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.