public class Solution
extends Object
1175 - Prime Arrangements\.
Easy
Return the number of permutations of 1 to `n` so that prime numbers are at prime indices (1-indexed.)
_(Recall that an integer is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers both smaller than it.)_
Since the answer may be large, return the answer **modulo `10^9 + 7` **.
**Example 1:**
**Input:** n = 5
**Output:** 12
**Explanation:** For example [1,2,5,4,3] is a valid permutation, but [5,2,3,4,1] is not because the prime number 5 is at index 1.
**Example 2:**
**Input:** n = 100
**Output:** 682289015
**Constraints:**
* `1 <= n <= 100`