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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 5 9 4 5 8 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 5 9 4 5 8 0 0 0 0 0

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