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 JavaApplication10 {
 
    public static void main(String[] args) {
        Scanner input = new Scanner (System.in);
        int x = input.nextInt();
        boolean a = false;
        for (int i=x;i>0;i--) {
        if (x==(i*(i+1)/2)) { a=true; break;}
        }
        if (a) System.out.println("YES");
        else System.out.print("NO");
        }
        
}    
    

