Gorilla Toe
------- ---

Gorilla Toe is a game just like Tic Tac Toe with the
following differences.  First, the game is played on
a board with N rows and M columns of squares, where
3 <= N,M <= 6.  Second, to win you must occupy min(N,M)
adjacent squares in a row or a column or a diagonal
(so on a board with 3 rows and 5 columns you must
occupy 3 adjacent squares in a row, a column, or a
diagonal).  Third, just before the game beings, a bunch
of gorillas rushes out and occupies some squares, where
they sit quietly during the rest of the game.  You
cannot occupy a square occupied by a gorilla - you just
will not fit!

You have been asked to write a player's assistant which,
when given a board state with P being the next player to
move, will label each unoccupied square according to the
fate of P if P moves next to that square and then both
players play optimally.

As in Tic Tac Toe, the players are X who moves first and
O who moves second.


Input
-----

For each of several test cases, first a line with the
test case name, then N lines of M columns, where N is
the number of rows and M the number of columns, and
then a single line containing just `.'.

The characters of the N lines of M columns describe the
state of the board, with one character for each square
containing:

	X	If the square is occupied by X.
	O	If the square is occupied by O.
	G	If the square is occupied by a gorilla.
	.	If the square is unoccupied.

No input line is longer than 80 characters.  Input ends
with an end of file.



Output
------

For each test case, an exact copy of the input, but with
the `.'s replaced by one of the following indicators of
what will happen if P moves to the `.'ed square and then
both players play optimally:

	W	if P will win
	L	if P will lose
	T	if the game will tie


Sample Input
------ -----

-- SAMPLE 1 -
...
.XO
...
.
-- SAMPLE 2 --
...G.
.OX.G
.....
.
-- SAMPLE 3 --
...GO
.GXOG
...XG
.


Sample Output
------ ------

-- SAMPLE 1 -
WWW
TXO
WWW
.
-- SAMPLE 2 --
TWTGL
LOXLG
TLTLL
.
-- SAMPLE 3 --
LWLGO
LGXOG
LLWXG
.


File:	   gorillatoe.txt
Author:	   Bob Walton <walton@seas.harvard.edu>
Date:	   Sat Sep  1 08:12:28 EDT 2012

The authors have placed this file in the public domain;
they make no warranty and accept no liability for this
file.

RCS Info (may not be true date or author):

    $Author: walton $
    $Date: 2012/09/01 12:16:39 $
    $RCSfile: gorillatoe.txt,v $
    $Revision: 1.4 $