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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;

//dijkstraによる解法
class Vertex{
	int x, y, dist;

	public Vertex(int x, int y, int dist) {
		super();
		this.x = x;
		this.y = y;
		this.dist = dist;
	}
}

public class Main {
	static final int mod = (int) 1e9 + 7;
	static final int DX[] = { -1, 0, 1, 0 }, DY[] = { 0, -1, 0, 1 };
	static final int[] DX8 = { -1, -1, -1, 0, 0, 1, 1, 1 }, DY8 = { -1, 0, 1, -1, 1, -1, 0, 1 };
	static final int INF = Integer.MAX_VALUE / 3;
	static final long LINF = Long.MAX_VALUE / 3;
	static final String nextLine = "\n";
	
	static int h, w;
	static char field[][];
	static int dist[][];

	public static void main(String[] args) {
		FastScanner fs = new FastScanner(System.in);
		h = fs.nextInt(); w = fs.nextInt();
		field = new char[h][w];
		for(int i=0;i<h;i++) {
			String s = fs.next();
			for(int j=0;j<w;j++) {
				field[i][j] = s.charAt(j);
			}
		}
		dist = new int[h][w];
		dijkstra(0,0);
		System.out.println(dist[h-1][w-1]);
	}
	
	static void dijkstra(int x, int y) {
		PriorityQueue<Vertex> pq = new PriorityQueue<>((p1,p2)->p1.dist-p2.dist);
		for(int i=0;i<h;i++)Arrays.fill(dist[i], INF);
		if(field[0][0] == '#')dist[0][0] = 1;
		else dist[0][0] = 0;
		pq.add(new Vertex(0,0,dist[0][0]));
		int DX2[] = {1,0}, DY2[]= {0,1};
		while(!pq.isEmpty()) {
			Vertex now = pq.poll();
			if(dist[now.x][now.y]<now.dist)continue;
			for(int i=0;i<2;i++) {
				int nx = now.x + DX2[i], ny = now.y + DY2[i];
				if(0<=nx&&nx<h&&0<=ny&&ny<w) {
					int cost = 0;
					if(field[now.x][now.y]=='.'&&field[nx][ny]=='#')cost = 1;
					if(dist[nx][ny] > dist[now.x][now.y] + cost) {
						dist[nx][ny] = dist[now.x][now.y] + cost;
						pq.add(new Vertex(nx,ny,dist[nx][ny]));
					}
				}
			}
		}
	}
	

	//MOD culculations
	static long plus(long x, long y) {
		long res = (x + y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long sub(long x, long y) {
		long res = (x - y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long mul(long x, long y) {
		long res = (x * y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long div(long x, long y) {
		long res = x * pow(y, mod - 2) % mod;
		return res < 0 ? res + mod : res;
	}

	static long pow(long x, long y) {
		if (y < 0)
			return 0;
		if (y == 0)
			return 1;
		if (y % 2 == 1)
			return (x * pow(x, y - 1)) % mod;
		long root = pow(x, y / 2);
		return root * root % mod;
	}
}

//高速なScanner
class FastScanner {
	private BufferedReader reader = null;
	private StringTokenizer tokenizer = null;

	public FastScanner(InputStream in) {
		reader = new BufferedReader(new InputStreamReader(in));
		tokenizer = null;
	}

	public String next() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	public String nextLine() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken("\n");
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}
}