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;
const string file = "A";
const string infile = file + ".in";
const string outfile = file + ".out";
int main() {
  ostream &fout = cout;
  istream &fin = cin;
  int N;
  fin >> N;
  long long cSum = 0;
  int idx = 1;
  while (cSum + idx * (idx + 1) / 2 <= N) {
    cSum += idx * (idx + 1) / 2;
    idx++;
  }
  fout << idx - 1 << "\n";
}
