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.PrintWriter;
import java.util.Scanner;

public class VanyaAndCubes_280_2 {
    public static void main (String[] args) {
        Scanner	sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int cubs =  sc.nextInt(), sum = 0, s, i = 0, level = 0;
        while (sum <= cubs) {
            i++;
            s = (i + i * i) / 2;
            sum += s;
            if (sum > cubs) {
                level = --i;
                break;
            }
        }
        pw.println(level);
        pw.close();
    }
}
