Just another storage question (from Japan)

Hey everybody, this is my first time posting here. I used to smoke cigars occasionally until I moved to Japan. Did I quit? No way. After discovering that Cubans are in ready supply over here (and having a real salary, aaaand the fact that smoking isn't as readily frowned upon as it is in the US), my smoking has increased by a bit. I have a humidor (unfortunately, discounts don't exist in Japan. Everything is sold at list price, so I had to get a cheap humidor for the price of a decent one), but have a question about cigar storage.

Although I've been smoking cigars since I was sixteen (now 26) I've never been a "serious" smoker. I'd like to think I have some knowledge about cutting, lighting, and etiquette, but my knowledge of storage is basically nil.

I regularly buy small boxes of club sized cigars (Partaga) and mini cigars (Cohiba). I'd like to keep them in my humidor, but I don't know if I can leave them in the box. Should I take them out before putting them in?

Thanks!