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

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

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

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