<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 1 3 9 8 6 4 0 4 2 8 6 4 3 5
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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user