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문제

The cows have taken up the game of checkers with a vengeance. Unfortunately, despite their unlimited enjoyment of playing, they are terrible at the endgame and want your help.

Given an NxN (4 <= N <= 500) checkboard, determine the optimal set of moves (i.e., smallest number 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 in the traditional way. 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 best solution requires the lower
- o - + - + - +  left 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 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. The king can jump a piece on every move of the optimal solution.

입력

  • Line 1: A single integer: N
  • Lines 2..N+1: Line i+1 contains N characters (each one of: '-', '+', 'K', or 'o') that represent row i of a proper checkboard. Line 2 always begins with '-'.

 

출력

  • Lines 1..?: If there is no winning sequence of jump, output "impossible" on a line by itself. If such a sequence exists, each line contains two space-separated integers that represent successive locations of a king whose moves will win the game. Any such sequence is acceptable.

 

예제 입력

8
-+-+-+-+
+-+-+-+-
-+-K-+-+
+-+-+-+-
-o-o-+-+
+-K-+-+-
-o-+-+-+
+-K-+-K-

예제 출력

8 3
6 1
4 3
6 5

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