The cows have a new laser-based system so they can have casual conversations while out in the pasture which is modeled as a $W x H$ grid of points $(1 \le W \le 100; 1 \le H \le 100)$.

The system requires a sort of line-of-sight connectivity in order to sustain communication. The pasture, of course, has rocks and trees that disrupt the communication but the cows have purchased diagonal mirrors ('/' and '\' below) that deflect the laser beam through a 90 degree turn. Below is a map that illustrates the problem.

$H$ is 8 and $W$ is 7 for this map. The two communicating cows are notated as '$C$'s; rocks and other blocking elements are notated as '*'s:

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

Determine the minimum number of mirrors $M$ that must be installed to maintain laser communication between the two cows, a feat which is always possible in the given test data.

Input

• Line 1: Two space separated integers: $W$ and $H$
• Lines $2,\ldots,H+1$: The entire pasture.

Output

• Line 1: A single integer: $M$

Examples

Input 1

7 8
.......
......C
......*
*****.*
....*..
....*..
.C..*..
.......

Output 1

3

Problem credits: Rob Kolstad, 2008