<|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:  1 6 2 2 2 2 2 7 3 6 5 1 3 2 2 7 4 8 9 3 8 4 2 9 7 1 7
Output: 2 2 2 7 3 6 5 1 3 2 2 7 4 8 9 3 8 4 2 9 7 1 7 1 6 2 2

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 8 4 5 6 7 7 5 8 5 7 1 0 0 0 0 0 1 8 5 4 3 8 6 1 7 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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user