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.io.IOException;
import java.util.Scanner;


public class Prob047A
{
    public static void main( String[] Args ) throws IOException
    {
        Scanner in = new Scanner( System.in );
        int x = in.nextInt();
        boolean t = false;
        int num = 0;
        for ( int a = 0; a < 150; a++ )
        {
            num += a;
            if ( x == num )
                t = true;
        }
        if ( t )
            System.out.println( "YES" );
        else
            System.out.println( "NO" );

    }
}