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

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

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

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