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

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

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

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