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: 

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import java.io.*;
import java.util.*;
import java.math.*;
import static java.lang.System.out;

public class CF492A
{
    public static void main(String[] args) throws IOException
    {
        //BufferedReader f = new BufferedReader(new FileReader("/Users/spencersharp/Desktop/input.txt"));
        
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(new BufferedOutputStream(System.out));
        
        String output = ""; //Write all output to this string

        //Code here
        int n = Integer.parseInt(f.readLine());
        int levelSize = 1;
        int numLevels = 0;
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < levelSize; j++)
                n--;
            levelSize+=i+2;
            numLevels++;
            //out.println(n);
        }
        if(n<0)
            numLevels--;
        output = ""+numLevels;
        
        
        //Code here

        //out.println(output);
        
        writer.println(output);
        writer.close();
        System.exit(0);
        
    }
}