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 1 1 7 9 8 7 9 2 8 8 8 7 2 2 6 4 0 0 0 0 0 0 1 5 5 8
Output: 8 5 1 1 7 9 8 7 9 2 8 8 8 7 2 2 6 4 0 0 0 0 0 0 1 5 5

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

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

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