Jumping Robot

Ali invents a jumping robot. This robot is controlled by a program {D_i}, which is a finite sequence of non-negative “jumping distances”. The program can’t be changed once the robot is made.
There are L boxes in a line. Each time the robot is placed in one of the boxes, facing left or right, and then it is turned on. It first jumps over D₁ boxes, then jumps over D₂ boxes ...
Ali writes a capital letter in each box. The robot prints out all the letter it touches, including the initial one. Now he wants to design a program with a length of p, so that for every kind of letters in the boxes, if you carefully choose the initial position and direction of the robot, it can print out a sequence of that letter of length p.
What’s the maximum possible p for the given letters in boxes?

The input consists several testcases.
The first line contains 2 integers n (4 <= n <= 8) and L (4 <= L <= 100), represents the number of different capital letters and the number of boxes.
The second line contains a string whose length is exactly L, represents the letters in each box. The string only contains the first n capital letters, and each letter appears at least once in the string.

Print an integer, the maximum length of the jumping program.

4 15
DABCDDCCBAACBBA

3

2011 Alibaba-Cup Campus Contest