Find a solution for an uncompleted [Sudoku](https://en.wikipedia.org/wiki/Sudoku) board. If there are more than 1 solutions, print any of them.
It is guaranteed that at least 1 solution exist.
### Input
- 9 lines, each line contains 9 integers in range $[0, 9]$. Number 0 means blank cell.
### Output
- 9 lines, each line contains 9 integers in range $[1, 9]$, one possible solution.
### Constraints
### Example
Input:
```
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
```
Output:
```
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
```
