Space Invaders

Yesterday my home was infiltrated by two space invaders.
Cockroaches as big as my fist that can fly! Which explains how they levitated up to the 15th floor.
But I still can't figure out how they got inside the apartment. I had the sliding doors open but the screens were closed.
Anyway-I heroically rose to the occasion. Blasting them at close range with the cockroach killer spray. Both struggled to survive-one flying through the room, me in chase and spraying madly. My friend who was visiting was completely useless. She ran screaming from the room. Ugh. Makes me want to move back to Alaska where there aren't any of these nasty creatures.