Implement a producer$-$consumer program using the semaphores in Linux with the following conditions:

a$.$

The buffer size is limited to $5$ items.

b$.$

The producer generates a total of $10$ items.

c$.$

The consumer should consume items only after at least $3$ items have been produced.

d$.$

The producer should wait if the buffer becomes full and can only resume once there are less than $5$ items in the buffer.

Requirements:

a$.$

Shared Buffer: Implement a shared buffer of a fixed size.

b$.$

Producer: The producer thread should generate data $($e$.$g$.,$ integers$)$ and place it into the buffer.

c$.$

Consumer: The consumer thread should take data from the buffer.

d$.$

Semaphore for Buffer Count: Use a semaphore to keep track of the number of items in the buffer.

e$.$

Mutex Lock: Use a mutex lock to ensure that only one thread $($producer or consumer$)$ can access the buffer at a time.

Expected Output:

The output should demonstrate the following sequence of events:

a$.$

The producer adds items to the buffer until it is full.

b$.$

The consumer starts consuming once there are at least $3$ items, and continues until the buffer is empty.

c$.$

This cycle continues until all $10$ items have been produced and consumed.