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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Threading.Tasks;
using System.Globalization;
namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            StreamScanner scan = new StreamScanner(System.Console.OpenStandardInput());
            h = scan.Integer();
            w = scan.Integer();
            char[,] map = new char[h, w];
            for (int i = 0; i < h; i++)
            {
                for (int k = 0; k < w; k++)
                {
                    map[i, k] = scan.Char();
                }
            }
            Console.WriteLine(myBFS(0, 0, map));

        }
        static long solve(int mae,int ushiro,long[,]dp,int[]a,bool taro)
        {
            if (dp[mae, ushiro] > long.MinValue)
            {
                return dp[mae, ushiro];
            }
            if (ushiro - mae == 1)
            {
                if (taro) { dp[mae, ushiro] = a[mae]; return dp[mae, ushiro]; }
                else { dp[mae, ushiro] = -a[mae]; return dp[mae, ushiro]; }
            }

            if(taro)
            {
                long max = Math.Max(a[mae] + solve(mae + 1, ushiro, dp, a, !taro),
                    a[ushiro-1] + solve(mae, ushiro - 1, dp, a, !taro));
                dp[mae, ushiro] = max;
                return dp[mae, ushiro];
                
            }
            else
            {
                long min= Math.Min(-a[mae] + solve(mae + 1, ushiro, dp, a, !taro),
                    -a[ushiro-1] + solve(mae, ushiro - 1, dp, a, !taro));
                dp[mae, ushiro] = min;
                return dp[mae, ushiro];
            }
            
        }

        static int nibutan(int med,int[]a)//med以上が何個あるか
        {
            int mae = 0;
            int ato = a.Length;
            while (true)
            {
                if (ato - mae <= 1) {
                    return mae; }
                int mid = (mae + ato) / 2;
                if (a[mid] > med) { ato = mid; }
                if (a[mid] <= med) { mae = mid; }
            }
        }


        public static int h;
        public static int w;
        public static int myBFS(int height, int width, char[,] map)
        {
            
            int[] dx = new int[] { 0, 1 };
            int[] dy = new int[] { 1, 0 };
            bool[,] visited = new bool[h, w];
            int[,] len = new int[h, w];
            if (map[0, 0] == '#') { len[0, 0] = 1; }
            var queue = new Queue<Tuple<int, int>>();
            queue.Enqueue(new Tuple<int, int>(height, width));
            int max = 0;
            visited[height, width] = true;
            while (queue.Count > 0)
            {
                var now = queue.Dequeue();
                for (int i = 0; i < 2; i++)
                {
                    int ny = now.Item1 + dy[i];
                    int nx = now.Item2 + dx[i];
                    if (ny >= h || ny < 0 || nx >= w || nx < 0)
                        continue;
                    if (visited[ny, nx]&&len[ny,nx]<=len[now.Item1,now.Item2])
                        continue;
                    visited[ny, nx] = true;
                    if (map[now.Item1, now.Item2] == '.' && map[ny, nx] == '#')
                    {
                        len[ny, nx] = len[now.Item1, now.Item2] + 1;
                    }
                    else { len[ny, nx] = len[now.Item1, now.Item2]; }
                    max = Math.Max(max, len[ny, nx]);
                    queue.Enqueue(new Tuple<int, int>(ny, nx));
                }
            }
            return len[h - 1, w - 1];
        }
        public static int BFS(int height, int width, char[,] map)
        {
            int[] dx = new int[] { -1, 0, 0, 1 };
            int[] dy = new int[] { 0, 1, -1, 0 };
            bool[,] visited = new bool[h, w];
            int[,] len = new int[h, w];
            var queue = new Queue<Tuple<int, int>>();
            queue.Enqueue(new Tuple<int, int>(height, width));
            int max = 0;
            visited[height, width] = true;

            while (queue.Count > 0)
            {
                var now = queue.Dequeue();
                for (int i = 0; i < 4; i++)
                {
                    int ny = now.Item1 + dy[i];
                    int nx = now.Item2 + dx[i];
                    if (ny >= h || ny < 0 || nx >= w || nx < 0)
                        continue;
                    if (visited[ny, nx] || map[ny, nx] == '#')
                        continue;
                    visited[ny, nx] = true;
                    len[ny, nx] = len[now.Item1, now.Item2] + 1;
                    max = Math.Max(max, len[ny, nx]);
                    queue.Enqueue(new Tuple<int, int>(ny, nx));
                }
            }
            return max;
        }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        private readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        public char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        public int Integer() { return (int)Long(); }
        public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    public class UnionFind
    {
        public int[] data;

        public UnionFind(int size)
        {
            data = new int[size];
            for (int i = 0; i < size; i++) data[i] = -1;
        }

        public bool Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);

            if (x != y)
            {
                if (data[y] < data[x])
                {
                    var tmp = y;
                    y = x;
                    x = tmp;
                }
                data[x] += data[y];
                data[y] = x;
            }
            return x != y;
        }

        public bool IsSameGroup(int x, int y)
        {
            return Root(x) == Root(y);
        }

        public int Root(int x)
        {
            return data[x] < 0 ? x : data[x] = Root(data[x]);
        }
    }
}