Soul Escape from Rough Blocks

One night a devil appeared at Daegu Science High School and trapped one student's soul in each of the $N$ blocks. The blocks are arranged in a row, and adjacent blocks are linked by a chain. Starting from some block and repeatedly moving to a linked block, the set of blocks you can reach is called a chain, and the number of blocks in a chain is its length. At the start, all $N$ blocks form one chain of length $N$.

Ian supports quantitative utilitarianism and wants to free as many souls as possible. He repeats the following process until no chain has length $3$ or more. Removing a block also removes every link directly attached to that block.

• Pick a chain $C$ with length $3$ or more.
• If the length of $C$ is $4$ or less, remove one block. Otherwise, remove two non-adjacent blocks. A removed block must satisfy these conditions:
  • The block must have two links attached to it. In other words, a block at either end of the chain cannot be removed.
  • After the removal, $C$ is no longer a chain, and $2$ or $3$ new chains are formed. The minimum length among the new chains should be as large as possible.

Find the maximum number of blocks Ian can remove.

The first line contains the number of blocks $N$.

Print the maximum number of blocks Ian can remove as a single integer.

$1 \le N \le 10^{18}$ is an integer.