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 TaskF {
    public static void main (String [] args) {
        Scanner sc = new Scanner (System.in);
        int a = sc.nextInt();
        int count = 2; int circle = 1; boolean f = false;
        for (int i = 0; i<500;i++){
            if (a == circle) {f = true; break;}
            if (i>a){break;}
            circle = circle+count;
            count++;
        }
        if (f) {System.out.println ("YES");}
        else {System.out.println ("NO");}
    }
}