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 in = new Scanner (System.in);
        int n = in.nextInt();
        int level = 0;
        while (true) {
            int block = ((level+1) * (level+2)) / 2;
            if (n - block >= 0) {
                n = n - block;
                level++;
            } else {
                break;
            }

        
        }
        System.out.println(level);
    }
}