During the Covid$-19$ pandemic, Bouncy Sports Equipment Inc. wants to limit the number of customers in their stores at a time.

For this purpose, they invested in visual people counting systems and barrier systems. Entry and exit doors are separated, so that the customer traffic is one$-$way at each door. Visual people counting camera systems are located at entry and exit doors. People counting systems and barrier systems are connected to the store local area network and each device receives a network IP address. The people counting systems and the door barriers communicate via local area network.

The people counting systems can recognize that a person is passing through the door. A signal is generated every time a person passes, and a file on the central computer that holds the number of customers in the store is updated.

The barriers on entry doors are triggered from the central computer after each change to number of customers in the store $($data kept in the above mentioned file$).$ When the number of customers in the store reaches to limit$,$ barriers at the entry doors will be closed. Barriers are kept closed until the number of customers in the store reduces below the limit$.$ There is a note on the barrier that explains the reason why entry is forbidden now. When some customers leave the store through the exit doors, the number of customers in the store decreases. When the number of customers in the store is below the limit$,$ the barriers at the entry doors will be opened and kept open until it is necessary to close $($as described above$).$

The store manager is allowed to connect to administration software that runs on the central computer to see how many people are in the store at the moment. The software also allows the store manager to change the in$-$store people limit$.($The requirements related to door barriers upon modifying the limit value are left to you. Please think about required behavior and consider it during your analysis.$)$

When store personnel enter the store, they should be able to open the barrier temporarily and pass. In order to detect store personnel, there is a card reader at the entry and exit doors. The personnel should always use their cards so that they can pass the barrier. They should use their cards during exit. So$,$ the movements of store personnel are not added to or subtracted from the people counter.