It’s possible to do a binary search on any ordered list: be it a list of increasing heights, integer numbers, floating-point numbers, etc. It can even be the set of integers , the set of natural numbers , or the set of rational numbers . We would still pick a range of possible solutions and throw away the unnecessary part on each iteration.

Challenge

Given a positive integer n, you are asked to check if it’s a full square without using the sqrt function.

Input

The input contains a single integer n (2 ≤ n ≤ ).

Output

The program should print Yes if n is a full square and No otherwise.

Examples

Input

Output

9

Yes

8

No

16

Yes

26

No

Hint

If n is a full square ⇒ there is another number x that . Therefore, you can try to find x on an interval [1, 2, …, n].