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

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

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

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