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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 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 4 7 1 6
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