The cows have taken up the game of checkers with a vengeance. Unfortunately, despite their infinite enjoyment of playing, they are terrible at the endgame. They want your help.
Given an NxN (4 <= N <= 30) checkboard, determine the optimal set of moves to end the game on the next move. Checkers move only on the '+' squares and capture by jumping 'over' an opponent's piece. The piece is removed as soon as it is jumped. See the example below where N=8:

- + - + - + - +  The K's mark Bessie's kings; the o's represent the
+ - + - + - + -  opponent's checkers. Bessie always moves next. The
- + - K - + - +  Kings jump opponent's checkers successively in any
+ - + - + - + -  diagonal direction (and removes pieces when jumped).
- o - o - + - +
+ - K - + - + -  For this board, the solution requires the lower left
- o - + - + - +  King to jump successively across all three of the
+ - K - + - K -  opponents' checkers, thus ending the game (moving K
                 marked as >K<):

   Original          After move 1       After move 2        After move 3
- + - + - + - +     - + - + - + - +    - + - + - + - +     - + - + - + - +
+ - + - + - + -     + - + - + - + -    + - + - + - + -     + - + - + - + -
- + - K - + - +     - + - K - + - +    - + - K - + - +     - + - K - + - +
+ - + - + - + -     + - + - + - + -    + ->K<- + - + -     + - + - + - + -
- o - o - + - +     - o - o - + - +    - + - o - + - +     - + - + - + - +
+ - K - + - + -    >K<- K - + - + -    + - K - + - + -     + - K ->K<- + -
- o - + - + - +     - + - + - + - +    - + - + - + - +     - + - + - + - +
+ ->K<- + - K -     + - + - + - K -    + - K - + - K -     + - K - + - K -

The moves traversed these squares:

  1 2 3 4 5 6 7 8           R C
1 - + - + - + - +    start: 8 3
2 + - + - + - + -    move:  6 1
3 - + - K - + - +    move:  4 3
4 + - * - + - + -    move:  6 5
5 - o - o - + - +
6 * - K - * - + - 
7 - o - + - + - + 
8 + - K - + - K - 

Write a program to determine the (unique, as it turns out) game-ending sequence for an NxN input board if it exists. There is at least a king and at least one opponent piece on the board.