<|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:  0 0 8 7 4 1 1 2 2 3 5 1 5 1 0
Output: 0 0 1 5 1 5 3 2 2 1 1 4 7 8 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 2 7 4 7 1 7 8 7 6 6 8 7 3 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