$2$ Supercomputer Scheduling $(15$ pt$)$

In the Computer$2000$ data center, you are tasked with managing the schedule of a supercomputer for various scientific calculations. To optimize usage, you need to plan the tasks so as to maximize the number of non$-$overlapping calculations.

Details:

$$ Task X starts on day $2$ and ends on day $6.$

$$ Task Y starts on day $9$ and ends on day $15.$

$$ Task Z starts on day $15$ and ends on day $20.$

$$ Task W starts on day $9$ and ends on day $11.$

In this scenario, not all tasks can be executed due to overlapping periods between tasks Y and W$.$ The maximum number of non$-$overlapping tasks that can be performed is $3,$ which includes tasks X$,$ W$,$ and Z$.$