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>
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  long long* arr = new long long[8000];
  arr[0] = 1;
  for (int i = 1; i < 1000; i++) arr[i] = arr[i - 1] + (i + 1);
  long long* pre = new long long[8000];
  pre[0] = arr[0];
  for (int i = 1; i < 8000; i++) pre[i] = pre[i - 1] + arr[i];
  int n;
  cin >> n;
  for (int i = 0; i < 8000; i++)
    if (pre[i] > n) {
      cout << i;
      break;
    }
  return 0;
}
