Problem: 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.

Examples

Input

3 3
.##
.#.
##.


Output

1


Input

3 3
.##
.#.
.


Output

1


Input

2 2
.
.#


Output

2


Input

4 4
..##
...
.
.


Output

0


Input

5 5
.#.#.
.#.#
.#.#.
.#.#
.#.#.


Output

4

Solution (in JAVA):

Solution:

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

public class Main {

	static long sx = 0, sy = 0, m = (long) (1e9 + 7);

	static ArrayList<Integer>[] a;
	static int[][][] dp;
	static long[] farr;
	// static boolean b = true;
	static HashMap<Integer, Integer> hm = new HashMap<>();

	// static TreeMap<Integer, Integer> hm = new TreeMap<>();
	public static PrintWriter out;
	// static ArrayList<pair> p = new ArrayList<>();
	static long[] fact = new long[(int) 1e6];
	static boolean b = false;
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long mod = 998244353;
	static int[] col;
	static String s;
	static int cnt;
	static int[][] p;

	public static void main(String[] args) throws IOException {

		Scanner scn = new Scanner(System.in);

		int n = scn.nextInt(), m = scn.nextInt();

		char[][] ch = new char[n][m];

		for (int i = 0; i < n; i++) {
			String s = scn.next();

			for (int j = 0; j < m; j++)
				ch[i][j] = s.charAt(j);
		}

		dp = new int[n][m][2];

		for (int i = 0; i < n; i++)
			for (int j = 0; j < m; j++)
				Arrays.fill(dp[i][j], -1);

		int ans = f(ch, 0, 0, 0);

		System.out.println(ans);
	}

	private static int f(char[][] ch, int i, int j, int k) {

		if (i == ch.length - 1 && j == ch[0].length - 1) {

			if (ch[i][j] == '.' ||(ch[i][j] == '#' && k == 1))
				return 0;
			else
				return 1;
		}

		if (i >= ch.length || j >= ch[0].length)
			return (int) 1e6;
		
		if (dp[i][j][k] != -1)
			return dp[i][j][k];

		if (ch[i][j] == '#') {

			if (k == 0) {

				int ans1 = f(ch, i + 1, j, 1) + 1;
				int ans2 = f(ch, i, j + 1, 1) + 1;

				return dp[i][j][k] = Math.min(ans1, ans2);
			}

			else {
				int ans1 = f(ch, i + 1, j, 1);
				int ans2 = f(ch, i, j + 1, 1);
				return dp[i][j][k] = Math.min(ans1, ans2);
			}
		}

		else {

			int ans1 = f(ch, i + 1, j, 0);
			int ans2 = f(ch, i, j + 1, 0);
			return dp[i][j][k] = Math.min(ans1, ans2);
		}
	}

	// _________________________TEMPLATE_____________________________________________________________

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

	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer o1, Integer o2) {
	// if (b[o1])
	// return -1;
	// else if (b[o2])
	// return 1;
	// else
	// return (int) (a[o2].size() - a[o1].size());
	// }
	//
	// }

	// public static long pow(long a, long b) {
	//
	// if(b<0)return 0;
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		int tb, tbw;

		pair() {
			tb = tbw = 0;
		}

		@Override
		public int compareTo(pair o) {

			return 1;
		}

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

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

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

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}