<|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
 Between 1 and 200, how many numbers have the sum of all their distinct prime factors equal to 16? (For example: The distinct prime factors of 12 are 2 and 3, and their sum is $2+3=5$). 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
Between 1 and 200, how many numbers have the sum of all their distinct prime factors equal to 16? (For example: The distinct prime factors of 12 are 2 and 3, and their sum is $2+3=5$).
test