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)

// mod custom_lib;
use std::cmp;

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

pub 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")
}

pub fn read_n<T: FromStr>(n: u32) -> Vec<T> {
  read_n_logic::<T>(n, vec![])
}

pub fn read_n_logic<T: FromStr>(n: u32, mut a: Vec<T>) -> Vec<T> {
  match n {
    0 => a,
    _ => {
      a.push(read::<T>());
      read_n_logic(n - 1, a)
    }
  }
}


fn main() {
  let h = read::<usize>();
  let w = read::<u32>();

  let mut s = Vec::new();
  let mut s_point = Vec::new();

  for _ in 0..h {
    let mut row = Vec::new();
    for c in read::<String>().chars() {
      row.push(c);
    }
    s_point.push(calc_width_lamb(&row));
    s.push(row);
  }

  for w_idx in 0..w {
    let height_point = calc_height_lamb(&s, w_idx as usize);
    for (h_idx, v) in height_point.iter().enumerate() {
      if v != &0 {
        s_point[h_idx as usize][w_idx as usize] += v - 1;
      }
    }
  }

  // 結果
  let mut answer = 0;
  for item in s_point {
    answer = cmp::max(*item.iter().max().unwrap(), answer)
  }

  println!("{}", answer);
}

fn calc_height_lamb(map: &Vec<Vec<char>>, w_idx: usize) -> Vec<u32> {
  let mut height_row = vec![];
  for row in map {
    height_row.push(row[w_idx])
  }
  calc_width_lamb(&height_row)
}

fn calc_width_lamb(row: &Vec<char>) -> Vec<u32> {
  let mut row_copy = row.clone();
  row_copy.insert(0, '#');
  let last_idx = row_copy.len();
  row_copy.insert(last_idx, '#');

  let mut prev_sharp = 0;
  let mut result_vec = vec![0; row_copy.len()];

  for (i, v) in row_copy.iter().enumerate() {
    if v == &'#' {
      for idx in prev_sharp..i {
        result_vec[idx] = (i - prev_sharp) as u32;
      }
      prev_sharp = i + 1;
    }
  }

  result_vec.remove(0);
  result_vec.remove(last_idx - 1);
  result_vec
}