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.*;
public class a47 {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[100];
        a[0]=0;
        int c=0;
        for(int i=1;i<100;i++)
        {
            a[i]=a[i-1]+i;
            if(a[i]>500)
                break;
        }
        for(int i=0;i<100;i++)
        {
            if(n==a[i])
            {
                c++;
                break;
            }
        }
        if(c==0)
            System.out.println("NO");
        else
            System.out.println("YES");
    }

}
