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 Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int x = scanner.nextInt();
        int [] ans = {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66,
                78, 91, 105, 120,136, 153, 171, 190, 210, 231, 253, 276,
                300, 325, 351, 378, 406, 435, 465, 496};
         boolean t = false;
        for(int i  = 0; i < ans.length; i++){
            if(ans[i]==x){
                System.out.println("YES");
                t=true;
            }
        }
        if(t==false){
            System.out.println("NO");
        }

    }
}
