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

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

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

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