<|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:  2 8 4 3 6 7 1 5 4 3 0 0 0 9 1 5
Output: 5 2 8 4 3 6 7 1 5 4 3 0 0 0 9 1

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 1 3 1 2 9 6 0 0 1 5 5 8 4 8 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