<|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:  2 4 0 0 1 9 7 4 5 8 7 2 2 3 8 2 2 4
Output: 0 0 1 9 7 4 5 8 7 2 2 3 8 2 2 4 2 4

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 9 7 5 1 2 3 9 5 5 6 5 1 1 5 9 9 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