<|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 5 4 2 7 3 8 8 2 0 0 0 0 0 0 0 5
Output: 7 3 8 8 2 0 0 0 0 0 0 0 5 1 5 4 2

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 8 6 9 8 5 0 0 9 2 3 1 9 9 3 5 4
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