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;
    import java.util.Vector;

    public class Main {
        public static void main(String[] args) {
            Scanner input = new Scanner(System.in);
            int cubes = input.nextInt();
            int x = 0 ;
            int total = 0 ;
            int count = 0 ;
            for(int i = 1 ; i <= cubes ; i++){
                x += i;
                total += x;
                if(total > cubes)
                    break;
                count++;
            }
            System.out.print(count);
        }
    }
