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.*;
import java.io.*;

public class Triangle
{
	public static void main(String[] args) throws IOException
	{
		BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
		int a = Integer.parseInt(r.readLine());
		Set<Integer> b = new HashSet<Integer>();
		for(int i = 1; i<=32; i++)
		{
			b.add(i*(i+1)/2);
		}

		if(b.contains(a)) System.out.println("YES");
		else System.out.println("NO");
	}
}

