Problem:
Score : 400 points

Problem Statement

Consider a grid with H rows and W columns of squares. Let (r, c) denote the square at the r-th row from the top and the c-th column from the left.
Each square is painted black or white.

The grid is said to be good if and only if the following condition is satisfied:

From (1, 1), we can reach (H, W) by moving one square right or down repeatedly, while always being on a white square.

Note that (1, 1) and (H, W) must be white if the grid is good.

Your task is to make the grid good by repeating the operation below. Find the minimum number of operations needed to complete the task. It can be proved that you can always complete the task in a finite number of operations.

Choose four integers r_0, c_0, r_1, c_1(1 \leq r_0 \leq r_1 \leq H, 1 \leq c_0 \leq c_1 \leq W). For each pair r, c (r_0 \leq r \leq r_1, c_0 \leq c \leq c_1), invert the color of (r, c) - that is, from white to black and vice versa.

Constraints

2 \leq H, W \leq 100

Input

Input is given from Standard Input in the following format:

H W
s_{11} s_{12} \cdots s_{1W}
s_{21} s_{22} \cdots s_{2W}
\vdots
s_{H1} s_{H2} \cdots s_{HW}

Here s_{rc} represents the color of (r, c) - # stands for black, and . stands for white.

Output

Print the minimum number of operations needed.

Sample Input 1

3 3
.##
.#.
##.

Sample Output 1

1

Do the operation with (r_0, c_0, r_1, c_1) = (2, 2, 2, 2) to change just the color of (2, 2), and we are done.

Sample Input 2

2 2
#.
.#

Sample Output 2

2

Sample Input 3

4 4
..##
#...
###.
###.

Sample Output 3

0

No operation may be needed.

Sample Input 4

5 5
.#.#.
#.#.#
.#.#.
#.#.#
.#.#.

Sample Output 4

4

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

module ch
  implicit none
  type char
     character(100)      :: n
  end type char
  type(char),allocatable :: s(:)
end module ch
program main
  
  use ch, only : s
  implicit none
  
  integer(8)              ::  h, w  
  integer(8)              ::  i, j
  integer(8),allocatable  ::  ss(:,:), sb(:,:)

  read(*,*) h, w
  allocate( s(h) )
  allocate( ss(h,w) )
  allocate( sb(h,w) )
  do i = 1, h
    read(*,*) s(i)%n
  end do
  
  ss = 0
  do i = 1, h
    do j = 1, w
    
      if( s(i)%n(j:j) == "#" ) then
        ss(i,j) = ss(i,j) + 1
      end if
      
      if( i == 1 .and. j /= 1 ) then
        ss(i,j) = ss(i,j) + ss(i,j-1) 
        if ( s(i)%n(j:j) == "#" .and. s(i)%n(j-1:j-1) == "#" ) then
          ss(i,j) = ss(i,j) - 1  
        end if
      end if

      if( i /= 1 .and. j == 1 ) then
        ss(i,j) = ss(i,j) + ss(i-1,j)
        if ( s(i)%n(j:j) == "#" .and. s(i-1)%n(j:j) == "#" ) then
          ss(i,j) = ss(i,j) - 1  
        end if
      end if

      if( i /= 1 .and. j /= 1 ) then
        if( ss(i,j-1) <= ss(i-1,j) ) then   
          ss(i,j) = ss(i,j) + ss(i,j-1) 
          if ( s(i)%n(j:j) == "#" .and. s(i)%n(j-1:j-1) == "#" ) then
            ss(i,j) = ss(i,j) - 1  
          end if
        else
          ss(i,j) = ss(i,j) + ss(i-1,j)
          if ( s(i)%n(j:j) == "#" .and. s(i-1)%n(j:j) == "#" ) then
            ss(i,j) = ss(i,j) - 1  
          end if
        end if
      end if

    end do
  end do
  
  !print*, ss(h,w)
  
  sb = 0
  do i = 1, h
    do j = 1, w
    
      if( s(i)%n(j:j) == "." ) then
        sb(i,j) = sb(i,j) + 1
      end if
      
      if( i == 1 .and. j /= 1 ) then
        sb(i,j) = sb(i,j) + sb(i,j-1) 
        if ( s(i)%n(j:j) == "." .and. s(i)%n(j-1:j-1) == "." ) then
          sb(i,j) = sb(i,j) - 1  
        end if
      end if
 
      if( i /= 1 .and. j == 1 ) then
        sb(i,j) = sb(i,j) + sb(i-1,j)
        if ( s(i)%n(j:j) == "." .and. s(i-1)%n(j:j) == "." ) then
          sb(i,j) = sb(i,j) - 1  
        end if
      end if
 
      if( i /= 1 .and. j /= 1 ) then
        if( sb(i,j-1) <= sb(i-1,j) ) then   
          sb(i,j) = sb(i,j) + sb(i,j-1) 
          if ( s(i)%n(j:j) == "." .and. s(i)%n(j-1:j-1) == "." ) then
            sb(i,j) = sb(i,j) - 1  
          end if
        else
          sb(i,j) = sb(i,j) + sb(i-1,j)
          if ( s(i)%n(j:j) == "." .and. s(i-1)%n(j:j) == "." ) then
            sb(i,j) = sb(i,j) - 1  
          end if
        end if
      end if
 
    end do
  end do
    
  if( ss(h,w) <= (sb(h,w)+1)) then
    print*, ss(h,w)
  else
    print*, sb(h,w)+1
  end if

end program main