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 TriangularNumber {

    public static void main(String args[]) {
        Scanner input = new Scanner(System.in);
        int n, t = 0, i, test = 0;
        n = input.nextInt();
        if (n <= 10)
        {
            for (i = 1; i <= n; i++)
            {
                t = t + i;
                if (t == n) 
                {
                    test = 1;
                    break;
                }
            }

        } 
        else if(n>10)
        {
            for (i = 1; i < n / 2; i++) 
            {
                t = t + i;
                if (t == n)
                {
                    test = 1;
                    break;
                }
            }
        }
        if(test==0)
        {
            System.out.println("NO");
        }
        else
        {
            System.out.println("YES");
        }

    }

}
