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:  3 3 4 0 0 7 0 0 9 3 0 0 9 0 9 4 6 0 0 6 0 4 7 0 0 3 5 9 0
Output: 5 5 5 0 0 5 0 0 5 5 0 0 5 0 5 5 5 0 0 5 0 5 5 0 0 5 5 5 0

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

Example 3:
Input:  4 7 8 8 0 8 3 7 7 4 0 0 0 5 0 0 5 3 6 0 7 2 8 0 7 0 0 4 1
Output: 5 5 5 5 0 5 5 5 5 5 0 0 0 5 0 0 5 5 5 0 5 5 5 0 5 0 0 5 5

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 0 4 0 8 0 6 0 3 5 5 0 0 8 0 3 0 0 1 3 0 5 2 7 7 8 2 9 8
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