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 Codeforces {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        //Variables
        int count;
        int cubeNumber;
        int currentNeeded = 0;

        cubeNumber = scan.nextInt();


       for ( count = 0 ; cubeNumber >= currentNeeded;) {
           cubeNumber -= currentNeeded;
           count++;
           currentNeeded += count;
       }

       System.out.println( count - 1 );




    }

}
