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.io.*;
import java.util.*;
 
public class Triangle
{
	public static void main(String[] args) throws IOException 
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
 
	      int n = Integer.parseInt(st.nextToken());
	      int count = 1;
	      boolean IsTriangularNum = false;
	      for(int i=1; i<=n; i+=count)
	      {
	            if(i == n)
	                  IsTriangularNum = true;
	            count++;
	      }
	      System.out.println(IsTriangularNum == true? "YES" : "NO");
	}
}