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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 9 4 1 7 4 7 1 7 9 7 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