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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 3 2 3 8 1 8 2 1 9 7 1 2 0 0 0 0 0 0 0 0 9 4 7 8 4 8 6 3
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