<|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:  0 0 0 9 9 6 1 9 9 9 9
Output: 0 0 0 9 9 9 9 9 9 9 9

Example 2:
Input:  3 8 6 6 6 8 6 6 6 0 0
Output: 6 6 6 6 6 6 6 6 6 0 0

Example 3:
Input:  3 3 3 1 1 3 3 3 3 3 0
Output: 3 3 3 3 3 3 3 3 3 3 0

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