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Perfect numbers

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Time limit 1000/1000/1000/1000 ms. Memory limit 65000/65000/65000/65000 Kb.

Problem description

A perfect number is a natural number and when you add up all of the factors less than that number, you get that number. The first two perfect numbers are 6 and 28. 1+2+3 = 6, and 1+2+4+7+14 = 28.

Make a program that finds out if the given number is perfect or not.

Input

There is a single integer N on the first line (0 < N < 10¹²).

Output

Write "Yes" if N is perfect and "No" otherwise.

Example

stdin	stdout
6	Yes
5	No

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