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const MOD: i64 = 1_000_000_007;
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const PRIME: [i32; 25] = [
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  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,
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];
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impl Solution {
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  pub fn num_prime_arrangements(n: i32) -> i32 {
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    let factorial_mod = |n: i32| -> i64 { (2..=n as i64).fold(1, |acc, x| (acc * x) % MOD) };
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    let num_primes = PRIME.iter().take_while(|&&x| x <= n).count() as i32;
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    ((factorial_mod(num_primes) * factorial_mod(n - num_primes)) % MOD) as i32
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  }
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}