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:  2 1 4 5 4 4 5 5 8 3 8 3 8 7 2 0 1
Output: 4 5 4 4 5 5 8 3 8 3 8 7 2 0 1 2 1

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

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

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