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

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

Example 3:
Input:  9 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 6 5
Output: 5 9 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 6

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