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.*;

public class VanyaAndCubes{
  public static void main(String[] args){
    Scanner gd = new Scanner(System.in);
    int num = gd.nextInt();
    int final_ans = 0;
    int sum = 1;
    int j = 2;
    int count = 0;
    while(final_ans<num){
      sum+=j;
      final_ans+=sum;
      j++;
      count++;
    }
    System.out.println(count);
  }
}
