Fox And Two Dots

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本文介绍了一款名为TwoDots的游戏，玩家需在n×m的棋盘上寻找同色圆点构成的循环。文章详细阐述了如何通过深度优先搜索(DFS)算法判断是否存在符合条件的循环，并提供了具体实现代码。

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Fox Ciel is playing a mobile puzzle game called "Two Dots". The basic levels are played on a board of size n × m cells, like this:

$\text{[math]}$

Each cell contains a dot that has some color. We will use different uppercase Latin characters to express different colors.

The key of this game is to find a cycle that contain dots of same color. Consider 4 blue dots on the picture forming a circle as an example. Formally, we call a sequence of dots d₁, d₂, ..., d_k a cycle if and only if it meets the following condition:

These k dots are different: if i ≠ j then d_i is different from d_j.
k is at least 4.
All dots belong to the same color.
For all 1 ≤ i ≤ k - 1: d_i and d_i + 1 are adjacent. Also, d_k and d₁ should also be adjacent. Cells x and y are called adjacent if they share an edge.

Determine if there exists a cycle on the field.

Input

The first line contains two integers n and m (2 ≤ n, m ≤ 50): the number of rows and columns of the board.

Then n lines follow, each line contains a string consisting of m characters, expressing colors of dots in each line. Each character is an uppercase Latin letter.

Output

Output "Yes" if there exists a cycle, and "No" otherwise.

Example

Input

3 4
AAAA
ABCA
AAAA

Output

Yes

Input

3 4
AAAA
ABCA
AADA

Output

No

Input

4 4
YYYR
BYBY
BBBY
BBBY

Output

Yes

Input

7 6
AAAAAB
ABBBAB
ABAAAB
ABABBB
ABAAAB
ABBBAB
AAAAAB

Output

Yes

Input

2 13
ABCDEFGHIJKLM
NOPQRSTUVWXYZ

Output

No

Note

In first sample test all 'A' form a cycle.

In second sample there is no such cycle.

The third sample is displayed on the picture above ('Y' = Yellow, 'B' = Blue, 'R' = Red).

代码：

#include<cstdio>
#include<algorithm>
#include<math.h>
#include<string.h>
using namespace std;
int vis[100][100];
char s[100][100];
int fxy[4][4]={{0,-1},{0,1},{-1,0},{1,0}},ex,ey,ok,n,m;
void dfs(int x,int y,int nl)
{  if(ok) return ;
vis[x][y]=1;
for(int i=0;i<4;i++)
{
	 int xx=x+fxy[i][0];
	 int yy=y+fxy[i][1];
	 if(xx==ex&&yy==ey&&nl>2)
	 {
	 	ok=1;
	 	return ;
	 }
	 if(xx>=0&&yy>=0&&xx<n&&yy<m&&!vis[xx][yy]&&s[xx][yy]==s[x][y])
	 dfs(xx,yy,nl+1);
}
}
int main()
{
  scanf("%d%d",&n,&m);
	{  ok=0;
	 for(int i = 0; i < n; i++)
            scanf("%s",s[i]);
		for(int i=0;i<n;i++)
		for(int j=0;j<m;j++)
		memset(vis,0,sizeof(vis)),ex=i,ey=j,dfs(i,j,0);
		if(ok)
		printf("Yes\n");
		else printf("No\n");	
	}
	return 0;
}