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

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

Example 3:
Input:  5 0 5 1 2 2 9 6 1 9 6 5 3 1 1
Output: 2 2 9 6 1 9 6 5 3 1 1 5 0 5 1

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 4 4 9 6 7 9 4 9 9 3 8 6
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