Suppose that we have a square city with straight streets. A map of a city is a square board with n rows and n columns, each representing a street or a piece of wall. 


A blockhouse is a small castle that has four openings through which to shoot. The four openings are facing North, East, South, and West, respectively. There will be one machine gun shooting through each opening. 

Here we assume that a bullet is so powerful that it can run across any distance and destroy a blockhouse on its way. On the other hand, a wall is so strongly built that can stop the bullets. 

The goal is to place as many blockhouses in a city as possible so that no two can destroy each other. A configuration of blockhouses is legal provided that no two blockhouses are on the same horizontal row or vertical column in a map unless there is at least one wall separating them. In this problem we will consider small square cities (at most 4x4) that contain walls through which bullets cannot run through. 


The following image shows five pictures of the same board. The first picture is the empty board, the second and third pictures show legal configurations, and the fourth and fifth pictures show illegal configurations. For this board, the maximum number of blockhouses in a legal configuration is 5; the second picture shows one way to do it, but there are several other ways. 


Your task is to write a program that, given a description of a map, calculates the maximum number of blockhouses that can be placed in the city in a legal configuration. 


InputThe input file contains one or more map descriptions, followed by a line containing the number 0 that signals the end of the file. Each map description begins with a line containing a positive integer n that is the size of the city; n will be at most 4. The next n lines each describe one row of the map, with a '.' indicating an open space and an uppercase 'X' indicating a wall. There are no spaces in the input file.


OutputFor each test case, output one line containing the maximum number of blockhouses that can be placed in the city in a legal configuration. 

Sample Input

4.X..
....
XX..
....
2
XX
.X
3
.X.
X.X
.X.
3
...
.XX
.XX
4
....
....
....
....
0

Sample Output

51
5
2
4


题目大概：

在一个矩形n*n中可以放很多车，两个车之间可以互相攻击到，但矩形中有很多墙可以使得两个车之间不能互相攻击到，问使得所有的车不互相攻击，最多放置多少个车。

思路：

可以按照正常的套路建模法，就是以列行为点，以一个点作为边，建模。但也不是按照正常套路，因为有墙间隔，所以要把有墙间隔的行作为两行或多行。列同理，然后给所有的行，列重新编号，最后再用套路法建模，跑一遍二分图。

代码：

#include <cstdio>
#include <cstring>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>
#define MAXN 10
using namespace std;
char map[MAXN][MAXN];
int hang[MAXN][MAXN];
int lie[MAXN][MAXN];
int G[110][110];
int pipei[MAXN];
bool used[MAXN];
int N, M;
void init()
{
    memset(G,0,sizeof(G));

}
void getMap()
{
    for(int i = 0; i < N; i++)
    {
        scanf("%s",map[i]);
    }
}
int find(int x,int n)
{
    for(int i = 0; i < n; i++)
    {
        int y = G[x][i];
        if(y&&!used[i])
        {
            used[i] = true;
            if(pipei[i] == -1 || find(pipei[i],n))
            {
                pipei[i] = x;
                return 1;
            }
        }
    }
    return 0;
}
void solve()
{
    int ans = 0;
    int an=0;
    for(int i=0;i<N;i++,an++)
    {

        for(int j=0;j<N;j++)
        {
            if(map[i][j]=='X'&&j+1<N&&map[i][j+1]!='X')an++;
            hang[i][j]=an;
        }

    }
    int ann=0;
    for(int j=0;j<N;j++,ann++)
    {

        for(int i=0;i<N;i++)
        {
            if(map[i][j]=='X'&&i+1<N&&map[i+1][j]!='X')ann++;
            lie[i][j]=ann;
        }

    }
    for(int i=0;i<N;i++)
    {
        for(int j=0;j<N;j++)
        {
            if(map[i][j]!='X')G[hang[i][j]][lie[i][j]]=1;
        }
    }
    memset(pipei, -1, sizeof(pipei));
    for(int i = 0; i <an; i++)
    {
        memset(used, false, sizeof(used));
        ans += find(i,ann);
    }
    printf("%d\n", ans);
}
int main()
{
    while(scanf("%d", &N)&&N)
    {
        init();
        getMap();
        solve();
    }
    return 0;
}