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 3 2 0 0 0 0 0 0 0 0 0 0 0 0 6 3 1
Output: 0 0 0 0 0 0 0 0 0 0 0 6 3 1 2 3 2 0

Example 2:
Input:  1 4 1 2 8 2 6 4 4 0 2 6 9 2 1 1 6 6
Output: 8 2 6 4 4 0 2 6 9 2 1 1 6 6 1 4 1 2

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

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