<|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
 While waiting for customers, a watermelon seller sequentially weighed 20 watermelons (weighing 1 kg, 2 kg, 3 kg, ..., 20 kg), balancing a watermelon on one side of the scale with one or two weights on the other side (possibly identical). The seller recorded the weights he used. What is the minimum number of different numbers that could appear in his records if the weight of each weight is an integer number of kilograms? 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
6
While waiting for customers, a watermelon seller sequentially weighed 20 watermelons (weighing 1 kg, 2 kg, 3 kg, ..., 20 kg), balancing a watermelon on one side of the scale with one or two weights on the other side (possibly identical). The seller recorded the weights he used. What is the minimum number of different numbers that could appear in his records if the weight of each weight is an integer number of kilograms?
test