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:  5 8 5 2 5 1 9 0 1 6 5 9 2 6 5 3 5 5
Output: 5 2 5 1 9 0 1 6 5 9 2 6 5 3 5 5 5 8

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

Example 3:
Input:  9 9 9 3 7 0 3 5 6 9 2 4 8 2 6 8 4 2
Output: 9 3 7 0 3 5 6 9 2 4 8 2 6 8 4 2 9 9

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