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.io.BufferedReader;
import java.io.InputStreamReader;


/**
 *
 * @author Hanif yang sangat mencintai indris
 */
public class Indris 
{
    public static void main(String args[])throws Exception
    {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        
        int input = Integer.parseInt(reader.readLine());
        input *= 2;
        boolean ok = false;
        for(int i = 1; i <= input; i++){
            int perhitungan = i*i + i;
            if(input == (perhitungan)){
                ok = true;
                break;
            }
        }
        
        if(ok){
            System.out.println("YES");
        }else{
            System.out.println("NO");
        }
            
  
        reader.close();
    }
    
  
    
   
}

