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

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

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

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