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 Vanya_and_Cubes {
    public static void main(String[] args){
        Scanner scn = new Scanner(System.in);
        int n = scn.nextInt();
        scn.close();

        for (int i=1; i<=n; i++){
            int x = i*(i+1)*(i+2);
            x = x/6;
            if (x==n){
                System.out.println(i);
                break;
            }
            else if (x>n){
                System.out.println(i-1);
                break;
            }
        }
    }
}