<|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:  9 2 2 6 4 8 8 6 5 1 8 7 5 5
Output: 5 5 7 8 1 5 6 8 8 4 6 2 2 9

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 9 4 1 5 0 0 0 0 0 0 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