There is a tournament with n players numbered from $1$ to n standing in a single row in increasing order of their numbers.

The tournament consists of multiple rounds. In each round:

• Players compete in pairs based on their positions in the row. The $i^{th}$ player from the front competes against the $i^{th}$ player from the back (the player at index $i$ faces the player at index $k - i + 1$, where $k$ is the total number of remaining players in the current round).

• If the number of players $k$ is odd, the middle player advances directly to the next round without playing a match.

• The winners of each match, along with any player who advanced directly, move on to the next round while preserving their relative order.

Two specific players, firstPlayer and secondPlayer, are the best players in the tournament. Each of them is guaranteed to win every match against any opponent other than each other. When firstPlayer and secondPlayer compete against each other, the tournament ends.

Return an array of two integers representing the earliest round number and the latest round number in which firstPlayer and secondPlayer can face each other. Round numbers start at $1$.

Constraints:

• $2 \leq$ n $\leq 28$

• $1 \leq$ firstPlayer $<$ secondPlayer $\leq$ n

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.