<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  9 2 2 8 6 8 3 7 7 3 3 9 2 3 2 6 3
Output: 3 2 6 3 9 2 2 8 6 8 3 7 7 3 3 9 2

Example 2:
Input:  5 4 9 9 0 0 1 6 1 7 7 1 1 1 8 4 6
Output: 1 8 4 6 5 4 9 9 0 0 1 6 1 7 7 1 1

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 7 7 8 7 1 0 0 0 0 0 0 0 0 0 8 2
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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user