can someone write detailed solution please ? with all SPNE. thanks in advance

Three players will open new shops in a linear city denoted by the [0,4] interval. There is no existing shop in the city. Players can locate their shops on integer values, so that they each have 5 potential locations: {0, 1, 2, 3, 4}. There can be multiple shops in one location. Player 1 chooses his/her shop location first. Observing this action, Player 2 chooses later. And then, observing those previous actions, Player 3 chooses the last. Players aim to maximize the number of customers they will serve.

The products to be sold in the shops will be identical, and their prices will be equal as well, so the only thing a potential customer cares about is the distance from his/her house to the shop. In particular, a customer shops from the closest shop. If a customers house is exactly in between multiple shops, he/she will choose either one with equal probabilities. All customers are discrete-uniformly distributed along the linear city: for the sake of simplicity, assume that there are 60 customers in each 1-unit distance, e.g., between 0-1, between 1-2, etc.

Example: If Player 1 has a shop in location 1 and the other players both have shops in location 4, here is the number of customers they serve. All 60 customers in the [0,1] interval shop from Player 1; all 60 customers in the [1, 2] interval shop from Player 1; customers in the [2, 3] interval can go to either shop with equal probabilities, so each player gains 20 customers from here; and customers in the [3, 4] interval can go to either Player 2s or Player 3s shop with equal probabilities, so each Player i {2, 3} gains 30 customers from here. As a result, Player 1 has a total of 140 customers, and Players 2 and 3 have a total of 50 customers each.

Find the number of customers each player will serve in every SPNE.

Two notes that will make your life easier: (1) For this quiz, you do not have to write the SPNE strategy profiles explicitly, you are allowed work on the equilibrium paths, however you still need to explain your work very clearly. (2) If a player is indifferent between two alternative locations, you can assume that he/she will choose the location with the highest index number. That is, if location a and location b yield the same number of customers, location a is preferred if a > b.