Prime Arrangements
<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>
Math
func numPrimeArrangements(n int) int {
	count := func(n int) int {
		cnt := 0
		primes := make([]bool, n+1)
		for i := range primes {
			primes[i] = true
		}
		for i := 2; i <= n; i++ {
			if primes[i] {
				cnt++
				for j := i + i; j <= n; j += i {
					primes[j] = false
				}
			}
		}
		return cnt
	}

	mod := int(1e9) + 7
	f := func(n int) int {
		ans := 1
		for i := 2; i <= n; i++ {
			ans = (ans * i) % mod
		}
		return ans
	}

	cnt := count(n)
	ans := f(cnt) * f(n-cnt)
	return ans % mod
}