<|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:  5 9 2 0 0 0 9 5 2 1 6 1 2 8 3 8
Output: 2 8 3 8 5 9 2 0 0 0 9 5 2 1 6 1

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

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

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