Next Prime Finder

You are given an integer n. Your task is to find the smallest prime number p such that p > n. A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself.

In mathematical terms, you need to find the smallest p satisfying:

[ p \text{ is prime} \quad \text{and} \quad p > n ]

Note that you may need to implement a helper function to check for primality efficiently.

inputFormat

The input consists of a single integer n provided via standard input (stdin).

outputFormat

Output the smallest prime number strictly greater than n to standard output (stdout).

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