Problem:
Score : 300 points

Problem Statement

You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black.
HW characters from A_{11} to A_{HW} represent the colors of the squares.
A_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.

We will repeatedly perform the following operation until all the squares are black:

Every white square that shares a side with a black square, becomes black.

Find the number of operations that will be performed.
The initial grid has at least one black square.

Constraints

1 \leq H,W \leq 1000

A_{ij} is # or ..

The given grid has at least one black square.

Input

Input is given from Standard Input in the following format:

H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}

Output

Print the number of operations that will be performed.

Sample Input 1

3 3
...
.#.
...

Sample Output 1

2

After one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.

Sample Input 2

6 6
..#..#
......
#..#..
......
.#....
....#.

Sample Output 2

3

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program agc033a
  implicit none
  character(1000) s
  integer h,w,x,y
  integer,allocatable :: grid(:,:)

  read *,h,w
  allocate(grid(w,h))

  do y = 1,h
     read *,s
     do x = 1,w
        grid(x,y) = merge(0,1000000,s(x:x)=='#')
     end do
  end do

  do x = 2,w
     grid(x,:) = merge(grid(x-1,:)+1,grid(x,:),grid(x,:)-grid(x-1,:)>1)
     grid(w-x+1,:) = merge(grid(w-x+2,:)+1,grid(w-x+1,:),grid(w-x+1,:)-grid(w-x+2,:)>1)
  end do

  do y = 2,h
     grid(:,y) = merge(grid(:,y-1)+1,grid(:,y),grid(:,y)-grid(:,y-1)>1)
     grid(:,h-y+1) = merge(grid(:,h-y+2)+1,grid(:,h-y+1),grid(:,h-y+1)-grid(:,h-y+2)>1)
  end do

  print *,maxval(grid)
end program agc033a