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.*;

public class Main {
    public static void main (String [] args ){
        Scanner t= new Scanner (System.in);
        int s,n=0,r=0,d;
        s=t.nextInt();
        d=s;
        for(int i=1;i<=s;i++){
            n+=i;
            d-=n;
            if (d>=0)
            r++;
            else
                break;
        }
        System.out.print(r);
    }
}