Problem
B: Fire!
Joe
works in a maze. Unfortunately, portions of the maze have caught on fire, and
the owner of the maze neglected to create a fire escape plan. Help Joe escape
the maze.
Given
Joe‘s location in the maze and which squares of the maze are on fire, you must
determine whether Joe can exit the maze before the fire reaches him, and how
fast he can do it.
Joe
and the fire each move one square per minute, vertically or horizontally (not
diagonally). The fire spreads all four directions from each square that is on
fire. Joe may exit the maze from any square that borders the edge of the maze.
Neither Joe nor the fire may enter a square that is occupied by a wall.
Input
Specification
The
first line of input contains a single integer, the number of test cases to
follow. The first line of each test case contains the two integers R and C,
separated by spaces, with 1 <= R, C<=
1000. The following R lines of the test case each contain
one row of the maze. Each of these lines contains exactly C characters, and each of these
characters is one of:
- #, a wall
- ., a passable square
- J, Joe‘s initial position in the maze, which is a passable
square - F, a square that is on fire
There
will be exactly one J in each test case.
Sample
Input
2
4 4
####
#JF#
#..#
#..#
3 3
###
#J.
#.F
Output
Specification
For
each test case, output a single line containing IMPOSSIBLE if Joe cannot exit the maze before
the fire reaches him, or an integer giving the earliest time Joe can safely exit
the maze, in minutes.
Output
for Sample Input
3
IMPOSSIBLE
?
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