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.*;
public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader scn = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int t = Integer.parseInt(scn.readLine());
        int i = 1;
        while (i <= t){
            if((i*(i+1))/2==t){
                out.write("YES");
                out.flush();
                return;
            }
            i++;
        }
        out.write("NO");
        out.flush();
    }
}

						 	 				 		 	 	 	 	 	 	  	