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Perfect Number ⭐⭐⭐

A perfect number is a positive integer that equals the sum of all its proper divisors (divisors smaller than the number itself).

For example, 6 is perfect because its divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.

Read a positive integer n and print Yes if it is a perfect number, or No otherwise.

Input

One positive integer:

  1. n

Output

Print Yes or No.

Examples

Input:

6

Output:

Yes

Input:

28

Output:

Yes

Input:

4

Output:

No