Problem: 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.

Examples

Input

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


Output

8


Input

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


Output

8


Input

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


Output

13

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Sparsh Sanchorawala
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DLamp solver = new DLamp();
        solver.solve(1, in, out);
        out.close();
    }

    static class DLamp {
        public void solve(int testNumber, InputReader s, PrintWriter w) {
            int n = s.nextInt(), m = s.nextInt();
            char[][] a = new char[n][];
            for (int i = 0; i < n; i++)
                a[i] = s.next().toCharArray();
            int[][][] dp = new int[4][n][m];

            for (int i = 0; i < n; i++) {

                if (a[i][0] == '.')
                    dp[0][i][0] = -1;

                for (int j = 1; j < m; j++)
                    if (a[i][j] == '.')
                        dp[0][i][j] = dp[0][i][j - 1];
                    else
                        dp[0][i][j] = j;
            }

            for (int i = 0; i < n; i++) {

                if (a[i][m - 1] == '.')
                    dp[2][i][m - 1] = m;
                else
                    dp[2][i][m - 1] = m - 1;

                for (int j = m - 2; j >= 0; j--) {
                    if (a[i][j] == '.')
                        dp[2][i][j] = dp[2][i][j + 1];
                    else
                        dp[2][i][j] = j;
                }
            }

            for (int j = 0; j < m; j++) {

                if (a[0][j] == '.')
                    dp[1][0][j] = -1;

                for (int i = 1; i < n; i++) {
                    if (a[i][j] == '.')
                        dp[1][i][j] = dp[1][i - 1][j];
                    else
                        dp[1][i][j] = i;
                }
            }

            for (int j = 0; j < m; j++) {

                if (a[n - 1][j] == '.')
                    dp[3][n - 1][j] = n;
                else
                    dp[3][n - 1][j] = n - 1;

                for (int i = n - 2; i >= 0; i--) {
                    if (a[i][j] == '.')
                        dp[3][i][j] = dp[3][i + 1][j];
                    else
                        dp[3][i][j] = i;
                }
            }

            int res = 0;

            for (int i = 0; i < n; i++) {

                for (int j = 0; j < m; j++) {

                    if (a[i][j] == '#')
                        continue;

                    int can = 1;
                    can += dp[3][i][j] - i - 1;
                    can += i - dp[1][i][j] - 1;
                    can += dp[2][i][j] - j - 1;
                    can += j - dp[0][i][j] - 1;
                    res = Math.max(can, res);
                }
            }

            w.println(res);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return nextString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}