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

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

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

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