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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6
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