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.math.*;
import java.util.*;

public class Olymp {
	public static void main(String[] args) 
	{
		Scanner in = new Scanner(System.in);

		int n;
		n=in.nextInt();
		boolean tr=false;
		
		int sum=0;
		
		for(int i=0;sum<n+1;i++)
		{
			sum+=i;
			if(sum==n)
			{
				tr=true;
				break;
			}
		}
			
		
		if(tr)
		{
			System.out.print("YES");
		}
		else
		{
			System.out.print("NO");
		}
	}
}
