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

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

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

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