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

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

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

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