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

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

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

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