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 Round44Div2A {
    public static void main(String[] args) throws IOException{
        BufferedReader rdr = new BufferedReader(new InputStreamReader(System.in)) ;
        int k = new Integer(rdr.readLine()) ;
        int root = (int)(Math.sqrt(1+8*k)) ;
        if(root*root == 1+8*k && (root-1)%2 == 0)
            System.out.println("YES");
        else
            System.out.println("NO");
            
    }
}
