human
I found an interesting problem on https://leetcode.com/problems/prime-arrangements/:
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

I tried it in Python, but could not do it. Can you solve it?
assistant
#Here is the Python program you requested.

class Solution:
    def numPrimeArrangements(self, n: int) -> int:
        primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,
                 61,67,71,73,79,83,89,97]
        r = sum(1 for p in primes if p <= n)
        a = 10**9 + 7
        ans = 1
        for i in range(1, min(r, n-r)+1):
            ans *= (i % a)**2
            ans %= a
        for i in range(min(r, n-r)+1, max(r, n-r)+1):
            ans *= i
            ans %= a
        return ans