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) {
	// write your code here
        Scanner scanner = new Scanner(System.in);
        String s[];
        int n = scanner.nextInt();
        boolean flag = false;
        for (int i = 1; i <= n; i++) {
            if (((i * (i + 1)) / 2) == n) {
                flag = true;
                System.out.println("YES");
                break;
            }
        }
        if (flag == false)
            System.out.println("NO");



    }
}

 		 	 	 			 	 	  	  		 		