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;
long long n;
bool check(long long mid) {
  long long res = 0;
  for (int i = 1; i <= mid; ++i) res += i * (i + 1) / 2;
  return res <= n;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> n;
  long long l = 1, r = 120;
  while (l < r) {
    long long mid = (l + r) / 2;
    if (check(mid))
      l = mid + 1;
    else
      r = mid;
  }
  if (!check(l)) --l;
  cout << l;
  return 0;
}
