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:  7 8 6 5 5 5 5 7 0 0 0 0 2 4 2 4 9 1
Output: 2 4 9 1 7 8 6 5 5 5 5 7 0 0 0 0 2 4

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

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

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