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 Main {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		
		HashSet<Integer> T = new HashSet<Integer>();
		int t;
		for (int i = 0; (t = i * (i + 1) / 2) <= 500; ++i)
			T.add(t);
		
		int N = Integer.parseInt(in.readLine());
		System.out.println(T.contains(N) ? "YES" : "NO");
		
		in.close();
		System.exit(0);
	}
}
