Problem $1$:

$[12$ pts$]$

The Metropolitan Transportation Authority $($MTA$)$ in New York City has introduced a new fare system based on the zones of the subway stations. The city is divided into three zones:

Zone $1$: Manhattan

Zone $2$: Brooklyn and Queens

Zone $3$: The Bronx and Staten Island

The fare rules are as follows:

Traveling within the same zone costs $$2\mathrm{.}50.$

Traveling between Zone $1$ and Zone $2$ costs $$3\mathrm{.}50.$

Traveling between Zone $1$ and Zone $3$ costs $$4\mathrm{.}50.$

Traveling between Zone $2$ and Zone $3$ costs $$3\mathrm{.}00.$

The MTA provides a map of stations and their corresponding zones as follows:

$\backslash$table$[[$Station$,$Zone$],[$Times Square,$1],[$Grand Central,$1],[$Williamsburg$,2],[$Astoria$,2],[$Bronx Zoo,$3],[$Staten Island Terminal,$3]]$

Define a function calculateFare that takes two arguments:

The starting station $($a string$),$

The ending station $($a string$).$

The function should return the total fare based on the zones of the starting and ending stations. Assume that the map of stations and their zones is available within the function using a simple associative map.

Example:

$\backslash$table$[[$Starting Station,Ending Station,Fare $($$$)],["$Times Square","Grand Central",$2\mathrm{.}5],["$Times Square","Williamsburg",$3\mathrm{.}5],["$Williamsburg$",$"Astoria",$2\mathrm{.}5],["$Astoria$",$"Bronx Zoo",$3\mathrm{.}0],["$Grand Central","Staten Island Terminal",$4\mathrm{.}5]]$

Note: Assume that the input will always contain a valid station name. You do not need to handle for invalid station names.