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:  6 2 1 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 1 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 0 0 4 5 8 4 6 8 1 8 1 9 2 1 7 5 9 7 3 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