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

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

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

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