Largest Prime Factor

Given a positive integer \(n\), your task is to determine its largest prime factor. A prime factor of \(n\) is a prime number that divides \(n\) without leaving a remainder. If \(n \leq 1\), then there is no prime factor and the output should be None.

For example, consider \(n = 13195\). The prime factors of 13195 are 5, 7, 13, and 29; hence, the largest prime factor is 29.

You are required to read the input from stdin and output the result to stdout.

inputFormat

The input consists of a single integer \(n\) provided on a single line through standard input.

outputFormat

Output a single line containing the largest prime factor of \(n\). If \(n \leq 1\), output None.

13195

29