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

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

Example 3:
Input:  1 6 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 8 1 1 9
Output: 1 9 1 6 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 8 1

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