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

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

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