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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 5 8 6 6 9 2 3 4 9 5 0 0 0 0 0 9 5 1 2 3 4 3 1 1
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