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

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

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