<|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
 From the 100 positive integers $1, 2, \cdots, 100$, remove 50 integers such that in the remaining integers, for any two different integers $a$ and $b$, the sum $a + b$ is not among the remaining integers. Find the maximum possible sum of the integers that are removed. 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
2165
From the 100 positive integers $1, 2, \cdots, 100$, remove 50 integers such that in the remaining integers, for any two different integers $a$ and $b$, the sum $a + b$ is not among the remaining integers. Find the maximum possible sum of the integers that are removed.
test