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

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

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

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