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

Example 2:
Input:  2 4 8 1 1 5 0 0 0 0 0 0 0 1 2 5 8 7
Output: 8 1 1 5 0 0 0 0 0 0 0 1 2 5 8 7 2 4

Example 3:
Input:  2 0 0 0 0 0 0 0 3 1 5 8 5 5 1 2 1 5
Output: 0 0 0 0 0 0 3 1 5 8 5 5 1 2 1 5 2 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 5 0 0 4 1 3 2 9 1 3 5 5 7 6 9 1 7
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