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

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

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

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