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

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

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

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