<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 {
    bool isPrime(int n) {
        if (n == 1) {
            return false;
        }
        for (int d = 2; d <= sqrt(n); d++) {
            if (n % d == 0) {
                return false;
            }
        }
        return true;
    }
    unsigned long long factorial (unsigned long long n) {
        cout << n << endl;
        unsigned long long f = 1;
        for (int i = 1; i <= n; i++) {
            f *= i;
            f %= (unsigned long long) (1e9 + 7);
        }
        return f;
    }
public:
    int numPrimeArrangements(int n) {
        int numP = 0;
        for (int i = 1; i <= n; i++) {
            if (isPrime(i)) {
                numP++;
            }
        }
        return factorial(numP) * factorial(n - numP) % (unsigned long long) (1e9 + 7);
    }
};
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