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

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

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