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.math.RoundingMode;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        Scanner scanner = new Scanner(System.in);
        //PrintWriter printWriter = new PrintWriter(new FileWriter("output.txt"));
        //Scanner scanner = new Scanner(new File("input.txt"));
        int n = scanner.nextInt();
        int sum = 0;
        int i = 0;
        if (n == 1) System.out.println(1);
        else {
            while (sum <= n) {
                i++;
                sum += sumInLine(i);
            }
            System.out.println(i - 1);
        }
    }

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

}









