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 codeforse {

    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub

 Scanner stdin = new Scanner(System.in);
 int n=stdin.nextInt();
 int sum=0;
 int i;int z=1;
 int count=0;int res=0;
 for ( i=1 ;i <= n ;i++ )
 { 
     sum+=i;
     res+=sum;
     count++;
     if (res>n)
     {    count=count-1; 
          break;
     }
     else
     {          
      continue;
     }}
     System.out.println(count);
 }}  