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.BufferedInputStream;
import java.io.IOException;
import java.util.Scanner;


public class A47 {
	public static void main(String[] args) throws IOException {
		solveTriangularNumbers();
	}
	public static void solveTriangularNumbers() throws IOException{
		Scanner scan = new Scanner(new BufferedInputStream(System.in));
		int N = scan.nextInt();
		int t = 1 + 8*N;
		double sqrt = Math.sqrt(t);
		int st = (int) sqrt;
		
		if(sqrt-st == 0){
			System.out.println("YES");
		}else{
			System.out.println("NO");
		}
	}
}
