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 B{
  public static void main(String[]args){
	  Scanner sc=new Scanner(System.in);
	  int n=sc.nextInt();
	  n*=2;int i=1;
	  while(i<=32 && i*(i+1)!=n) {
		  i++;
	  }
	  if(i>32) {
		  System.out.println("NO");
	  }else {
		  System.out.println("YES");
	  }
		  
   }
}
