<|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 6 2 6 7 1 8 6 4 9 1 6 9 5 9 9 9 5 2 6 3 2 7 1 1 1 0 0
Output: 2 6 7 1 8 6 4 9 1 6 9 5 9 9 9 5 2 6 3 2 7 1 1 1 0 0 0 0 6

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

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

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 0 0 0 0 0 0 8 8 9 3 6 2 6 5 8 5 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