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

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

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

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 8 3 6 2 8 8 1 6 3 8 6 7 2 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