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 Main {
	public static void main (String[] args){
	    Scanner sc = new Scanner(System.in);
	    int n = sc.nextInt();
	    int tot = 0, add = 0;
	    int i = 1;
	    while(true){
	        add += i;
	        if(tot + add > n){
	            System.out.println(i - 1);
	            return;
	        }
	        tot += add;
	        i++;
	    }
	}
}