Write efficient C++ code for the following program.Also explain your logic

You are given two sequences A₁,A₂,,A_N and B₁,B₂,,B_N. You should choose a permutation P₁,P₂,,P_N of the integers 1 through N and construct N rectangles with dimensions A₁BP₁,A₂B_P2,,A_NB_PN Then, for each of these rectangles, you should construct an inscribed circle, i.e. a circle with the maximum possible area that is completely contained in that rectangle.

Let S be the sum of diameters of these N circles. Your task is to find the maximum value of S