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おじゃまします ojama shimasu
Sorry to intrude — said at every door.
What does ojama shimasu mean?
Announced as you step into someone's home, even a close friend's. Literally I'm about to be a nuisance, which is charmingly pessimistic for a greeting.
Example
おじゃまします、と言って玄関を上がった。
I said "sorry to intrude" and stepped up into the house.
Vibe
Who you can say this to, and how it lands.
Safe to use Fine in ordinary conversation.
The story behind ojama shimasu
Announced in the doorway of any home you enter, including your best friend's, this greeting literally declares that you are about to be an obstruction. Jama comes from Buddhist vocabulary, where it named the demonic interference that blocks a practitioner's path, which makes it a wonderfully dramatic ancestor for a phrase you say while taking off your shoes.
The grammar is the polite part. You flag the trouble first so the host can wave it away. On the way out you switch to the past tense, ojama shimashita, sorry for having been in the way, and the same phrase softens a phone call, a shop visit, even leaving a video meeting early. Politeness here is mostly good timing.