Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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Unknown Language Round #2:

- Io-2008-01-07 (Win32)

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C. Extraordinarily Nice Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe positive integer *a* is a divisor of the positive integer *b* if and only if there exists a positive integer *c* such that *a* × *c* = *b*.

King Astyages thinks a positive integer *x* is extraordinarily nice if the number of its even divisors is equal to the number of its odd divisors.

For example 3 has two positive divisors 3 and 1, both of which are odd, so 3 is not extraordinarily nice. On the other hand 2 is only divisible by 2 and 1, so it has one odd and one even divisor. Therefore 2 is extraordinarily nice.

Given a positive integer *x* determine whether it's extraordinarily nice.

Input

The input contains only a single integer *x* (1 ≤ *x* ≤ 10^{3}).

Output

Write a single yes or no. Write yes if the number is extraordinarily nice and no otherwise.

You don't need to care about capital or small letters. The output is case-insensitive.

Examples

Input

2

Output

yes

Input

3

Output

no

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