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

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

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