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 2 3 7 6 3 2 2 3 7 8 3 4 6 6 6 8 2 8 4 7 8 8 2
Output: 7 8 8 2 6 2 3 7 6 3 2 2 3 7 8 3 4 6 6 6 8 2 8 4

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

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

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