Smallest Prime Divisor

Given an integer \(n\), find its smallest prime divisor. If \(n\) is composite, the answer is the smallest prime number that divides \(n\). If \(n\) is a prime number, then its smallest prime divisor is \(n\) itself. For \(n \le 1\), output None.

For example, for \(n = 15\) the smallest prime divisor is \(3\) since \(3\) divides \(15\) and is prime. Similarly, for \(n = 7\), the answer is \(7\).

inputFormat

The input begins with an integer \(T\) denoting the number of test cases. Each of the following \(T\) lines contains a single integer \(n\).

outputFormat

For each test case, output a single line containing the smallest prime divisor of \(n\). If \(n \le 1\), output None.

3
15
2
77

3
2
7