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.io.*;
import java.util.*;


public class SolutionA {
    public void solve() throws Exception{
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = Integer.parseInt(bf.readLine());
        int f = 0;
        int i = 1;
        int ans = 0;
        while(n - (f+i) >= 0){
            n = n - (f+i);
            ans++;
            f = f+i;
            i++;
        }
            
        out.println(ans);
        out.flush();
    }
    public static void main(String args[]) throws Exception{
        new SolutionA().solve();
    }

}