<|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 2 6 3 7 1 8 9 9 6 2 2 6 2 6 8 0 0 0 0 0 0 0
Output: 6 3 7 1 8 9 9 6 2 2 6 2 6 8 0 0 0 0 0 0 0 0 0 0 2

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

Example 3:
Input:  1 4 4 1 3 4 5 3 9 4 2 5 7 1 8 1 0 0 0 0 0 6 2 5 6
Output: 3 4 5 3 9 4 2 5 7 1 8 1 0 0 0 0 0 6 2 5 6 1 4 4 1

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 2 1 1 9 6 6 3 0 0 0 0 0 0 0 0 0 0 0 0 3 7 7 7 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