MAKEMAZE - VALIDATE THE MAZE

There are many algorithms to generate maze. (http://en.wikipedia.org/wiki/Maze_generation_algorithm). After generating the maze we’ve to validate whether it’s a valid maze or not. A valid maze has exactly one entry point and exactly one exit point (exactly 2 openings in the edges) and there must be at least one path from the entry point to exit point.

Given a maze, just find whether the maze is "valid" or "invalid".

Input

The first line consists of an integer t, the number of test cases. Then for each test case, the first line consists of two integers m and n, the number of rows and columns in the maze. Then contains the description of the matrix M of order mxn. M[i][j]=# represents a wall and M[i][j]='.' represents a space.

Output

For each test case find whether the maze is "valid" or "invalid".

Constraints

1<=t<=10000

1<=m<=20

1<=n<=20

Example

Input:
6
4 4
####
#...
#.##
#.##
5 5
#.###
#..##
##..#
#.#.#
###.#
1 1
.
5 1
#
#
.
.
#
2 2
#.
.#
3 4
#..#
#.##
#.##

Output:
valid
valid
invalid
valid
invalid
invalid

Added by:cegprakash
Date:2012-05-11
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU

hide comments
2017-08-03 22:00:51
.


Last edit: 2017-08-07 10:31:15
2017-06-18 20:59:23
good problem to try :) [spoiler] figure out base cases ac in 5 th go :)

Last edit: 2017-08-02 13:07:16
2017-04-12 20:59:56 candide
The problem is well settled and the description is clear although the question being academic. The problem receives a [big spoiler sentence] (i implemented both for comparison purpose).

Last edit: 2017-08-02 13:08:15
2017-03-15 21:24:27
AC :) Just apply [spoiler]

Last edit: 2017-03-22 18:44:46
2017-03-15 04:43:26
AC in 1 go . used backtracking.
Thanks @s1234 for the hint . Key point ...
More than two opening even if they are not connected will cause invalid:
##.#
.#.#
##.#
##.# is invalid.


Last edit: 2017-03-15 04:44:56
2017-02-27 15:30:07
can be solved with backtracking
2016-10-21 15:05:18 cegprakash
vandan1177 : invalid
2016-10-16 13:19:21
Is "....." valid or invalid?
2016-10-04 22:25:04
finally understood [spoiler] ^_^ credits @pulkitgulati

Last edit: 2016-10-21 15:05:55
2016-09-21 15:05:09
đm ez vcl các bạn ei
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