Given an unsorted array $A=($:$a_1,a_2,$dots,$a_n$:$)$ of $n$ arbitrary numbers, which may be positive, negative, or zero. Design a divide and conquer algorithm to compute the maximum value of $a_i{a}_j$ with $1ij.$ Your algorithm should run in $O(n)$ time in the worst case. Present your algorithm as one Python function: def maxProduct $(($:$a_1,a_2,$dots,$a_n$:$))$ :

The algorithm should return minimum elements as well $($it must work for negative input numbers$).$