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

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

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

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