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

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

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

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