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Many people think that Tetris was invented by two Russian programmers. But that is not the whole truth.
The idea of the game is very old - even the Egyptians had something similar. But they did not use it as a game.
Instead, it was used as a very complicated lock. The lock was made of wood and consisted of a large number
of square fields, laid out in regular rows and columns. Each field was either completely filled with wood, or empty.
The key for this lock was two-dimensional and it was made by joining square parts of the same size as
the fields of the lock. So they had a 2D lock and 2D key that could be inserted into the lock from the top.
The key was designed so that it was not possible to move it upwards. It could only fall down and it could
slide sideways - exactly like in a Tetris game. The only difference is that the key could not be rotated.
Rotation in Tetris is really a Russian invention.
Input
The input consists of T test cases. The number of them (T) is given on the first line of the input file.
Each test case begins with a line containing two integers R and C (1<=R,C<=100) indicating the key size.
Then exactly R rows follow, each containing C characters. Each character is either a hash mark (#) or a period (.).
A hash mark represents one square field made of wood; a period is an empty field. The wooden fields
are always connected, i.e. the whole key is made of one piece. Moreover, the key remains connected even
if we cut off arbitrary number of rows from its top. There is always at least one non-empty field in
the top-most and bottom-most rows and the left-most and right-most columns.
After the key description, there is a line containing two integers D and W (1<=D<=10000, 1<=W<=1000).
The number W is the lock width, and D is its depth. The next D lines contain W characters each.
The character may be either a hash mark (representing the wood) or a period (the free space).
Output
Your program should print one line of output for each test case. The line should contain the statement
"The key falls to depth X.". Replace X with the maximum depth to which the key can be inserted by moving
it down and sliding it to the left or right only. The depth is measured as the distance between the bottom side
of the key and the top side of the lock. If it is possible to move the key through the whole lock and take
it away at the bottom side, output the sentence "The key can fall through.".
Sample
| Input | Output |
|---|
4
2 4
#.##
###.
3 6
#....#
#....#
#..###
2 3
##.
.##
2 7
#.#.#.#
.#.#.#.
1 1
#
1 10
###....###
3 2
##
.#
.#
1 5
#.#.# | The key falls to depth 2.
The key falls to depth 0.
The key can fall through.
The key falls to depth 2. |
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