Perfect Number Checker

A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself). In other words, for a number \(n\), if

[ n = \sum_{\substack{d|n \ d < n}} d ]

holds true, then \(n\) is considered perfect. For example, 6 is a perfect number because its divisors 1, 2, and 3 add up to 6.

Your task is to write a program that reads a single integer \(n\) from standard input and determines whether it is a perfect number. The program should output "True" if \(n\) is a perfect number, or "False" otherwise.

inputFormat

A single integer (n), provided via standard input.

outputFormat

Print "True" if the input integer is a perfect number. Otherwise, print "False".## sample

6

True