<p>Return the number of permutations of 1 to <code>n</code> so that prime numbers are at prime indices (1-indexed.)</p>

<p><em>(Recall that an integer&nbsp;is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers&nbsp;both smaller than it.)</em></p>

<p>Since the answer may be large, return the answer <strong>modulo <code>10^9 + 7</code></strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 5
<strong>Output:</strong> 12
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 100
<strong>Output:</strong> 682289015
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
</ul>

class Solution {
public:
    int numPrimeArrangements(int n) {
        const int MOD = 1e9 + 7;
        vector<bool> is_prime(n + 1, true);
        is_prime[0] = is_prime[1] = false;
        for (int i = 2; i * i <= n; ++i) {
            if (is_prime[i]) {
                for (int j = i * i; j <= n; j += i) {
                    is_prime[j] = false;
                }
            }
        }
        int prime_count = count(is_prime.begin(), is_prime.end(), true);
        long long result = 1;
        for (int i = 1; i <= prime_count; ++i) {
            result = result * i % MOD;
        }
        for (int i = 1; i <= n - prime_count; ++i) {
            result = result * i % MOD;
        }
        return result;
    }
};
7700