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:  6 7 0 0 0 0 0 0 0 0 0 0 0 7 5 8 4 5 5 6 5 3 4 6 1
Output: 3 4 6 1 6 7 0 0 0 0 0 0 0 0 0 0 0 7 5 8 4 5 5 6 5

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

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

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