<|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 3 2 7 2 0 0 0 0 6 6 6 4
Output: 2 0 0 0 0 6 6 6 4 7 3 2 7

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

Example 3:
Input:  1 4 7 8 3 7 3 1 7 3 2 4 3
Output: 3 7 3 1 7 3 2 4 3 1 4 7 8

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