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

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

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

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