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.Arrays;
import java.util.Scanner;


public class Main {
    public static void main(String[]args){
        
        Scanner sc = new Scanner (System.in);
        double in = sc.nextInt();
        if ((-1+Math.sqrt(1+8*in))/2 - (int)(-1+Math.sqrt(1+8*in))/2 == 0 && (-1+Math.sqrt(1+8*in))/2!=0){
        System.out.println("YES");} else System.out.println("NO");
    }
    
    
}
