On a $2 ext{D}$ campus grid, there are n workers and m bikes, where each worker and bike is positioned at integer coordinates. You are given two arrays: workers, where workers[i] = [$x_i$, $y_i$] represents the position of the $i$-th worker, and bikes, where bikes[j] = [$x_j$, $y_j$] represents the position of the $j$-th bike.

Each worker must be assigned exactly one unique bike, meaning no two workers may be assigned the same bike.

The Manhattan distance between two locations $(x_1, y_1)$ and $(x_2, y_2)$ is defined as $|x_1 - x_2| + |y_1 - y_2|$.

Return the minimum possible sum of Manhattan distances between each worker and their assigned bike.

Constraints:

• n $= $ workers.length

• m $= $ bikes.length

• $1 \leq$ n $\leq$ m $\leq 10$

• workers[i].length $= 2$

• bikes[i].length $= 2$

• $0 \leq$ workers[i][0], workers[i][1], bikes[i][0], bikes[i][1] $< 1000$

• All worker and bike locations are unique.

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.