Consider a robot moving in an n $$ n grid. It starts at the coordinate $(1,1)($say representing the bottom left conner cell$)$ and it moves either one square up or one square right, i$.$e$.$ it increases either one $($but not both$)$ of its coordinates by exactly one $($if not already equal to n$).$ Eventually the robot will arrive at the coordinate $($n$,$ n$).$ You also know, from past observations, the robot$$s probability of various moves. In particular, if the robot is at position $($x$,$ y$),$ its next move will be $$move up$$ with probability u$($x$,$ y$)$ and will be $$move right$$ with probability r$($x$,$ y$)=1$ u$($x$,$ y$).$ You want to prevent this robot from reaching its destination by placing one single block along its path $($you cannot place the block in $(1,1)$ or $($n$,$ n$)).$ Describe an algorithm to find the best place to place the block that will maximize the probability that the robot will enter the chosen location during its trip. Your algorithm should run in O$($n$2)$ time.