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 test {
   public static boolean contains(int[] arr, int item) {
      for (int n : arr) {
         if (item == n) {
            return true;
         }
      }
      return false;
   }
   public static void main(String[] args) {

      Scanner in = new Scanner(System.in);
      int a = in.nextInt();    
      int[] tri = { 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528 };  
      if (contains(tri, a) == true) {
         System.out.println("YES");
      }  else {
         System.out.println("NO");
      }

      in.close();

   }
}