<|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:  6 9 4 8 2 9 6 2 1 1 4 8 4 2 8 1 2 2 7 9 9 1 0 0 0 0 8 4 7 8
Output: 4 8 2 9 6 2 1 1 4 8 4 2 8 1 2 2 7 9 9 1 0 0 0 0 8 4 7 8 6 9

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 2 0 0 0 0 0 0 0 0 3 3 6 2 2 5 6 7 5 9 4 2 1 2 4 2 7 1 7 5
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