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 VanyaandCubes
{
	public static void main(String[] args) 
	{
		Scanner sc=new Scanner(System.in);
		long n=sc.nextInt();
		long j,count=1,s=0,sum=0;
		while(true)
		{
		    s=0;
		    for(j=1;j<=count;j++)
		    {
		        s=s+j;
		    }
		    sum=sum+s;
		    if(sum>n)
		    {
		        count--;
		        break;
		    }
		    else if (sum==n)
		    break;
		    else
		    count++;
		}
		System.out.println(count);
		
	}
}
