<|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 class has 25 students. The teacher wants to prepare $N$ candies for a competition and distribute them according to scores (students with the same score get the same number of candies, and those with lower scores get fewer candies, which can be 0). What is the minimum value of $N$ that allows such distribution, regardless of how many questions there are in the competition or how the students perform? 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
600
A class has 25 students. The teacher wants to prepare $N$ candies for a competition and distribute them according to scores (students with the same score get the same number of candies, and those with lower scores get fewer candies, which can be 0). What is the minimum value of $N$ that allows such distribution, regardless of how many questions there are in the competition or how the students perform?
test