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

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

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

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