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

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

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

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