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 0 0 0 0 0 0 0 0 0 0 0 6 3 2 6 2 7 7 4 4 8 1 6
Output: 4 8 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 3 2 6 2 7 7 4

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

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

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