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

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

Example 3:
Input:  5 5 3 4 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6 5
Output: 6 5 5 5 3 4 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8

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