Perfect Number Checker

A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself). For example, the number 6 is perfect since \(6 = 1 + 2 + 3\).

Your task is to determine whether a given positive integer \(n\) is a perfect number. If it is, print True; otherwise, print False. The underlying condition can be mathematically expressed as:

\( n = \sum_{d|n, \; d<n} d \)

inputFormat

The input consists of a single line containing one positive integer \(n\).

outputFormat

Output a single line: True if \(n\) is a perfect number, or False otherwise.

6

True