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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 2 9 2 7 9 6 3 7 4 6 9 6 6 7
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