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

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

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

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