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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 1 1 1 4 4 8 4 1 3 3 3 4 6 8 7 8 7 2 6 5 1 4 6 3 3 3
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