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.HashMap;
import java.util.Map;
import java.util.Scanner;
public class Main {
 public static void main(String[] args){
     Scanner sc=new Scanner(System.in);
    int a=sc.nextInt();
    int height=0,itr=1;
    for(int i=2;;i++){
        
        a=a-itr;
    if(a<0)
        break;
        itr=itr+i;
        height++;
        
    }
    System.out.println(height);
     
 }
}
