44. Perfect Donation Amount

Difficulty: easy · Math, Number Theory

Problem

A charity considers a donation amount **perfect** if it equals the sum of its proper divisors (all positive divisors other than the number itself). For example `28 = 1 + 2 + 4 + 7 + 14`. Given a donation amount `n`, print `true` if it is perfect and `false` otherwise.

Input

A single line containing the integer `n`.

Output

Print `true` or `false`.

Example 1

Input:
28
Output:
true

Explanation: The proper divisors 1, 2, 4, 7 and 14 add up to 28.

Example 2

Input:
12
Output:
false

Explanation: 1 + 2 + 3 + 4 + 6 = 16, which is not 12.

Constraints

- 1 <= n <= 10^12

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