For how many integers $n$ where $2 \le n \le 100$ is $\binom{n}{2}$ odd?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For how many integers $n$ where $2 \le n \le 100$ is $\binom{n}{2}$ odd?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
50
For how many integers $n$ where $2 \le n \le 100$ is $\binom{n}{2}$ odd?
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