490. Figure ans Spots

Time limit per test: 0.25 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard



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-neigbours if they share a side or a corner. An 8-path between black cells A and B is a sequence of cells X 0 = A, X 1, ·s, 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 X 0 = A, X 1, ·s, 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 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.

Input
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.

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

Example(s)
sample input
sample output
3
7 9 2
20 20 22
5 5 10
#......##
#.#.....#
#.##.....
....####.
.#..##.#.
.#..##.#.
.#.......

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

Impossible