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:  4 2 7 9 8 4 6 5 7 3 5 8 0 0 0 0 0 0 0 0 0 5 6 6 9 5 1 8 5 3
Output: 8 4 6 5 7 3 5 8 0 0 0 0 0 0 0 0 0 5 6 6 9 5 1 8 5 3 4 2 7 9

Example 2:
Input:  2 4 1 9 6 8 6 4 8 3 9 8 1 7 0 0 0 0 0 0 9 1 8 3 7 9 6 9 9 5
Output: 6 8 6 4 8 3 9 8 1 7 0 0 0 0 0 0 9 1 8 3 7 9 6 9 9 5 2 4 1 9

Example 3:
Input:  2 7 7 1 4 5 3 3 5 6 7 2 1 9 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 4 5 3 3 5 6 7 2 1 9 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 7 1

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