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 TriangularNumbers {
    public static void main(String[] args) {
        int n = new Scanner(System.in).nextInt();
        double k = n;
        k *= 2;
        k += 0.25;
        double t =Math.sqrt(k)-0.5;
        int i = (int) t;
        if (t == i){
            System.out.println("YES");
        }else{
            System.out.println("NO");
        }
    }
}
