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.*;
import java.util.*;

public class a
{
	public static void main( String arg[] )
	{
		Scanner s = new Scanner( System.in );

		int n = s.nextInt();

		boolean ok = false;
		int i=1;
		while( i*(i+1)/2 <= n )
		{
			if ( i*(i+1)/2 == n )
				ok = true;
			++i;
		}

		if ( ok )
			System.out.println( "YES" );
		else
			System.out.println( "NO" );
		System.out.flush();
	}
}




