Time Limit: 3000 MS Memory Limit: 65536 K
Have you ever read any description of some encryption algorithm? These descriptions almost
always include messages being sent between Alice and Bob. We (the people organizing the
2011 Central Europe Regional Contest) think that those descriptions are too impersonal ¡ª
considering these two people are probably the most famous cryptographers in the whole world,
we know so little about them. They deserve more attention, don¡¯t you think? We can learn
about their hobbies, for instance.
In their free time, Alice and Bob like to play a game inspired by Tron. In this game, you race a car
through a square grid and you need to avoid hitting obstacles placed in the grid. Furthermore,
the car leaves a permanent trail, which you also need to avoid. The car only moves in the four
cardinal directions (east, west, north, or south). In their version of the game, Alice and Bob
alternate in controling the car¡ªAlice starts, moves the car from its initial position to one of the
adjacent positions in the grid, then Bob takes over and moves the same car to another adjacent
The player who crashes the car (i.e., moves it to a position occupied by an obstacle, or to one
of the previously visited positions) loses. Both Alice and Bob are incredibly skilled players and
never make mistakes; in particular, they only crash if there is no possible move from their current
position that would avoid it. Given the map of the obstacles, your task is to determine which
player wins from which initial position.
The input contains descriptions of several game fields. The first line of each description contains
two integers N and E (1 <= N,E <= 100) ¡ª the size of the grid in the north-south and in the
east-west directions. The following N lines describe the map. Each of the lines contains a string
of E characters, where the j-th character on the i-th line determines the state of the position
with coordinates (j, i). The possible characters are ¡°.¡± (a dot) if the position is empty and
the uppercase letter ¡°X¡± if there is an obstacle. All positions not covered by the map (i.e., with
coordinates (j, i) such that i <= 0 or j <= 0 or i > N or j > E) are forbidden and not used in the
game, they work as if there were obstacles.
The last game field is followed by a line containing two zeros.
For each game field, output N lines of strings of length E, showing whether Alice or Bob wins
when the game starts from the given location. The j-th character on the i-th line should be
¡°A¡± if Alice wins when starting from the position (j, i), ¡°B¡± if Bob wins, or ¡°X¡± if the position
contains an obstacle.
After each output, print one empty line.