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: Time Limit Exceeded)

import java.io.*;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.NoSuchElementException;
import java.util.Queue;
import java.util.concurrent.DelayQueue;

public class Main {

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int h = fs.nextInt();
        int w = fs.nextInt();
        String[][] ss = new String[h][w];
        for( int i = 0 ; i < h ; i++ ){
            ss[i] = fs.next().split("" );
        }

        int count = 1000000;

        Deque<Integer> posQueue = new ArrayDeque();

        // 変換カウント(3桁) + 白かどうか(1桁) + 縦座標(2桁) + 横座標(2桁)
        // 200 + 1 + 99 + 99
        posQueue.add(("#".equals(ss[0][0]) ? 1 : 0) * 10000 + ("#".equals(ss[0][0]) ? 0 : 1) * 1000); // 白かどうか　+ 縦座標 * 100 + 横座標

        while( !posQueue.isEmpty() ) {

            // 今いる場所
            int item = posQueue.poll();
            int changeCount = item / 10000;
            int isWhite = (item % 10000) / 1000;
            int hPos = (item % 1000) / 100;
            int wPos = item % 100;

            // 今いる場所が最終地点なら集計して終了
            if (hPos == h - 1 && wPos == w - 1) {
                count = Math.min(count, changeCount);
                continue;
            }

            // 下を見る
            if (hPos != h - 1) {
                // 白い場所から黒い場所へ移る場合のみカウントを増加
                int addCount = (isWhite == 1 && "#".equals(ss[hPos + 1][wPos])) ? 1 : 0;
                posQueue.add((changeCount+addCount)*10000 + (".".equals(ss[hPos + 1][wPos]) ? 1 : 0) * 1000 + (hPos + 1) * 100 + wPos);
            }
            // 右を見る
            if (wPos != w - 1) {
                // 白い場所から黒い場所へ移る場合のみカウントを増加
                int addCount = (isWhite == 1 && "#".equals(ss[hPos][wPos + 1])) ? 1 : 0;
                posQueue.add((changeCount+addCount)*10000 + (".".equals(ss[hPos][wPos+1]) ? 1 : 0) * 1000 + hPos * 100 + wPos + 1 );
            }
        }

        System.out.println( count );

    }

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

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

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

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

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

        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();
        }

        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());
        }
    }
}