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

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

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

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