The 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 ≤ 103).

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

Source: codeforces | Difficulty: EASY
Tags: Mathematics


Solutions: