"If the gym is too hot, I get a headache, " said Marquez-Munoz.

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Other than the prospect of modestly lower electricity rates a year or two down the road, all they would get out of the deal is a headache.

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He has a pounding sinus headache that he needs to get rid of so he can return to his job as a logistics manager at his dad's chemical company.

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It's an odd predicament, to say the least, but if you're familiar with the kind of off-field trouble that professional athletes can get into, an imaginary girlfriend doesn't sound like much of a headache for human resources.

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