$3.(12$ pts$.)$ There are $\backslash ($ m $\backslash )$ mice and $\backslash ($ n $\backslash )$ holes on the ground of a warehouse; each is represented with a distinct $2$D $\backslash (($x$,$ y$)\backslash )$ coordinates. A cat is coming and all mice are running to try to hide in a hole. Each hole can hide at most $\backslash ($ k $\backslash )$ mice. All mice run at the same velocity $\backslash ($ v $\backslash ).$ A mouse is eventually safe if it reaches a hole $($with at most $\backslash ($ k $\backslash )$ mice including itself$)$ in $\backslash ($ s $\backslash )$ seconds. Design a polynomial$-$time algorithm $($in $\backslash ($ m $\backslash )$ and $\backslash ($ n $\backslash ))$ to find the maximum number of mice that can be safe. Hint: reduce this problem to a network flow problem.