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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 3 6 8 4 4 9 3 2 9 9 3 7 3 2 0 0 0 0 0 0 6 4 1 4
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