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 TriangularNumbers {
    private static boolean[] flag = new boolean[501];
    private static Scanner sc=new Scanner(System.in);
    public static void init(){
        for(int i = 1; ; i++){
            int n = i * (i + 1) / 2;
            if(n > 500){
                break;
            }
            flag[n] = true;
        }
    }
    public static void main(String[] args) {
        init();
        while(sc.hasNext()){
            int num = sc.nextInt();
            if(flag[num]){
                System.out.println("YES");
            }
            else{
                System.out.println("NO");
            }
        }
    }
}
