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 in = new Scanner(System.in);
        
        boolean a = false;
        int []ar = new int [33];
        
        for (int i = 0; i <= 32; i++) {
            ar[i]= (i*(i+1))/2 ;           
        }
       
        int n = in.nextInt();
        
        for (int i = 0; i < 33; i++) {
            if(n==ar[i])
                a=true;
        }
        
        if(a)
            System.out.println("YES");
        else
            System.out.println("NO");
        
    }
    
}
