<|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 5 9 6 2 0 0 0 5 2 2 6 8 6 5
Output: 6 2 0 0 0 5 2 2 6 8 6 5 1 5 9

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 5 7 8 2 8 2 5 4 1 3 1 3 2 7
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