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

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

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

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