Solve a 9x9 Sudoku puzzle

Q: Solve a 9x9 Sudoku puzzle

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Question

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.

Solve a 9x9 Sudoku puzzle

Input

Output

Assumptions / Constraints

Example

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