a$)$ Design a UML Statechart that will model a simple lighting system with the following characteristics:

$-$ Manual mode $-$ allows the user to manually switch on and off a light using $\backslash ($ O N $\backslash )$ and an OFF buttons respectively. This is the default mode.

$-$ Automatic mode $-$ turns the light on when it gets dark. Turns the light off when it gets bright.

$-$ A MODE button is used switch between manual and automatic modes. Only this button can change modes of the system.

$-$ Assume a luminosity sensor is polled every second and raises either a bright or dark event dependant on a simple threshold value.

$-$ Ensure the system does not flicker the light as darkness falls or daylight approaches or shadowing occurs. It can be assumed that a stable situation has been reached after one minute.

Note any assumptions made about the system as part of your answer.