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

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

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

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 1 5 9 6 5 5 1 0 0 0 0 0 0 0 0 0 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