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

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

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

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