Create a simple client$-$server interaction using socket programming in C$.$ The server should listen for incoming connections and display messages received from the client. The client, on the other hand, should allow users to input messages to be sent to the server. Implement a mechanism for the client to signal the end of the conversation, and ensure that the server reacts accordingly by displaying the messages and terminating the connection. Provide both the client and server source code along with instructions for running the programs.