<|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:  6 8 8 0 0 0 0 0 0 0 4 6 5 4 2 9 9 1
Output: 9 1 6 8 8 0 0 0 0 0 0 0 4 6 5 4 2 9

Example 2:
Input:  8 8 7 4 0 0 0 0 0 0 0 0 0 0 0 7 4 3
Output: 4 3 8 8 7 4 0 0 0 0 0 0 0 0 0 0 0 7

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 5 9 9 8 9 1 8 1 8 1 5 9 8 9 2 7 7
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