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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 8 0 0 0 0 0 0 0 0 0 3 1 7 2 7 9 2 5 8 5 5 2 2 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