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
//Written by Shagoto
import java.util.*;
public class Main
{
  public static void main(String[]args)
  {
    Scanner read = new Scanner(System.in);
    
    int n = read.nextInt();
    
    for(int i = 1; i<=32; i++)
    {
      if((i*(i+1)) / 2 == n)
      {
        System.out.println("YES");
        break;
      }
      else if((i*(i+1)) / 2 > n)
      {
        System.out.println("NO");
        break;
      }
      else
      {
        continue;
      }
    }
  }
}