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

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

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