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Night travel to Cappadocia from Istanbul?

I've seen that there are pretty cheap buses to Cappadocia from Istanbul (about $35 and 10 hours) to Urgup. I would really like to make this an adventure from my trip to turkey, but I would like to conserve on time. Is it possible to take a bus/train/other mode of transport overnight to Urgup from Istanbul? I would fit me best to travel like this: night of April 18:travel overnight to Urgup April 19: Explore Urgup, stay here overnight April 20: Continue exploring, travel back to Istanbul this night. April 21: Fly back to central europe for school on the 22. (havn't scheduled flight yet, could make it later in the day or whatever is necesary)
-Also approximate costs would be greatly appreciated as well, Thanks!