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 A47 {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		Integer N = Integer.parseInt(br.readLine());
		
		int tri = 0;
		boolean f = false;
		for(int i = 1; i <= 500;i++){
			tri = i+tri;
			if(tri == N){
				f = true;
				break;
			}			
		}
		System.out.println(f?"YES":"NO");		
	}

}
