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 9 6 2 0 0 0 0 0 0 0 9 9 4 8 7 6 1 7 8 1 7 8 8 5
Output: 7 8 8 5 2 8 9 6 2 0 0 0 0 0 0 0 9 9 4 8 7 6 1 7 8 1

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

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

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