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.*;

public class Main {
    public static ArrayList<Integer> tri = new ArrayList<Integer>();
    
    public static void init() {
        for(int i = 0; i <= 31; i++) {
            tri.add(i*(i+1)/2);
        }
    }
    
    public static void main (String[] args) {
        init();
        Scanner sc = new Scanner(System.in);
        while(sc.hasNext()) {
            int n = sc.nextInt();
            System.out.println((tri.contains(n)) ? "YES" : "NO"); 
        }
    }
}