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>
int n, a[1000], sum[1000];
int main() {
  scanf("%d", &n);
  for (int i = 1;; i++) {
    a[i] = a[i - 1] + i;
    sum[i] = sum[i - 1] + a[i];
    if (n < sum[i] && n >= sum[i - 1]) {
      printf("%d", i - 1);
      return 0;
    }
  }
}
