3D Printed Statues

Picture by
Ariosvaldo GonzĂˇfoles, cc-by

You have a single 3D printer, and would like to use it to produce $n$ statues. However, printing the statues one by one on the 3D printer takes a long time, so it may be more time-efficient to first use the 3D printer to print a new printer. That new printer may then in turn be used to print statues or even more printers. Print jobs take a full day, and every day you can choose for each printer in your possession to have it print a statue, or to have it 3D print a new printer (which becomes available for use the next day).

What is the minimum possible number of days needed to print at least $n$ statues?

The input contains a single integer $n$ ($1 \le n \le 10\, 000$), the number of statues you need to print.

Output a single integer, the minimum number of days needed to print at least $n$ statues.

Sample Input 1 | Sample Output 1 |
---|---|

1 |
1 |

Sample Input 2 | Sample Output 2 |
---|---|

5 |
4 |