<|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 9 4 6 7 3 3 9 7 1 3 0 0 0 0 0 0 2 6 8 2 8 8 5
Output: 6 7 3 3 9 7 1 3 0 0 0 0 0 0 2 6 8 2 8 8 5 5 9 4

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 9 6 8 6 3 6 3 9 1 6 0 0 0 0 3 5 3 1 4 1 1 8 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