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.io.*;
import java.util.*;

public class Main {
    static boolean OFFLINE = false;

    public static int level(int i) {
        return i * (i + 1) / 2;
    }

    public static void main(String[] args) throws IOException {
        Scanner scanner;
        if (OFFLINE) {
            scanner = new Scanner(new FileReader("input.txt"));
        } else {
            scanner = new Scanner(System.in);
        }

        int N = scanner.nextInt();

        int tmp;
        int nextLevel = 1;

        while (true) {
            tmp = level(nextLevel);
            if (tmp > N) {
                break;
            }

            N -= tmp;
            ++nextLevel;
        }

        System.out.println(nextLevel - 1);
    }
}