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.*;import java.util.*;import java.math.*;
public class Main
{
	static long mod=1000000007l;
    static int max=Integer.MAX_VALUE,min=Integer.MIN_VALUE;
    static long maxl=Long.MAX_VALUE,minl=Long.MIN_VALUE;
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    
    
    static public void main(String[] args)throws Exception
    {
    	st=new StringTokenizer(br.readLine());
    	int r=i();
    	int c=i();
    	char ch[][]=new char[r][c];
    	int ar[][]=new int[r][c];
    	for(int x=0;x<r;x++)
    	{
    		String s=s();
    		for(int y=0;y<c;y++)ch[x][y]=s.charAt(y);
    	}
    	ar[r-1][c-1]=0;
    	if(ch[r-1][c-1]=='#')ar[r-1][c-1]=1;
    	for(int x=c-2;x>=0;x--)
		{
    		if(ch[r-1][x]=='.')ar[r-1][x]=ar[r-1][x+1];
    		else ar[r-1][x]=ar[r-1][x+1]+1;
		}
    	for(int x=r-2;x>=0;x--)
		{
    		if(ch[x][c-1]=='.')ar[x][c-1]=ar[x+1][c-1];
    		else ar[x][c-1]=ar[x+1][c-1]+1;
		}
    	for(int x=r-2;x>=0;x--)
    	{
    		for(int y=c-2;y>=0;y--)
    		{
    			ar[x][y]=min(ar[x+1][y],ar[x][y+1]);
    			if(ch[x][y]=='#')ar[x][y]++;
    		}
    	}
    	pl(ar[0][0]);
//    	for(int x=0;x<r;x++)
//    	{
//    		for(int y=0;y<c;y++)p(ar[x][y]+" ");
//    		pl();
//    	}
	}
    static int max(int a,int b){return Math.max(a,b);}
    static int min(int a,int b){return Math.min(a,b);}
    static int abs(int a){return Math.abs(a);}
    static long max(long a,long b){return Math.max(a,b);}
    static long min(long a,long b){return Math.min(a,b);}
    static long abs(long a){return Math.abs(a);}
    static int sq(int a){return (int)Math.sqrt(a);}
    static long sq(long a){return (long)Math.sqrt(a);}
    static int gcd(int a,int b) {return b==0?a:gcd(b,a%b);}
    static int ncr(int n,int c,long m)
    {
        long a=1l;
        for(int x=n-c+1;x<=n;x++)a=((a*x)%m);
        long b=1l;
        for(int x=2;x<=c;x++)b=((b*x)%m);
        long v=(div((int)b,m-2,m)%m);
        return (int)((a*v)%m);
    }
    static int fib(int n) 
    { 
        double p=(1+Math.sqrt(5))/2; 
        return (int)Math.round(Math.pow(p,n)/Math.sqrt(5)); 
    }
    static boolean[] sieve(int n)
    {
        boolean bo[]=new boolean[n+1];
        bo[0]=true;bo[1]=true;
        for(int x=4;x<=n;x+=2)bo[x]=true;
        for(int x=3;x*x<=n;x+=2)
        {
            if(!bo[x])
            {
                for(int y=x*x;y<=n;y+=x)bo[y]=true;
            }
        }
        return bo;
    }
    static int[] fac(int n)
    {
        int bo[]=new int[n+1];
        bo[0]=0;bo[1]=1;
        for(int x=1;x<=n;x++)
        {
            for(int y=x;y<=n;y+=x)bo[y]++;
        }
        return bo;
    }
    static long div(long a,long b,long m) 
    {
        long r=1l;
        a%=m;  
        while(b>0)
        {
            if((b&1)==1)r=(r*a)%m; 
            b>>=1;
            a=(a*a)%m;  
        } 
        return r; 
    }
    static int i()throws IOException
    {
        if(!st.hasMoreTokens()) st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    static long l()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    static String s()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    static double d()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Double.parseDouble(st.nextToken());
    }
    static void p(Object p){System.out.print(p);}
    static void p(String p){System.out.print(p);}
    static void p(int p){System.out.print(p);}
    static void p(double p){System.out.print(p);}
    static void p(long p){System.out.print(p);}
    static void p(char p){System.out.print(p);}
    static void p(boolean p){System.out.print(p);}
    static void pl(Object p){System.out.println(p);}
    static void pl(String p){System.out.println(p);}
    static void pl(int p){System.out.println(p);}
    static void pl(char p){System.out.println(p);}
    static void pl(double p){System.out.println(p);}
    static void pl(long p){System.out.println(p);}
    static void pl(boolean p){System.out.println(p);}
    static void pl(){System.out.println();}
    static int[] ari(int n)throws IOException
    {
        int ar[]=new int[n];
        st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=Integer.parseInt(st.nextToken());
        return ar;
    }
    static int[][] ari(int n,int m)throws IOException
    {
        int ar[][]=new int[n][m];
        for(int x=0;x<n;x++)
        {
            st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Integer.parseInt(st.nextToken());
        }
        return ar;
    }
    static long[] arl(int n)throws IOException
    {
        long ar[]=new long[n];
        st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=Long.parseLong(st.nextToken());
        return ar;
    }
    static long[][] arl(int n,int m)throws IOException
    {
        long ar[][]=new long[n][m];
        for(int x=0;x<n;x++)
        {
            st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Long.parseLong(st.nextToken());
        }
        return ar;
    }
    static String[] ars(int n)throws IOException
    {
        String ar[]=new String[n];
        st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=st.nextToken();
        return ar;
    }
    static double[] ard(int n)throws IOException
    {
        double ar[]=new double[n];
        st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Double.parseDouble(st.nextToken());
        return ar;
    }
    static double[][] ard(int n,int m)throws IOException
    {
        double ar[][]=new double[n][m];
        for(int x=0;x<n;x++)
        {
            st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Double.parseDouble(st.nextToken());
        }
        return ar;
    }
    static char[] arc(int n)throws IOException
    {
        char ar[]=new char[n];
        st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=st.nextToken().charAt(0);
        return ar;
    }
    static char[][] arc(int n,int m)throws IOException
    {
        char ar[][]=new char[n][m];
        for(int x=0;x<n;x++)
        {
            String s=br.readLine();
            for(int y=0;y<m;y++)ar[x][y]=s.charAt(y);
        }
        return ar;
    }
    static void p(int ar[])
    {
        StringBuilder sb=new StringBuilder("");;
        for(int a:ar) sb.append(a+" ");
        System.out.println(sb);
    }
    static void p(int ar[][])
    {
        StringBuilder sb;
        for(int a[]:ar)
        {
            sb=new StringBuilder("");
            for(int aa:a) sb.append(aa+" ");
            System.out.println(sb);
        }
    }
    static void p(long ar[])
    {
        StringBuilder sb=new StringBuilder("");
        for(long a:ar)sb.append(a+" ");
        System.out.println(sb);
    }
    static void p(long ar[][])
    {
        StringBuilder sb;
        for(long a[]:ar)
        {
            sb=new StringBuilder("");
            for(long aa:a)sb.append(aa+" ");
            System.out.println(sb);
        }
    }
    static void p(String ar[])
    {
        StringBuilder sb=new StringBuilder("");
        for(String a:ar)sb.append(a+" ");
        System.out.println(sb);
    }
    static void p(double ar[])
    {
        StringBuilder sb=new StringBuilder("");
        for(double a:ar)sb.append(a+" ");
        System.out.println(sb);
    }
    static void p(double ar[][])
    {
        StringBuilder sb;
        for(double a[]:ar)
        {
            sb=new StringBuilder("");
            for(double aa:a)sb.append(aa+" ");
            System.out.println(sb);
        }
    }
    static void p(char ar[])
    {
        StringBuilder sb=new StringBuilder("");
        for(char aa:ar)sb.append(aa+" ");
        System.out.println(sb);
    }
    static void p(char ar[][])
    {
        StringBuilder sb;
        for(char a[]:ar)
        {
            sb=new StringBuilder("");
            for(char aa:a)sb.append(aa+" ");
            System.out.println(sb);
        }
    }
}