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:  2 3 5 6 8 8 6 0 6 5 7 5 5 8 5 3 2
Output: 3 2 2 3 5 6 8 8 6 0 6 5 7 5 5 8 5

Example 2:
Input:  5 8 6 3 8 8 9 1 4 8 8 8 1 0 8 6 8
Output: 6 8 5 8 6 3 8 8 9 1 4 8 8 8 1 0 8

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 1 4 2 2 9 9 0
Output: 9 0 0 0 0 0 0 0 0 0 0 0 1 4 2 2 9

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