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.*;
public class A {

    public static void main(String[] args) throws IOException{
        BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
        int m = Integer.parseInt(stdin.readLine());
        double x =  ((Math.sqrt(8*m + 1) - 1) / 2);
        if (x - (int)x > 0 )System.out.println("NO");
        else System.out.println("YES");
}
}