Consider two possible investments A and B; each year, an oracle tells you the return of the

investments for the each of the n next years. This can be represented by arrays A $=[$a$1,...,$ an$]$

and B $=[$b$1,...,$ bn$]($you can assume that these are always correct$).$ At the beginning of each year

i$,$ you can place all your investment money entirely in A or entirely in B$.$ It is guaranteed that

your money should multiply by ai $($if you invested in A$)$ or by bi $($if you invested in B$)$ by the end

of year i$.$ However, if you move your money from A to B or B to A when transitioning to the next

year, you lose half your money.

Given the return on investments for the next n years as arrays of multipliers A $=[$a$1,...,$ an$]$

and B $=[$b$1,...,$ bn$],$ design an algorithm to determine the maximum multiplier you can achieve

on your initial investment by the end of year n$.$

Example: Lets say that A $=[4,2,3,1]$ and B $=[1,2,3,3].$ You should place your money in

investment A in years $1,2,$ and $3($to have your initial investment multiply by $423=24).$ Then,

you would transfer your money from A to B$,$ which would cut your money in half $($now you only

have a $12$x multiplier on your initial investment$).$ By the end of year $4,$ you would achieve a $36$x

multipler on your initial investment. Your algorithm should return $36$ in this case.