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.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;


public class cubes {

    public static int fib(int n){
        if(n > 0) return n + fib(n-1);
        else return n;
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int i = sc.nextInt();

        int numLayers = 0; 
        int allCubes = 0;

        while(true){
            allCubes = allCubes + fib(numLayers+1);
            if(allCubes > i) break;
            numLayers++;
        }

        System.out.println(numLayers);    
    }
    
}
