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.*;

public class Solution1 {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String s = in.readLine();
        int num2 = Integer.parseInt(s);
      

        int resultado = 0;
        int check = 0;
        
        

        for (int i = 1; i <= num2; i++) {
            resultado = resultado + i;


            if (resultado == num2) {
               // System.out.println("YES");
                check = 1;
              
                
            }
            //System.out.println("NO");
            
           
        }

        if(check == 1){
            System.out.println("YES");
        }else{
            System.out.println("NO");
        }



    
        

    }
}

