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.PrintWriter;
import java.util.Scanner;


public class A {
	static int max = 510;
	static long[] all = new long[max];
	static {
		for(int i=1; i<max; i++)
			all[i] = all[i-1] + i;
	}
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		boolean found = false;
		for(int i=0; i < all.length; i++)
			if (all[i] == n) {
				found = true;
				break;
			}
			
		out.println(found ? "YES" : "NO");
		out.close();
	}
}
