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.Scanner;

public class TriangularNumbers {
	static final int[] a = new int[] { 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78,
			91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325,
			351, 378, 406, 435, 465, 496 };

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		boolean f = false;
		for(int i : a)
			if(i == n)
				f = true;
		System.out.println(f ? "YES" : "NO");
	}	
}
