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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] input = br.readLine().split(" ");
        int h = Integer.parseInt(input[0]);
        int w = Integer.parseInt(input[1]);
        char[][] mat  = new char[h][w];
        for(int i=0; i<h; i++) {
            mat[i] = br.readLine().toCharArray();
        }
        if(h == 1 && w == 1) {
            System.out.println(mat[0][0] == '.' ? 0 : 1);
        } else {
            Graph g = new Graph(h * w, mat);
            for (int i = 1; i < w; i++) {
                int left = getIndex(w, 0, i - 1);
                int index = getIndex(w, 0, i);
                if (mat[0][i - 1] == '.') {
                    if (mat[0][i] == '.')
                        g.addEdge(left, index, 0);
                    else
                        g.addEdge(left, index, 1);
                } else {
                    if (i == 1)
                        g.addEdge(left, index, 1);
                    else {
                        g.addEdge(left, index, 0);
                    }
                }
            }
            for (int i = 0; i < w; i++) {
                for (int j = 1; j < h; j++) {
                    if (i == 0) {
                        int index = getIndex(w, j, i);
                        int prev = getIndex(w, j - 1, i);
                        //System.out.println(index +  " " + prev);
                        if (j == 1) {
                            if (mat[j - 1][i] == '.') {
                                if (mat[j][i] == '.')
                                    g.addEdge(prev, index, 0);
                                else
                                    g.addEdge(prev, index, 1);
                            } else {
                                g.addEdge(prev, index, 1);
                            }
                        } else {
                            if (mat[j - 1][i] == '.') {
                                if (mat[j][i] == '.') {
                                    g.addEdge(prev, index, 0);
                                } else {
                                    g.addEdge(prev, index, 1);
                                }
                            } else {
                                g.addEdge(prev, index, 0);
                            }
                        }
                    } else {
                        int up = getIndex(w, j - 1, i);
                        int left = getIndex(w, j, i - 1);
                        int index = getIndex(w, j, i);
                        if (mat[j][i - 1] == '.') {
                            if (mat[j][i] == '.')
                                g.addEdge(left, index, 0);
                            else
                                g.addEdge(left, index, 1);
                        } else {
                            g.addEdge(left, index, 0);
                        }
                        if (j == 1) {
                            if (mat[j - 1][i] == '.') {
                                if (mat[j][i] == '.')
                                    g.addEdge(up, index, 0);
                                else
                                    g.addEdge(up, index, 1);
                            } else {
                                g.addEdge(up, index, 1);
                            }
                        } else {
                            if (mat[j - 1][i] == '.') {
                                if (mat[j][i] == '.') {
                                    g.addEdge(up, index, 0);
                                } else {
                                    g.addEdge(up, index, 1);
                                }
                            } else {
                                g.addEdge(up, index, 0);
                            }
                        }
                    }
                }
            }
            g.dijsktra(0);
            System.out.println(g.getAns());
        }
        br.close();
    }

    private static int getIndex(int w, int i, int j) {
        return w*i + j;
    }

    static class Node implements Comparator<Node> {
        int s, e, cost;

        Node(int s, int e, int cost) {
            this.s = s;
            this.e = e;
            this.cost = cost;
        }

        Node() {}

        public int compare(Node a, Node b) {
            return a.cost - b.cost;
        }
    }

    static class Graph {
        int V;
        ArrayList<Node> list[];
        int dist[];
        char[][] mat;

        Graph(int v, char[][] mat) {
            V = v;
            list = new ArrayList[V];
            dist = new int[V];
            for(int i=0; i<V; i++) {
                list[i] = new ArrayList<>();
            }
            this.mat = mat;
        }

        void addEdge(int u, int v, int cost) {
            list[u].add(new Node(u, v, cost));
        }

        void dijsktra(int s) {
            boolean[] visited = new boolean[V];
            PriorityQueue<Node> pq = new PriorityQueue<>(V, new Node());
            pq.add(new Node(s, s, mat[0][0] == '.' ? 0 : 1));
            Arrays.fill(dist, Integer.MAX_VALUE);
            dist[s] = 0;
            while(!pq.isEmpty()) {
                Node u = pq.poll();
                if(visited[u.s])
                    continue;
                visited[u.s] = true;
                for(int i=0; i<list[u.s].size(); i++) {
                    Node v = list[u.s].get(i);
                    if(dist[v.e] > dist[u.s] + v.cost) {
                        dist[v.e] = dist[u.s] + v.cost;
                    }
                    if(!visited[v.e]) {
                        pq.add(new Node(v.e, v.e, dist[v.e]));
                    }
                }
            }
        }

        int getAns() {
            //for(int i=0; i<V; i++)
                //System.out.println(i + " = " + dist[i]);
            return dist[dist.length-1];
        }
    }
}