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

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

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

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