Prime Number Checker

You are given a single input from stdin that represents a value. Your task is to determine whether the given value (if it is an integer) is a prime number.

For the purposes of this problem, a prime number is defined as an integer \( n \) such that \( n \ge 2 \) and the only divisors of \( n \) are 1 and \( n \) itself. If the input is not a valid integer, you should output None (without quotes). Note that numbers less than 2 are not considered prime.

Examples:

• Input: 2 → Output: True
• Input: 4 → Output: False
• Input: abc → Output: None

inputFormat

The input consists of a single line read from stdin. The line contains either an integer (possibly with a leading + or - sign) or a non-integer string.

outputFormat

Print one of the following outputs to stdout:

• True if the input represents a prime number.
• False if the input is an integer but not a prime number (including when it is less than 2).
• None if the input does not represent a valid integer.
## sample

2

True