#include <iostream>
#include <vector>
#include <queue>
using namespace std;

const int MAXN = 2e5 + 10;
bool a[MAXN], dl[MAXN];
int n, m, deg[MAXN][2];
vector<int> Mat[MAXN];
queue<int> del;

void ers(int v) {
	for (int i = 0; i < Mat[v].size(); i++) {
		if (dl[Mat[v][i]])
			continue;
		deg[Mat[v][i]][a[v]]--;
		if (deg[Mat[v][i]][0] == 0 || deg[Mat[v][i]][1] == 0)
			del.push(Mat[v][i]), dl[Mat[v][i]] = true;
	}
}

int main() {
	cin >> n >> m;
	for (int i = 1; i <= n; i++) {
		char tmp;
		cin >> tmp;
		a[i] = (tmp == 'A');
	}
	for (int i = 0; i < m; i++) {
		int v, u;
		cin >> v >> u;
		Mat[u].push_back(v);
		Mat[v].push_back(u);
		deg[u][a[v]]++;
		deg[v][a[u]]++;
	}
	for (int i = 1; i <= n; i++)
		if (deg[i][0] == 0 || deg[i][1] == 0)
			del.push(i), dl[i] = true;
	while (!del.empty()) {
		ers(del.front());
		del.pop();
	}
	int ans = 0;
	for (int i = 1; i <= n; i++)
		ans += !dl[i];
	if (ans)
		cout << "Yes";
	else
		cout << "No";
}
### Prompt

Your task is to create a CPP solution 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 <iostream>
#include <vector>
#include <queue>
using namespace std;

const int MAXN = 2e5 + 10;
bool a[MAXN], dl[MAXN];
int n, m, deg[MAXN][2];
vector<int> Mat[MAXN];
queue<int> del;

void ers(int v) {
	for (int i = 0; i < Mat[v].size(); i++) {
		if (dl[Mat[v][i]])
			continue;
		deg[Mat[v][i]][a[v]]--;
		if (deg[Mat[v][i]][0] == 0 || deg[Mat[v][i]][1] == 0)
			del.push(Mat[v][i]), dl[Mat[v][i]] = true;
	}
}

int main() {
	cin >> n >> m;
	for (int i = 1; i <= n; i++) {
		char tmp;
		cin >> tmp;
		a[i] = (tmp == 'A');
	}
	for (int i = 0; i < m; i++) {
		int v, u;
		cin >> v >> u;
		Mat[u].push_back(v);
		Mat[v].push_back(u);
		deg[u][a[v]]++;
		deg[v][a[u]]++;
	}
	for (int i = 1; i <= n; i++)
		if (deg[i][0] == 0 || deg[i][1] == 0)
			del.push(i), dl[i] = true;
	while (!del.empty()) {
		ers(del.front());
		del.pop();
	}
	int ans = 0;
	for (int i = 1; i <= n; i++)
		ans += !dl[i];
	if (ans)
		cout << "Yes";
	else
		cout << "No";
}
```