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

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

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

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 0 7 5 8 6 8 7 5 7 3 7 3 4 8 6 9 5 1 9 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