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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 2 9 2 7 4 9 6 2 6 3 2 8 4 6 1 0 0
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