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

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

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

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