On a campus represented by a $2$D grid, there are n workers and m bikes, where $n \leq m$.

You are given an array workers of length n where workers[i] = [x_i, y_i] represents the position of the $i^{ ext{th}}$ worker, and an array bikes of length m where bikes[j] = [x_j, y_j] represents the position of the $j^{ ext{th}}$ bike. All coordinates are given on a $2$D plane.

Each worker must be assigned exactly one bike, and each bike can be assigned to at most one worker. The assignments are made greedily according to the following priority rules:

1. Pairs of (worker, bike) with a smaller Manhattan distance are assigned first. The Manhattan distance between worker i and bike j is $|x_i - x_j| + |y_i - y_j|$.

2. If multiple pairs share the same distance, priority is given to the pair with the smaller worker index.

3. If multiple pairs share the same distance and worker index, priority is given to the pair with the smaller bike index.

Once a worker is assigned a bike or a bike is taken by a worker, neither can be part of any future assignment.

Return an array result of length n, where result[i] is the $0$ indexed index of the bike assigned to the $i^{ ext{th}}$ worker.

Constraints:

• n == workers.length

• m == bikes.length

• $1 \leq$ n $\leq$ m $\leq 1000$

• workers[i].length == bikes[j].length == $2$

• $0 \leq x_i, y_i < 1000$

• $0 \leq x_j, y_j < 1000$

• 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.