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

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

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

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