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Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Goal

A (2-)neighbor-sum grid is a 5×5 matrix containing each number from 1 to 25 exactly once and where each value that is at least 3 can be obtained as the sum of two distinct values among its direct neighbors (horizontally, vertically and diagonally, so that an inner cell has 8 neighbors, a border cell has 5 neighbors and a corner cell has 3 neighbors).

Example: (21 = 4+17, 14 = 4+10, 10 = 4+6, 16 = 6+10, 22 = 6+16, etc for every value >2 of the grid)
`21 14 10 16 2217  4  1  6 1912  3  5 11 1315  8  2  7 1823 24  9 20 25`

It can be proven that there are 56816 such grids (or 7102 up to the 8 symmetries of the square).

In this problem, you are given a partially completed grid (in which unknown values are indicated by a 0 in the input) and you are asked to complete it. It is guaranteed for each given testcase that there exists a unique solution.
Input
5 lines of 5 space-separated numbers between 0 and 25, 0 indicating an unknown value.
Output
5 lines of 5 space-separated numbers between 1 and 25 corresponding to the unique complete solution.
Constraints
Example
Input
```21 14 10 0 0
0 4 1 6 0
0 3 5 11 13
15 0 0 0 0
23 24 0 20 25
```
Output
```21 14 10 16 22
17 4 1 6 19
12 3 5 11 13
15 8 2 7 18
23 24 9 20 25
```

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