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

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

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

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