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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;


/**
 *
 * @author xergioalex
 */
public class Main {

    
    public static void main(String[] args) throws IOException {
        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));        
        StringTokenizer token;
        String in= input.readLine();        
        while(in != null){             
            int n = Integer.valueOf(in);
            double root = n;
            root = Math.sqrt(8*n+1);
            n = (int) root;
            if(root == n){                
                System.out.println("YES");
            }
            else{
                System.out.println("NO");
            }
            in= input.readLine();
        }
    
    }
}