A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  8 3 6 7 1 6 1 3 1 1 1 3 1 7 6
Output: 6 7 1 3 1 1 1 3 1 6 1 7 6 3 8

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 5 5 6 3 6 1 6 2 1 2 4 6 5 7
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>.
Assistant: Let me solve this step by step.
<think>
user