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.InputStream;
import java.io.IOException;
import java.io.PrintStream;
import java.math.*;
import java.util.*;

public class Main {

  public static void main(String[] args) {
    solve(System.in, System.out);
  }

  static void solve(InputStream is, PrintStream os) {
    Scanner sc = new Scanner(is);

    /* read */
    int h = sc.nextInt();
    int w = sc.nextInt();

    boolean[][] grid = new boolean[h][w];

    for (int r = 0; r < h; r++) {
      String line = sc.next();
      for (int c = 0; c < w; c++) {
        grid[r][c] = line.charAt(c) == '.';
      }
    }
    os.println(travel(0, 0, true, grid, new HashMap<>(), new HashMap<>()));
  }

  private static int travel(int r, int c, boolean status, boolean[][] grid, Map<Integer, Integer> memoT, Map<Integer, Integer> memoF) {

    int w = grid[0].length;
    int h = grid.length;

    if (r == h || c == w) return Integer.MAX_VALUE;

    int ans = 0;
    if (status && !grid[r][c]) {
      ans++;
    }
    if (r == h - 1 && c == w - 1) return ans;

    int x = r * w + c;
    if (status) {
      if (memoT.containsKey(x)) return memoT.get(x);
    } else {
      if (memoF.containsKey(x)) return memoF.get(x);
    }

    int right = travel(r, c + 1, grid[r][c], grid, memoT, memoF);
    int down = travel(r + 1, c, grid[r][c], grid, memoT, memoF);
    ans += Math.min(down, right);
    if (status) {
      memoT.put(x, ans);
    } else {
      memoF.put(x, ans);
    }

    return ans;
  }

  private static long gcd(long m, long n) {
    if (m < n) return gcd(n, m);
    if (n == 0) return m;
    return gcd(n, m % n);
  }

  private static long lcm(long m, long n) {
    return m / gcd(m, n) * n;
  }

  private static class Modular {

    private final long mod;

    private Modular(long mod) {
      this.mod = mod;
    }

    private long inverse(long n) {
      return pow(n, mod - 2) % mod;
    }

    private long pow(long x, long n) {
      /*
      long ans = 1;
      while (n > 0) {
        if ((n & 1) == 1) {
          ans = ans * x % mod;
        }
        x = x * x % mod;
        n >>= 1;
      }
      return ans;
      */
      if (n == 0) {
        return 1;
      }
      return n % 2 == 0 ?
          pow(x * x % mod, n / 2) % mod :
          x % mod * pow(x, n - 1) % mod;
    }
  }

  private static class ModularNFixedCombination {

    private final Modular modular;
    private final long[] comb;
    private final long N;

    public ModularNFixedCombination(long N, int size, long mod) {
      this.modular = new Modular(mod);
      this.comb = new long[size + 1];
      this.N = N;

      comb[0] = 1;

      for (int i = 1; i <= size; i++) {
        comb[i] = ((comb[i - 1] * (N - (i - 1))) % mod * modular.inverse(i)) % mod;
      }
    }

    long combination(int n, int k) {
      if (n != N) {
        throw new IllegalStateException();
      }
      return comb[k];
    }

    long repeatedCombination(int n, int k) {
      return combination(n + k - 1, k);
    }
  }

  private static class ModularCombination {

    private final long fact[];
    private final long mod;
    private final Modular modular;

    public ModularCombination(int size, long mod) {
      this.fact = new long[size + 1];
      this.mod = mod;
      this.modular = new Modular(mod);

      this.fact[0] = 1;
      for (int i = 1; i <= size; i++) {
        fact[i] = (fact[i - 1] * i) % mod;
      }
    }

    private long factorial(int n) {
      return fact[n];
    }

    long combination(int n, int k) {
      return
          (
              (
                  (
                      factorial(n) * modular.inverse(factorial(n - k))
                  ) % mod
              ) * modular.inverse(factorial(k))
          ) % mod;
    }

    long repeatedCombination(int n, int k) {
      return combination(n + k - 1, k);
    }
  }

  private static class Scanner {

    private final InputStream is;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    Scanner(InputStream is) {
      this.is = is;
    }

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = is.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 static 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());
    }
  }
}