<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 8 4 7 2 5 1 7 1 3 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8
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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user