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.util.*;
public class A
{
    public static void main(String [] args)
    {
 
    Scanner s=new Scanner(System.in);
    int i=1;
    HashSet h=new HashSet<Integer>();
    while(i<32)
    {
        int t=i*(i+1);
        t=t/2;
        h.add(t);
        i++;
    }
    
    int m=s.nextInt();
    if(h.contains(m))
    System.out.println("YES");
    else
    System.out.println("NO");
    }
}