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.*;
import java.io.*;
public class Problem{
	public static void main(String [] args)throws IOException{
		BufferedReader b = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		 int N = Integer.parseInt(b.readLine());
		 ArrayList<Integer> t = new ArrayList<Integer>();
		 for(int i = 1; i <= 35; i++){
			 t.add((i) * (i + 1) / 2);
		 }
		 String ans = t.contains(N) ? "YES" : "NO";
		 out.println(ans);
		 out.close();
	}
}
