There are two candy shops, both of which have N candies for sale. The first shop sells each candy for one golde coin; the second shop sells each candy for one silver coin. You have N$/2$ golden coins and N$/2$ silver ones $($Nis even$).$ Each candy is of some particular type $($not necessarily unique$),$ represented by an integer. What is the maximum number of different types of candy that you can buy? Write a function: class Solution $\{$ public int solution$($int$[]$ A$,$ int $[]$ B$)$; $\}$ that, given two arrays A and B of N integers, representing types of candies in the first and second shop respectively, returns the maximum possible number of different types of candy that you can buy. For example, given: A$=[1,2,3,4]$ B$=[3,3,3,7]$ the function should return $4.$ You can, for example, buy candies of types $1,2$ in the first shop and then candies of types $3,7$ in the second shop. A$=[1,2,3,4]$ B$=[3,3,3,7]$ the function should return $4.$ You can, for example, buy candies of types $1,2$ in the first shop and then candies types $3,7$ in the second shop. Given: A$=[2,2,2,2,2,2]$ B$=[7,4,2,5,1,2]$ the function should also return $4.$ In the first shop you can only buy candies of type $2,$ but then you can buy thre candies of other types $($for example, $7,4$ and $5)$ in the second shop. Write an efificient algorithm for the following assumptions: N is an integer within the range $[2\mathrm{.}100,000]$; N is even; each element of arrays A and B is an integer within the range $1.\mathrm{.}1,000,000,000.$