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 JavaApplication1 {

    static Scanner input = new Scanner(System.in);
    public static void main(String[] args) {
        
        
        int n=input.nextInt();
        int sum=0;
        int i=1;
        
        while(sum<=n){
            sum+=i;
            if(sum==n){
                System.out.println("YES");
                return;
            }
            i++;
            
        }
        
        System.out.println("NO");
    }
}
