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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 6 9 6 8 0
Output: 9 6 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 6

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

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