<|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:  3 5 3 3 4 0 4 1 5 6 7 7 4 1 7 4 1 1 9
Output: 5 3 3 4 0 4 1 5 6 7 7 4 1 7 4 1 1 9 3

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 2 1 5 3 2 0 0 0 0 0 0 0 0 8 5 2 7 5
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