While on a globetrotting spree, Ted and Darren kept in touch with each other via the Internet, mostly through chat rooms. Whenever a user logged out of the chat room, the chat applet showed the logout time, like your computer clock, to the other person.

Here is a sample of their conversation.

Ted: Today I saw a statue with the head of a lion and the body of a fish.
Darren: Hey, I was just visiting a structure with the head of a man and the body of a lion.

At the end of the chat, Ted logged out, and Darren immediately followed suit.They chatted again some time later, and their logout times were exactly the reverse of their earlier logout times. In other words, Ted's logout time was the same as Darren's earlier logout time. And Darren's logout time ws the same as Ted's earlier time. Quite a coincidence!
Can you guess where Ted and Darren are?