Children of the Candy Corn

Description

The cornfield maze is a popular Halloween treat.
Visitors are shown the entrance and must wander through the maze facing zombies,
chainsaw-wielding psychopaths, hippies, and other terrors on their quest to find
the exit.

One popular maze-walking strategy guarantees that the visitor
will eventually find the exit. Simply choose either the right or left wall,
and follow it. Of course, there‘s no guarantee which strategy (left or right)
will be better, and the path taken is seldom the most efficient. (It also
doesn‘t work on mazes with exits that are not on the edge; those types of mazes
are not represented in this problem.)

As the proprieter of a cornfield
that is about to be converted into a maze, you‘d like to have a computer program
that can determine the left and right-hand paths along with the shortest path so
that you can figure out which layout has the best chance of confounding
visitors.

Input

Input to this problem will begin with a line
containing a single integer n indicating the number of mazes. Each maze will
consist of one line with a width, w, and height, h (3 <= w, h <= 40),
followed by h lines of w characters each that represent the maze layout. Walls
are represented by hash marks (‘#‘), empty space by periods (‘.‘), the start by
an ‘S‘ and the exit by an ‘E‘.

Exactly one ‘S‘ and one ‘E‘ will be
present in the maze, and they will always be located along one of the maze
edges and never in a corner. The maze will be fully enclosed by walls (‘#‘),
with the only openings being the ‘S‘ and ‘E‘. The ‘S‘ and ‘E‘ will also be
separated by at least one wall (‘#‘).

You may assume that the maze exit
is always reachable from the start point.

Output

For each maze in the input, output on a single
line the number of (not necessarily unique) squares that a person would visit
(including the ‘S‘ and ‘E‘) for (in order) the left, right, and shortest paths,
separated by a single space each. Movement from one square to another is only
allowed in the horizontal or vertical direction; movement along the diagonals
is not allowed.

Sample Input

2

8 8

########

#......#

#.####.#

#.####.#

#.####.#

#.####.#

#...#..#

#S#E####

9 5

#########

#.#.#.#.#

S.......E

#.#.#.#.#

#########

Sample Output

37 5 5

17 17 9