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 8 1 6 1 2 3 2 4 0 4 8 8 3 7 7 5
Output: 3 7 7 5 1 5 8 1 6 1 2 3 2 4 0 4 8 8

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 4 9 1 2 6 9 1 6 9 9 9 1 7 5 9 3 1
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