A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangular number. The n-th triangular number is the number of dots in a triangle with n dots on a side. <image>. You can learn more about these numbers from Wikipedia (http://en.wikipedia.org/wiki/Triangular_number).

Your task is to find out if a given integer is a triangular number.

Input

The first line contains the single number n (1 ≤ n ≤ 500) — the given integer.

Output

If the given integer is a triangular number output YES, otherwise output NO.

Examples

Input

1


Output

YES


Input

2


Output

NO


Input

3


Output

YES
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;
public class S {
	public static void main (String[] args) {
		Scanner in=new Scanner(System.in);
		int x=in.nextInt();
		int z=(x*2*4)+1;
		if(Math.ceil(Math.sqrt((double)z))==Math.floor(Math.sqrt((double)z)))
		{
		    System.out.print("YES");
		}
		else
		{
		    System.out.print("NO");
		}
	}
}