Sudoku Solver

Solve the classic Sudoku puzzle. Given a partially filled \(9\times 9\) grid, complete the grid so that every row, every column, and every \(3\times 3\) sub-grid contains all of the digits from 1 to 9 exactly once.

You are guaranteed that the puzzle has a unique solution. Use backtracking or any efficient algorithm to fill in the missing cells (represented by 0).

inputFormat

The input consists of 9 lines. Each line contains 9 space-separated integers, where 0 represents an empty cell and the numbers 1-9 represent the digits already filled in the Sudoku board.

outputFormat

Output the solved Sudoku board in exactly 9 lines, where each line contains 9 space‐separated integers.

5 3 0 0 7 0 0 0 0
6 0 0 1 9 5 0 0 0
0 9 8 0 0 0 0 6 0
8 0 0 0 6 0 0 0 3
4 0 0 8 0 3 0 0 1
7 0 0 0 2 0 0 0 6
0 6 0 0 0 0 2 8 0
0 0 0 4 1 9 0 0 5
0 0 0 0 8 0 0 7 9

5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9