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
]
MOD = 10**9 + 7

def calc_num_primes(n: int) -> int:
    return len([p for p in PRIMES if p <= n])
def factorial(n):
    ans = 1
    for i in range(1, n + 1):
        ans *= i
        ans %= MOD
    return ans

class Solution:
    def numPrimeArrangements(self, n: int) -> int:
        return (
            lambda n, num_primes, factorial: factorial(num_primes) * factorial(n - num_primes) % MOD
        )(
            n,
            calc_num_primes(n),
            factorial
        )