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.Scanner;

public class tri{
        
        public static void main(String eww[]){
                Scanner rm=new Scanner(System.in);
      	
      	int n = rm.nextInt();	
      	int c = 0;
      	int d = 1;
      	while(n>c){
      	 c = c + d;
      	 d++;
      	 
      	}
      	
      	if(c == n){p("YES");
      	}else{p("NO");}

        }
        
        static<R>void p(R M){System.out.print(M);}
}