## PUCMM223 - C You and Me

You and Me is a board game between two players, the board is MxN, with 1 ≤ M,N ≤ 20. Initially each player has one piece, piece 'a' and piece 'b', both players move at the same time its piece, a valid move is to move the piece one square on each of the 4 cardinal directions (North, South, East, West),or stay in the same square, that is, if a piece is at x,y it can move to(x-1, y), (x, y-1), (x, y), (x, y+1), (x+1, y), so with the two pieces combined there are 5x5=25 possibilities in one move. The game has a goal, piece 'a' must finish at position initially accupied by 'b', and viceversa. To make this game more interesting the cells can be occupied by a block('#'), or can be unocuppied('.'). What is the minimum number of moves required to achieve this goal, if the pieces cannot occupy the same square at a given time and can't cross each other. See examples for further details.

### Input

For each test case the first line contains two separated integers, M and N, rows and columns of the board.

then M strings of N characters follow.

Each character could be '.', '#', 'a', 'b'.

Just one 'a' and one 'b' exists.

The last case is followed by 0 0.

### Output

Output the minimum number of moves required to achieve the goal. Output IMPOSSIBLE if it is not possible.

### Example

Input:

3 4

#..#

a..b

####

3 7

#######

#a...b#

#######

4 4

a...

###.

##..

b...

0 0

Output:

5

IMPOSSIBLE

11

Note:

1st case:

one possibility is

#..# #..# #.b# #..# #..# #..#

a..b--->.ab.--->..a.--->..ba--->.b.a--->b..a

#### #### #### #### #### ####

Added by: | Olson Ortiz |

Date: | 2012-07-27 |

Time limit: | 0.130s-0.391s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | CSHARP CPP C++ 4.3.2 JAVA |

Resource: | Used in 3rd PUCMM Olympiad 2012 (1st phase) |