I had a sex dream and didn't ejaculate

I had a sex dream last night (there was no penetration but there was other sexual activities). There was no orgasm during the dream and when I woke up, I didn't find anything on my clothes, so basically I didn't ejaculate. My question is, do I have to take a shower(ghusl) even though I didn't ejaculate? Just because I had a dream about something sexual? If I don't take a shower, will that break my fast?