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

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

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

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