There were so much mind swaps in this ep I am not sure if I can recall them all, let's see...
The plots are: Fansworth and Amy build a mind sapping machine, after heaps of dead monkeys. Farnworth: Science can't move forward without heaps!
Then Leela thinks Fry only likes her because of her looks, and Bender wants to steal a crwn from the robt emperor of robo-hungary.
First Amy and Farnworth swap, and them Bender swpa with Farnworth, meaning Amy is in the prof's body, Bender in Amy's and Farnworth in Bender's. At the emperor's ship, Bender isn't believed to be a robot, and he proves it by moonwalking. He meets the emperor and as the emperor wishes to be a normal guy, Bender takes him to the Planet Express. Meanwhile Amy and Leela swap as Leela wants to see a movie with a discount. So now Leela is on the professor's body and Amy is in Leela's.
Professor: I'm afraid we will have to use...........math!
The Professor is trying to figure out a solution, but then deicdes to run away onto a circus. Meanwhile, Fry tries to porve Leela wrong, and swaps with Zoidberg. Then FRy and Leela go out ( in Zoidberg and Farnworth bodies) to Elzar's. Bender and the emperor return and then, Bender's in the emperor's body, the emperor is on a robotic wash bucket's and the wash bucket is on Amy's.
so, Bender is at the UN when the emperor's fiancee and cousin come to kill him and unmask him, , but then Farnworth sees it on the TVbot and launches himself to the UN via Big BErtha (a robot cannon) to save him. A japanses gets his arm cut, only to find out moments later via translator LOL. Then Fry and Leela have sex in Dr. and Prof bodies(DISTURBING DISTURBING!). Wash bucket proclaims his love to Scruffy but he says their love is forbidden and leaves her. Zoidberg tries to convince the emperor he is Fry and blows up the apartment
Zoidberg: The person who owns this body has a friend!
Then Hermes and amy swap as Leela's body was to fat, and they both get their bodsies thinner, and then when they all want to return to their bodies, with a little help of the Harlem Globetrotters, they all go back to their bodies (the writers inventes and proved a theorem just for this ep, and the theorem itself appeared for seconds!)
The epiosde was amazing, non-stop comedy. 10/10.