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

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

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

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