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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 8 9 2 2 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 8 8 3 3 7 6 6 8
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