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.*;
import java.io.*;
 
public class Main{
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        int sum=0;
        int n=sc.nextInt();
        if(n<0){
            System.out.println("NO");
        }
        for(int i=1;i <= n;i++){
           // sum=sum+i;
            if(i*(i+1)/2 == n){
                System.out.println("YES");
                return;
            }
        }
                System.out.println("NO");
            
        }
        
    }
