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.*;
import java.io.InputStreamReader;
public class Main{
  public static void main(String args[]) throws IOException{
    BufferedReader br=new BufferedReader( new InputStreamReader(System.in));
      int n=Integer.parseInt(br.readLine());
      int sum=0;
      boolean num=true;
      for(int i=1;sum<=500;i++){
        sum=sum+i;
   if(sum==n){
     System.out.println("YES");
     num=true;
     break;
       }
   else
     num=false;
      }
      if(num==false){
          System.out.println("NO");
      }
  }
}
 	 			 	 		   			 			  		  		 	