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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int h = cin.Int();
			int w = cin.Int();
			var s = new string[h];
			for (int i = 0; i < h; i++) {
				s[i] = cin.Next();
			}

			var d = new int[h, w];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					d[i, j] = int.MaxValue;
				}
			}

			d[0, 0] = 0;
			var q = new Queue<Position>();
			q.Enqueue(new Position {
				X = 0,
				Y = 0,
				D = s[0][0] == '#' ? 1 : 0,
				IsBlack = s[0][0] == '#' });
			while (q.Count > 0) {
				var cur = q.Dequeue();
				if (cur.X < w - 1) {
					int nd = 0;
					if (cur.IsBlack) {
						nd = cur.D;
					} else {
						if (s[cur.Y][cur.X + 1] == '#') {
							nd = cur.D + 1;
						} else {
							nd = cur.D;
						}
					}

					if (d[cur.Y, cur.X + 1] > nd) {
						d[cur.Y, cur.X + 1] = nd;
						q.Enqueue(new Position { 
							X = cur.X + 1,
							Y = cur.Y,
							D = nd,
							IsBlack = s[cur.Y][cur.X + 1] == '#' });
					}
				}

				if (cur.Y < h - 1) {
					int nd = 0;
					if (cur.IsBlack) {
						nd = cur.D;
					} else {
						if (s[cur.Y + 1][cur.X] == '#') {
							nd = cur.D + 1;
						} else {
							nd = cur.D;
						}
					}

					if (d[cur.Y + 1, cur.X] > nd) {
						d[cur.Y + 1, cur.X] = nd;
						q.Enqueue(new Position {
							X = cur.X,
							Y = cur.Y + 1,
							D = nd,
							IsBlack = s[cur.Y + 1][cur.X] == '#'
						});
					}
				}
			}

			int ans = d[h - 1, w - 1];
			Console.WriteLine(ans);
		}

		struct Position
		{
			public int X { get; set; }
			public int Y { get; set; }
			public int D { get; set; }
			public bool IsBlack { get; set; }
		}
	}

	public static class Helper
	{
		public static void UpdateMin32<T>(T array, int index, int value) where T : IList<int>
			=> array[index] = Math.Min(array[index], value);
		public static void UpdateMax32<T>(T array, int index, int value) where T : IList<int>
			=> array[index] = Math.Max(array[index], value);
		public static void UpdateMin64<T>(T array, int index, long value) where T : IList<long>
			=> array[index] = Math.Min(array[index], value);
		public static void UpdateMax64<T>(T array, int index, long value) where T : IList<long>
			=> array[index] = Math.Max(array[index], value);

		public static T[] Array<T>(int n, Func<int, T> init)
			=> Enumerable.Range(0, n).Select(x => init(x)).ToArray();
		public static List<T> List<T>(int n, Func<int, T> init)
			=> Enumerable.Range(0, n).Select(x => init(x)).ToList();
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private readonly Func<string> reader_;
		private string[] buf_;
		private int index_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}