<|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:  5 6 4 7 8 7 7 0 9 2 8 4 3 9 2 1 6 2 3 7 7 2 8 1 3 3 2
Output: 8 7 7 0 9 2 8 4 3 9 2 1 6 2 3 7 7 2 8 1 3 3 2 5 6 4 7

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

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

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