Authorities say the blaze broke out at around 2:15 am Monday on the third floor of the building.
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Firefighters arrived at the scene on East Gun Hill Road and spent about an hour extinguishing the flames.
The three people who were injured in the fire are all expected to recover.
Citizen app video shows a large presence of fire trucks and a ladder extended upward near the building.
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Officials are investigating the cause of the fire.
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