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

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

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