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

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

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

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