Closest Primes

Given an integer \(n\), your task is to find the two closest prime numbers: one that is less than or equal to \(n\) and one that is greater than or equal to \(n\). If there is no prime number less than or equal to \(n\), output "None" for that side.

The solution requires you to determine if a number is prime, and then from \(n\) search downward for the closest lower prime and upward for the closest higher prime.

inputFormat

The input contains a single integer \(n\) provided in the standard input.

outputFormat

Output exactly two lines. The first line contains the closest prime number less than or equal to \(n\) (or "None" if such a prime does not exist). The second line contains the closest prime number greater than or equal to \(n\).

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