about the singular values of $D$ with respect to the singular values of $C$ ?

Thank you,