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

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

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

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