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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 2 7 2 2 1 8 2 4 5 3 8 3 7 3 7 4 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