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 triangularNumbers_payay{
    static int input;
    static int trial=1;
        
    public static void getInput(){
        Scanner kb = new Scanner(System.in);
        while (input <=0 || input >=501){   
        System.out.println("");
        input = kb.nextInt();   
        }           
    }
    public static void check(){
        
        for(int x=1;trial<input;x++){
            trial=x*(x+1)/2;
        }
        
    }
    public static void print(){
        if(input==trial)
        System.out.println("YES");
        else
        System.out.println("NO");
    }
        
    public static void main(String[]args){
        getInput();
        check();
        print();
    }
}