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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<string.h>

int main(){
  //variable to height, and width
  int h, w;
  //variable to drive for syntax
  int i, j, k, l;
  //variable to max
  int max = 0;
  //reading
  scanf("%d %d", &h, &w);
  char grid[h][w+1];
  //文字列の読み込みを行う
  for(i = 0; i < h; i++){
    char temp[w+1];
    scanf("%s", temp);
    strcpy(grid[i],temp);
  }
  //i行目までの行で横の最大値を格納
  int rawmax=1;
  int colmax=1;
  //一行ずつみていき、横の最大を探す
  for(i = 0; i<h; i++){
    char temp[w+2];
    strcpy(temp, strcat(grid[i], "#"));
    /*printf("%s\n", temp);*/
    //横幅で何マス照らせるのかを保存する
    int rawtmp = 0;
    int coltmp = 0;
    int start=0, end=0;
    for(j=0; j<w+1; j++){
      //障害物発見時 or 終端到達
      if( grid[i][j] == '#') {
        //もし幅の最大値以上のマスが照らせるならば、縦で何マス塗れるかを確認する
        if(rawmax <= rawtmp){
          //横幅最大値の更新
          rawmax=rawtmp;
          //その区間での見る位置の終点を更新して、縦ラインで何マス塗れるかを確認
          end=j-1;
          for(k = start; k<=end; k++){
            //上方向への探索
            for(l = i-1; l>0&&grid[l][k]!='#'; l--){
              coltmp++;
            }
            //下方向への探索
            for(l = i+1; l<h&&grid[l][k]!='#'; l++){
              coltmp++;
            }
            if(colmax < coltmp) colmax = coltmp;
            /*printf("colmax = %d\n", colmax);*/
            coltmp=0;
          }
          //この区間までで最大値を更新していればアップデート
          if(max < rawmax+colmax) max = rawmax+colmax;
        }
      //rawtmpの値をクリアする
      rawtmp=0;
      //始点を次の位置に持ってくる
      start=j+1;
      }else{
        //障害物ない限りrawtmpを増加
        rawtmp++;
        /*printf("naw looking grid[%d][%d], rawtmp = %d\n", i, j, rawtmp);*/
      }
    }
  }
  /*
  printf("rawmax = %d\n", rawmax);
  printf("colmax = %d\n", colmax);
  */
  //output max
  printf("%d", max);
  return 0;
}