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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 5 6 1 4 2 9 8 9 7 1 1 1 8 6 2 5 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