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;
//import java.math.*;

public class TriangleNumbers {

    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        if(n == 1){
            System.out.println("YES");
        } else {
            double a = Math.sqrt(n*8+1);
            a -= Math.floor(Math.sqrt(n*8+1));
            System.out.println( a == 0 ? "YES" : "NO");
        }
    }

}
