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.Scanner;

public class VanyaandCubes
{
    public static void main(String[] main)
    {
        Scanner cin= new Scanner(System.in);
        int n = cin.nextInt();
        int d = 0 ;
        int flag = 0 ;
        int index = 1 ;
        while ( index == 1 ) 
        {
            flag ++ ;
            d = d +  flag * (flag + 1) / 2 ;
            if(d > n)
                index = 0;
        }
        System.out.println(flag - 1);
    }
}