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
2015-11-02 06:03:58 Anubhav Gupta
Input contains spaces!!! lots of WA's because of that
2015-10-24 12:16:39 jarvis
Detained from class tests :P :P AC :D here!
2015-10-23 13:47:36 hardik agrawal
first bfs! nice problem... my 101st.. :)
2015-09-11 09:22:10 sri
####
#...
#.##
#.##
is this valid or not?
how?
2015-08-09 21:00:04 AJEET KUMAR
constraint for m and n in question is not valid. take your array size much greater for example 1000.
2015-06-06 17:57:40 viraj
Pay special attention to "(exactly 2 openings in the edges)".
2015-04-28 14:28:47 Usama
what are the answer of these

.#.
.##

and

#...#

?

Last edit: 2015-04-28 14:32:12
2015-02-26 15:04:16 Subrat Singh
finally done :)

Last edit: 2015-02-27 15:29:33
2014-12-15 13:13:03 Malfple
I don't get it...Checked overbound already~~WA. Used another absurd checking~~AC
2014-09-09 13:39:08 Girish Rathi
easy one with simple solution
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