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

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

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

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