OSN 2017 Problem 2

Five people are gathered in a meeting. Some pairs of people shakes hands. An ordered triple of people $(A,B,C)$ is a trio if one of the following is true:

• A shakes hands with B, and B shakes hands with C, or
• A doesn't shake hands with B, and B doesn't shake hands with C.

If we consider $(A,B,C)$ and $(C,B,A)$ as the same trio, find the minimum possible number of trios.