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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 8 6 1 8 4 9 8 0 0 0 1 7 8 8 6 4 5 4 7 8 5 7 7 6 4 7
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