<|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:  4 3 9 1 6 2 6 1 3 1 9 2 4 1 8 6 2 4 6 1 2 7 4
Output: 9 1 6 2 6 1 3 1 9 2 4 1 8 6 2 4 6 1 2 7 4 4 3

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 8 6 6 3 6 5 3 2 6 0 9 5 6 1 4 6 4 7 6 7 6 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