PROBLEM STATEMENT
As a result of ever increasing traffic jams, subway transportation in big cities has become a 
must. A train can actually take you from your home to your office faster than a car can. But what 
happens if you have your office in another city? In this problem we consider three different 
cities: A, B and C. Each of these cities has its own subway transportation system and you can go 
from a station to any other in the same city without having to leave the underground. A big 
project is now underway, and the goal is to merge the subway lines such that transportation 
between these cities becomes available soon. In order to achieve this, it was decided that two 
tunnels would be constructed, each of them connecting two subway stations in two different cities. 
This has to be done at a minimal cost, so it is important which subway stations are chosen. Also 
consider that the only factor in determining the cost is the distance between the two subway 
stations connected by a tunnel. 

You will be given a int[] ax, a int[] ay, a int[] bx, a int[] by, a int[] cx and a int[] cy with 
the following signification: 
 ax and ay represent the coordinates of the subway stations in city A  i.e (ax[i],ay[i]) is the 
 point denoting the place of the i-th station
 bx and by represent the coordinates of the subway stations in city B  i.e (bx[i],by[i]) is the 
 point denoting the place of the i-th station
 cx and cy represent the coordinates of the subway stations in city C  i.e (cx[i],cy[i]) is the 
 point denoting the place of the i-th station

Return the minimal added distance of the two tunnels such that all three cities become connected.



  
  

DEFINITION
Class:ATaleOfThreeCities
Method:connect
Parameters:vector <int>, vector <int>, vector <int>, vector <int>, vector <int>, vector <int>
Returns:double
Method signature:double connect(vector <int> ax, vector <int> ay, vector <int> bx, vector <int> 
by, vector <int> cx, vector <int> cy)


NOTES
-Your return value must have an absolute or relative error less than 1e-9.


CONSTRAINTS
-ax, ay, bx, by, cx, and cy will each contain between 2 and 50 elements, inclusive.
-Each element of ax, ay, bx, by, cx, and cy is between -100 and 100, inclusive.
-The number of elements in ax is equal to the number of elements in ay.
-The number of elements in bx is equal to the number of elements in by.
-The number of elements in cx is equal to the number of elements in cy.
-There are no subway stations with identical coordinates.


EXAMPLES

0)
{0,0,0}
{0,1,2}
{2,3}
{1,1}
{1,5}
{3,28}

Returns: 3.414213562373095

The tunnel connecting the subway station in city A at (0,2) with the subway station in city C at 
(1,3) has a length of about 1.41 and the tunnel connecting the subway station in city A at (0,1) 
with the subway station in city B at (2,1) has a length of 2.

1)
{-2,-1,0,1,2}
{0,0,0,0,0}
{-2,-1,0,1,2}
{1,1,1,1,1}
{-2,-1,0,1,2}
{2,2,2,2,2}

Returns: 2.0

2)
{4,5,11,21,8,10,3,9,5,6}
{12,8,9,12,2,3,5,7,10,13}
{34,35,36,41,32,39,41,37,39,50}
{51,33,41,45,48,22,33,51,41,40}
{86,75,78,81,89,77,83,88,99,77}
{10,20,30,40,50,60,70,80,90,100}

Returns: 50.323397776611024

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