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:  9 2 6 7 4 1 9 4 8 5 9 9 5 5 2 3 8
Output: 4 1 9 4 8 5 9 9 5 5 2 3 8 9 2 6 7

Example 2:
Input:  9 3 1 9 5 0 0 0 0 0 0 5 1 4 1 2 9
Output: 5 0 0 0 0 0 0 5 1 4 1 2 9 9 3 1 9

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 4 5 6 1 8 9 2 7 7 9 8 8 6 7 8 8
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