Ensuring Minimum Manhattan Distance

Given a grid of characters with 'B' representing special markers and other cells containing digits, your task is to verify that every pair of 'B' in the grid is at least a specified Manhattan distance d apart. The Manhattan distance between two cells at coordinates \((i_1,j_1)\) and \((i_2,j_2)\) is defined as \(|i_1-i_2|+|j_1-j_2|\). If any two 'B' cells are closer than d, the configuration is invalid and you must output "Impossible". Otherwise, output the grid in the same format (each row as a string).

The input starts with an integer t specifying the number of test cases. For each test case, the first line contains three integers n, m, and d — the number of rows, columns, and the required minimum Manhattan distance. This is followed by n lines each consisting of a string that represents a row of the grid.

For each test case, if the grid satisfies the condition, output the grid with each row on a new line. Otherwise, output a single line with the word "Impossible".

inputFormat

The input is given via standard input and has the following format:

t
n m d
row1
row2
... 
rown
... (repeated t times)

Here, t is the number of test cases. For each test case, n and m denote the number of rows and columns of the grid, and d is the required minimum Manhattan distance. Each of the following n lines represents a row of the grid.

outputFormat

For each test case, output the result on standard output. If the grid satisfies the condition (i.e. every two 'B' cells are at least a Manhattan distance of d apart), then output n lines representing the modified grid. If the condition is not satisfied, output a single line: Impossible.

Note: For multiple test cases, outputs are printed consecutively in the order of input.

## sample

3
3 3 2
B0B
000
B0B
4 5 3
B302B
00000
00000
B400B
3 3 2
BBB
000
BBB

B0B
000
B0B
B302B
00000
00000
B400B
Impossible

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