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 A47 
{
	public static void main (String[] args)
{ Scanner in=new Scanner(System.in);
int n=in.nextInt();
boolean check=false; int s=0;
for(int i=1;i<=n ;i++)
{ s+=i;
if(s==n)
{ check=true;
  break;
}
}
if(check)
System.out.println("YES");
else System.out.println("NO");
}
}