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.*;
public class Sample {
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int cubeR = (int)Math.pow(n, 1 / (3.0));
        for(int i = cubeR; ; i++) {
            int x = getSum(i);
            if(x == n) {
                System.out.println(i);
                break;
            } else if(x > n) {
                System.out.println(i - 1);
                break;
            }
        }
    }
    
    public static int getSum(int n) {
        int sum = 0;
        int temp = n;
        for(int i = 1; i <= temp; i++) {
            sum =  sum + (n * i);
            n--;
        }
        return sum;
    }
}