Titanic

Three friends are big film geeks.  One of them knows how many times two of them have seeen titanic. She sends a text letting them know that they have each seen titanic and that one of them has seen it one more time than the other. The respond with the following:

"Did you watch Titanic more than I did?"

"I have no idea!"

"Me neither, do you know now?"

Yes, indeed"

"Really? Then so do I!"

So, the question is: What is the sum of the possible number of times that one of them watched titanic