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

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

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

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