<|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
 There are 5 mathematics trainee teachers to be allocated among three second-year high school classes for internship, with at least 1 and at most 2 teachers in each class. How many different allocation schemes are there? 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
90
There are 5 mathematics trainee teachers to be allocated among three second-year high school classes for internship, with at least 1 and at most 2 teachers in each class. How many different allocation schemes are there?
test