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

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

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

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