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 A {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        while(s.hasNext()){
            int a = s.nextInt();
            boolean ok = false;
            for(int i=0;i<=100;i++){
                if (i*(i+1) == 2 * a) {
                    ok = true;
                    break;
                }
            }
            if(ok)
            System.out.println("YES");
            else System.out.println("NO");
            
        }
    }

}
