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

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

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

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