Prove that regular languages and context-free languages aren't closed under $Perm(L)$
Hints:


For regular languages, consider $Perm((01)^*) \cap 0^* 1^*$.
For context-free languages, consider $Perm(0^n 1^n 2^m 3^m) \cap 0^* 2^* 1^* 3^*$.