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.*;

public class cf47A {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		float r = 1 ,m = 0 ;
		int x,i ;
		List <Integer> arr = new ArrayList <> () ;
		while (m <= 500) {
			m = ((r+1)/2 ) * r ;
			arr.add((int)m);
			r += 1;
		}
		//System.out.println(arr);
		x = sc.nextInt() ;
		for (i = arr.size() - 1 ; i >= 0 ;i--) {
			if (arr.get(i) == x) {
				System.out.println("YES");
				System.exit(0);
			}
		}
		System.out.println("NO");
	}
}