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

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

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

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