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.*;
import java.io.*;
import java.lang.*;
import java.text.*;
import java.math.*;
public class A
{
    public static void main(String args[]) throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
        int n=Integer.parseInt(br.readLine());
        int i=0,last=0,cur=0;
        while(n>0)
        {
            i++;
            cur=last+i;
            last=cur;
            n-=cur;
            if(n<0)
            {
                i--;
            }
        }
        bw.write(i+"\n");
        bw.flush();
    }
}