Maximize 1D deliveries within distance and minimize total distance

You are given positions on a 1D line:

• people : an array of N integers (positions of people)
• shops : an array of M integers (positions of milk-tea shops)

You may match a shop to a person if the delivery distance is within a fixed limit D:

$|shops[k] - people[i]| \le D$

Constraints:

• Each shop can deliver to at most one person.
• Each person can receive from at most one shop.

Objective (lexicographic)

1. Maximize the number of deliveries (matched pairs).
2. Among all matchings that achieve the maximum number of deliveries, minimize the total delivery distance:

$\sum |shops[k] - people[i]|$

Task

Given people, shops, and D (e.g., D = 5), return:

• maxDeliveries : the maximum number of deliveries possible
• minTotalDistance : the minimum total distance among matchings that achieve maxDeliveries

Notes

• Positions may be unsorted; you may sort them.
• Specify and handle edge cases such as duplicates, empty arrays, and when no pairs are feasible.