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 Rust (1.42.0) (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;

//https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

//https://qiita.com/maguro_tuna/items/fab200fdc1efde1612e7
macro_rules! min {
    // 引数が 1 個だけの場合は、そのまま返す
    ($a:expr ) => {
        $a
    };
    // 引数が 2 個の場合は、std::cmp::minを使用して小さい方を返す
    ($a:expr, $b:expr) => {
        std::cmp::min($a, $b)
    };
    // 引数が 3 個以上ある場合は、再帰的に min! マクロを呼び出す
    ($a:expr, $($rest:expr),+ ) => {
        std::cmp::min($a, min!($($rest),+)) // 第2引数以降の部分に対して再帰呼び出し
    };
}

macro_rules! chmin {
    ($base:expr, $($cmps:expr),+) => {
        // 第2引数以降の部分に関して、min! を使用して最小値を求める
        let cmp_min = min!($($cmps),+);
        // それが第1引数より小さかったら、更新して true を返す
        if $base > cmp_min{
            $base = cmp_min;
            true
        }else{
            // 更新が不要なので、false を返す
            false
        }
    };
}

//https://drken1215.hatenablog.com/entry/2020/03/22/154300
fn main() {
    //方向ベクトル
    let dx = vec![1, 0];
    let dy = vec![0, 1];
    //入力処理
    let h: usize = read();
    let w: usize = read();
    let mut fi: Vec<Vec<char>> = vec![vec![' '; w]; h];
    for i in 0..h {
        fi[i] = read::<String>().chars().collect();
    }

    //dpテーブル初期化
    let mut dp: Vec<Vec<u64>> = vec![vec![std::u64::MAX; w]; h];
    //dp初期値セット
    if fi[0][0] == '#' {
        dp[0][0] = 1;
    } else {
        dp[0][0] = 0
    }

    //dp更新
    for i in 0..h {
        for j in 0..w {
            for dir in 0..2 {
                let ni = i + dx[dir];
                let nj = j + dy[dir];
                //場外の場合は処理しない
                if ni >= h || nj >= w {
                    continue;
                }
                let mut add = 0;
                //通路から壁へ移動する時はコスト１増加
                if fi[ni][nj] == '#' && fi[i][j] == '.' {
                    add = 1;
                }
                //dpテーブルを最小値で更新する
                chmin!(dp[ni][nj], dp[i][j] + add);
            }
        }
    }
    //println!("{:?}", dp);
    println!("{}", dp[h-1][w-1]);
}