There is an $8 imes 8$ chessboard with $n$ pieces placed on it. You are given two arrays: an array of strings pieces and a $2$D integer array positions, each of length n, where pieces[i] represents the type of the $i$-th piece and positions[i] = [r_i, c_i] represents its starting square using $1$ based indexing.

Each piece can be one of three types:

• A "rook" can move in any of the $4$ horizontal or vertical directions.

• A "queen" can move in any of the $8$ horizontal, vertical, or diagonal directions.

• A "bishop" can move in any of the $4$ diagonal directions.

Every piece independently selects a destination square and travels toward it along a straight line at a speed of $1$ square per unit time. A piece may also choose to stay on its starting square. All pieces begin moving simultaneously at time $t = 0$. When a piece reaches its chosen destination, it stops and stays on that square for all subsequent moments.

A move combination is considered valid if at no time $t \geq 0$ do two pieces occupy the same square.

Return the total number of valid move combinations.

Constraints:

• n $==$ pieces.length

• n $==$ positions.length

• $1 \leq$ n $\leq 4$

• pieces only contains the strings "rook", "queen", and "bishop".

• There will be at most $1$ queen on the chessboard.

• $1 \leq r_i, c_i \leq 8$

• Each positions[i] is distinct.

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.