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

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

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

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