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

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

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