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
{
    public static void main( String [] args )
    {
        Scanner input = new Scanner( System.in );

        int n = input.nextInt();

        for( int i = 1; i <= n; i++ )
        {
            if( (i * ( i + 1 )) / 2 == n )
            {
                System.out.println( "YES" );
                return;
            }
        }

        System.out.println( "NO" );
    }
}