Find the coefficient of $x^{49}$ in the expansion of
\[(x + 1)(x + 3)(x + 5) \dotsm (x + 95)(x + 97)(x + 99).\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the coefficient of $x^{49}$ in the expansion of
\[(x + 1)(x + 3)(x + 5) \dotsm (x + 95)(x + 97)(x + 99).\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2500
Find the coefficient of $x^{49}$ in the expansion of
\[(x + 1)(x + 3)(x + 5) \dotsm (x + 95)(x + 97)(x + 99).\]
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