Factorial Divisibility

Given a positive integer n, find the smallest positive integer m such that m! is divisible by n. In other words, determine the minimum m satisfying $$ n \mid m! $$, where $$m! = 1 \times 2 \times \cdots \times m.$$

For example, if n = 6, we have 3! = 6 which is divisible by 6, so the answer is 3. Your solution should read the input from standard input (stdin) and output the result to standard output (stdout).

inputFormat

The input consists of a single line containing one positive integer n (n ≥ 1).

outputFormat

Output a single integer: the smallest m such that m! is divisible by n.

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2