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 3 6 5 9 8 8 1 2 0 0 0 0 0 9 9
Output: 0 9 9 4 3 6 5 9 8 8 1 2 0 0 0 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 4 9 5 5 0 0 0 2 8 3 6 8 7 9 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>.
Assistant: Let me solve this step by step.
<think>
user