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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 3 1 3 8 1 3 8 3 8 8 7 4 3 6 7 3 2 3 7 3 3 7 1 8 3 3 2 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