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

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

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

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