Next Prime Number

Given an integer \(N\), your task is to compute the smallest prime number greater than \(N\). A prime number \(p\) is a number that has no divisors other than 1 and itself. Formally, you need to find the smallest integer \(p\) such that \(p > N\) and \(p\) is prime.

The definition of a prime number can be stated as follows:

( p \text{ is prime if } \forall d \in \mathbb{Z},\ 1<d<p \Rightarrow d \nmid p ).

inputFormat

The input consists of a single line containing one integer \(N\) (\(0 \leq N \leq 10^7\)).

outputFormat

Output the smallest prime number strictly greater than \(N\) on a single line.

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