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

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

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

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