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 input = new Scanner(System.in);

		int x = input.nextInt();
		int count = 0, i = 0;
		while(x >= sum(i))
		{
			x -= sum(i);
			i++;
			count++;
		}
		System.out.println(count-1);
	}

	public static int sum(int x)
	{
		int sum = 0;
		for(int i=1 ; i<=x ; i++)
		sum += i;
		return sum;
	}
}