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;

public class Test {
	
	public static void main(String[] args){
			
		Scanner sc = new Scanner(System.in);
		long m = sc.nextInt();
		long n = 0 ;
	    long somme = 0 ;	
			while(somme <= m ){
				if(somme == m ){ break ;}
				else {somme =  n*(n+1)/2 ;
			    n ++ ;}
			    
			}
			if (somme == m ) { System.out.println("YES"); }
			else { System.out.println("NO"); }
		}
			
}