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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 4 3 0 0 0 0 6 4 4 3 8 4 8 8 3 6 2 8 4 6 3 7
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