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: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Queue;
import java.util.function.Consumer;

public class Main {
    final static long MOD07 = 1_000_000_007;
    final static long MOD09 = 1_000_000_009;

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        Integer H = fs.nextInt();
        Integer W = fs.nextInt();
        char[][] s = new char[H][];
        for (int i = 0; i < H; i++) {
            s[i] = fs.next().toCharArray();
        }
        Queue<Pair<Pair<Integer, Integer>, Integer>>  queue = new LinkedList<>();

        queue.add(new Pair(new Pair(0, 0), s[0][0] == '.' ? 0 : 1));
        int min = Integer.MAX_VALUE;

        while (!queue.isEmpty()) {
            Pair<Pair<Integer, Integer>, Integer> p = queue.poll();
            Pair<Integer, Integer> position = p.f;
            Integer count = p.s;
            if (count >= min || count > H - 1) {
                continue;
            }

            if (position.f == H -1 && position.s == W-1) {
                min = Math.min(min,  (int) Math.ceil((double) count / 2.0));
                continue;
            }
            Integer h = position.f;
            Integer w = position.s;

            // going down
            Integer nextH = h + 1;
            Integer nextW = w;
            if (0 <= nextH && nextH < H && 0 <= nextW && nextW < W) {
                p.f.f = nextH;
                p.f.s = nextW;
                p.s = count + ((s[h][w] == s[nextH][nextW]) ? 0 : 1);
                queue.add(p);
            }

            // going right
            nextH = h;
            nextW = w + 1;
            if (0 <= nextH && nextH < H && 0 <= nextW && nextW < W) {
                queue.add(new Pair(new Pair(nextH, nextW), count + ((s[h][w] == s[nextH][nextW]) ? 0 : 1)));
            }
        }

        out.println(min);
        out.flush();
    }


    static void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }



    // Execute func for all patterns can be represented with n bit.
    // O(n2^n)
    static void forAllBit(int n, Consumer<List<Boolean>> func) {
        for (int i = 0; i < (1 << n); i++) {
            List<Boolean> arg = new ArrayList();
            for (int j = 0; j < n; j++) {
                boolean isJthBitSet = ((i >> j) & 1) == 1;
                arg.add(isJthBitSet);
            }
            func.accept(arg);
        }
    }



    private static boolean nextPermutation(int[] arr) {
        // Find the start index of descending part.
        int descendingStart = -1;

        int previous = Integer.MIN_VALUE;
        for (int i = arr.length-1; i>=0; i--) {
            if (arr[i] >= previous ) {
                descendingStart = i;
            } else {
                break;
            }
            previous = arr[i];
        }

        if (descendingStart == 0) {
            return false;
        }

        int target = arr[descendingStart - 1];
        int swapIndex = descendingStart;
        for (int i = descendingStart; i < arr.length;i++) {
            if (arr[i] > target) {
                swapIndex = i;
            }
        }

        swap(arr, descendingStart - 1, swapIndex);
        reverse(arr, descendingStart, arr.length -1);
        return true;
    }

    private static void reverse(int[] arr, int from, int to) {
        while (from < to) {
            swap(arr, from, to);
            from++;
            to--;
        }
    }

    private static void swap(int[] arr, int i, int j) {
        int tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }

    static class Pair<F extends Comparable<F>, S extends Comparable<S>> implements Comparable<Pair<F, S>> {
        F f;
        S s;

        Pair() {
        }

        Pair(F f, S s) {
            this.f = f;
            this.s = s;
        }

        Pair(Pair<F, S> p) {
            f = p.f;
            s = p.s;
        }

        @Override
        public int compareTo(Pair<F, S> p) {
            if (f.compareTo(p.f) != 0) {
                return f.compareTo(p.f);
            }
            return s.compareTo(p.s);
        }

        @Override
        public int hashCode() {
            return f.hashCode() ^ s.hashCode();
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || this.f == null || this.s == null) {
                return false;
            }
            if (this.getClass() != o.getClass()) {
                return false;
            }
            Pair p = (Pair) o;
            return this.f.equals(p.f) && this.s.equals(p.s);
        }

        @Override
        public String toString() {
            return "{" + f.toString() + ", " + s.toString() + "}";
        }
    }

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static boolean isPrime(int n) {
        for (int i = 2; i <= ((int) Math.sqrt(n)); i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return n != 1;
    }

    public static void reverse(int[] array) {
        for (int i = 0; i < array.length / 2; i++) {
            int temp = array[i];
            array[i] = array[array.length - i - 1];
            array[array.length - i - 1] = temp;
        }
    }

    public static void reverse(long[] array) {
        for (int i = 0; i < array.length / 2; i++) {
            long temp = array[i];
            array[i] = array[array.length - i - 1];
            array[array.length - i - 1] = temp;
        }
    }

    public static boolean isPrime(long n) {
        for (long i = 2; i <= ((long) Math.sqrt(n)); i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return n != 1;
    }

    public static Map<Long, Long> primeFactor(long n) {
        Map<Long, Long> map = new HashMap<>();
        long num = n;
        for (long i = 2; i <= ((long) Math.sqrt(n)); i++) {
            while (num % i == 0L) {
                map.put(i, map.getOrDefault(i, 0L) + 1L);
                num /= i;
            }
        }
        if (num != 1) {
            map.put(num, 1L);
        }

        return map;
    }

    public static List<Long> divisors(long n) {
        List<Long> list = new ArrayList<>();
        for (long i = 1; i <= ((long) Math.sqrt(n)); i++) {
            if (n % i == 0) {
                list.add(i);
                if (i != n / i) {
                    list.add(n / i);
                }
            }
        }

        return list;
    }

    public static int lcm(int a, int b) {
        return a / gcd(a, b) * b;
    }

    public static int nCk(int n, int k, int M) {
        long ret = 1;
        int min = Math.min(k, n - k);
        for (int i = 1; i <= min; i++) {
            ret = (ret * pow(i, M - 2, M)) % M;
        }
        for (int i = n - min + 1; i <= n; i++) {
            ret = (ret * i) % M;
        }
        return (int) ret;
    }

    //return a^b mod M O(logB)
    public static long pow(long a, long b, int M) {
        long ret = 1;
        long tmp = a;
        while (b > 0) {
            if ((b & 1) == 1) ret = (ret * tmp) % M;
            tmp = (tmp * tmp) % M;
            b = b >> 1;
        }
        return ret;
    }


    public static int find(int[] tree, int idx) {
        if (tree[idx] == idx) return idx;
        else return tree[idx] = find(tree, tree[idx]);
    }

    public static void union(int[] tree, int idx1, int idx2) {
        int root1 = find(tree, idx1);
        int root2 = find(tree, idx2);
        tree[root2] = root1;
    }

    public static int lowerBound(int[] list, int target) {
        int ok = list.length;
        int ng = -1;
        while (Math.abs(ok - ng) > 1) {
            int mid = (ok + ng) / 2;
            if (list[mid] >= target) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        return ok;
    }

    public static int lowerBound(long[] list, long target) {
        int ok = list.length;
        int ng = -1;
        while (Math.abs(ok - ng) > 1) {
            int mid = (ok + ng) / 2;
            if (list[mid] >= target) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        return ok;
    }

    public static <T extends Comparable<? super T>> int lowerBound(List<T> list, T target) {
        return ~Collections.binarySearch(list, target, (x, y) -> (x.compareTo(y) >= 0) ? 1 : -1);
    }

    public static <T extends Comparable<? super T>> int upperBound(List<T> list, T target) {
        return ~Collections.binarySearch(list, target, (x, y) -> (x.compareTo(y) > 0) ? 1 : -1);
    }
}


class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte()) return buffer[ptr++];
        else return -1;
    }

    private boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }

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