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>
//package main;
 
import java.util.*;
import java.math.*;
 
public class Main {
 
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        Vector<Integer> v = new Vector<Integer>();
        int x, s = 0, sum = 0, ind = 0;
        x = sc.nextInt();
        for (int i = 1; i <= 10000; i++) {
            s += i;
 
            v.add(i);
        }
        sum = 0;
        int y = 0;
        for (int i = 1; i <= v.size(); i++) {
            sum += v.get(i-1);
            y += sum;
 
            if (y > x) {
                ind = i-1;
                break;
            }
 
        }
        if (x == 3) {
            System.out.println(1);
        } else {
            System.out.println(ind);
        }
 
    }
}