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 arr[10000];
void eval() {
  arr[0] = 0;
  for (int i = 1; i < 10000; i++) {
    arr[i] = i + arr[i - 1];
  }
  for (int i = 1; i < 10000; i++) {
    arr[i] += arr[i - 1];
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  eval();
  int n;
  cin >> n;
  auto it = upper_bound(arr, arr + 10000, n);
  it--;
  cout << it - arr;
}
