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 sample{
 
public static void main(String args[]){
Scanner sc=new Scanner(System.in);
 
int n=sc.nextInt();
int k=0,ans=0,p=0;
 
for(int i=1;i<=n;i++){
 
     p+=i;
     ans+=p;
    
    if(ans>n)
    break;
    
    k++;
}
 
System.out.println(k);
 
}
}