<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:
    def numPrimeArrangements(self, n: int) -> int:
        
        if n <= 2:
            return 1

        def is_prime(n):
            for i in range(2, int(sqrt(n))+1):
                if n % i == 0:
                    return 0 # not prime
            return 1

        def comb(n):
            out = 1
            for i in range(1, 1+n):
                out = out * i
            return out
        
        prime = 0
        for i in range(2, n+1):
            prime += is_prime(i)

        
        non_prime = n - prime
        # print(prime, non_prime)
        # A(p, p) * A(np, np)
        return comb(prime)*comb(non_prime) % (10**9+7)

28