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

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

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

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