In a car factory there are two assembly lines, called A and $B.$ Each of them consists of $N$ positions numbered from $0$ to $N-1.$ In each position, some component is installed

into the car being assembled. The lines are symmetric; that is$,$ the same component is installed into the car in the corresponding positions of A and B$.$

In order to assemble a car, it needs to get through all of the positions on the assembly lines. It takes $A[K]$ minutes to install the component in the K$-$th position on line $A,$ and

$B[K]$ minutes to install it on line $B.$

After installing a component in the K$-$th position, the car can either be moved to the next position on the same line $($which happens automatically and takes $0mi$

$u$ tes or it

can be moved to the other line. Switching from line A to line B takes $x$ minutes, and switching from line $B$ to line A takes $Y$ minutes.

The assembly process can be started in either line.

Write a function:

def solution$(A,B,x,Y)$

that, given arrays A and $B$ consisting of $N$ integers each, and integers $x$ and $Y,$ returns the minimum time required to assemble an entire car.

Examples:

Given $A=[1,6,2],B=[3,2,5],x=2$ and $Y=1,$ the function should return $8.$ The assembly of the car can start in line A$.$ After installing the component in position number $0$

$(1$ minute$),$ the car can be moved to assembly line $B(2$ minutes$)$ to install the component in position number $1(2$ minutes$),$ and move the car back to line A $(1$ minute$),$ where

the last component would be installed $(2$ minutes$).$ The total time is $1+2+2+1+2=8.$

Given $A=[2,11,4,4],B=[9,2,5,11],x=8$ and $Y=4,$ the function should return $21.$ It is optimal to assemble the entire car on line A$.$

Given $A=[1,10,1],B=[10,1,10],x=1$ and $Y=5,$ the function should return $9.$

Given $A=[8,3,3],B=[6,1,10],x=4$ and $Y=3,$ the function should return $13.$

Write an efficient algorithm for the following assumptions:

$N$ is an integer within the range $[1.\mathrm{.}100,000]$;

each element of arrays A and B is an integer within the range $[1.\mathrm{.}20,000]$;

$x$ and $Y$ are integers within the range $[1.\mathrm{.}20,000].$