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:  0 0 8 3 7 2 8 9 5 7 8 6 9 8 2 8 2 6
Output: 0 8 3 7 2 8 9 5 7 8 6 9 8 2 8 2 6 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 7 4 4 5 6 6 1 1 5 5 4 2 3 3 9 9 6
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