Perfect Number

MediumMathNumber-TheoryDivisors5 hidden tests

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

Decide whether n is perfect.

Input format

One line: a positive integer n.

Output format

Print YES if n is perfect, otherwise NO.

Constraints

1 <= n <= 100000000

Examples

Example 1

Input

Expected

YES

Explanation

Divisors of 28 excluding itself are 1,2,4,7,14 which sum to 28, so YES.

Example 2

Input

Expected

NO

Explanation

1+2+3+4+6 = 16, not 12, so NO.

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