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:  0 0 0 0 0 0 3 5 2 4 2 5 5 9 5 2 9 4 9 9 1 1 4 1 1 2 1 3 0 0
Output: 3 0 0 0 0 0 0 0 0 3 5 2 4 2 5 5 9 5 2 9 4 9 9 1 1 4 1 1 2 1

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

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

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