#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
using namespace std;
struct node{
	int y,next;
}a[800010];int len=0,last[400010];
int n,m,c[400010],dis[400010];
bool vis[400010];
char s[200010];
void ins(int x,int y)
{
	a[++len].y=y;
	a[len].next=last[x];last[x]=len;
}
void insert(int x,int y,int c)
{
	int X=x+n,Y=y+n;
	if(c==1) ins(x,Y),ins(y,X);
	else ins(X,y),ins(Y,x);
}
bool dfs(int x)
{
	if(vis[x]) return true;
	vis[x]=true;
	for(int i=last[x];i;i=a[i].next)
	{
		int y=a[i].y;
		if(dis[y]<dis[x]+1)
		{
			dis[y]=dis[x]+1;
			if(dfs(y)) return true;
		}
	}
	vis[x]=false;
	return false;
}
int main()
{
	scanf("%d %d",&n,&m);
	scanf("%s",s+1);
	for(int i=1;i<=n;i++) c[i]=s[i]-'A';
	for(int i=1;i<=m;i++)
	{
		int x,y;scanf("%d %d",&x,&y);
		//ins(x,y);ins(y,x);
		if(c[x]==c[y]) insert(x,y,1);
		else insert(x,y,0);
	}
	memset(vis,false,sizeof(vis));
	for(int i=1;i<=n;i++)
		if(dfs(i)) {printf("Yes");return 0;}
	printf("No");
}
### Prompt

Please create a solution in cpp to the following problem:

You are given an undirected graph consisting of N vertices and M edges. The vertices are numbered 1 to N, and the edges are numbered 1 to M. In addition, each vertex has a label, `A` or `B`. The label of Vertex i is s_i. Edge i bidirectionally connects vertex a_i and b_i.

The phantom thief Nusook likes to choose some vertex as the startpoint and traverse an edge zero or more times. Today, he will make a string after traveling as above, by placing the labels of the visited vertices in the order visited, beginning from the startpoint.

For example, in a graph where Vertex 1 has the label `A` and Vertex 2 has the label `B`, if Nusook travels along the path 1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 2, the resulting string is `ABABB`.

Determine if Nusook can make all strings consisting of `A` and `B`.

Constraints

* 2 \leq N \leq 2 \times 10^{5}
* 1 \leq M \leq 2 \times 10^{5}
* |s| = N
* s_i is `A` or `B`.
* 1 \leq a_i, b_i \leq N
* The given graph may NOT be simple or connected.

Input

Input is given from Standard Input in the following format:


N M
s
a_1 b_1
:
a_{M} b_{M}


Output

If Nusook can make all strings consisting of `A` and `B`, print `Yes`; otherwise, print `No`.

Examples

Input

2 3
AB
1 1
1 2
2 2


Output

Yes


Input

4 3
ABAB
1 2
2 3
3 1


Output

No


Input

13 23
ABAAAABBBBAAB
7 1
10 6
1 11
2 10
2 8
2 11
11 12
8 3
7 12
11 2
13 13
11 9
4 1
9 7
9 6
8 13
8 6
4 10
8 7
4 3
2 1
8 12
6 9


Output

Yes


Input

13 17
BBABBBAABABBA
7 1
7 9
11 12
3 9
11 9
2 1
11 5
12 11
10 8
1 11
1 8
7 7
9 10
8 8
8 12
6 2
13 11


Output

No

### Response

```cpp
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
using namespace std;
struct node{
	int y,next;
}a[800010];int len=0,last[400010];
int n,m,c[400010],dis[400010];
bool vis[400010];
char s[200010];
void ins(int x,int y)
{
	a[++len].y=y;
	a[len].next=last[x];last[x]=len;
}
void insert(int x,int y,int c)
{
	int X=x+n,Y=y+n;
	if(c==1) ins(x,Y),ins(y,X);
	else ins(X,y),ins(Y,x);
}
bool dfs(int x)
{
	if(vis[x]) return true;
	vis[x]=true;
	for(int i=last[x];i;i=a[i].next)
	{
		int y=a[i].y;
		if(dis[y]<dis[x]+1)
		{
			dis[y]=dis[x]+1;
			if(dfs(y)) return true;
		}
	}
	vis[x]=false;
	return false;
}
int main()
{
	scanf("%d %d",&n,&m);
	scanf("%s",s+1);
	for(int i=1;i<=n;i++) c[i]=s[i]-'A';
	for(int i=1;i<=m;i++)
	{
		int x,y;scanf("%d %d",&x,&y);
		//ins(x,y);ins(y,x);
		if(c[x]==c[y]) insert(x,y,1);
		else insert(x,y,0);
	}
	memset(vis,false,sizeof(vis));
	for(int i=1;i<=n;i++)
		if(dfs(i)) {printf("Yes");return 0;}
	printf("No");
}
```