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:  2 5 5 6 8 0 0 0 0 0 0 0 8 6 7 2 8 3 2 9 5
Output: 6 8 0 0 0 0 0 0 0 8 6 7 2 8 3 2 9 5 2 5 5

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

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

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