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

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

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

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