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.math.BigInteger;
import java.util.*;
public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int a=scan.nextInt();
        int i=0;
        while (true){
            a=a-i;
            i++;
            if(a==0){
                break;
            }
            else if(a<0){
                break;
            }
        }
        if(a==0){
            System.out.println("YES");
        }
        else {
            System.out.println("NO");
        }
    }
}