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;

/**
 *
 * @author Refat
 */
public class Main
{
    /**
     * @param args the command line arguments
     */
    public static void main(String[] args)
    {
        Scanner scanner=new Scanner(System.in);

        int dp[]=new int[1000+1];
        for(int i=0;i<=1000;i++)
            dp[i]=0;

        int k=1;
        int sum=0;
        for(;sum<=500;)
        {
            sum+=k;
            dp[sum]=1;
            k++;
        }


        int x=scanner.nextInt();
        if(dp[x]==0)
            System.out.println("NO");
        else
            System.out.println("YES");


        // TODO code application logic here
    }
}