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

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

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

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