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.*;
public class Main
{
    public static void main(String[] args) 
	{
		int x=0,y,z,res,w,n,m,i,j,p,q,k=0,b=0,c=0,max=0,sum=0,ans=0,flag=0;
		Scanner sc=new Scanner(System.in);
		n=sc.nextInt();
		ans=0;
		i=1;
		j=1;
		if(n==1){
		System.out.println(i);
		return;}
		while(ans+j<=n)
		{
		    ans+=j;
		i++;
		    j+=i;
		    
		}
		System.out.println(i-1);
	}
}
