## 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

hide comments
 rp007: 2015-07-24 09:27:41 Awesome Question (BFS+BFS) "Maja aa gaya Tel Laga Ke" .... :-) goyal: 2015-07-11 16:24:40 maja aa gaya tel laga k:) i think first try pt07z and then this tarunsai: 2015-07-06 09:21:23 very easy BFS+BFS :) SangKuan: 2015-07-01 05:30:55 17 wa,now got ac...o(∩∩)o...use dfs or bfs,not esay Rishabh: 2015-06-08 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: 2015-05-18 16:04:01 sometimes something easy may also be misleading :-P eightnoteight: 2015-01-09 07:38:32 after solving this question, try to solve PT07Z damn i'm tired of translating my python code to cpp code whenever there are strict constraints. please increase the time limit. there isn't a single submission in python Mitch Schwartz: 2014-08-08 15:34:53 @arbit: Read the problem statement carefully. arbit: 2014-08-08 11:24:10 Can I assume that there will not be any inputs like this? ##### #...# #...# #...# ##### I mean where there are more than one paths from a dot to another. Should we expect inputs like this too? Francky: 2013-04-29 23:17:57 @ Mohammed El-Ansary: Read description -> "The labyrinth is designed in such a way that there is exactly one path between any two free blocks", so your sample is impossible according to this rule.

 Added by: adrian Date: 2004-06-06 Time limit: 5s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All Resource: ACM Central European Programming Contest, Prague 1999