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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 4 6 8 9 1 5 6 9 1 5 5 0 0 0 0 0 0 0 0 3 4 6 1 1 3
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