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:  4 4 9 5 3 4 1 4 3 6 6 9 6 6 6 7 5 5 3 6 5 0 0 0 0 0 0 0 0
Output: 5 3 4 1 4 3 6 6 9 6 6 6 7 5 5 3 6 5 0 0 0 0 0 0 0 0 4 4 9

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

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

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