Perfect Number Checker

Given a positive integer n, determine whether it is a perfect number. A number is considered perfect if it is equal to the sum of its proper divisors (i.e., all divisors excluding the number itself). Mathematically, n is perfect if

$$ n = \sum_{d|n, d<n} d $$

Your task is to check whether the given number satisfies this property.

inputFormat

The input consists of a single integer n (1 ≤ n ≤ 10^5). It is read from standard input.

outputFormat

Output a single line containing "YES" if n is a perfect number; otherwise, output "NO". The output is written to standard output.## sample

6

YES