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 int N = 100000 + 10;
int n, a[N];
int main() {
  cin >> n;
  a[1] = 1;
  for (int i = 1; i < N; i++) {
    a[i] = (i * (i + 1)) / 2;
    if (i > 1) a[i] += a[i - 1];
    if (a[i] > n) {
      cout << i - 1;
      return 0;
    }
  }
  return 0;
}
