##
2000/2001 ACM SOUTHERN CALIFORNIA REGIONAL

SCHOLASTIC PROGRAMMING CONTEST

####
Problem 6

Team Packing

file: teampack.cc

Every year Swamp County holds its regional collegiate programming contest. One
part of running the programming contest is assigning teams to workstations. The
organizers attempt to locate teams such that teams from the same school are not
assigned workstations close to each other. In the past this has been an ad hoc
process. Your team will develop an application to allow the organizers to compare
their ad hoc workstation assignments with the best possible layout. Input to
your program is a list of Cartesian coordinates of workstation locations (in
integer feet) followed by one line per school giving the number of teams from the
school and the school name. There will be a maximum of 14 workstations, and 4
teams per school. The last workstation will always be located at `0,0'. The
dimensions of the largest possible workstation lab are 200 by 200 feet. Also, the
number of teams will not exceed the number of workstations, and there will always
be at least one school with at least two teams. The input file may contain
more than one scenario; in this case, the scenarios will be separated by a
line of ten dashes (see the sample input below).

Output from your program is the
square of the minimum distance between any two teams from the same school after
teams have been assigned workstations that maximize this distance. The output is
one line containing the left-justified integer value that is the squared
distance.

#### Sample Input

3,0 6,0 9,0
0,2 3,2 6,2 9,2
0,5 3,5 6,5 9,5 14,3 14,6 0,0
3 Bogy U
3 Gator State
1 Armadillo Tech
2 CFTBL City College
1 Moss Institute
3 SC Polytechnic
----------
100,100 0,100 100,0 0,0
2 HMC
1 BYU
1 UVM

#### Sample Output

34
20000