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 power(int x, int y) {
  int a = x;
  for (int i = 0; i < y; i++) {
    x = x * a;
  }
  return x;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int c = 2, c2 = 1, c3 = 0;
  int sum = 1;
  int x;
  cin >> x;
  while (true) {
    c3++;
    if (sum == x) {
      cout << c3;
      break;
    } else if (sum > x) {
      cout << c3 - 1;
      break;
    }
    c2 += c;
    sum += c2;
    c++;
  }
  return 0;
}
