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 0 0 0 7 2 4 9 6 2 4 9 1 3 4 7 4 3 5 8 2 5 0 0 0
Output: 0 0 0 0 0 7 2 4 9 6 2 4 9 1 3 4 7 4 3 5 8 2 5 0 0 0 0 0 0 0

Example 2:
Input:  9 4 6 5 5 7 3 1 7 8 5 4 4 2 7 4 8 1 3 1 5 4 3 5 6 4 1 9 4 6
Output: 5 7 3 1 7 8 5 4 4 2 7 4 8 1 3 1 5 4 3 5 6 4 1 9 4 6 9 4 6 5

Example 3:
Input:  8 4 4 2 9 1 9 9 8 4 3 6 5 8 5 1 2 3 7 9 8 6 2 7 1 9 9 0 0 2
Output: 9 1 9 9 8 4 3 6 5 8 5 1 2 3 7 9 8 6 2 7 1 9 9 0 0 2 8 4 4 2

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