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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0
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