Given an integer n, return the number of permutations of numbers from $1$ to n such that prime numbers are placed at prime indices ($1$ indexed).

Since the answer may be large, return it modulo $10^9 + 7$.

Note: A positive integer is prime if it is strictly greater than $1$ and cannot be formed by multiplying two smaller positive integers. Indices are $1$ indexed.

Constraints:

• $1 \leq$ n $\leq 100$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.