21761_FigureansSpots

Let's consider an infinite sheet of grid paper. Initially all the cells are white and you can paint some of them black.

Two cells are called 8-neighbours if they share a side or a corner. An 8-path between black cells A and B is a sequence of cells X₀ = A , X₁, ..., X_L-1, X_L = B such that all cells in the sequence are black and for all 0 ≤ i < L the cells X_i and X_i+1 are 8-neighbours. A set of black cells is called a figure if there is an 8-path from each of them into each other.

Two cells are called 4-neighbours if they share a side. A 4-path between white cells A and B is a sequence of cells X₀ = A, X₁, ..., X_L-1 , X_L = B such that all cells in the sequence are white and for all 0 ≤ i < L the cells X_i and X_i+1 are 4-neigbours. A finite set of white cells is called a spot if:

• There is a 4-path from each of them into each other.

• The previous condition is broken when any other white cell is added to the set.

We say that a figure has the height H and the width W if it fits in a rectangle H rows high and W columns wide, but does not fit in a rectangle H-1 rows high and W columns wide nor in a rectangle H-1 rows high and W columns wide.

The image above shows a figure with height 7 and width 9 and containing two spots.

Given the numbers H, W and N, construct a figure with height exactly H and width exactly W and containing exactly N spots.

The input file contains several test cases. The first line of the file contains T (1 ≤ T ≤ 100), the number of test cases. Each of the following T lines describes one test case and contains three integers H, W and N (1 ≤ H, W ≤ 20, 1 ≤ N ≤ 200), separated by spaces.

The output file should contain the following data for each test case:

• If it is possible to construct a figure with the given parameters, output any of the possible figures as H rows consisting of W characters each; output the character "." for a black cell and the character "#" for a white cell.

• If it is impossible to construct the required figure, output a single line containing the word Impossible.

The output data for two different test cases should be separated by an empty line.

37
9 2
20 20 22
5 5 10

#......##
#.#.....#
#.##.....
....####.
.#..##.#.
.#..##.#.
.#.......

.#####.######.#####.
..###...####...###..
...#.....##.....#...
....................
....##..##..#...#...
...#.#.#..#.##.##...
...###.#....#.#.#...
...#.#.#..#.#...#...
...#.#..##..#...#...
....................
....................
.###..##..###...##..
..#..#..#.#..#.#..#.
..#..#....###..#....
..#..#..#.#....#..#.
.###..##..#.....##..
....................
...#.....##.....#...
..###...####...###..
.#####.######.#####.

Impossible