<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Compute the number of ways to select 99 cells of a $19 \times 19$ square grid such that no two selected cells share an edge or vertex. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
1000
Compute the number of ways to select 99 cells of a $19 \times 19$ square grid such that no two selected cells share an edge or vertex.
test