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.io.*;
import java.util.Scanner;

public class Main {
   private static int from;
   private static int to;
   
   public static void main(String[] args) {
	   
      Scanner sc = new Scanner(System.in);
      int times = sc.nextInt();
      String value = "NO";
      
      for (int i = 1; i <= 500 ; i++) {
    	  if(times == i*(i+1)/2) {
    		  
    		  value = "YES";
    		  break;
    	  }
      }
      System.out.println(value);
   }
   
   

}