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

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

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

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