<|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 4 4 3 3 5 3 5 8 8 0 0 0 0 3 8 4 6 1 1 7 3
Output: 3 5 3 5 8 8 0 0 0 0 3 8 4 6 1 1 7 3 1 4 4 3

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

Example 3:
Input:  5 2 9 3 9 9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
Output: 9 9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 2 9 3

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