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Problem Description

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.

Input

The 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.

Output

For 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

5 1 5 2 4 这个题因为数据量比较小，所以可以直接dfs+回溯去做。 不过这里还有一个比较巧妙的解法，就是二分图匹配。 对于每一行来说，没有方块间隔的那些地方就相当于一个点，类似于缩点。每一列也是一样。 这样的话，每中数字代表的地方就只能安置一个炮弹，就转化成了二分图匹配求最大匹配。 代码如下：

#include
   
    #define ll long longusing namespace std;const int maxx=1e3+100;char s[maxx][maxx];int cntx[maxx][maxx];int cnty[maxx][maxx];int mzp[maxx][maxx];int pre[maxx];int vis[maxx];int n;inline void init(){
   	memset(cntx,0,sizeof(cntx));	memset(cnty,0,sizeof(cnty));	memset(mzp,0,sizeof(mzp));	memset(pre,-1,sizeof(pre));}inline int dfs(int cur,int y){
   	for(int i=1;i<=y;i++)	{
   		if(mzp[cur][i]&&!vis[i])		{
   			vis[i]=1;			if(pre[i]==-1||dfs(pre[i],y))			{
   				pre[i]=cur;				return 1;			}		}	}	return 0;}inline int match(int x,int y){
   	int ans=0;	for(int i=1;i<=x;i++)	{
   		memset(vis,0,sizeof(vis));		ans+=dfs(i,y);	}	return ans;}int main(){
   	while(scanf("%d",&n),n)	{
   		init();		for(int i=0;i
   

努力加油a啊，(^o)/~

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