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

Example 2:
Input:  3 1 2 4 6 7 2 8 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 3 3 2 4
Output: 2 4 6 7 2 8 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 3 3 2 4 3 1

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 2 8 6 9 5 7 5 4 6 5 4 3 7 9 2 3 6 8 5 9 7 9 9 9 9 2
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