Bayan 2015 Contest Warm Up C题（DP+模拟）

C. Kamal-ol-molk's Painting

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Rumors say that one of Kamal-ol-molk's paintings has been altered. A rectangular brush has been moved right and down on the painting.

Consider the painting as a n × m rectangular grid. At the beginning an x × y rectangular brush is placed somewhere in the frame, with edges parallel to the frame, (1 ≤ x ≤ n, 1 ≤ y ≤ m). Then the brush is moved several times. Each time the brush is moved one unit right or down. The brush has been strictly inside the frame during the painting. The brush alters every cell it has covered at some moment.

You have found one of the old Kamal-ol-molk's paintings. You want to know if it's possible that it has been altered in described manner. If yes, you also want to know minimum possible area of the brush.

Input

The first line of input contains two integers n and m, (1 ≤ n, m ≤ 1000), denoting the height and width of the painting.

The next n lines contain the painting. Each line has m characters. Character 'X' denotes an altered cell, otherwise it's showed by '.'. There will be at least one altered cell in the painting.

Output

Print the minimum area of the brush in a line, if the painting is possibly altered, otherwise print  - 1.

Sample test(s)

input

4 4
XX..
XX..
XXXX
XXXX

output

4

input

4 4
....
.XXX
.XXX
....

output

2

input

4 5
XXXX.
XXXX.
.XX..
.XX..

output

-1

题意：给出一个n*m的图，X是可以被涂色的点，问你能不能找出一个面积最小的刷子给所有X点刷上颜色，刷子每次只能往下或右移动一格

思路：首先用sum[i][j]表示从i到n，从j到m的X的格子个数，这个直接DP求就好了

            然后就是判断的部分，枚举刷子的面积就好了

            对于每个枚举的刷子面积，从图的最左最上的点开始图（一定是这样，要知道任何时刻刷子左上方的点是一定涂不到的）

            然后判断当前能不能刷满，如果能够，就判断刷子下一步是往下还是往右移动（如果右边方向的最上一排和下边方向的最左边一排都同时有格子一定不可以）

            细节看代码吧~