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

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

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

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