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 TriangularNumber {

	public static void main(String[] args){
		Scanner input = new Scanner(System.in);
		int n = input.nextInt()*2;
        int   temp = (int)Math.ceil((-1+Math.sqrt(1+4*n))/2);		
	  if((temp*(temp+1))==n)System.out.println("YES");
	  else
		  System.out.println("NO");
	}

}
