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

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

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