LABYR1  Labyrinth
The northern part of the Pyramid contains a very large and complicated labyrinth. The labyrinth is divided into square blocks, each of them either filled by rock, or free. There is also a little hook on the floor in the center of every free block. The ACM have found that two of the hooks must be connected by a rope that runs through the hooks in every block on the path between the connected ones. When the rope is fastened, a secret door opens. The problem is that we do not know which hooks to connect. That means also that the neccessary length of the rope is unknown. Your task is to determine the maximum length of the rope we could need for a given labyrinth.
Input
The input consists of T test cases. The number of them (T) is given on the first line of the input file.
Each test case begins with a line containing two integers C and R (3 <= C,R <= 1000) indicating the number of columns and rows. Then exactly R lines follow, each containing C characters. These characters specify the labyrinth. Each of them is either a hash mark (#
) or a period (.
). Hash marks represent rocks, periods are free blocks. It is possible to walk between neighbouring blocks only, where neighbouring blocks are blocks sharing a common side. We cannot walk diagonally and we cannot step out of the labyrinth.
The labyrinth is designed in such a way that there is exactly one path between any two free blocks. Consequently, if we find the proper hooks to connect, it is easy to find the right path connecting them.
Output
Your program must print exactly one line of output for each test case. The line must contain the sentence "Maximum rope length is X.
" where Xis the length of the longest path between any two free blocks, measured in blocks.
Example
Sample Input: 2 3 3 ### #.# ### 7 6 ####### #.#.### #.#.### #.#.#.# #.....# ####### Sample output: Maximum rope length is 0. Maximum rope length is 8.Warning: large Input/Output data, be careful with certain languages
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Rishabh:
20150608 11:50:46
"there is exactly one path between any two free blocks". Does this means that there will be only one connected component (island) ? 

Shubham Bansal:
20150518 16:04:01
sometimes something easy may also be misleading :P


eightnoteight:
20150109 07:38:32
after solving this question, try to solve PT07Z


Mitch Schwartz:
20140808 15:34:53
@arbit: Read the problem statement carefully. 

arbit:
20140808 11:24:10
Can I assume that there will not be any inputs like this?


Francky:
20130429 23:17:57
@ Mohammed ElAnsary:


Mohammed ElAnsary:
20130429 22:26:28
Can an input be in this format?


যোবায়ের:
20091006 19:17:22
Similar problem http://www.spoj.pl/problems/PT07Z/ 
Added by:  adrian 
Date:  20040606 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  ACM Central European Programming Contest, Prague 1999 