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: Accepted)

@file:Suppress("DuplicatedCode")

import java.io.IOException
import java.io.InputStream
import java.io.PrintWriter
import java.util.NoSuchElementException

fun main(args: Array<String>) {
    PrintWriter(System.out).use { out ->
        D.solve(D.FastScanner(), out)
        out.flush()
    }
}

private fun D.solve(sc: D.FastScanner, out: PrintWriter) {
    val h = sc.nextInt()
    val w = sc.nextInt()
    val fs = '.'.toInt()

    val map = Array(h) {
        IntArray(w) {
            sc.readByteAsInt() - fs
        }.let {
            sc.readByte()
            it
        }
    }

    for((height, row) in map.withIndex()) {
        var lastWall = -1
        for ((width, c) in row.withIndex()) {
            if (c < 0) {
                if (lastWall != width - 1) {
                    val len = width - lastWall - 1
                    for (i in (lastWall + 1) until width) {
                        map[height][i] = len
                    }
                }
                lastWall = width
            }
        }

        if (lastWall != w - 1) {
            val len = w - lastWall - 1
            for (i in (lastWall + 1) until w) {
                map[height][i] = len
            }
        }
    }

    for (width in 0 until w) {
        var lastWall = -1
        for (height in 0 until h) {
            val c = map[height][width]
            if (c < 0) {
                if (lastWall != height - 1) {
                    val len = height - lastWall - 1
                    for (i in (lastWall + 1) until height) {
                        map[i][width] += len
                    }
                }
                lastWall = height
            }
        }

        if (lastWall != h - 1) {
            val len = h - lastWall - 1
            for (i in (lastWall + 1) until h) {
                map[i][width] += len
            }
        }
    }

    var max = 0
    for (i in 0 until h) {
        for (j in 0 until w) {
            val v = map[i][j]
            if (v > max) max = v
        }
    }

    out.println(max - 1)
}

@Suppress("MemberVisibilityCanBePrivate")
private object D {
    private const val zeroCode = '0'.toInt()
    private const val nineCode = '9'.toInt()

    class FastScanner {
        private val `in`: InputStream = System.`in`
        private val buffer = ByteArray(2048)
        private var ptr = 0
        private var buflen = 0

        private fun hasNextByte(): Boolean {
            if (ptr < buflen) {
                return true
            } else {
                ptr = 0
                try {
                    buflen = `in`.read(buffer)
                } catch (e: IOException) {
                    e.printStackTrace()
                }
                if (buflen <= 0) {
                    return false
                }
            }
            return true
        }

        fun readByte(): Byte = if (hasNextByte()) buffer[ptr++] else -1

        fun readByteAsInt(): Int = if (hasNextByte()) buffer[ptr++].toInt() else -1

        operator fun hasNext(): Boolean {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++
            return hasNextByte()
        }

        operator fun next(): String {
            if (!hasNext()) throw NoSuchElementException()

            return buildString {
                var b = readByteAsInt()

                while (isPrintableChar(b)) {
                    appendCodePoint(b)
                    b = readByteAsInt()
                }
            }
        }

        fun toCharIterator(): CharIterator = object : CharIterator() {
            private var nextByte: Byte = readByte()

            override fun hasNext(): Boolean = isPrintableChar(nextByte)

            override fun nextChar(): Char {
                val res = nextByte
                nextByte = readByte()
                return res.toChar()
            }

        }

        fun nextLong(): Long {
            if (!hasNext()) throw NoSuchElementException()
            var n: Long = 0
            var minus = false
            var b = readByteAsInt()

            if (b == '-'.toInt()) {
                minus = true
                b = readByteAsInt()
            }

            if (b !in zeroCode..nineCode) {
                throw NumberFormatException()
            }

            while (true) {
                if (b in zeroCode..nineCode) {
                    n *= 10
                    n += b - zeroCode.toLong()
                } else if (b == -1 || !isPrintableChar(b)) {
                    return if (minus) -n else n
                } else {
                    throw NumberFormatException()
                }

                b = readByteAsInt()
            }
        }

        fun nextInt(): Int {
            val nl = nextLong()
            if (nl < Int.MIN_VALUE || nl > Int.MAX_VALUE) throw NumberFormatException()
            return nl.toInt()
        }

        fun nextDouble(): Double {
            return next().toDouble()
        }

        fun readIntArray(n: Int): IntArray {
            val arr = IntArray(n)

            for (i in 0 until n) {
                arr[i] = nextInt()
            }

            return arr
        }

        fun readBigInt(capacity: Int): IntArray {
            if (!hasNext()) throw NoSuchElementException()

            val arr = IntArray(capacity)
            var len = 0
            arr[0] = readByteAsInt() - zeroCode
            while (arr[len] in 0..9) {
                len++
                arr[len] = readByteAsInt() - zeroCode
            }

            return arr.sliceArray(0 until len)
        }

        companion object {
            private inline fun isPrintableChar(c: Int): Boolean {
                return c in 33..126
            }

            private inline fun isPrintableChar(c: Byte): Boolean {
                return c in 33..126
            }
        }
    }
}