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.*;
import java.lang.*;
import java.io.*;

public class Main
{
    public static void main (String[] args) throws java.lang.Exception
    {
        Scanner sc = new Scanner(System.in);
        int cant = sc.nextInt();
        if(cant > 1)
          System.out.println(nivel(cant, 1, 1));
          else
          System.out.println(1);
    }
    
    private static int nivel(int cant, int i, int sum){
        int res;
        if( sum > cant)
            res = 0;
            else {
                res = nivel(cant - sum, i + 1, sum + i + 1 )+ 1;
            }
            return res;
    }
}