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)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
 
use std::cmp::Ordering;
use std::cmp;
use std::cmp::min;
use std::collections::BTreeMap;
use std::process;
use std::cmp::Ord;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::collections::BTreeSet;
use std::mem;
use std::collections::BinaryHeap;
/// Equivalent to std::lowerbound and std::upperbound in c++
pub trait BinarySearch<T> {
    fn lower_bound(&self, &T) -> usize;
    fn upper_bound(&self, &T) -> usize;
}
 
impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}
 
fn matmul(A:&Vec<Vec<i64>>, B:&Vec<Vec<i64>>) -> Vec<Vec<i64>>{
    let mut C = vec![vec![0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
                C[i][j] %= MOD;
            }
        }
    }
    return C;
}
fn matpow(A:&mut Vec<Vec<i64>>, n:usize) -> Vec<Vec<i64>>{
    let mut B = vec![vec![0;A.len()];A.len()];
    for i in 0..A.len(){
        B[i][i] = 1;
    }
    let mut n = n;
    let mut tmp = A.clone();
    while(n>0){
        if n&1 == 1{B = matmul(&B, &tmp);}
        tmp = matmul(&tmp, &tmp);
        n>>=1;
    }
    return B;
}

 
 
 

/*
subset enumeration
let mut set;
let mut subset = set;
        for sm2 in 0..1<<n{
            if subset==0{
                break;
            }

            hogehoge


            subset = (subset-1)&set;
        }
*/
/*
全方位木
    fn dfs(s:usize,bef:usize,m:i64, g:&Vec<Vec<usize>>, dp:&mut Vec<Vec<i64>>)->i64{
        let mut res = 1;
        for i in 0..g[s].len(){
            let e = g[s][i];
            if e != bef{
                dp[s][i] = dfs(e, s, m, g, dp);
                res *= (1 + dp[s][i]);
                res %= m;
            }
        }
        return res;
    }
    let tmp = dfs(0, n, m, &g, &mut dp);
    fn dfs2(s:usize, bef:usize, p:i64, m:i64, g:&Vec<Vec<usize>>, dp:&mut Vec<Vec<i64>>){
        for i in 0..g[s].len(){
            let e = g[s][i];
            if e == bef{dp[s][i] = p;}
        }
        let mut L = vec![0;g[s].len()];
        let mut R = vec![0;g[s].len()];

        for i in 0..g[s].len(){
            L[i] = {
                let mut tmp = 1+dp[s][i];
                tmp %= m;
                if i != 0{
                    tmp *= L[i-1];
                }
                tmp%m
            }
        }

        for i in (0..g[s].len()).rev(){
            if i+1<g[s].len(){
                R[i] = (R[i+1]*((1+dp[s][i])%m))%m;
            }
            else{
                R[i] = (1+dp[s][i])%m;
            }

            if g[s][i] == bef{
                continue;
            }  
            let mut tmp = 1;
            if i != 0{
                tmp *= L[i-1];
                tmp %= m;
            }
            if i+1 != g[s].len(){
                tmp *= R[i+1];
                tmp %= m;
            }
            dfs2(g[s][i], s, tmp, m, g, dp);
        }
    }

    */
fn divisor(n:usize) -> Vec<usize>{
    let mut res:Vec<usize> = Vec::new(); 
    for i in 1..n+1{
        if i*i>n{break;}
        if n%i == 0{
            res.push(i);
            if i != n/i{
                res.push(n/i);    
            }    
        }    
    }
    res
}
struct UnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    size:Vec<usize>,
    size_edge:Vec<usize>,
}
impl UnionFind{
    fn init(n:usize) -> UnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        UnionFind{
            par:par,
            rank:vec![0;n],
            size:vec![1;n],
            size_edge:vec![0;n],
        }
    }
    fn find(&mut self, x:usize) ->usize{
        if(self.par[x] == x){
            x
        }
        else{
            let p = self.par[x];
            let res = self.find(p);
            self.par[x] = res;
            res
        }
    }
    fn same(&mut self, a:usize, b:usize)->bool{
        self.find(a) == self.find(b)
    }
    fn unite(&mut self, a:usize, b:usize){
        let x = self.find(a);
        let y = self.find(b);
        if x != y{
            if (self.rank[x] < self.rank[y]){
                self.par[x] = y;
                self.size[y] += self.size[x];
                self.size_edge[y] += self.size_edge[x];
                self.size_edge[y] += 1;
            }
            else{
                self.par[y] = x;
                self.size[x] += self.size[y];
                self.size_edge[x] += self.size_edge[y];
                self.size_edge[x] += 1;
                if(self.rank[x] == self.rank[y]){ self.rank[x]+=1;}
            }
            
        }
        else{
            self.size_edge[x] += 1;
        }
    }
    fn check_size(&mut self, a:usize) -> usize{
        let x = self.find(a);
        let s = self.size[x];
        s
    }
}
struct SegTree<I, BiOp> {
    n: usize,
    dat: Vec<I>,
    op: BiOp,
    e: I,
}

impl<I, BiOp> SegTree<I, BiOp>
    where BiOp: Fn(I, I) -> I,
          I: Copy {
    pub fn new(n_: usize, op: BiOp, e: I) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2
        SegTree {n: n, dat: vec![e; 2 * n - 1], op: op, e: e}
    }
    /* ary[k] <- v */
    pub fn update(&mut self, idx: usize, v: I) {
        let mut k = idx + self.n - 1;
        self.dat[k] = v;
        while k > 0 {
            k = (k - 1) / 2;
            self.dat[k] = (self.op)(self.dat[2 * k + 1], self.dat[2 * k + 2]);
        }
    }
    /* [a, b) (note: half-inclusive)
     * http://proc-cpuinfo.fixstars.com/2017/07/optimize-segment-tree/ */
    pub fn query(&self, mut a: usize, mut b: usize) -> I {
        let mut left = self.e;
        let mut right = self.e;
        a += self.n - 1;
        b += self.n - 1;
        while a < b {
            if (a & 1) == 0 {
                left = (self.op)(left, self.dat[a]);
            }
            if (b & 1) == 0 {
                right = (self.op)(self.dat[b - 1], right);
            }
            a = a / 2;
            b = (b - 1) / 2;
        }
        (self.op)(left, right)
    }
}
pub mod FenwickTree {
    use std::ops::{AddAssign, Sub};
    pub struct FenwickTree<i64> {
        n: usize,
        data: Vec<i64>,
        init: i64,
    }
 
    impl<i64: Copy + AddAssign + Sub<Output = i64>> FenwickTree<i64> {
        pub fn new(size: usize, init: i64) -> FenwickTree<i64> {
            FenwickTree {
                n: size + 1,
                data: vec![init; size + 1],
                init: init,
            }
        }
 
        pub fn add(&mut self, k: usize, value: i64) {
            let mut x = k;
            while x < self.n {
                self.data[x] += value;
                x |= x + 1;
            }
        }
 
        /// Returns a sum of range `[l, r)`
        pub fn sum(&self, l: usize, r: usize) -> i64 {
            self.sum_one(r) - self.sum_one(l)
        }
 
        /// Returns a sum of range `[0, k)`
        pub fn sum_one(&self, k: usize) -> i64 {
            assert!(k < self.n, "k={} n={}", k, self.n);
 
            let mut result = self.init;
            let mut x = k as i32 - 1;
            while x >= 0 {
                result += self.data[x as usize];
                x = (x & (x + 1)) - 1;
            }
 
            result
        }
    }
}

pub mod FenwickTree_MOD {
    use std::ops::{AddAssign, Sub};
    use std::ops::RemAssign;
    pub struct FenwickTree<i64> {
        n: usize,
        data: Vec<i64>,
        init: i64,
        MOD:  i64,
    }
 
    impl<i64:Copy + AddAssign+ RemAssign + Sub<Output = i64>> FenwickTree<i64> {
        pub fn new(size: usize, init: i64, MOD:i64) -> FenwickTree<i64> {
            FenwickTree {
                n: size + 1,
                data: vec![init; size + 1],
                init: init,
                MOD:MOD,
            }
        }
 
        pub fn add(&mut self, k: usize, value: i64) {
            let mut x = k;
            while x < self.n {
                self.data[x] += value;
                self.data[x] %= self.MOD;
                x |= x + 1;
            }
        }
 
        /// Returns a sum of range `[l, r)`
        pub fn sum(&self, l: usize, r: usize) -> i64 {
            self.sum_one(r) - self.sum_one(l)
        }
 
        /// Returns a sum of range `[0, k)`
        pub fn sum_one(&self, k: usize) -> i64 {
            assert!(k < self.n, "k={} n={}", k, self.n);
 
            let mut result = self.init;
            let mut x = k as i32 - 1;
            while x >= 0 {
                result += self.data[x as usize];
                result %= self.MOD;
                x = (x & (x + 1)) - 1;
            }
 
            result
        }
    }
}
pub struct Scanner<R> {
    stdin: R,
}
 
impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
struct LazySegTree<BiOp> {
    n: usize,
    val: Vec<i64>,
    ma:Vec<i64>,
    op: BiOp,
    e: i64,
    upe:i64,
    inf:i64,
}

impl<BiOp> LazySegTree<BiOp>
    where BiOp: Fn(i64, i64) -> i64,
          i64: Copy {
    pub fn new(n_: usize, op: BiOp, e: i64, upe:i64, inf:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2

        LazySegTree {n: n, val: vec![e; 2 * n ], ma:vec![upe;2*n], op: op, e: e, upe:upe, inf:inf}
    }
    pub fn query(&self, x:usize, y:usize, l:usize, r:usize, k:usize) -> i64 {
        if (r<=x || y<=l) {return self.inf;}
        if (x<=l && r<=y) {return self.ma[k];}
        let mut L = self.query(x,y,l,(l+r)/2, k*2);
        let mut R = self.query(x,y,(l+r)/2,r, k*2+1);
        return self.val[k] + (self.op)(L, R);

    }
    
    pub fn update(&mut self, x:usize, y:usize, v:i64, l:usize,r:usize, k:usize) {
        if (l>=r) {return;}
        if (x<=l && r<=y){
            self.val[k]+=v;
            self.ma[k]+=v;
        }
        else if(l<y && x<r){
            self.update(x, y, v, l, (l+r)/2, k*2);
            self.update(x,y,v,(l+r)/2,r, k*2+1);
            self.ma[k] = self.val[k] + (self.op)(self.ma[k*2], self.ma[k*2+1]);
        }
    }
}
fn lab(a:usize, b:usize, c:&mut usize) -> usize{
    if (b==0){return a;}
    let mut x = c.clone();
    *c = x+1;
    println!("{} {} {}", a,b,c);
    return lab(b, a%b, c);
}
fn dist_1(x0:f64, y0:f64, x1:f64, y1:f64, x2:f64, y2:f64) -> f64{
    let mut a = x2-x1;
    let mut b= y2-y1;
    let mut a2 = a*a;
    let mut b2 = b*b;
    let mut r2 = a2+b2;
    let mut tt = -(a*(x1-x0) + b*(y1-y0));
    if tt<0.0{
        return (x1 - x0)*(x1-x0) + (y1-y0)*(y1-y0);
    }
    if (tt>r2){
        return (x2-x0)*(x2-x0) + (y2-y0)*(y2-y0);
    }
    let mut f1 = a*(y1-y0)-b*(x1-x0);
    return (f1*f1)/r2;
}
fn modinv(a:usize)->usize{
    let mut b = MODu as i64;
    let mut u = 1 as i64;
    let mut v = 0 as i64;
    let mut a = a as i64;
    let mut m = MODu as i64;
    while(b>0){
        let mut t = a/b;
        a -= t*b;
        mem::swap(&mut a, &mut b);
        u-=t*v;
        mem::swap(&mut u, &mut v);    
    }
    u%=m;
    if u<0{u+=m;}
    return u as usize;

}
fn modpow(x:usize, n:usize) -> usize{
        let mut ans = 1;
        let mut n = n;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x%MODu;}
            x = x*x%MODu;
            n = n>>1;
        }
        ans
}
fn comb(a:usize, b:usize,  fac:&Vec<usize>, ifac:&Vec<usize>)->usize{
        let mut a = a;
        let mut b = b;
        if a == 0 && b == 0{return 1;}
        if a<b || a<0{return 0;}
        let mut tmp = ifac[a-b]*ifac[b] % MODu;
        return tmp * fac[a] % MODu;
}

fn invs()->(Vec<usize>, Vec<usize>){
    let mut fac = vec![0;300001];
    let mut ifac = vec![0;300001];
    fac[0] = 1;
    ifac[0] = 1;
    for i in 0..300000{
        fac[i+1] = fac[i] * (i+1) % MODu;
        ifac[i+1] = ifac[i] * modpow(i+1, MODu - 2) % MODu;
    }
    (fac, ifac)
}

struct ConvexHallTrick {
    Q: Vec<(i64, i64)>,
}

impl ConvexHallTrick{
    pub fn new() -> Self {

        ConvexHallTrick {Q: Vec::new()}
    }
    pub fn calc(&self, p:(i64, i64), x:i64)->i64{
        return p.0 * x + p.1;
    }
    pub fn dodo(& self, A:(i64, i64), B:(i64, i64), C:(i64, i64)) -> bool{
        //max or min
        (A.1 - C.1) * (B.0 - A.0) <= (A.1 - B.1)*(C.0 - A.0)
    }
    pub fn add(&mut self, a:i64, b:i64){
        self.Q.push((a, b));
        let mut v = self.Q.len();
        while(v >=3 && self.dodo(self.Q[v-3], self.Q[v-2], self.Q[v-1])){
            self.Q[v-2] = self.Q[v-1];
            self.Q.pop();
            v = self.Q.len();
        }
    }
    pub fn query(& self, x:i64) -> i64{
        let mut L = -1;
        let mut R = (self.Q.len() - 1) as i64;
        while(R-L>1){
            let mut m = (L+R)/2;
            if self.calc(self.Q[m as usize], x)>=self.calc(self.Q[m as usize+1], x){
                L=m;
            }
            else{
                R=m;
            }

        }
        return self.calc(self.Q[R as usize], x);
    }
}
#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);
impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}
fn main(){
    //let s = std::io::stdin();
    //let mut sc = Scanner { stdin: s.lock() };
    input!{
        h:usize,
        w:usize,
        map:[chars;h],
    }
    let mut x = Vec::new();
    let mut y = Vec::new();
    for i in 0..h{
        x.push(Vec::new());
        for j in 0..w{
            if map[i][j] == '#'{
                x[i].push(j);
            }
        }
        x[i].push(w);
    }
    
    for i in 0..w{
        y.push(Vec::new());
        for j in 0..h{
            if map[j][i] == '#'{
                y[i].push(j);
            }
        }
        y[i].push(h);
    }
    
    let mut xm = Vec::new();
    let mut ym = Vec::new();
    for i in 0..h{
        xm.push(Vec::new());
        for j in 0..w{
            if map[i][j] == '#'{
                xm[i].push(-(j as i64));
            }
        }
        xm[i].reverse();
        xm[i].push(1);
    }
    
    for i in 0..w{
        ym.push(Vec::new());
        for j in 0..h{
            if map[j][i] == '#'{
                ym[i].push(-(j as i64));
            }
        }
        ym[i].reverse();
        ym[i].push(1);
    }
    let mut res = 0;
    for j in 0..h{
        for i in 0..w{
            if map[j][i] != '#'{
                let a = x[j].lower_bound(&i);
                let b = xm[j].lower_bound(&-(i as i64));
                let c = y[i].lower_bound(&j);
                let d = ym[i].lower_bound(&-(j as i64));
                let ax = x[j][a];
                let bx = -1 * xm[j][b];
                let ay = y[i][c];
                let by = -1 * ym[i][d];
                res = cmp::max(res,1+ i as i64 - bx -1 + ax as i64 - i as i64 -1+
                                    j as i64 - by -1 + ay as i64 - j as i64 -1);
            }
        }
    }
    println!("{}", res);
     
}
pub static MOD:i64 = 1000000007;
pub static MODu:usize = 1000000007;
const INF: i64 = 1 << 60;