Vanya got n cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes, and so on. Thus, the i-th level of the pyramid must have 1 + 2 + ... + (i - 1) + i cubes.

Vanya wants to know what is the maximum height of the pyramid that he can make using the given cubes.

Input

The first line contains integer n (1 ≤ n ≤ 104) — the number of cubes given to Vanya.

Output

Print the maximum possible height of the pyramid in the single line.

Examples

Input

1


Output

1


Input

25


Output

4

Note

Illustration to the second sample: 

<image>
import java.util.ArrayList;
import java.util.Scanner;

/**
 *
 * @author muath
 */
public class Codef {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
      Scanner input = new Scanner (System.in);
      int x=input.nextInt();
      int y = x;
      int nextline=1;
      int counter=0;
      int temp=2;
      
      while (nextline <=x)
      {
          
          y-=nextline;
          nextline=nextline+temp;
          
          temp+=1;
          counter+=1;
          
          
          if(nextline > y)
              break;
      }
      
      System.out.println(counter);
   
    
}
}