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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Numerics;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
using static AtCoder.CalcL;
namespace AtCoder
{
    class AC
    {
        //const int MOD = 1000000007;
        const int MOD = 998244353;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dI = { 0, 1, 0, -1 };
        static readonly int[] dJ = { 1, 0, -1, 0 };
        static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>> G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var input = cin.ReadSplitInt();
            int H = input[0];
            int W = input[1];
            var map = new string[H];
            for(var i = 0; i < H; i++)
            {
                map[i] = Console.ReadLine();
            }
            var ans = new int[H, W];
            var used = new bool[H, W];
            for (var i = 0; i < H; i++) for (var j = 0; j < W; j++) { ans[i, j] = INF; used[i, j] = false; }
            var bfs = new Queue<Tuple<int, int>>();
            bfs.Enqueue(new Tuple<int, int>(0, 0));
            ans[0, 0] = map[0][0] == '#' ? 1 : 0;
            while (bfs.Any())
            {
                var tp = bfs.Dequeue();
                int x = tp.Item1;
                int y = tp.Item2;
                if (x + 1 < H)
                {
                    int d = map[x][y] == '.' && map[x + 1][y] == '#' ? 1 : 0;
                    ans[x + 1, y] = Min(ans[x + 1, y], ans[x, y] + d);
                    if (!used[x + 1, y]) bfs.Enqueue(new Tuple<int, int>(x + 1, y));
                }
                if (y + 1 < W)
                {
                    int d = (map[x][y] == '.' && map[x][y + 1] == '#') ? 1 : 0;
                    ans[x, y + 1] = Min(ans[x, y + 1], ans[x, y] + d);
                    if (!used[x, y + 1]) bfs.Enqueue(new Tuple<int, int>(x, y + 1));
                }
            }
            Console.WriteLine(ans[H - 1, W - 1]);
            //Display(ans, H, W);
            //Console.Out.Flush();
        }
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
    }
    public class Scanner
    {
        public int[] ReadSplitInt()
        {
            return ConvertAll(Console.ReadLine().Split(), int.Parse);
        }
        public long[] ReadSplitLong()
        {
            return ConvertAll(Console.ReadLine().Split(), long.Parse);
        }
        public double[] ReadSplit_Double()
        {
            return ConvertAll(Console.ReadLine().Split(), double.Parse);
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

        static public long LPow(int a, int b)
        {
            return (long)Pow(a, b);
        }
    }
    static public class CalcI
    {
        public static int Gcd(int a, int b)
        {
            if (a * b == 0) { return Max(a, b); }
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        public static int Lcm(int a, int b)
        {
            int g = Gcd(a, b);
            return a / g * b;
        }
        public static int Ceil(int n, int div)
        {
            return (n + div - 1) / div;
        }
    }
    static public class CalcL
    {
        public static long Gcd(long a, long b)
        {
            if (a * b == 0) { return Max(a, b); }
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        public static long Lcm(long a, long b)
        {
            long g = Gcd(a, b);
            return a / g * b;
        }
        public static long Ceil(long n, long div)
        {
            return (n + div - 1) / div;
        }
    }
    class Modulo
    {
        private int M;
        private readonly long[] m_facs;
        public long Mul(long a, long b)
        {
            return ((a * b) % M);
        }
        public Modulo(long n, int m)
        {
            M = m;
            m_facs = new long[n + 1];
            m_facs[0] = 1;
            for (long i = 1; i <= n; ++i)
            {
                m_facs[i] = Mul(m_facs[i - 1], i);
            }
        }
        public long Fac(long n)
        {
            return m_facs[n];
        }
        public long Pow(long a, long m)
        {
            switch (m)
            {
                case 0:
                    return 1L;
                case 1:
                    return a;
                default:
                    long p1 = Pow(a, m / 2);
                    long p2 = Mul(p1, p1);
                    return ((m % 2) == 0) ? p2 : Mul(p2, a);
            }
        }
        public long Div(long a, long b)
        {
            return Mul(a, Pow(b, M - 2));
        }
        public long Ncr(long n, long r)
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            long res = Fac(n);
            res = Div(res, Fac(r));
            res = Div(res, Fac(n - r));
            return res;
        }
    }
}