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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 3 2 9 8 2 2 6 7 8 7 1 0 0 0 0 9 1 5 2 7 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