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:  0 0 0 0 0 0 0 2 5 3 4 4 5 3 1 4 5 3 7 6 3 5 0
Output: 0 0 0 0 0 0 0 5 3 6 7 3 5 4 1 3 5 4 4 3 5 2 0

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

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

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