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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 8 0 0 5 1 9 4 5 1 2 5 4 8 3 6 2 9 8 4 1 4 8 7 2
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