Minimum Time to Generate Text

You are given an integer n. Initially the text is empty, and you want to generate a text with a length of at least n characters. There are three operations available:

• Type a single letter at a cost of $1$.
• Copy the entire current text to the clipboard at a cost of $5$ (this operation is equivalent to pressing Ctrl+A, Ctrl+C, and then deselecting the text).
• Paste the entire content of the clipboard at the end of the text at a cost of $2$.

Note that if you use the copy operation when you have i characters, you can then paste repeatedly. After copying, every paste appends exactly i characters. Formally, if you are at a state with i characters, and you decide to copy (cost $5$) and then paste k times (each paste costs $2$, so total paste cost is $2k$), then the text length becomes i × (k+1) and the total additional cost is $5+2k$.

Your task is to find the minimum total time required to obtain a text of length at least n.

Note: The data range in this problem is slightly different from the original version.

inputFormat

The input consists of a single integer n (where n ≥ 1), representing the minimum length of the text.

outputFormat

Output a single integer, the minimum time required to generate a text of length at least n.

sample

1

1