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.*;
import java.util.*;
public class A47 {
    public static void main(String[] args) throws IOException   {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        Set<Integer> set = new HashSet<Integer>();
        for(int i = 1; i <= 500; i++)
            set.add((i*i+i)/2);
        System.out.println(set.contains(Integer.parseInt(br.readLine())) ? "YES" : "NO");
    }
}
