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

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

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