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 randomQues {
    static boolean isTrain(int num){
        if(num<0){
            return false;
        }
        int sum=0;
        for (int i = 1; sum <=num ; i++) {
            sum+=i;
            if (sum==num){
                return true;
            }
        }
        return false;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int num=sc.nextInt();
      if (isTrain(num)){
          System.out.println("YES");
      }
      else {
          System.out.println("NO");
      }
    }
}