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:  5 8 1 7 7 4 4 8 8 6 1 0 0 0 0 0 0 9 9 2 5
Output: 5 5 8 1 7 7 4 4 8 8 6 1 0 0 0 0 0 0 9 9 2

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 8 5 3 8 2 5 6 0 0 0 0 0 0 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