Solve a 9x9 Sudoku puzzle

Given a partially filled **9×9 Sudoku** board, fill the empty cells so that the completed board is valid. A valid Sudoku satisfies: - Each row contains digits **1–9** with no repetition. - Each column contains digits **1–9** with no repetition. - Each of the nine **3×3 sub-boxes** contains digits **1–9** with no repetition. ### Input - A 9×9 grid of characters where each cell is either `'1'..'9'` or `'.'` (empty). ### Output - Modify the board in-place (or return the completed board) so it becomes a valid solved Sudoku. ### Assumptions / Constraints - The input is guaranteed to have **at least one solution**. - You may assume the puzzle has a **unique solution** unless stated otherwise. ### Example Input: - Row 1: `5 3 . . 7 . . . .` - Row 2: `6 . . 1 9 5 . . .` - ... Output: a completed valid Sudoku grid.