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;


public class A {

	/**
	 * @param args
	 * @throws IOException 
	 * @throws NumberFormatException 
	 */
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(in.readLine());
		int num;
		for (int i = 1;; i++) {
			num = (i*(i+1))/2;
			if(num == n) {
				System.out.println("YES");
				break;
			} else if(num > n) {
				System.out.println("NO");
				break;
			}
		}
	}

}
