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
import java.util.Scanner;
public class Ishu
{
    	public static void main(String[] args)
    	{
	 Scanner scan=new Scanner(System.in); 
	 int n,T,i=1;
	 boolean flag=false;
	 n=scan.nextInt();
	 while(true)
		{
		 T=(i*i+i)/2;
		 if(T==n)	
			{
			 flag=true;
			 break;
			}
		 else if(T>n)
			break;
		 ++i;
		}
	 if(flag)
		System.out.println("YES");
	 else
		System.out.println("NO");
	}
}