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 8 2 3 0 0 0 0 0 0 0 0 0 3 1 8 2 5 9
Output: 9 9 1 8 2 3 0 0 0 0 0 0 0 0 0 3 1 8 2 5

Example 2:
Input:  9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6 5
Output: 5 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6

Example 3:
Input:  1 4 9 8 7 8 4 1 8 7 5 8 0 0 5 7 2 3 7 8
Output: 8 1 4 9 8 7 8 4 1 8 7 5 8 0 0 5 7 2 3 7

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 5 4 4 3 5 3 8 4 4 9 0 1 8 4 2 2 7 1 1
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