UVA Don't Get Rooked

主题如以下：

 Don't Get Rooked 

In chess, the rook is a piece that can move any number of squaresvertically or horizontally. In this problem we will consider smallchess boards (at most 44)
that can also contain walls through whichrooks cannot move. The goal is to place as many rooks on a board aspossible so that no two can capture each other. A configuration ofrooks is
legal provided that no two rooks are on the samehorizontal row or vertical column unless there is at least one wallseparating them.

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

Your task is to write a program that, given a description of a board,calculates the maximum number of rooks that can be placed on theboard in a legal configuration.

Input

The input file contains one or more board descriptions, followed bya line containing the number 0 that signals the end of the file. Eachboard description begins with a line containing a positive integer
nthat is the size of the board; n will be at most 4. The next
nlines each describe one row of the board, with a `.' indicating anopen space and an uppercase `X' indicating a wall. There are nospaces in the input file.

Output

For each test case, output one line containing themaximum number of rooks that can be placed on the boardin 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

跟八皇后问题差点儿相同，就是多了墙而已，这样不一定每行每列仅仅有一个点，中间可能隔着墙。所以用一个函数推断两点之间是否有墙。

用一个函数推断一个点能否被放置，可以的条件是它与所在行所在列的不论什么一个已经放置的点之间都有墙。有了这个函数后就行对每一个点展开DFS，更新最大值。

AC的代码例如以下：

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