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.lang.*;
import java.util.*;
import java.io.*;
public class test
{  
  
  Scanner sc=new Scanner(System.in);
  PrintWriter pr=new PrintWriter(System.out,true);
  public static void main(String... args) 
  {
       test c=new test();
       c.prop();
  }
  public void prop() 
  {
    int n,a ;
     n=sc.nextInt();
        for (int i=1; ;++i) {
           a=i*(i+1) ;
           a=a/2 ;
              if(a==n)
              {
                pr.println("YES");
                break ;
              }else if(a>n)
                {
                  pr.println("NO");
                  break ;
                }
        }
      
  }
 
}