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

Example 2:
Input:  9 2 3 2 6 6 3 6 1 1 9 7 0 0 0 0 0
Output: 6 6 3 6 1 1 9 7 0 0 0 0 0 9 2 3 2

Example 3:
Input:  1 9 9 7 3 7 2 6 6 0 0 0 0 6 5 6 5
Output: 3 7 2 6 6 0 0 0 0 6 5 6 5 1 9 9 7

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 4 3 1 9 2 9 2 0 0 0 0 0 0 0 0 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