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Problem of the day

You have been given a 9x9 2d integer matrix 'MAT' representing a Sudoku puzzle. The empty cells of the Sudoku are filled with zeros, and the rest of the cells are filled with integers from 1 to 9. Your task is to fill all the empty cells such that the final matrix represents a Sudoku solution.

```
A Sudoku solution must satisfy all the following conditions-
1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
3. Each of the digits 1-9 must occur exactly once in each of the 9, 3x3 sub-grids of the grid.
You can also assume that there will be only one sudoku solution for the given matrix.
```

Detailed explanation

```
Size of MAT is 9x9
0 <= MAT[i][j] <= 9
where an empty cell is given by 0 in the matrix.
```

```
The output is consists of 9 lines. Each line contains 9 single space-separated integers where the empty cells from the input matrix are replaced by some integers.
```

```
You are not required to print anything, and it has already been taken care of. Just implement the function.
```

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

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

```
In the output:
In each row, each of the digits 1-9 is occurring exactly once.
In each column, each of the digits 1-9 is occurring exactly once.
In each 3x3 sub-grids of the grid, each of the digits is occurring exactly once.
```