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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

#define DEBUG 0

#define int long long
#define for0(i,n) for (int i=0; i<n; i++)
#define fill1(a,z) fill_n(a, sizeof(a)/sizeof(a[0]), z)
#define fill2(a,z) fill_n(a[0], sizeof(a)/sizeof(a[0][0]), z)
#define fill3(a,z) fill_n(a[0][0], sizeof(a)/sizeof(a[0][0][0]), z)
#define mp make_pair
#define X first
#define Y second
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
#define all(a) a.begin(),a.end()
#define sz(x) (int)(x).size()
#define pmod(x,m) (((x)%(m)+m)%m)
#ifdef int
#define read(x) scanf("%lld",&x);
#else
#define read(x) scanf("%d",&x);
#endif

#ifdef DEBUG
#define nl cout<<"\n";
#define pr(x) cout<<(x)<<" ";
#define prl(x) cout<<#x " = "<<x<<endl;
#define prp(x) cout<<"("<<(x).first<<" "<<(x).second<<") ";
#define printv(v) {for(int _=0; _<sz(v); _++) cout<<v[_]<<" "; cout<<"\n";}
#define printa(a,s) {for (int _=0; _<s; _++) cout<<a[_]<<" "; cout<<"\n";}
#define print2D(a,m,n) {for (int _=0; _<m; _++) {for (int __=0; __<n; __++) cout<<a[_][__]<<" "; cout<<"\n";} cout<<"\n";}
#define priter(v) {for (auto x : v) {pr(x)} nl}
#define debug cout<<"ok at line "<<__LINE__<<endl;
#else
#define nl
#define pr(x)
#define prl(x)
#define prp(x)
#define printv(v)
#define printa(a,s)
#define print2D(a,m,n)
#define priter(v)
#define debug
#endif
#define MAXN 100000

using namespace std;

typedef long long ll;

const int INF = 2147483647;
const long long INFL = 9223372036854775807LL;
const double EPSILON = 0.00000001;
const long long MOD = 1000000007;

int32_t main()
{
    #ifdef DEBUG
    //freopen("A.txt","r",stdin);
    //freopen("","w",stdout);
    #endif
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    
    int h,w;
    cin >> h >> w;
    vector<string> grid;
    for0(i,h) {
        string row;
        cin >> row;
        grid.push_back(row);
    }
    
    int dp[h+1][w+1];
    fill2(dp, INF);
    dp[0][0] = grid[0][0] == '#';
    
    for (int i=0; i<h; i++) {
        for (int j=0; j<w; j++) {
            if (i == 0 && j == 0)
                continue;
            int a = INF, b = INF;
            if (i > 0) {
                a = dp[i-1][j] + (grid[i][j] != grid[i-1][j] and grid[i][j] == '#');
            }
            if (j > 0) {
                b = dp[i][j-1] + (grid[i][j] != grid[i][j-1] and grid[i][j] == '#');
            }
            dp[i][j] = min(a,b);
        }
    }
    
    int ans = dp[h-1][w-1];
    cout << ans << endl;
    
    return 0;
}