A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  1 3 2 0 0 0 5 4 1 6 0 5 4 2 0 5 0 0 5 0 5 2 0 0 2 0 0 6
Output: 1 3 2 5 4 1 6 5 4 2 5 5 5 2 2 6 0 0 0 0 0 0 0 0 0 0 0 0

Example 2:
Input:  0 7 0 8 6 0 1 6 3 0 1 1 0 0 8 0 9 0 7 2 2 8 6 9 2 7 5 8
Output: 7 8 6 1 6 3 1 1 8 9 7 2 2 8 6 9 2 7 5 8 0 0 0 0 0 0 0 0

Example 3:
Input:  3 9 3 0 0 0 0 0 0 6 0 0 0 0 2 5 5 0 8 1 1 3 3 8 0 0 9 4
Output: 3 9 3 6 2 5 5 8 1 1 3 3 8 9 4 0 0 0 0 0 0 0 0 0 0 0 0 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 0 0 5 0 0 0 0 0 4 8 9 5 7 0 5 2 0 0 0 9 2 5 3 0 0 0 7
Show your work in <think> </think> tags, and return the answer in <answer> </answer> tags with space between each number. For example <answer> 1 3 5 7 </answer>.
Assistant: Let me solve this step by step.
<think>
user