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.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;


public class Solution {
    
    public static void main(String[] args) throws Exception{
        StreamTokenizer in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));     
        
        in.nextToken();     
        int n = (int)(in.nval);
        
        String res = "NO";

        for(int i = 1; i<=32; i++){
            if(i*(i+1) == 2*n){
                System.out.print("YES");
                return;
            }
        }
        
        System.out.print("NO");
        
    }

}
