Sudoku

You get an unfinished Sudoku board with 9 rows and 9 columns. Each cell is a char. It is a digit from '1' to '9', or '.' for an empty cell.

Return the board with every empty cell filled in.

The finished board must follow three rules:

1. Each row holds the digits 1 to 9 once.
2. Each column holds the digits 1 to 9 once.
3. Each 3 x 3 block holds the digits 1 to 9 once. The thick lines in the picture below mark the nine blocks.

The digits already on the board stay where they are.

Example 1:

Input: board = [
  [".","3","8",".",".","2",".",".","."],
  [".","1",".","3",".",".","2",".","."],
  [".",".",".",".","7","4","5",".","."],
  [".",".",".",".","5","6",".","7","."],
  ["6",".","5","7",".","1","3",".","4"],
  [".","7",".","8","4",".",".",".","."],
  [".",".","3","2","6",".",".",".","."],
  [".",".","6",".",".","8",".","5","."],
  [".",".",".","5",".",".","7","2","."]
]
Output: [
  ["5","3","8","6","9","2","4","1","7"],
  ["4","1","7","3","8","5","2","6","9"],
  ["2","6","9","1","7","4","5","3","8"],
  ["3","8","4","9","5","6","1","7","2"],
  ["6","9","5","7","2","1","3","8","4"],
  ["1","7","2","8","4","3","6","9","5"],
  ["9","5","3","2","6","7","8","4","1"],
  ["7","2","6","4","1","8","9","5","3"],
  ["8","4","1","5","3","9","7","2","6"]
]
Explanation: The puzzle is drawn above.
It has exactly one solution, drawn below.
The digits you add are in blue.

Constraints:

• The board is always 9 rows of 9 cells.
• A cell is a digit from '1' to '9' or '.' (empty).
• Every puzzle you get has exactly one solution.