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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 9 7 3 6 7
Output: 3 6 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 9 7

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 8 8 5 4 3 0 2 1 9 5 3 5 4 2 4 3 7 3 1 6 4 7 6 3 9 4 6 6
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