Algorithms and Data Structures

Perfect number

A number is considered perfect if it’s the sum of all its divisors except itself. For instance, the divisors of 6 are 1, 2, and 3, we exclude 6. 1 + 2 + 3 = 6 ⇒ 6 is a perfect number.

Input

The input contains a single integer n (1 ≤ n ≤ ).

Output

The program should print Yes if the given number is perfect and No otherwise.

Examples

Input
Output
6
Yes
8
No

Explanation

  1. 6 → 1 + 2 + 3 = 6 ⇒ 6 is perfect
  1. 8 → 1 + 2 + 4 = 7 ⇒ 8 is not perfect
 

Constraints

Time limit: 0.2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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