Codeforce#385B.Hongcow Solves A Puzzle

B. Hongcow Solves A Puzzle

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Hongcow likes solving puzzles.

One day, Hongcow finds two identical puzzle pieces, with the instructions "make a rectangle" next to them. The pieces can be described by an n by m grid of characters, where the character 'X' denotes a part of the puzzle and '.' denotes an empty part of the grid. It is guaranteed that the puzzle pieces are one 4-connected piece. See the input format and samples for the exact details on how a jigsaw piece will be specified.

The puzzle pieces are very heavy, so Hongcow cannot rotate or flip the puzzle pieces. However, he is allowed to move them in any directions. The puzzle pieces also cannot overlap.

You are given as input the description of one of the pieces. Determine if it is possible to make a rectangle from two identical copies of the given input. The rectangle should be solid, i.e. there should be no empty holes inside it or on its border. Keep in mind that Hongcow is not allowed to flip or rotate pieces and they cannot overlap, i.e. no two 'X' from different pieces can share the same position.

Input

The first line of input will contain two integers n and m (1 ≤ n, m ≤ 500), the dimensions of the puzzle piece.

The next n lines will describe the jigsaw piece. Each line will have length m and will consist of characters '.' and 'X' only. 'X' corresponds to a part of the puzzle piece, '.' is an empty space.

It is guaranteed there is at least one 'X' character in the input and that the 'X' characters form a 4-connected region.

Output

Output "YES" if it is possible for Hongcow to make a rectangle. Output "NO" otherwise.

Examples

input

2 3XXXXXX

output

YES

input

2 2.XXX

output

NO

input

5 5.......X.................

output

YES

Note

For the first sample, one example of a rectangle we can form is as follows

111222111222

For the second sample, it is impossible to put two of those pieces without rotating or flipping to form a rectangle.

In the third sample, we can shift the first tile by one to the right, and then compose the following rectangle:

.......XX................

大体题意：

给你一个n*m 的矩阵，  你要用两个同样的图形构造出一个矩形来，问是否可以？   .表示 这个地方是空地，X表示是一个小元素!你不可以旋转覆盖， 只能移动整体！其实可以把.给忽略。

思路：

逆向思考，一个矩形需要被两个相同的图形拼接起来，那么这个图形就必须是矩形。然后判断X覆盖的部分是不是矩形就可以了。计算出能套住所有X的最小矩形，然后把这个矩形扫一遍就可以判断里面是不是都是X了。

本弱ji本来就渣，题目还这么迷！无力吐槽！

AC代码：

#include<bits/stdc++.h>using namespace std;const int INF = 0x3f3f3f3f;char a[505][505];int main(){    int n, m;    while(cin >> n >> m)    {        for(int i = 0; i < n; i++)            cin >> a[i];        int left = INF, right = -INF, top = INF, bottom = - INF;        for(int i = 0; i < n; i++)            for(int j = 0; j < m; j++)                if(a[i][j] == 'X')                {                    left = min(left, j);                    right = max(right, j);                    top = min(top, i);                    bottom = max(bottom, i);                }        int flag = 1;        for(int i = top; i <= bottom && flag; i++)            for(int j = left; j <= right && flag; j++)                if(a[i][j] != 'X')                {                    puts("NO");                    flag = 0;                }        if(flag)            puts("YES");    }    return 0;}