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:  5 1 6 1 1 6 2 5 1 2 6 5 0 7
Output: 7 5 1 6 1 1 6 2 5 1 2 6 5 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 3 5 5 6 6 0 0 0 0 0 0 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