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

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

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

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