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:  0 0 0 0 0 0 1 5 1 7 3 1 6 4 6 3 6 3 2 1 1 1 3 0 0 0
Output: 0 0 0 0 0 0 0 0 0 1 5 1 7 3 1 6 4 6 3 6 3 2 1 1 1 3

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 7 6 3 6 4 4 4 4 6 8 1 8 6 7 4 9 8 2 5 9 7 0 8 3 2
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