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 HelloWorld
{

	static boolean ans = true;

	public static void main(String[] args) throws Exception {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(System.out);
		int n = Integer.parseInt(br.readLine());
		for(int i = 1; i <= 500; i++) {
			int val = i*(i+1);
			val /= 2;
			if(val == n) {
				writer.println("YES");
				writer.close();
				return;
			}
		}
		writer.println("NO");
    br.close();
    writer.close();
	}
}
