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:  4 4 7 2 3 3 9 8 9 7 7 8 7 3 6
Output: 8 7 3 6 4 4 7 2 3 3 9 8 9 7 7

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 9 5 5 9 4 9 9 4 0 0 0 0 9 9
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