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:  9 1 4 3 4 1 4 7 2 0 0 0 0 0 0 0 5 9 6 5 3 3
Output: 1 4 3 4 1 4 7 2 0 0 0 0 0 0 0 5 9 6 5 3 3 9

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

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

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