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.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class Main
{
    public static void main(String[] args) {
        Scanner s=new Scanner(System.in);
        int n=s.nextInt(),ans=0,i=0;
        if(n==1)
        System.out.println("YES");
        else
        {
        for(i=0;i<n;i++)
        {
            ans=ans+i;
            if(ans==n)
            {
                 System.out.println("YES");
                 break;
            }
        }
        if(n==i)
            System.out.println("NO");
        }
       
    }
}