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.Scanner;

public class MAIN 
{
    public static void main(String[] args) 
    {
        Scanner in = new Scanner(System.in);
        int C = in.nextInt();
        int T=1;
        int c=0;
        for(int i=2;T<=C;i++)
        {
            if(T==C)
            {
                c++;
                break;
            }
            T+=i;
            
        }
        if(c==1)
        {
            System.out.print("YES");
        }
        else
        {
            System.out.print("NO");
        }
        
    }

}
