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

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

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

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