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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 8 1 1 0 0 0 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