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>
const double pi = acos(-1.0);
const long long mod = 1e9 + 7;
using namespace std;
int a[10005];
int sum[10005];
int main() {
  int N;
  scanf("%d", &N);
  a[1] = 1;
  sum[1] = 1;
  for (int i = 1; i <= 10000; i++) a[i + 1] = a[i] + i + 1;
  for (int i = 1; i <= 10000; i++) sum[i + 1] = sum[i] + a[i + 1];
  for (int i = 1; i <= 10000; i++) {
    if (N >= sum[i] && N < sum[i + 1]) {
      printf("%d\n", i);
      break;
    }
  }
  return 0;
}
