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 1 4 7 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 3 7 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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

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