FDNY to the Rescue!

Time Limit: 2 Seconds
Memory Limit: 65536 KB

The Fire Department of New York (FDNY) has always been proud of their response
time to fires in New York City, but they want to make their response time even
better. To help them with their response time, they want to make sure that the
dispatchers know the closest firehouse to any address in the city. You have
been hired to write this software and are entrusted with maintaining the proud
tradition of FDNY. Conceptually, the software will be given the address of the
fire, the locations of the firehouses, street intersections, and the time it
takes to cover the distance between each intersection. It will then use this
information to calculate how long it takes to reach an address from each firehouse.

Given a specific fire location in the city, the software will calculate the
time taken from all the fire stations located in the city to reach the fire
location. The list of fire stations will be sorted from shortest time to longest
time. The dispatcher can then pick the closest firestation with available firefighters
and equipment to dispatch to the fire.

**Input Format:**

Line 1:

# of intersections in the city, a single integer (henceforth referred to as
N) N<20

Lines 2 to N+1:

A table (square matrix of integer values separated by one or more spaces) representing
the time taken in minutes between every pair of intersections in the city. In
the sample input shown below the value ��3�� on the 1st row and the 2nd column
represents the time taken from intersection #1 to reach intersection #2.

Similarly the value ��9�� on the 4th row and the 2nd column represents the time
taken from intersection #4 to reach intersection #2.

A value of -1 for time means that it is not possible to go directly from the
origin intersection (row #) to the destination intersection (column #). All
other values in the table are non-negative.

Line N+2:

An integer value n (<= N) indicating the intersection closest to the fire
location followed by one or more integer values for the intersections closest
to the fire stations (all on one line, separated by one or more spaces) will
follow the input matrix.

Notes on input format:

1. The rows and columns are numbered from 1 to N.

2. All input values are integers

3. All fire locations are guaranteed reachable from all firehouses.

4. All distance calculations are made from the intersection closest to each
firehouse to the intersection closest to the fire.

**Output Format:**

Line 1:

A label line with the headings for each column, exactly as shown in the example.

Line 2 onwards (one line for each fire station):

A sorted list (based on time) showing the fire station (origin), the destination
site, time taken and a complete shortest path of nodes from the originating
fire station to the fire location.

Notes on output format:

1. Columns are tab separated.

2. If two or more firehouses are tied in time they can be printed in any order.

3. If more than one path exists that has the same minimal time for a given location
& firehouse, either one can be printed on the output.

4. If the fire location and the fire station locations happen to be the same
intersection, the output will indicate that the origin and destination have
the same intersection number, the time will be ��0�� and the nodes in the shortest
path will show just one number, the fire location.

**This problem contains multiple test cases!**

The first line of a multiple input is an integer N, then a blank line followed
by N input blocks. Each input block is in the format indicated in the problem
description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between
output blocks.

**Sample Input:**

1

6

0 3 4 -1 -1 -1

-1 0 4 5 -1 -1

2 3 0 -1 -1 2

8 9 5 0 1 -1

7 2 1 -1 0 -1

5 -1 4 5 4 0

2 4 5 6

In the above input the last line indicates that ��2�� is the location of the
fire and ��4��, ��5�� and ��6�� are the intersections where fire stations are located.

Sample Output:

Org Dest Time Path

5 2 2 5 2

4 2 3 4 5 2

6 2 6 6 5 2

Source:

**Mid-Atlantic USA 2001**
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