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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 4 6 1 0 0 2 8 5 9 9 7 5 5 9 7 2 5 2
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