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:  3 6 0 0 0 0 0 0 0 8 4 3 3 2 8 2 8 8 3 2 9 5 8
Output: 5 8 3 6 0 0 0 0 0 0 0 8 4 3 3 2 8 2 8 8 3 2 9

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

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

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