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 Main2 {
        public static void main(String[] args){            
            Scanner sc = new Scanner(System.in);
            int N = sc.nextInt();
            String S = Double.toString( (-1 + Math.sqrt(1 + 8*N))/2 );
            String y[] = S.split("\\.");
            if (y[1].equals("0")){System.out.println("YES");} else {System.out.println("NO");}  
        }  
    }