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

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

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

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