Description

There is a train at station A with an initial speed of $0$. Every second, you can choose to set the acceleration of the train to $1$ or $-1$. After leaving station A, the speed of the train cannot be $0$ until it reaches station B. The distance between station A and station B is $L$. Given the distance $L$, can the train stop exactly at station B if the acceleration is set properly?

The train stops exactly at station B which means that when the train arrives at station B, its speed should be exactly $0$.

$^\dagger$ The relationship between initial speed ($v_0$), acceleration ($a$), time ($t$) and distance ($s$) can be described by the equation: $s=v_0t+\frac{1}{2} at^2$.

Input

A single integer $L$ ($1\le L\le 10^9$), denoting the distance between station A and station B.

Output

Output YES if it is possible to stop at station B. Otherwise, output NO.

Samples

4

YES

7

YES

5

NO

Note

For the second example, the following $v-t$ graph shows a possible way.

Resources

电子科技大学第十五届 ACM 趣味程序设计竞赛