This problem is about the "busy beaver" function.

Look carefully at the $3-$state$-$busy$-$beaver and $4-$state$-$busy$-$beaver examples, including all the comments that discuss the busy beaver function. Write a pseudocode to check all $2-$state $2-$symbol Turing machines and find busy beavers among them which has either the most non$-$blank symbols or which took the most steps. Use function simulate$2$state$2$symbolTM$($A$0\_$transition, A$1\_$transition, B$0\_$transition, B$1\_$transition$)$ to simulate a $2-$state $2-$symbol Turing machine that returns a list including the number of steps it took and the number of non$-$blank symbols. You can use transition as follows:

For example for A$0\_$transition which is the transition when current state is A and input symbol is $0,$ you can use string $"1$LB$"$ which writes $1$ to tapehead, then moves tapehead to left and sets current state to B$.$

Finally describe how this implementation can be generalized into all types of Turing machines and discuss whether this is a good or bad solution for finding busy beavers.