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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    partial class Program
    {
        static long mod = 1000000007;
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            Solve();
            Console.Out.Flush();
            Console.ReadKey();
        }

        //ここから
        static int H;
        static int W;
        static char[][] S;
        static void Solve()
        {
            Multi(out H, out W);
            S = GetCharJaggedArray(H);

            var ans = Dijkstra();
            if (S[0][0] == '#') ans++;
            Console.WriteLine(ans);

        }

        static long Dijkstra()
        {
            var dx = new int[] { 1, 0};
            var dy = new int[] { 0, 1};
            var A = Enumerable.Repeat(0, H * W).Select(s => new List<Edge>()).ToArray();
            int start = 0;
            int goal = H * W - 1;
            for (int y = 0; y < H; y++)
            {
                for (int x = 0; x < W; x++)
                {
                    var pos = y * W + x;
                    for (int v = 0; v < 2; v++)
                    {
                        var ny = y + dy[v];
                        var nx = x + dx[v];
                        var npos = ny * W + nx;
                        if (nx < 0 || W <= nx || ny < 0 || H <= ny) continue;
                        var edge = new Edge();
                        edge.to = npos;
                        if (S[y][x]=='.' && S[ny][nx] == '#') edge.cost = 1;
                        else edge.cost = 0;
                        A[pos].Add(edge);
                    }
                }
            }

            var dist = Enumerable.Repeat((long)(int.MaxValue), H * W).ToArray();
            dist[start] = 0;
            var prev = Enumerable.Repeat(0, H * W).ToArray();
            var next = new PriorityQueue<Node>();

            next.Push(new Node(start, 0));
            while (next.Count > 0)
            {
                var n = next.Peek();
                next.Pop();
                foreach (var a in A[n.node])
                {
                    var alt = dist[n.node] + a.cost;
                    if (dist[a.to] > alt)
                    {
                        dist[a.to] = alt;
                        prev[a.to] = n.node;
                        next.Push(new Node(a.to, alt));
                    }
                }
            }
            return dist[goal];
        }
    }
    class Edge
    {
        public int to;
        public long cost;
    }
    class Node : IComparable<Node>
    {
        public Node(int n, long c)
        {
            node = n; cost = c;
        }
        public int node;
        public long cost;
        public int CompareTo(Node other)
        {
            return cost < other.cost ? 1 : cost == other.cost ? 0 : -1;
        }
    }

    class PriorityQueue<T> where T : IComparable<T>
    {
        public PriorityQueue()
        {
            buffer = new List<T>();
        }


        List<T> buffer;
        public void Push(T elem)
        {
            int n = buffer.Count;
            buffer.Add(elem);
            while (n != 0)
            {
                int i = (n - 1) / 2;
                if (buffer[n].CompareTo(buffer[i]) > 0)
                {
                    T temp = buffer[n];
                    buffer[n] = buffer[i];
                    buffer[i] = temp;
                }
                n = i;
            }
        }

        public void Pop()
        {
            int n = buffer.Count - 1;
            buffer[0] = buffer[n];
            buffer.RemoveAt(n);
            for (int i = 0, j; (j = 2 * i + 1) < n;)
            {
                if ((j != n - 1) && (buffer[j].CompareTo(buffer[j + 1]) < 0)) { j++; }
                if (buffer[i].CompareTo(buffer[j]) < 0)
                {
                    T temp = buffer[j];
                    buffer[j] = buffer[i];
                    buffer[i] = temp;
                }
                i = j;
            }
        }

        public T Peek()
        {
            return buffer[0];
        }

        public int Count { get { return buffer.Count; } }
    }



    //拡張メソッド
    public static class Ex
    {
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.Ordinal); return s.ToList(); }
        public static string yesno(this bool b) { return b ? "yes" : "no"; }
        public static string YesNo(this bool b) { return b ? "Yes" : "No"; }
        public static string YESNO(this bool b) { return b ? "YES" : "NO"; }
    }

    partial class Program
    {
        static public string GetStr() { return Console.ReadLine().Trim(); }
        static public char GetChar() { return Console.ReadLine().Trim()[0]; }
        static public int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
        static public long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
        static public double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
        static public string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
        static public int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
        static public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
        static public char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
        static public double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
        static public T[][] CreateJaggedArray<T>(int H, int W, T value) { return Enumerable.Repeat(0, H).Select(s => Enumerable.Repeat(value, W).ToArray()).ToArray(); }
        static public int[][] GetIntJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetIntArray().ToArray()).ToArray(); }
        static public long[][] GetLongJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetLongArray().ToArray()).ToArray(); }
        static public char[][] GetCharJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetStr().ToCharArray()).ToArray(); }
        static public double[][] GetDoubleJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetDoubleArray()).ToArray(); }

        static public void WriteObjects<T>(IReadOnlyCollection<T> values) { var array = values.ToArray(); var num = array.Length; if (num == 0) return; Console.Write(array[0]); for (int i = 1; i < num; i++) { Console.Write(" " + array[i]); } Console.WriteLine(); }

        static bool eq<T, U>() => typeof(T).Equals(typeof(U));
        static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        static T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                           : eq<T, long>() ? ct<T, long>(long.Parse(s))
                           : eq<T, double>() ? ct<T, double>(double.Parse(s))
                           : eq<T, char>() ? ct<T, char>(s[0])
                                             : ct<T, string>(s);
        static void Multi<T>(out T a) => a = cv<T>(GetStr());
        static void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        static void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        static void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
        }
        static void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
        }
        static void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);
        }
    }
}