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

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

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

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