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

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

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

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