Largest Prime Factor

Given a positive integer n, your task is to find its largest prime factor. A prime factor of a number is a prime number that divides it exactly without leaving a remainder. If n ≤ 1, output None since the number does not have a prime factor.

The problem can be formally defined as: Given a positive integer \( n \), find \( p \) such that \( p \) is prime, \( p | n \), and for every other prime \( q \) with \( q | n \), \( p \ge q \).

inputFormat

The input consists of a single integer n provided via standard input (stdin). The integer is on one line.

outputFormat

Output the largest prime factor of n on a single line to standard output (stdout). If n ≤ 1, output the string None.

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