A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 1 6 6 8 0 0 0 0 0 0 0 0 0 0 7 8 2 3 5 5 8 8 1 9 9
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>.
Assistant: Let me solve this step by step.
<think>
user