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

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

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