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

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

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

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