SOLVE B$.$ A company is planuing to interview $2$n people. Given a $2-$D array costs of size $2$n x $2$ where costs$[$i$][1]$ is the cost of flying the ith person to city A$,$ and costs$[$i$][2]$ is the cost of flying the ith person to city B$.$ We want to return the minimum cost to fly every person to a city such that exactly n people arrive in each city.

Example $1$ Input: costs $=[[10,20],[30,200],[400,50],[30,20]]$ Output: $110$

Explanation: The first person goes to city A for a cost of $10.$ The second person goes to city A for a cost of $30.$ The third person goes to city B for a cost of $50.$ The fourth person goes to city B for a cost of $20.$ The total

minimum cost is $10+30+50+20=110$ to have half the people interviewing in each city. Example $2$ Input: costs a$)(10$ points$)$ Write down a recursive formulation of the minimum cost, minCost$($z$,$y$),$ which is the minimum cost of sending a people to city A and y people to city B where minCost$($n$,$ n$)$ is actually the answer to the original problem. In the solution, consider the possibilities when sending $($a $+$ y$)$t person into a city.

minCost$($x$,$y$)=[[259,770],[448,54],[926,667],[184,139],[840,118],[577,469]]$ Output: $1859$

Explanation: The first person goes to city A for a cost of $259.$ The second person goes to city B for a cost of $54.$ The third person goes to city B for a cost of $667.$ The fourth person goes to city A for a cost of $184.$ The fifth person goes to city B for a cost of $118.$ The sixth person goes to city A for a cost of $577.$ The total

minimum cost is $259+54+667+184+118+577=1859$ to have half the people interviewing in each city.

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$($b$)(10$ points$)$ Write a dynamic programming algorithm for finding the minimum cost to fly every person to a city, such that exactly n people arrive in each city. Also, give the running time of your algorithm.