D - Fox And Two Dots DFS

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.

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).

题目大意：判断图中是否有些相同字母组成的环，如果有的话直接出书YES，没有输出NO

思路：图中的每个点都有可能构成循环，所以要逐一遍历，如果该点可以构成循环的环那么起点是该点，，终点也是该点，环至少是4个点构成，所以如果有环的话再次回到起点时步数一定大于等于四。

AC代码：

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int n,m,end_i,end_j;
char aa;
char arr[100][100];
int mark[100][100]={0};
int d[4][2]={{1,0},{-1,0},{0,1},{0,-1}};
int flag=0;
void dfs(int x,int y,int step)
{
    if(flag==1) return;
    if(step>=4&&x==end_i&&y==end_j)如果回到了起点且步数大于等于4  则找到环了。
    {
        flag=1;
        return;
    }
    for(int i=0;i<4;i++){
        int dx=x+d[i][0];
        int dy=y+d[i][1];
        if(dx>=0&&dy>=0&&dx<n&&dy<m&&mark[dx][dy]==0&&arr[dx][dy]==aa){
            if(dx==end_i&&y==end_j&&step<3)//起点就是终点所以起点没有被标记，当进入到第二个点时，可能会回到起点，所以要对步数进行判断，看是否大于等于3
                continue;
            mark[dx][dy]=1;
            dfs(dx,dy,step+1);
        }
    }
}
int main()
{
    cin>>n>>m;//n行m列 
    for(int i=0;i<n;i++)    scanf("%s",&arr[i]);//存图
    
    for(int i=0;i<n;i++)
    {    
        for(int j=0;j<m;j++)
        {
            memset(mark,0,sizeof(mark));
            end_i=i;
            end_j=j;//起点与终点 
            aa=arr[i][j];//搜索的字符
            dfs(i,j,0);
            if(flag==1)
                break;
        }
        if(flag==1) break;
    }
    if(flag==1) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
}

D - Fox And Two Dots DFS

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