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.Scanner;
import java.math.BigInteger;

public class Main {
	
	public static BigInteger suma(BigInteger n){
		BigInteger uno = new BigInteger("1");
		BigInteger dos = new BigInteger("2");
		return n.multiply(n.add(uno)).divide(dos);
	}
	
	public static void main (String args[]) {
		Scanner sc = new Scanner(System.in);
		BigInteger n = sc.nextBigInteger();
		BigInteger cero = new BigInteger("0");
		BigInteger dos = new BigInteger("2");
		BigInteger uno = new BigInteger("1");
		BigInteger l = new BigInteger("0");
		BigInteger r = l;
		BigInteger m = l;
			l = new BigInteger("0");
			r = n;
			while(l.compareTo(r) < 0){
				m = l.add(r).divide(dos);
				if(suma(m).compareTo(n) < 0){
					l = m.add(uno);
				}else{
					r = m;
				}
			}
			if(suma(l).compareTo(n) == 0){
				System.out.println("YES");
			}else{
				System.out.println("NO");
			}
			
		
	}
}