CF 510b Fox And Two Dots

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:

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, ..., dk a cycle if and only if it meets the following condition:

1. These k dots are different: if i ≠ j then di is different from dj.
2. k is at least 4.
3. All dots belong to the same color.
4. For all 1 ≤ i ≤ k - 1: di and di + 1 are adjacent. Also, dk 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.

Examples

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).

 主要是用dfs判断有没有回到出发的点，并保证不走回头路（所以dfs函数里定义四个变量）

#include<cstdio>
#include<cstring>
int flag[55][55];
char str[55][55];
int n,m,k;
int dx[4]={-1,1,0,0};
int dy[4]={0,0,-1,1};
void dfs(int x,int y,int cx,int cy)
{
    if(flag[x][y] == 1)
    {
        k=1;
        return ;
    }
    flag[x][y]=1;
    int i,nx,ny;
    for(i = 0 ; i < 4 ; i++)
    {
        
        nx=x+dx[i];
        ny=y+dy[i];
        if(str[nx][ny] == str[x][y] && (nx != cx || ny != cy))
        {
        
                dfs(nx,ny,x,y);
            
        }
    }
    
}
int main()
{
    while(scanf("%d %d",&n,&m)!=EOF)
    {
        k=0;
        int i,j;
        memset(flag,0,sizeof(flag));
        for(i = 1 ; i <= n ; i++)
        {
            scanf("%s",str[i]+1);
        }
        for(i = 1 ; i <= n ; i++)
        {
            for(j = 1 ; j <= m ; j++)
            {
                if(flag[i][j] == 1)
                
                    continue;
                    
                    dfs(i,j,i,j);
                
                if(k == 1)
                
                    break;
            }
            if(k == 1)
                break;
        } 
        if(k == 1)
            printf("Yes\n");
        else
            printf("No\n");
    }
}