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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 9 2 7 1 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 4
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