<|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 8 6 5 7 4 7 2 7 2 6 5 6 2 7 3
Output: 0 3 7 2 6 5 6 2 7 2 7 4 7 5 6 8

Example 2:
Input:  9 1 1 2 8 3 5 8 6 2 7 1 8 6 1 2
Output: 2 1 6 8 1 7 2 6 8 5 3 8 2 1 1 9

Example 3:
Input:  0 0 0 0 9 8 3 2 4 1 6 5 7 3 4 5
Output: 0 0 0 0 5 4 3 7 5 6 1 4 2 3 8 9

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 1 3 7 7 8 5 4 7 2 5 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