<|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:  7 9 9 1 7 6 3 2 7 3 3 4 7 0 1 9 6
Output: 9 6 7 9 9 1 7 6 3 2 7 3 3 4 7 0 1

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 2 6 4 8 5 7 3 3 3 4 3 6 9 0 0 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