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 4 4 4 4 6 3 8 8 7 6 3 3 1 4 2 7 7
Output: 4 4 6 3 8 8 7 6 3 3 1 4 2 7 7 7 4 4

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

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

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