<|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:  8 0 0 6 8 9 1 2 4 7 1 2 6 1 3
Output: 2 6 1 3 8 0 0 6 8 9 1 2 4 7 1

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

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

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