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.*;
import java.math.*;

public class Main {
	public static StreamTokenizer in = new StreamTokenizer(System.in);
	public static boolean bg = true;

	public static void main(String[] args) throws Exception {
		HashSet<Integer> s1 = new HashSet();
		for (int i=1;i<=100;i++){
			s1.add(i*(i+1)/2);
		}
		int n1 = ni();
		if (s1.contains(n1)) pn("YES");
		else pn("NO");
	}

	private static int ni() throws Exception {
		in.nextToken();
		return (int) in.nval;
	}

	private static long nl() throws Exception {
		in.nextToken();
		return (long) in.nval;
	}

	private static double nd() throws Exception {
		in.nextToken();
		return in.nval;
	}

	private static void pn(Object o1) {
		System.out.println(o1);
	}
}
