<|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:  8 4 1 4 0 0 0 0 0 0 0 8 1 7 1 8 6 4 2 4 6
Output: 4 6 8 4 1 4 0 0 0 0 0 0 0 8 1 7 1 8 6 4 2

Example 2:
Input:  3 2 2 7 7 9 5 6 8 0 0 0 5 4 1 2 2 2 3 9 7
Output: 9 7 3 2 2 7 7 9 5 6 8 0 0 0 5 4 1 2 2 2 3

Example 3:
Input:  5 5 2 3 6 7 3 3 1 7 7 0 0 0 1 7 2 9 7 2 3
Output: 2 3 5 5 2 3 6 7 3 3 1 7 7 0 0 0 1 7 2 9 7

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 2 7 1 4 2 8 7 3 9 8 7 9 1 1 1 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