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:  3 4 4 2 5 9 1 6 7 2 5 1 5 3 5 7 9 5 8 3 7 3 8 6 9 8 7
Output: 9 8 7 3 4 4 2 5 9 1 6 7 2 5 1 5 3 5 7 9 5 8 3 7 3 8 6

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

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

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