Sliding Block Puzzle#5416
In sliding block puzzles, we repeatedly slide pieces (blocks) to open spaces within a frame to establish a goal placement of pieces.
A puzzle creator has designed a new puzzle by combining the ideas of sliding block puzzles and mazes. The puzzle is played in a rectangular frame segmented into unit squares. Some squares are pre-occupied by obstacles. There are a number of pieces placed in the frame, one 2 \times 2 king piece and some number of 1 \times 1 pawn pieces. Exactly two 1 \times 1 squares are left open. If a pawn piece is adjacent to an open square, we can slide the piece there. If a whole edge of the king piece is adjacent to two open squares, we can slide the king piece. We cannot move the obstacles. Starting from a given initial placement, the objective of the puzzle is to move the king piece to the upper-left corner of the frame.
The following figure illustrates the initial placement of the fourth dataset of the sample input.
Figure 1: The fourth dataset of the sample input.
Your task is to write a program that computes the minimum number of moves to solve the puzzle from a given placement of pieces. Here, one move means sliding either king or pawn piece to an adjacent position.
The input is a sequence of datasets. The first line of a dataset consists of two integers and separated by a space, where and are the height and the width of the frame. The following lines, each consisting of characters, denote the initial placement of pieces. In those lines, 'X', 'o', '*', and '.' denote a part of the king piece, a pawn piece, an obstacle, and an open square, respectively. There are no other characters in those lines. You may assume that 3 \leq H \leq 50 and 3 \leq W \leq 50.
A line containing two zeros separated by a space indicates the end of the input.
For each dataset, output a line containing the minimum number of moves required to move the king piece to the upper-left corner. If there is no way to do so, output -1.
Example 1