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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;


public class TriangularNumbers {

    void run() {
        try {
            BufferedReader bfd = new BufferedReader(new InputStreamReader(
                    System.in));
            int n = Integer.parseInt(bfd.readLine());
            boolean b = false;
            for(int i = 0 ; i < 2*n; ++i)
                if(i*i + i == 2*n){
                    b = true; 
                    break;
                }
            System.out.println( b ? "YES" : "NO");
            
        } catch (Exception e) {
        }
    }
    public static void main(String[] args) {
        new TriangularNumbers().run();
    }

}
