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.*;

public class Main 
{
public static void main(String []args)throws IOException
{
 	BufferedReader var=new BufferedReader(new InputStreamReader(System.in));
int arr[]=new int[500];
int ban=0;
for(int c=1;c<=500;c++)
{
	arr[c-1]=(c*(c+1))/2;
}
int num=Integer.parseInt(var.readLine());
for(int c2=0;c2<500;c2++)
{
	if(arr[c2]==num)
	{
		ban++;
		
	}
}
if(ban>=1)
{
	System.out.println("YES");
}
else
{
	System.out.println("NO");
}
}
}
	    			 	 		       	 		 	