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 0 0 0 0 0 0 3 4 2 2 4 7 8
Output: 7 8 1 5 0 0 0 0 0 0 3 4 2 2 4

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 3 0 5 4 3 8 9 7 3 3 3 9 3 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