Get The Treasure

One day, a team of archaeologists found a figure and some ancient charactors at a relique. The figure was made up of n points distributing on a circle symmetrically.
After investigating the charactors, they got to know that a treasure was hid beneath the figure. In order to open the door to the treasure, they must redraw all the lines between any two points in the figure with some colors. If the figure was right, the door would open.
Now they want to know how many times they have to try at most to open the door, and they ask you for help.

Each test case contains an integer n and a string S in a line. n is the number of points in the figure and S is a string made up of distinct capital letters, each indicating a color that can be used to redraw the figure. 3 <= n <= 50.

Each case outputs the maximum times they may try in one line. Note that two figures are considered the same if one can be obtained by having rotation and mirroring on the other one.

3 BW
3 RGB
4 RG

4
10
19

GUAN, Yao

ZOJ Monthly - October 2006