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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 5 4 6 7 0 0 7 5 8 4 1 1 7 8 3 1 9 8 6 4 4 8 3
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