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 Main {
	public static void main(String[] args) {
		new Main().solve();
	}
	
	void solve() {
		Scanner cin = new Scanner(System.in);
		int a = cin.nextInt();
		boolean good = false;
		for(int i = 1; ; i ++) {
			int sum = i * (i + 1) / 2;
			if(sum == a) good = true;
			if(sum >= a) break;
		}
		System.out.println(good ? "YES" : "NO");
		
	}
}
