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 input=new Scanner(System.in);
   long x;
   x=input.nextLong();
   long j=1+8*x;
   double p=Math.sqrt((long)j);
  
   if(Math.ceil(p)==Math.floor(p)){
     System.out.println("YES");
   }
   else{
     System.out.println("NO");
   }
  }
}
