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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

def mapend(h,w,h_now,w_now,map)
    if h-1 == h_now && w-1 == w_now then
        return true
    else
        return false
    end
end

def check(h,w,map)
    if map[h][w] == "." then
        return true
    else
        return false
    end
end

def move(h,w,h_now,w_now,map,count)
    #タイルが黒なら白に変更
    if check(h_now,w_now,map) == false then 
        count += 1
    end
    #マップ終了時 
    if mapend(h,w,h_now,w_now,map) then
            return count
    end
    #右に移動
    if (w_now+1) < w then
        count_a = move(h,w,h_now,w_now+1,map,count)
    else
        count_a = 100000000000000
    end
    #下に移動
    if (h_now+1) < h then
        count_b = move(h,w,h_now+1,w_now,map,count)
    else
        count_b = 100000000000000
    end
    if count_a < count_b then return count_a 
    else                      return count_b
    end
end
h,w = gets.split.map(&:to_i)
map = []
h.times{|i|
    #1行ずつ読み込み
    str = gets.chomp.to_s
    map << str.chars
}
#-----------------------------
h_now = 0
w_now = 0
count = 0

p move(h,w,h_now,w_now,map,count)