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 Triangularnums {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int num = s.nextInt();
		int sum = 0;
		boolean answered = false;
		for (int n = 1; sum <= num; n++) { 
            sum = sum + n; 
            if (sum == num) {
                System.out.println("YES");
            	answered = true;
            }
        } 
		if(answered == false) {
			System.out.println("NO");
		}
		
	}
}
