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

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

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

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