Candy Cross

This problem is a heavily simplified version of a popular candy game, which we call Candy Cross. The board is a single column of $R$ cells. Each cell holds a candy of one of three kinds, A, B, or C. You may make up to $N$ moves. In each move, you swap two adjacent candies so that a row of at least three equal candies forms. If no move is possible, the game ends.

After a move, every candy that belongs to such a row disappears. If several rows form at once, they all disappear together. The candies above the holes then fall down to fill them. The column is always refilled to full height with new candies. To decide which new candies fall in, imagine the original column copied upward into an infinitely tall column.

Once the holes are filled, a new situation may arise, and the process repeats automatically. Candies in rows disappear, and the holes are refilled. This continues until no rows remain on the board. Then the next move is made.

Scoring is simple. Each time a row of at least three candies appears, whether from your move or from falling candies, you get $(2L-5)$ points, where $L$ is the length of the row. A row of three candies gives 1 point, a row of four gives 3 points, and so on.

Write a program that, given the initial column and the maximum number of moves, computes the maximum score you can achieve.

The first line contains the integer $N$, the maximum number of moves ($1 \le N \le 5$). The second line contains a string of $R$ letters ($3 \le R \le 20$), each one of A, B, or C. This is the initial column, listed from bottom to top. The initial column never has three equal letters in a row. The input is chosen so that no infinite loop of falling candies can occur.

Print a single integer, the maximum score you can achieve.

$2 \le N \le 5$