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

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

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

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