<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:

        cnt = 0
        flag = 0
        tmp = 0
        for j in range(2, n + 1):   
            flag = False
            tmp = 0
            for i in range(2, int(n ** 0.5) + 1):
                if j % i == 0 and i != j:
                    tmp += 1
                if tmp >= 1:
                    flag = True
                    break
            if not flag:
                cnt += 1
        
        print()

        return (math.factorial(cnt) * math.factorial(n - cnt)) % (10 ** 9 + 7) 
16300