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

Example 2:
Input:  7 9 2 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3 4 4 7 1 7 9
Output: 7 9 7 9 2 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3 4 4 7 1

Example 3:
Input:  7 8 7 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 2 3 9 8 1 1 7 5
Output: 7 5 7 8 7 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 2 3 9 8 1 1

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