Perfect Number Checker

Determine whether a given positive integer n is a perfect number. A number is called perfect if it is equal to the sum of its proper divisors (divisors excluding itself). In mathematical terms, a number \(n\) is perfect if it satisfies the equation:

\[ n = \sum_{d \mid n,\ d < n} d \]

For example, 6 is perfect because \(6 = 1 + 2 + 3\), and 28 is perfect because \(28 = 1 + 2 + 4 + 7 + 14\). Conversely, numbers like 10 or 1 are not perfect.

inputFormat

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

Note: You can assume that 1 \le n \le 10^8.

outputFormat

Output a single line with True if n is a perfect number, otherwise output False.

## sample

6

True

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