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

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

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

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