A smart office security IoT application allows authenticated employees $($users$)$ to open the entrance barrier for visitors. The user authentication is performed by employees keying their passwords, and $3$ consecutive incorrect passwords will trigger the alarm of the entrance system. The initial state of the system is IDLE and the barrier is closed. If a login is successful, the system transits to SUCC state and the barrier is opened. Otherwise, if $3$ consecutive incorrect passwords are entered, the system transits to FAILED state and the user must wait $60$ seconds before he$/$she can login again.

i$)$ Implement a finite state machine $($FSM$)$ to describe a login procedure of the system. In your design, you must specify and list all appropriate events, actions, states and their transitions. You may include any additional state where appropriate.

ii$)$ Draw an FSM state transition table to satisfy these workflows.