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

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

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

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