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

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

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

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