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

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

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