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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 4 4 2 6 4 1 4 1 2 8 4 0 0 2
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