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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 6 2 5 3 5 8
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 8 5 3 5 2 6

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