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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.io.PrintWriter
import java.util.*
import java.math.*
import java.lang.*
import kotlin.comparisons.*

val pw = PrintWriter(System.out)
val MOD: Long = (1e+9 + 7).toLong()

fun main(args: Array<String>) {
    val (h, w) = readListOfInt()
    val s = mutableListOf<List<Char>>()
    for(i in 0 until h) {
        s.add(read().toList())
    }
    
    val left = Array(h, { IntArray(w).toMutableList() }).toMutableList()
    val right = Array(h, { IntArray(w).toMutableList() }).toMutableList()
    val top = Array(h, { IntArray(w).toMutableList() }).toMutableList()
    val down = Array(h, { IntArray(w).toMutableList() }).toMutableList()

    for(i in 0 until h) {
        for(j in 0 until w) {
            if(s[i][j] == '.') {
                left[i][j] = if(j == 0) 1 else left[i][j-1] + 1
            } else {
                left[i][j] = 0
            }
        }
        for(j in w-1 downTo 0) {
            if(s[i][j] == '.') {
                right[i][j] = if(j == w-1) 1 else right[i][j+1] + 1
            } else {
                right[i][j] = 0
            }
        }
    }
    for(j in 0 until w) {
        for(i in 0 until h) {
            if(s[i][j] == '.') {
                top[i][j] = if(i == 0) 1 else top[i-1][j] + 1
            } else {
                top[i][j] = 0
            }
        }
        for(i in h-1 downTo 0) {
            if(s[i][j] == '.') {
                down[i][j] = if(i == h-1) 1 else down[i+1][j] + 1
            } else {
                down[i][j] = 0
            }
        }
    }
    var max = left[0][0] + right[0][0] + top[0][0] + down[0][0] - 3
    for(i in 0 until h) {
        for(j in 0 until w) {
            val tmp = left[i][j] + right[i][j] + top[i][j] + down[i][j] - 3
            max = Math.max(max, tmp)
        }
    }
    println(max)

    pw.flush()
}

/****** Declared Functions and Data Structures ******/
// IO
fun read() = readLine()!!
fun readInt() = read().toInt()
fun readLong() = read().toLong()
fun readDouble() = read().toDouble()
fun readListOfString() = read().split(" ")
fun readListOfInt() = readListOfString().map { it.toInt() }
fun readListOfLong() = readListOfString().map { it.toLong() }
fun readListOfDouble() = readListOfString().map { it.toDouble() }

fun Double.format(digits: Int) = String.format("%.${digits}f", this)
fun Float.format(digits: Int) = String.format("%.${digits}f", this)

fun print(value: Any) { pw.print(value) }
fun println(value : Any) { pw.println(value) }

// Extensions
fun<T> List<T>.toBuckets(): Map<T, Int>
    = this.groupBy { it }.mapValues { it.value.size }

fun<T: Comparable<T>> List<T>.upperBound(element: T, fromIndex: Int=0, toIndex: Int=this.size): Int {
    var l = fromIndex
    var r = toIndex
    while(l < r) {
        val mid = (l+r) / 2
        if(element >= this[mid]) { 
            l = mid + 1
        } else {
            r = mid
        }
    }
    return l
}

fun<T: Comparable<T>> List<T>.lowerBound(element: T, fromIndex: Int=0, toIndex: Int=this.size): Int {
    var l = fromIndex
    var r = toIndex
    while(l < r) {
        val mid = (l+r) / 2
        if(element <= this[mid]) { 
            r = mid
        } else {
            l = mid + 1
        }
    }
    return r 
}

fun <K, V> Map<K, V>.toMutableMap(): MutableMap<K, V> = HashMap(this)

// Util Functions
fun makeDivisors(n: Long): List<Long> {
    val divisors = mutableListOf<Long>()
    for(i in 1L .. Math.sqrt(n.toDouble()).toLong()+1L) {
        if(n % i == 0L) {
            divisors.add(i)
            if(i != n/i) {
                divisors.add(n/i)
            }
        }
    }
    return divisors.distinct().sorted()
}

fun<T> permutations(src: List<T>): List<List<T>> {
    if(src.size == 1) return listOf(src)
    val perms = mutableListOf<List<T>>()
    val insertElement = src[0]
    permutations(src.drop(1)).forEach { perm ->
        for(i in 0..perm.size) {
            val newPerm = perm.toMutableList()
            newPerm.add(i, insertElement)
            perms.add(newPerm.toList())
        }
    }
    return perms
}

// return nCr, if you want nCr, please access v[n][r]
fun combinations(n: Long): List<List<Long>> {
    val v = (0..n).map { (0..n).map{0L}.toMutableList() }.toMutableList()
    for(i in 0 until v.size) {
        v[i][0] = 1L
        v[i][i] = 1L
    }
    for(i in 0 until v.size) {
        for(j in 1 until i) {
            v[i][j] = (v[i-1][j-1] + v[i-1][j]) % MOD
        }
    }
    return v.map { it.toList() }.toList()
}

// should be a >= b
fun gcd(a: Long, b: Long): Long = 
    if(b == 0L) a else gcd(b, a % b)

// shoud be a >= b
fun lcm(a: Long, b: Long): Long = 
    a / gcd(a, b) * b

fun sumDigits(num_: Long): Long {
    var num = num_
    var rtn: Long = 0
    while(num != 0.toLong()) {
        val tmp = num % 10
        rtn += tmp
        num /= 10
    }
    return rtn
}

fun Double.isDecimal(): Boolean = ((this - Math.floor(this)) != 0.0)

// Data Structures
class Stack<T>(private var st: MutableList<T> = mutableListOf<T>()) {
    fun isEmpty() = st.isEmpty()
    fun top(): T = st.last()
    fun push(e: T) { st.add(e) }
    fun pop() { st = st.dropLast(1).toMutableList() }
}

class Queue<T>(private var que: MutableList<T> = mutableListOf<T>()) {
    fun isEmpty() = que.isEmpty()
    fun top(): T = que.first()
    fun push(e: T) { que.add(e) }
    fun pop() { que = que.drop(1).toMutableList() }
}