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.io.*;
import java.util.Scanner;
public class Main {
public static void main(String[] args) throws IOException{
	Scanner sc = new Scanner(System.in);
	int remaining = sc.nextInt();
	int height = 0;
	for(int i=1;i<=remaining;i++){
		int minus = 0;
		int temp = 0;
		for(int j=1;j<=i;j++){
			 minus+=j;
			 temp = j;
		}
		remaining = remaining-minus;
		height++;
		if(remaining<(minus+temp+1))
			break;
	}
System.out.println(height);}
}