Consider the following problem. Given a set A of n distinct positive integers $($represented using an array$)$ as input, return true if there are two subsets of A$,$ call these subsets S and T$,$ such that S $$ T $=$ A$,$ S $$ T $=,$ and $\backslash$Sigma $$ in $=4\backslash$Sigma $$ in $,$ and return false otherwise. That is$,$ is there a way to partition the set A into two disjoint$$subsets S and T such that the sum of the elements in S is equal to four times the sum of the elements in T$?$ Write in pseudocode an exhaustive search algorithm that solves this problem. You may use a mixture of high$-$level and low$-$level pseudocode, as in the example on page $3$ of the pseudocode handout that shows how to write pseudocode for the Knapsack problem. Briefly explain how your algorithm works $($and$/$or use comments in your pseudocode$).$ Also, describe the problem that your algorithm in terms of input and output. $($For example, see the examples in Section $2\mathrm{.}3$ to see how the author describes the input and output of the algorithms.$)$ Explain what the running time of your algorithm is$.$