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.*;
public class A47 {
	
	public static void main(String args[]){
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		
		int sum=0;
		int i=0;
		while(n>sum){
			i++;
			sum =i*(i+1)/2;
		}
		if(n==sum) System.out.println("YES");
		else System.out.println("NO");
		
	}

}
