<|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:  5 1 3 7 7 1 5 6 4 1 2 6 7 4 7 2
Output: 7 2 5 1 3 7 7 1 5 6 4 1 2 6 7 4

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

Example 3:
Input:  4 1 3 4 4 8 7 0 0 0 0 0 0 0 7 4
Output: 7 4 4 1 3 4 4 8 7 0 0 0 0 0 0 0

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