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

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

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

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