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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 1 7 4 1 5 3 5 1 9 0
Output: 5 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 1 7 4 1 5 3

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