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

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

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

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