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 5 6 5 5 9 2 0 0 0 0 3 1 1 9 6 4 4 1
Output: 5 6 5 5 9 2 0 0 0 0 3 1 1 9 6 4 4 1 8

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

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

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