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 cubes {
    public  static void main(String args[]){
        Scanner input=new Scanner(System.in);
        int n=input.nextInt();
        int temp=0;
        int m=0;
        int p=0;
        for(int i=1;i<=n;i++){
        if(n==1){
          temp=1;
         break;
    }
            if(p+m+i>n){
                break;
            }
            m+=i;
                p+=m;
                temp+=1;

        }
        System.out.println(temp);
    }
}
