<|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
 A magician has a set of $20^{2}$ different cards. Each card has one red side and one blue side; on each card, there is a natural number from 1 to 20 written on both sides. We call a card a double if the numbers on both sides of the card are the same. The magician wants to draw two cards in such a way that at least one of them is a double, and no number appears simultaneously on both drawn cards. In how many ways can he do this? 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
7030
A magician has a set of $20^{2}$ different cards. Each card has one red side and one blue side; on each card, there is a natural number from 1 to 20 written on both sides. We call a card a double if the numbers on both sides of the card are the same. The magician wants to draw two cards in such a way that at least one of them is a double, and no number appears simultaneously on both drawn cards. In how many ways can he do this?
test