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.io.*;
    public class Cf280a {
        public static void main(String[] args) throws IOException {
            InputStreamReader fin = new InputStreamReader(System.in);
            Scanner scr = new Scanner(fin);
            int n = scr.nextInt();
            int h = 0;
            int sum = 0;
            while (true) {
                h++;
                sum += h;
                n -= sum;
                if (n < 0) {
                    h--;
                    break;
                }
            }
            PrintWriter fout = new PrintWriter(System.out);
            fout.print(h);
            fout.flush();
            fout.close();
        }
    }