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.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	     Scanner SC=new Scanner(System.in);
	     BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	     int n=0;
	     int m=0;
	     
	     if(SC.hasNext())
	     n=SC.nextInt();
	     
	     String s="NO";
	     int x=1;
	     int temp=0;
	     while(temp<=n)
	     {
	          int t2=(x*(x+1))/2;
	          if(t2==n)
	          {
	               s="YES";
	               break;
	          }
	          
	          temp=t2;
	          x++;
	     }
	     
	    
	   
	   System.out.print(s);
	    
		
     }
}