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

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

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

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