<image>On a certain railway line, including the starting and ending stations, there were originally 6 stations. Now, 3 new stations have been added. The tickets for a round trip between two stations are different. How many different types of tickets need to be added?

Hint: According to the given problem, draw the line segment diagram of the original six stations A, B, C, D, E, and F, along with the newly added stations X, Y, and Z. (The positions of X, Y, and Z are not fixed; take one example for reference.)

From the above line segment diagram, it can be seen that each time a new station is added, new tickets are required between the new station and the old stations ____ (types). When 3 new stations are added, ____ types of tickets need to be added. Additionally, between the 3 newly added stations, ____ (types) of different tickets are required. Thus, a total of ____ (types) different tickets need to be added.
