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.*;

public class Start{
    public static void main(String[] Args){
        int T,n;
        Scanner sc = new Scanner(System.in);
        T = sc.nextInt();
        T = T*2;
        boolean b = false;
        for(int i=1; i<T; i++){
            n=i*(i+1);
            if(n == T){ b = true; break; }
            if(n>T){ break; }

        }

        if(b==true){
            System.out.println("YES");

        }else{System.out.println("NO");}
        sc.close();

    }
}