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 LuaJIT (2.0.4) (judge verdict: Accepted)

local h, w = io.read("*n", "*n", "*l")
local map = {}
for i = 1, h do
  local s = io.read()
  for j = 1, w do
    map[(i - 1) * w + j] = s:sub(j, j) == "."
  end
end

local taskstate = {}
for i = 1, h * w do taskstate[i] = false end
local tasks = {}
local tasknum = 0
local done = 0
local tasklim = h * w

local function addtask(idx)
  if not taskstate[idx] then
    taskstate[idx] = true
    tasknum = tasknum + 1
    local taskidx = tasknum % tasklim
    if taskidx == 0 then taskidx = tasklim end
    tasks[taskidx] = idx
  end
end

local inf = 1000000007
local len = {}
for i = 1, h * w do
  len[i] = inf
end
if not map[1] then
  len[1] = 1
else
  len[1] = 0
end


local function walk(src, dst)
  if map[src] == map[dst] then
    if len[src] < len[dst] then
      len[dst] = len[src]
      addtask(dst)
    end
  else
    if len[src] + 1 < len[dst] then
      len[dst] = len[src] + 1
      addtask(dst)
    end
  end
end

addtask(1)

while done < tasknum do
  done = done + 1
  local taskidx = done % tasklim
  if taskidx == 0 then taskidx = tasklim end
  local idx = tasks[taskidx]
  taskstate[idx] = false

  if idx <= (h - 1) * w then walk(idx, idx + w) end
  if 1 < w then
    if idx % w ~= 0 then walk(idx, idx + 1) end
  end
end
local ret = len[h * w]
print(math.ceil(ret / 2))