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 3 4 9 1 7 2 1 2 2 7 1 1 3 9 9 8
Output: 9 9 8 9 3 4 9 1 7 2 1 2 2 7 1 1 3

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

Example 3:
Input:  2 5 1 7 1 4 0 0 0 0 0 0 8 6 2 8 9
Output: 2 8 9 2 5 1 7 1 4 0 0 0 0 0 0 8 6

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 9 4 9 7 5 3 0 0 0 0 0 0 0 7 1 6
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