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

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

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

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