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

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

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

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