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 8 6 9 9 2 2 3 5 3 7 5 4 6 9 8 1 1 3 4 1 7
Output: 8 6 9 9 2 2 3 5 3 7 5 4 6 9 8 1 1 3 4 1 7 5

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

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

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