Problem:
Score : 400 points

Problem Statement

There is a grid with H horizontal rows and W vertical columns, and there are obstacles on some of the squares.

Snuke is going to choose one of the squares not occupied by an obstacle and place a lamp on it.
The lamp placed on the square will emit straight beams of light in four cardinal directions: up, down, left, and right.
In each direction, the beam will continue traveling until it hits a square occupied by an obstacle or it hits the border of the grid. It will light all the squares on the way, including the square on which the lamp is placed, but not the square occupied by an obstacle.

Snuke wants to maximize the number of squares lighted by the lamp.

You are given H strings S_i (1 \leq i \leq H), each of length W. If the j-th character (1 \leq j \leq W) of S_i is #, there is an obstacle on the square at the i-th row from the top and the j-th column from the left; if that character is ., there is no obstacle on that square.

Find the maximum possible number of squares lighted by the lamp.

Constraints

1 \leq H \leq 2,000

1 \leq W \leq 2,000

S_i is a string of length W consisting of # and ..

. occurs at least once in one of the strings S_i (1 \leq i \leq H).

Input

Input is given from Standard Input in the following format:

H W
S_1
:
S_H

Output

Print the maximum possible number of squares lighted by the lamp.

Sample Input 1

4 6
#..#..
.....#
....#.
#.#...

Sample Output 1

8

If Snuke places the lamp on the square at the second row from the top and the second column from the left, it will light the following squares: the first through fifth squares from the left in the second row, and the first through fourth squares from the top in the second column, for a total of eight squares.

Sample Input 2

8 8
..#...#.
....#...
##......
..###..#
...#..#.
##....#.
#...#...
###.#..#

Sample Output 2

13

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

use std::io::*;

const SP: u8 = b' ';
const LF: u8 = b'\n';

struct CharacterInput<'a> {
    locked_stdin: StdinLock<'a>,
    bytes_buffer: Vec<u8>,
}

impl<'a> CharacterInput<'a> {
    fn read(&mut self, delimiter: u8) -> &[u8] {
        self.bytes_buffer.clear();

        let mut len = self
            .locked_stdin
            .read_until(delimiter, &mut self.bytes_buffer)
            .unwrap();

        if len > 0 {
            len -= 1;
        }

        &self.bytes_buffer[0..len]
    }

    fn scan_u(&mut self, delimiter: u8) -> u32 {
        self.read(delimiter)
            .into_iter()
            .fold(0, |accumulator, byte| {
                (byte - b'0') as u32 + accumulator * 10
            })
    }
}

fn create_cin<'a>(input: StdinLock<'a>, buffer_capacity: usize) -> CharacterInput {
    CharacterInput {
        locked_stdin: input,
        bytes_buffer: Vec::with_capacity(buffer_capacity),
    }
}

fn println<T: std::string::ToString>(s: T) {
    println!("{}", s.to_string());
}

// ------------------------------------------------------------------------

struct Grid<T> {
    vec: Vec<T>,
    row_count: usize,
    column_count: usize
}

impl<T> Grid<T>
where
    T: Clone + Copy,
{
    fn new(initial_value: T, column_count: usize, row_count: usize) -> Grid<T> {
        Grid {
            vec: vec![initial_value; column_count * row_count],
            row_count: row_count,
            column_count: column_count
        }
    }
}

use std::ops::{Index, IndexMut};

impl<T> Index<usize> for Grid<T> {
    type Output = [T];
    fn index(&self, row: usize) -> &[T] {
        debug_assert!(row < self.row_count);
        let start_index = row * self.column_count;
        &self.vec[start_index..start_index + self.column_count]
    }
}

impl<T> IndexMut<usize> for Grid<T> {
    fn index_mut(&mut self, row: usize) -> &mut [T] {
        debug_assert!(row < self.row_count);
        let start_index = row * self.column_count;
        &mut self.vec[start_index..start_index + self.column_count]
    }
}


trait ExIterator: Iterator {
    fn foreach<F>(self, mut callback: F)
    where
        Self: Sized,
        F: FnMut(Self::Item),
    {
        self.fold((), move |(), item| callback(item));
    }
}

impl<I: Iterator> ExIterator for I {}


trait GridReader<T> {
    fn scan_grid(
        &mut self,
        width: usize,
        height: usize,
        initial_value: T,
        key_value_arrays: &[(u8, T)],
    ) -> Grid<T>;
}

impl<'a, T> GridReader<T> for CharacterInput<'a>
where
    T: Clone + Copy,
{
    /**
     * Example:
     * let mut grid = cin.scan_grid(w, h, 0 as u32, &[(b'#', 1)]);
     */
    fn scan_grid(
        &mut self,
        column_count: usize,
        row_count: usize,
        initial_value: T,
        key_value_arrays: &[(u8, T)],
    ) -> Grid<T> {
        let mut grid = Grid::new(initial_value, column_count, row_count);

        for row_index in 0..row_count {
            let byte_row = self.read(LF);
            let grid_row = &mut grid[row_index];

            (0..column_count)
                .filter_map(|x| {
                    key_value_arrays
                        .into_iter()
                        .filter(|entry| byte_row[x] == entry.0)
                        .map(|entry| (x, entry.1))
                        .next()
                })
                .foreach(|(x, value)| grid_row[x] = value);
        }

        grid
    }
}

// ------------------------------------------------------------------------

fn main() {
    let cin = stdin();
    let cin = &mut create_cin(cin.lock(), 32);

    let h = cin.scan_u(SP) as usize;
    let w = cin.scan_u(LF) as usize;

    let mut grid = cin.scan_grid(w, h, 0 as i32, &[(b'#', -1)]);

    for y in 0..h {
        let row = &mut grid[y];
        let mut x = 0;
        while x < w {
            if row[x] != -1 {
                let mut next_x = x + 1;
                while next_x < w && row[next_x] != -1 {
                    next_x += 1;
                }
                let count = next_x - x;

                for x in x..next_x {
                    row[x] = count as i32;
                }
                x = next_x + 1;
            } else {
                x += 1;
            }
        }
    }

    let mut max_count = -1;

    for x in 0..w {
        let mut y = 0;
        while y < h {
            if grid[y][x] != -1 {
                let mut next_y = y + 1;
                while next_y < h && grid[next_y][x] != -1 {
                    next_y += 1;
                }
                let count = next_y - y;

                for y in y..next_y {
                    let mut row = &mut grid[y];
                    row[x] += count as i32;
                    if row[x] > max_count { max_count = row[x]; }
                }

                y = next_y + 1;
            } else {
                y += 1;
            }
        }
    }

    println(max_count - 1);
}