Laser Communication

There is a $W \times H$ map divided into $1 \times 1$ square cells. Each cell is either empty or a wall, and exactly two of the cells are marked with the letter C.

You want to connect the two cells marked C with a laser. A laser is fired from a C cell in one of the four directions (up, down, left, or right). By placing a mirror / or \ on an empty cell, you can turn the laser's direction by 90 degrees at that cell. A laser cannot pass through a wall cell.

Write a program that finds the minimum number of mirrors that must be placed so that the two C cells are connected by a laser.

The figure below shows an example with $H = 8$ and $W = 7$, where empty cells are drawn as . and walls as *. The left side is the initial state, and the right side shows the two C cells connected using the minimum number of mirrors.

7 . . . . . . .         7 . . . . . . .
6 . . . . . . C         6 . . . . . /-C
5 . . . . . . *         5 . . . . . | *
4 * * * * * . *         4 * * * * * | *
3 . . . . * . .         3 . . . . * | .
2 . . . . * . .         2 . . . . * | .
1 . C . . * . .         1 . C . . * | .
0 . . . . . . .         0 . \-------/ .
  0 1 2 3 4 5 6           0 1 2 3 4 5 6

The first line contains the map's width $W$ and height $H$. ($1 \le W, H \le 100$)

From the second line, the map is given over $H$ lines, each consisting of $W$ characters. The characters mean:

• .: an empty cell
• *: a wall
• C: a cell that must be connected by the laser

There are always exactly two C cells, and only inputs in which the two cells can be connected by a laser are given.

On the first line, print the minimum number of mirrors that must be placed to connect the two C cells.