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

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

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

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