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.Scanner;

public class Vanya_and_Cubes {

    private static final Scanner SCANNER = new Scanner(System.in);

    public static void main(String[] args) {
        int amount = 0 , sum_line = 0 , line = 0 ,  sum = 0 , answer = 0;

        amount = SCANNER.nextInt();

        while(true){
            line++;
            sum_line += line;
            sum += sum_line;
            if(sum > amount)
            {
                break;
            }
            answer++;
        }

        System.out.print(answer);
    }
}
