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 geniosity {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        ArrayList<Integer> ar = new ArrayList<Integer>();
        int[] arr= new int[10005];
        for(int i = 0; i <= 10004; ++i){
            arr[i] = (i * (i+1))/2;
//            System.out.println(arr[i]);
        }

        int n = in.nextInt();
        int ans = 0;
        long sum = 0;
        if(n == 1){
            System.out.println(1);
        }
        else{
            boolean flag = false;
            for(int i = 0; i < n; ++i){
                sum += arr[i];
                if(sum <= (long) n){
                    ans = Math.max(ans, i);
                }
                else{
                    break;
                }
            }
            System.out.println(ans);
        }

    }
}
