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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 3 2 3 6 3 1 8 2 6 9 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
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