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 Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		PrintStream out = System.out;
		
		HashSet<Integer> t = new HashSet<Integer>();
		
		for (int i = 0; i < 501; i++) {
			t.add(i*(i+1) / 2);
		}
		
		int n = in.nextInt();
		if(t.contains(n)){
			out.print("YES");
		}else{
			out.print("NO");
		}
		
		
		in.close();
		out.flush();
	}

}
