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

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

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

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