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:  4 7 2 8 4 5 5 6 3 3 0 0 0 0 0 7 9 7 2 7 9
Output: 7 9 4 7 2 8 4 5 5 6 3 3 0 0 0 0 0 7 9 7 2

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 2 3 0 0 0 0 0 0 0 0 1 5 4 8 6 8 7 5 3 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