Problem:
Score: 300 points

Problem Statement

We have a canvas divided into a grid with H rows and W columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j).

Initially, all the squares are white. square1001 wants to draw a picture with black paint. His specific objective is to make Square (i, j) black when s_{i, j}= #, and to make Square (i, j) white when s_{i, j}= ..

However, since he is not a good painter, he can only choose two squares that are horizontally or vertically adjacent and paint those squares black, for some number of times (possibly zero). He may choose squares that are already painted black, in which case the color of those squares remain black.

Determine if square1001 can achieve his objective.

Constraints

H is an integer between 1 and 50 (inclusive).

W is an integer between 1 and 50 (inclusive).

For every (i, j) (1 \leq i \leq H, 1 \leq j \leq W), s_{i, j} is # or ..

Input

Input is given from Standard Input in the following format:

H W
s_{1, 1} s_{1, 2} s_{1, 3} ... s_{1, W}
s_{2, 1} s_{2, 2} s_{2, 3} ... s_{2, W}
: :
s_{H, 1} s_{H, 2} s_{H, 3} ... s_{H, W}

Output

If square1001 can achieve his objective, print Yes; if he cannot, print No.

Sample Input 1

3 3
.#.
###
.#.

Sample Output 1

Yes

One possible way to achieve the objective is shown in the figure below. Here, the squares being painted are marked by stars.

Sample Input 2

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

Sample Output 2

No

square1001 cannot achieve his objective here.

Sample Input 3

11 11
...#####...
.##.....##.
#..##.##..#
#..##.##..#
#.........#
#...###...#
.#########.
.#.#.#.#.#.
##.#.#.#.##
..##.#.##..
.##..#..##.

Sample Output 3

Yes

Solution in Rust (1.15.1) (judge verdict: Accepted)

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

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(i.lock(), &mut o);
    stdout().write_all(&o).unwrap();
}

fn run<R: BufRead, W: Write>(i: R, o: &mut W) {
    let mut i = AtRead::from(i);
    let (h, w) = i.read2::<usize, usize>();
    let mut s = Vec::new();
    s.push(vec![false; w + 2]);
    for _ in 0..h {
        let mut sy: Vec<_> = i.read_line()
            .as_bytes()
            .iter()
            .map(|&x| x == b'#')
            .collect();
        sy.insert(0, false);
        sy.push(false);
        s.push(sy);
    }
    s.push(vec![false; w + 2]);

    let r = if solve(&s, h, w) { "Yes" } else { "No" };
    writeln!(o, "{}", r).unwrap();
}
fn solve(s: &[Vec<bool>], h: usize, w: usize) -> bool {
    for y in 0..h {
        for x in 0..w {
            if s[1 + y][1 + x] && !s[y][1 + x] && !s[2 + y][1 + x] && !s[1 + y][x]
                && !s[1 + y][2 + x]
            {
                return false;
            }
        }
    }
    true
}

mod utils {
    #![allow(dead_code)]
    use super::*;
    use std::ops::*;

    pub struct AtRead<R: BufRead> {
        r: R,
        s: String,
    }

    macro_rules! fn_read {
        {$f:ident($($v:ident: $t:ident),*)} => {
            pub fn $f<$($t: FromStr),*>(&mut self) -> ($($t),*) {
                let i = &mut self.read_line().split(' ');
                $(
                    let $v = next(i);
                )*
                ($($v),*)
            }
        };
    }

    impl<R: BufRead> AtRead<R> {
        pub fn from(r: R) -> Self {
            AtRead {
                r: r,
                s: String::new(),
            }
        }
        pub fn read_line(&mut self) -> &str {
            self.s.clear();
            self.r.read_line(&mut self.s).unwrap();
            self.s.trim()
        }

        pub fn read<T: FromStr>(&mut self) -> T {
            self.read_line().parse().ok().unwrap()
        }
        fn_read! { read2(v1: T1, v2: T2) }
        fn_read! { read3(v1: T1, v2: T2, v3: T3) }
        fn_read! { read4(v1: T1, v2: T2, v3: T3, v4: T4) }
        fn_read! { read5(v1: T1, v2: T2, v3: T3, v4: T4, v5: T5) }

        pub fn read_vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
            self.read_line()
                .split(' ')
                .take(n)
                .map(|x| x.parse().ok().unwrap())
                .collect()
        }
        pub fn read_array<A: AsMut<[T]> + Default, T: FromStr>(&mut self) -> A {
            let mut a: A = Default::default();
            {
                let a: &mut [T] = a.as_mut();
                let i = &mut self.read_line().split(' ');
                for n in 0..a.len() {
                    a[n] = next(i);
                }
            }
            a
        }
    }

    fn next<'a, T: FromStr, I: std::iter::Iterator<Item = &'a str>>(i: &mut I) -> T {
        i.next().unwrap().parse().ok().unwrap()
    }

    #[derive(Debug, Clone, Copy)]
    pub struct ModInt(pub usize);

    const MOD_BASE: usize = 1000000007;
    const MOD_INV_POW: usize = 1000000005;

    impl ModInt {
        pub fn new(n: usize) -> Self {
            ModInt(n % MOD_BASE)
        }
        pub fn pow(self, mut exp: usize) -> Self {
            let mut b = self;
            let mut r = ModInt(1);
            while exp != 0 {
                if exp % 2 == 1 {
                    r *= b;
                }
                exp /= 2;
                b = b * b;
            }
            r
        }
        pub fn inverse_element(self) -> Self {
            self.pow(MOD_INV_POW)
        }
    }

    macro_rules! ModInt_op {
        (($ot:ident, $f:ident), ($ot_a:ident, $f_a:ident), $($rhs:ty, $e:expr,)*) => {
            $(
            impl $ot<$rhs> for ModInt {
                type Output = Self;
                fn $f(self, rhs: $rhs) -> Self {
                    Self::new(($e)(self, rhs))
                }
            }
            impl $ot_a<$rhs> for ModInt {
                fn $f_a(&mut self, rhs: $rhs) {
                    *self = Self::new(($e)(*self, rhs))
                }
            }
            )*
        }
    }

    ModInt_op!(
        (Add, add),
        (AddAssign, add_assign),
        ModInt,
        |l: ModInt, r: ModInt| l.0 + r.0,
        usize,
        |l: ModInt, r: usize| l.0 + r,
    );

    ModInt_op!(
        (Mul, mul),
        (MulAssign, mul_assign),
        ModInt,
        |l: ModInt, r: ModInt| l.0 * r.0,
        usize,
        |l: ModInt, r: usize| l.0 * r,
    );

    ModInt_op!(
        (Sub, sub),
        (SubAssign, sub_assign),
        ModInt,
        |l: ModInt, r: ModInt| MOD_BASE + l.0 - r.0,
        usize,
        |l: ModInt, r: usize| MOD_BASE + l.0 - r,
    );

    // std::cmp::Reverseと同じ
    #[derive(PartialEq, Eq)]
    pub struct RevCmp<T>(pub T);

    impl<T: PartialOrd> PartialOrd for RevCmp<T> {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            other.0.partial_cmp(&self.0)
        }
    }
    impl<T: Ord> Ord for RevCmp<T> {
        fn cmp(&self, other: &Self) -> Ordering {
            other.0.cmp(&self.0)
        }
    }

    pub struct PascalsTriangle<T> {
        buf: Vec<T>,
        n: usize,
    }

    impl<T: One> PascalsTriangle<T> {
        pub fn new(n: usize) -> Self {
            let mut s = PascalsTriangle {
                buf: vec![T::one()],
                n: 1,
            };
            while s.n <= n {
                let i = s.buf.len() - s.n;
                s.buf.push(T::one());
                for m in 1..s.n {
                    let v = s.buf[i + m - 1] + s.buf[i + m];
                    s.buf.push(v);
                }
                s.buf.push(T::one());
                s.n += 1;
            }
            s
        }
        pub fn get(&mut self, n: usize, m: usize) -> T {
            debug_assert!(n <= self.n);
            debug_assert!(m <= n);
            self.buf[n * (n + 1) / 2 + m]
        }
    }

    pub struct PascalsTriangleIter<T> {
        buf: Vec<T>,
    }
    impl<T: One> PascalsTriangleIter<T> {
        pub fn new(n: usize) -> Self {
            let mut s = PascalsTriangleIter {
                buf: Vec::with_capacity(n + 1),
            };
            for _ in 0..n + 1 {
                s.next();
            }
            s
        }
        pub fn next(&mut self) {
            for i in (1..self.buf.len()).rev() {
                self.buf[i] = self.buf[i] + self.buf[i - 1];
            }
            self.buf.push(T::one());
        }
        pub fn get(&self) -> &[T] {
            &self.buf
        }
    }

    pub struct ModIntFacts {
        f: Vec<ModInt>,
        rf: Vec<ModInt>,
    }
    impl ModIntFacts {
        pub fn new(n: usize) -> Self {
            let mut s = ModIntFacts {
                f: vec![ModInt(0); n + 1],
                rf: vec![ModInt(0); n + 1],
            };

            let v = ModInt(1);
            s.f[0] = v;
            for i in 1..n + 1 {
                s.f[i] = s.f[i - 1] * i;
            }
            s.rf[n] = s.f[n].inverse_element();
            for i in (1..n + 1).rev() {
                s.rf[i - 1] = s.rf[i] * i;
            }
            s
        }
        pub fn fact(&self, n: usize) -> ModInt {
            self.f[n]
        }
        pub fn comb(&self, n: usize, c: usize) -> ModInt {
            self.f[n] * self.rf[c] * self.rf[n - c]
        }
    }

    pub trait Zero: Add<Output = Self> + Sized + Copy {
        fn zero() -> Self;
    }
    pub trait One: Zero {
        fn one() -> Self;
    }

    macro_rules! impl_zero {
        ($t:ty, $e:expr) => {
            impl Zero for $t {
                fn zero() -> Self {
                    $e
                }
            }
        }
    }
    macro_rules! impl_one {
        ($t:ty, $e1:expr, $e0:expr) => {
            impl One for $t {
                fn one() -> Self {
                    $e1
                }
            }
            impl_zero!($t, $e0);
        }
    }

    impl_one!(usize, 1, 0);
    impl_one!(u32, 1, 0);
    impl_one!(i32, 1, 0);
    impl_one!(f64, 1.0, 0.0);
    impl_one!(ModInt, ModInt(1), ModInt(0));

    pub trait BinarySearchExt<T> {
        fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize;
        fn lower_bound(&self, x: &T) -> usize;
        fn upper_bound(&self, x: &T) -> usize;
    }
    impl<T: Ord> BinarySearchExt<T> for [T] {
        fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize {
            let mut low = 0;
            let mut high = self.len();
            while low < high {
                let mid = (low + high) / 2;
                if f(&self[mid]) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }
            low
        }
        fn lower_bound(&self, x: &T) -> usize {
            self.lower_bound_by(|y| x <= y)
        }
        fn upper_bound(&self, x: &T) -> usize {
            self.lower_bound_by(|y| x < y)
        }
    }

    pub trait AtSliceExt<T> {
        fn rotate(&mut self, mid: usize);
    }
    impl<T> AtSliceExt<T> for [T] {
        fn rotate(&mut self, mid: usize) {
            {
                let (l, r) = self.split_at_mut(mid);
                l.reverse();
                r.reverse();
            }
            self.reverse()
        }
    }

}